Bayesian inversion analysis of nonlinear dynamics in surface heterogeneous reactions.
Omori, Toshiaki; Kuwatani, Tatsu; Okamoto, Atsushi; Hukushima, Koji
2016-09-01
It is essential to extract nonlinear dynamics from time-series data as an inverse problem in natural sciences. We propose a Bayesian statistical framework for extracting nonlinear dynamics of surface heterogeneous reactions from sparse and noisy observable data. Surface heterogeneous reactions are chemical reactions with conjugation of multiple phases, and they have the intrinsic nonlinearity of their dynamics caused by the effect of surface-area between different phases. We adapt a belief propagation method and an expectation-maximization (EM) algorithm to partial observation problem, in order to simultaneously estimate the time course of hidden variables and the kinetic parameters underlying dynamics. The proposed belief propagation method is performed by using sequential Monte Carlo algorithm in order to estimate nonlinear dynamical system. Using our proposed method, we show that the rate constants of dissolution and precipitation reactions, which are typical examples of surface heterogeneous reactions, as well as the temporal changes of solid reactants and products, were successfully estimated only from the observable temporal changes in the concentration of the dissolved intermediate product.
Output Feedback for Stochastic Nonlinear Systems with Unmeasurable Inverse Dynamics
Institute of Scientific and Technical Information of China (English)
Xin Yu; Na Duan
2009-01-01
This paper considers a concrete stochastic nonlinear system with stochastic unmeasurable inverse dynamics. Motivated by the concept of integral input-to-state stability (iISS) in deterministic systems and stochastic input-to-state stability (SISS) in stochastic systems, a concept of stochastic integral input-to-state stability (SiISS) using Lyapunov functions is first introduced. A constructive strategy is proposed to design a dynamic output feedback control law, which drives the state to the origin almost surely while keeping all other closed-loop signals almost surely bounded. At last, a simulation is given to verify the effectiveness of the control law.
Success Stories in Control: Nonlinear Dynamic Inversion Control
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.
Nonlinear Damping Identification in Nonlinear Dynamic System Based on Stochastic Inverse Approach
2012-01-01
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...
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.
Designing a Robust Nonlinear Dynamic Inversion Controller for Spacecraft Formation Flying
Directory of Open Access Journals (Sweden)
Inseok Yang
2014-01-01
Full Text Available The robust nonlinear dynamic inversion (RNDI control technique is proposed to keep the relative position of spacecrafts while formation flying. The proposed RNDI control method is based on nonlinear dynamic inversion (NDI. NDI is nonlinear control method that replaces the original dynamics into the user-selected desired dynamics. Because NDI removes nonlinearities in the model by inverting the original dynamics directly, it also eliminates the need of designing suitable controllers for each equilibrium point; that is, NDI works as self-scheduled controller. Removing the original model also provides advantages of ease to satisfy the specific requirements by simply handling desired dynamics. Therefore, NDI is simple and has many similarities to classical control. In real applications, however, it is difficult to achieve perfect cancellation of the original dynamics due to uncertainties that lead to performance degradation and even make the system unstable. This paper proposes robustness assurance method for NDI. The proposed RNDI is designed by combining NDI and sliding mode control (SMC. SMC is inherently robust using high-speed switching inputs. This paper verifies similarities of NDI and SMC, firstly. And then RNDI control method is proposed. The performance of the proposed method is evaluated by simulations applied to spacecraft formation flying problem.
Directory of Open Access Journals (Sweden)
Yu-Chi Wang
2015-01-01
Full Text Available This paper presents a unified approach to nonlinear dynamic inversion control algorithm with the parameters for desired dynamics determined by using an eigenvalue assignment method, which may be applied in a very straightforward and convenient way. By using this method, it is not necessary to transform the nonlinear equations into linear equations by feedback linearization before beginning control designs. The applications of this method are not limited to affine nonlinear control systems or limited to minimum phase problems if the eigenvalues of error dynamics are carefully assigned so that the desired dynamics is stable. The control design by using this method is shown to be robust to modeling uncertainties. To validate the theory, the design of a UAV control system is presented as an example. Numerical simulations show the performance of the design to be quite remarkable.
DEFF Research Database (Denmark)
Mosegaard, Klaus
2012-01-01
For non-linear inverse problems, the mathematical structure of the mapping from model parameters to data is usually unknown or partly unknown. Absence of information about the mathematical structure of this function prevents us from presenting an analytical solution, so our solution depends on our......-heuristics are inefficient for large-scale, non-linear inverse problems, and that the 'no-free-lunch' theorem holds. We discuss typical objections to the relevance of this theorem. A consequence of the no-free-lunch theorem is that algorithms adapted to the mathematical structure of the problem perform more efficiently than...
Directory of Open Access Journals (Sweden)
Na Duan
2012-01-01
Full Text Available The adaptive stabilization scheme based on tuning function for stochastic nonlinear systems with stochastic integral input-to-state stability (SiISS inverse dynamics is investigated. By combining the stochastic LaSalle theorem and small-gain type conditions on SiISS, an adaptive output feedback controller is constructively designed. It is shown that all the closed-loop signals are bounded almost surely and the stochastic closed-loop system is globally stable in probability.
Nonlinear system compound inverse control method
Institute of Scientific and Technical Information of China (English)
Yan ZHANG; Zengqiang CHEN; Peng YANG; Zhuzhi YUAN
2005-01-01
A compound neural network is utilized to identify the dynamic nonlinear system.This network is composed of two parts: one is a linear neural network,and the other is a recurrent neural network.Based on the inverse theory a compound inverse control method is proposed.The controller has also two parts:a linear controller and a nonlinear neural network controller.The stability condition of the closed-loop neural network-based compound inverse control system is demonstrated based on the Lyapunov theory.Simulation studies have shown that this scheme is simple and has good control accuracy and robustness.
Directory of Open Access Journals (Sweden)
Murray L. Ireland
2015-06-01
Full Text Available Multirotor is the umbrella term for the family of unmanned aircraft, which include the quadrotor, hexarotor and other vertical take-off and landing (VTOL aircraft that employ multiple main rotors for lift and control. Development and testing of novel multirotor designs has been aided by the proliferation of 3D printing and inexpensive flight controllers and components. Different multirotor configurations exhibit specific strengths, while presenting unique challenges with regards to design and control. This article highlights the primary differences between three multirotor platforms: a quadrotor; a fully-actuated hexarotor; and an octorotor. Each platform is modelled and then controlled using non-linear dynamic inversion. The differences in dynamics, control and performance are then discussed.
Energy Technology Data Exchange (ETDEWEB)
Turchetti, G. (Bologna Univ. (Italy). Dipt. di Fisica)
1989-01-01
Research in nonlinear dynamics is rapidly expanding and its range of applications is extending beyond the traditional areas of science where it was first developed. Indeed while linear analysis and modelling, which has been very successful in mathematical physics and engineering, has become a mature science, many elementary phenomena of intrinsic nonlinear nature were recently experimentally detected and investigated, suggesting new theoretical work. Complex systems, as turbulent fluids, were known to be governed by intrinsically nonlinear laws since a long time ago, but received purely phenomenological descriptions. The pioneering works of Boltzmann and Poincare, probably because of their intrinsic difficulty, did not have a revolutionary impact at their time; it is only very recently that their message is reaching a significant number of mathematicians and physicists. Certainly the development of computers and computer graphics played an important role in developing geometric intuition of complex phenomena through simple numerical experiments, while a new mathematical framework to understand them was being developed.
Gladwell, Graham ML
2011-01-01
The papers in this volume present an overview of the general aspects and practical applications of dynamic inverse methods, through the interaction of several topics, ranging from classical and advanced inverse problems in vibration, isospectral systems, dynamic methods for structural identification, active vibration control and damage detection, imaging shear stiffness in biological tissues, wave propagation, to computational and experimental aspects relevant for engineering problems.
Nonlinear Least Squares for Inverse Problems
Chavent, Guy
2009-01-01
Presents an introduction into the least squares resolution of nonlinear inverse problems. This title intends to develop a geometrical theory to analyze nonlinear least square (NLS) problems with respect to their quadratic wellposedness, that is, both wellposedness and optimizability
Nonlinear inversion flight control for a supermaneuverable aircraft
Snell, S. Antony; Garrard, William L., Jr.; Enns, Dale F.
1990-01-01
This paper describes the use of nonlinear dynamic inversion for the design of a flight control system for a supermaneuverable aircraft. First, the dynamics to be controlled were separated into fast and slow variables. The fast variables were the angular rates and the slow variables were the attitude angles. Then a nonlinear inversion controller was designed for the fast variables. This stabilized the longitudinal short-period and improved the lateral-directional responses over a wide range of angle of attack by making use of a combination for aerodynamic surfaces and thrust vectoring control. Outer loops were then closed to allow the pilot to control the slow dynamics, the angle of attack, side-slip angle and the velocity bank angle. Nonlinear inversion was also used to design of the outer loop control laws. The dynamic inversion control laws were compared with more conventional, gain-scheduled control laws and were shown to yield much better performance.
High resolution 3D nonlinear integrated inversion
Institute of Scientific and Technical Information of China (English)
Li Yong; Wang Xuben; Li Zhirong; Li Qiong; Li Zhengwen
2009-01-01
The high resolution 3D nonlinear integrated inversion method is based on nonlinear theory. Under layer control, the log data from several wells (or all wells) in the study area and seismic trace data adjacent to the wells are input to a network with multiple inputs and outputs and are integratedly trained to obtain an adaptive weight function of the entire study area. Integrated nonlinear mapping relationships are built and updated by the lateral and vertical geologic variations of the reservoirs. Therefore, the inversion process and its inversion results can be constrained and controlled and a stable seismic inversion section with high resolution with velocity inversion, impedance inversion, and density inversion sections, can be gained. Good geologic effects have been obtained in model computation tests and real data processing, which verified that this method has high precision, good practicality, and can be used for quantitative reservoir analysis.
Non-Linear Logging Parameters Inversion
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
The non-linear logging parameters inversion is based on the field theory, information optimization and predication theory. It uses seismic charaoters,geological model and logging data as a restriction to inverse 2D, 3D logging parameters data volume. Using this method,
Institute of Scientific and Technical Information of China (English)
1996-01-01
3.1 A Unified Nonlinear Feedback Functional Method for Study Both Control and Synchronization of Spatiotemporal Chaos Fang Jinqing Ali M. K. (Department of Physics, The University of Lethbridge,Lethbridge, Alberta T1K 3M4,Canada) Two fundamental questions dominate future chaos control theories.The first is the problem of controlling hyperchaos in higher dimensional systems.The second question has yet to be addressed:the problem of controlling spatiotemporal chaos in a spatiotemporal system.In recent years, control and synchronization of spatiotemporal chaos and hyperchaos have became a much more important and challenging subject. The reason for this is the control and synchronism of such behaviours have extensive and great potential of interdisciplinary applications, such as security communication, information processing, medicine and so on. However, this subject is not much known and remains an outstanding open.
Smith, G. A.; Meyer, G.
1981-01-01
A full envelope automatic flight control system based on nonlinear inverse systems concepts has been applied to a vertical attitude takeoff and landing (VATOL) fighter aircraft. A new method for using an airborne digital aircraft model to perform the inversion of a nonlinear aircraft model is presented together with the results of a simulation study of the nonlinear inverse system concept for the vertical-attitude hover mode. The system response to maneuver commands in the vertical attitude was found to be excellent; and recovery from large initial offsets and large disturbances was found to be very satisfactory.
Smith, G. A.; Meyer, G.
1981-01-01
A full envelope automatic flight control system based on nonlinear inverse systems concepts has been applied to a vertical attitude takeoff and landing (VATOL) fighter aircraft. A new method for using an airborne digital aircraft model to perform the inversion of a nonlinear aircraft model is presented together with the results of a simulation study of the nonlinear inverse system concept for the vertical-attitude hover mode. The system response to maneuver commands in the vertical attitude was found to be excellent; and recovery from large initial offsets and large disturbances was found to be very satisfactory.
The role of nonlinearity in inverse problems
Snieder, Roel
1998-06-01
In many practical inverse problems, one aims to retrieve a model that has infinitely many degrees of freedom from a finite amount of data. It follows from a simple variable count that this cannot be done in a unique way. Therefore, inversion entails more than estimating a model: any inversion is not complete without a description of the class of models that is consistent with the data; this is called the appraisal problem. Nonlinearity makes the appraisal problem particularly difficult. The first reason for this is that nonlinear error propagation is a difficult problem. The second reason is that for some nonlinear problems the model parameters affect the way in which the model is being interrogated by the data. Two examples are given of this, and it is shown how the nonlinearity may make the problem more ill-posed. Finally, three attempts are shown to carry out the model appraisal for nonlinear inverse problems that are based on an analytical approach, a numerical approach and a common sense approach.
Nonlinear dynamics and complexity
Luo, Albert; Fu, Xilin
2014-01-01
This important collection presents recent advances in nonlinear dynamics including analytical solutions, chaos in Hamiltonian systems, time-delay, uncertainty, and bio-network dynamics. Nonlinear Dynamics and Complexity equips readers to appreciate this increasingly main-stream approach to understanding complex phenomena in nonlinear systems as they are examined in a broad array of disciplines. The book facilitates a better understanding of the mechanisms and phenomena in nonlinear dynamics and develops the corresponding mathematical theory to apply nonlinear design to practical engineering.
Nonlinear approximation with dictionaries,.. II: Inverse estimates
DEFF Research Database (Denmark)
Gribonval, Rémi; Nielsen, Morten
In this paper we study inverse estimates of the Bernstein type for nonlinear approximation with structured redundant dictionaries in a Banach space. The main results are for separated decomposable dictionaries in Hilbert spaces, which generalize the notion of joint block-diagonal mutually...
Nonlinear approximation with dictionaries. II. Inverse Estimates
DEFF Research Database (Denmark)
Gribonval, Rémi; Nielsen, Morten
2006-01-01
In this paper, which is the sequel to [16], we study inverse estimates of the Bernstein type for nonlinear approximation with structured redundant dictionaries in a Banach space. The main results are for blockwise incoherent dictionaries in Hilbert spaces, which generalize the notion of joint block-diagonal...
Intramolecular and nonlinear dynamics
Energy Technology Data Exchange (ETDEWEB)
Davis, M.J. [Argonne National Laboratory, IL (United States)
1993-12-01
Research in this program focuses on three interconnected areas. The first involves the study of intramolecular dynamics, particularly of highly excited systems. The second area involves the use of nonlinear dynamics as a tool for the study of molecular dynamics and complex kinetics. The third area is the study of the classical/quantum correspondence for highly excited systems, particularly systems exhibiting classical chaos.
Nonlinear dynamics of structures
Oller, Sergio
2014-01-01
This book lays the foundation of knowledge that will allow a better understanding of nonlinear phenomena that occur in structural dynamics. This work is intended for graduate engineering students who want to expand their knowledge on the dynamic behavior of structures, specifically in the nonlinear field, by presenting the basis of dynamic balance in non‐linear behavior structures due to the material and kinematics mechanical effects. Particularly, this publication shows the solution of the equation of dynamic equilibrium for structure with nonlinear time‐independent materials (plasticity, damage and frequencies evolution), as well as those time dependent non‐linear behavior materials (viscoelasticity and viscoplasticity). The convergence conditions for the non‐linear dynamic structure solution are studied, and the theoretical concepts and its programming algorithms are presented.
Full Waveform Inversion Using Nonlinearly Smoothed Wavefields
Li, Y.
2017-05-26
The lack of low frequency information in the acquired data makes full waveform inversion (FWI) conditionally converge to the accurate solution. An initial velocity model that results in data with events within a half cycle of their location in the observed data was required to converge. The multiplication of wavefields with slightly different frequencies generates artificial low frequency components. This can be effectively utilized by multiplying the wavefield with itself, which is nonlinear operation, followed by a smoothing operator to extract the artificially produced low frequency information. We construct the objective function using the nonlinearly smoothed wavefields with a global-correlation norm to properly handle the energy imbalance in the nonlinearly smoothed wavefield. Similar to the multi-scale strategy, we progressively reduce the smoothing width applied to the multiplied wavefield to welcome higher resolution. We calculate the gradient of the objective function using the adjoint-state technique, which is similar to the conventional FWI except for the adjoint source. Examples on the Marmousi 2 model demonstrate the feasibility of the proposed FWI method to mitigate the cycle-skipping problem in the case of a lack of low frequency information.
DEFF Research Database (Denmark)
Mosekilde, Erik
Through a significant number of detailed and realistic examples this book illustrates how the insights gained over the past couple of decades in the fields of nonlinear dynamics and chaos theory can be applied in practice. Aomng the topics considered are microbiological reaction systems, ecological...
Inverse problem for multi-body interaction of nonlinear waves
Marruzzo, Alessia; Antenucci, Fabrizio; Pagnani, Andrea; Leuzzi, Luca
2016-01-01
The inverse problem is studied in multi-body systems with nonlinear dynamics representing, e.g., phase-locked wave systems, standard multimode and random lasers. Using a general model for four-body interacting complex-valued variables we test two methods based on pseudolikelihood, respectively with regularization and with decimation, to determine the coupling constants from sets of measured configurations. We test statistical inference predictions for increasing number of sampled configurations and for an externally tunable {\\em temperature}-like parameter mimicing real data noise and helping minimization procedures. Analyzed models with phasors and rotors are generalizations of problems of real-valued spherical problems (e.g., density fluctuations), discrete spins (Ising and vectorial Potts) or finite number of states (standard Potts): inference methods presented here can, then, be straightforward applied to a large class of inverse problems.
Learning Inverse Rig Mappings by Nonlinear Regression.
Holden, Daniel; Saito, Jun; Komura, Taku
2016-11-11
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.
Galerkin approximation for inverse problems for nonautonomous nonlinear distributed systems
Banks, H. T.; Reich, Simeon; Rosen, I. G.
1988-01-01
An abstract framework and convergence theory is developed for Galerkin approximation for inverse problems involving the identification of nonautonomous nonlinear distributed parameter systems. A set of relatively easily verified conditions is provided which are sufficient to guarantee the existence of optimal solutions and their approximation by a sequence of solutions to a sequence of approximating finite dimensional identification problems. The approach is based on the theory of monotone operators in Banach spaces and is applicable to a reasonably broad class of nonlinear distributed systems. Operator theoretic and variational techniques are used to establish a fundamental convergence result. An example involving evolution systems with dynamics described by nonstationary quasilinear elliptic operators along with some applications are presented and discussed.
Nonlinear Dynamic Force Spectroscopy
Björnham, Oscar
2016-01-01
Dynamic force spectroscopy (DFS) is an experimental technique that is commonly used to assess information of the strength, energy landscape, and lifetime of noncovalent bio-molecular interactions. DFS traditionally requires an applied force that increases linearly with time so that the bio-complex under investigation is exposed to a constant loading rate. However, tethers or polymers can modulate the applied force in a nonlinear regime. For example, bacterial adhesion pili and polymers with worm-like chain properties are examples of structures that show nonlinear force responses. In these situations, the theory for traditional DFS cannot be readily applied. In this work we expand the theory for DFS to also include nonlinear external forces while still maintaining compatibility with the linear DFS theory. To validate the theory we modeled a bio-complex expressed on a stiff, an elastic and a worm-like chain polymer, using Monte Carlo methods, and assessed the corresponding rupture force spectra. It was found th...
Nonlinear dynamics by mode superposition
Energy Technology Data Exchange (ETDEWEB)
Nickell, R.E.
1976-01-01
A mode superposition technique for approximately solving nonlinear initial-boundary-value problems of structural dynamics is discussed, and results for examples involving large deformation are compared to those obtained with implicit direct integration methods such as the Newmark generalized acceleration and Houbolt backward-difference operators. The initial natural frequencies and mode shapes are found by inverse power iteration with the trial vectors for successively higher modes being swept by Gram-Schmidt orthonormalization at each iteration. The subsequent modal spectrum for nonlinear states is based upon the tangent stiffness of the structure and is calculated by a subspace iteration procedure that involves matrix multiplication only, using the most recently computed spectrum as an initial estimate. Then, a precise time integration algorithm that has no artificial damping or phase velocity error for linear problems is applied to the uncoupled modal equations of motion. Squared-frequency extrapolation is examined for nonlinear problems as a means by which these qualities of accuracy and precision can be maintained when the state of the system (and, thus, the modal spectrum) is changing rapidly. The results indicate that a number of important advantages accrue to nonlinear mode superposition: (a) there is no significant difference in total solution time between mode superposition and implicit direct integration analyses for problems having narrow matric half-bandwidth (in fact, as bandwidth increases, mode superposition becomes more economical), (b) solution accuracy is under better control since the analyst has ready access to modal participation factors and the ratios of time step size to modal period, and (c) physical understanding of nonlinear dynamic response is improved since the analyst is able to observe the changes in the modal spectrum as deformation proceeds.
Analysis of nonlinear channel friction inverse problem
Institute of Scientific and Technical Information of China (English)
CHENG Weiping; LIU Guohua
2007-01-01
Based on the Backus-Gilbert inverse theory, the singular value decomposition (SVD) for general inverse matrices and the optimization algorithm are used to solve the channel friction inverse problem. The resolution and covari- ance friction inverse model in matrix form is developed to examine the reliability of solutions. Theoretical analyses demonstrate that the convergence rate of the general Newton optimization algorithm is in the second-order. The Wiggins method is also incorporated into the algorithm. Using the method, noise can be suppressed effectively, and the results are close to accurate solutions with proper control parameters. Also, the numerical stability can be improved.
Inverse Coefficient Problems for Nonlinear Elliptic Variational Inequalities
Institute of Scientific and Technical Information of China (English)
Run-sheng Yang; Yun-hua Ou
2011-01-01
This paper is devoted to a class of inverse coefficient problems for nonlinear elliptic variational inequalities. The unknown coefficient of elliptic variational inequalities depends on the gradient of the solution and belongs to a set of admissible coefficients. It is shown that the nonlinear elliptic variational inequalities is unique solvable for the given class of coefficients. The existence of quasisolutions of the inverse problems is obtained.
Nonlinear dynamics in psychology
Directory of Open Access Journals (Sweden)
Stephen J. Guastello
2001-01-01
Full Text Available This article provides a survey of the applications of nonlinear dynamical systems theory to substantive problems encountered in the full scope of psychological science. Applications are organized into three topical areas – cognitive science, social and organizational psychology, and personality and clinical psychology. Both theoretical and empirical studies are considered with an emphasis on works that capture the broadest scope of issues that are of substantive interest to psychological theory. A budding literature on the implications of NDS principles in professional practice is reported also.
A nonlinear model reference adaptive inverse control algorithm with pre-compensator
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
In this paper, the reduced-order modeling (ROM)technology and its corresponding linear theory are expanded from the linear dynamic system to the nonlinear one, and H∞ control theory is employed in the frequency domain to design some nonlinear system' s pre-compensator in some special way. The adaptive model inverse control (AMIC)theory coping with nonlinear system is improved as well. Such is the model reference adaptive inverse control with pre-compensator (PCMRAIC). The aim of that algorithm is to construct a strategy of control as a whole. As a practical example of the application, the numerical simulation has been given on matlab software packages. The numerical result is given. The proposed strategy realizes the linearization control of nonlinear dynamic system. And it carries out a good performance to deal with the nonlinear system.
Global Analysis of Nonlinear Dynamics
Luo, Albert
2012-01-01
Global Analysis of Nonlinear Dynamics collects chapters on recent developments in global analysis of non-linear dynamical systems with a particular emphasis on cell mapping methods developed by Professor C.S. Hsu of the University of California, Berkeley. This collection of contributions prepared by a diverse group of internationally recognized researchers is intended to stimulate interests in global analysis of complex and high-dimensional nonlinear dynamical systems, whose global properties are largely unexplored at this time. This book also: Presents recent developments in global analysis of non-linear dynamical systems Provides in-depth considerations and extensions of cell mapping methods Adopts an inclusive style accessible to non-specialists and graduate students Global Analysis of Nonlinear Dynamics is an ideal reference for the community of nonlinear dynamics in different disciplines including engineering, applied mathematics, meteorology, life science, computational science, and medicine.
Discrete-time inverse optimal control for nonlinear systems
Sanchez, Edgar N
2013-01-01
Discrete-Time Inverse Optimal Control for Nonlinear Systems proposes a novel inverse optimal control scheme for stabilization and trajectory tracking of discrete-time nonlinear systems. This avoids the need to solve the associated Hamilton-Jacobi-Bellman equation and minimizes a cost functional, resulting in a more efficient controller. Design More Efficient Controllers for Stabilization and Trajectory Tracking of Discrete-Time Nonlinear Systems The book presents two approaches for controller synthesis: the first based on passivity theory and the second on a control Lyapunov function (CLF). Th
Minimax theory for a class of nonlinear statistical inverse problems
Ray, Kolyan; Schmidt-Hieber, Johannes
2016-06-01
We study a class of statistical inverse problems with nonlinear pointwise operators motivated by concrete statistical applications. A two-step procedure is proposed, where the first step smoothes the data and inverts the nonlinearity. This reduces the initial nonlinear problem to a linear inverse problem with deterministic noise, which is then solved in a second step. The noise reduction step is based on wavelet thresholding and is shown to be minimax optimal (up to logarithmic factors) in a pointwise function-dependent sense. Our analysis is based on a modified notion of Hölder smoothness scales that are natural in this setting.
Nonlinear inversion schemes for fluorescence optical tomography.
Freiberger, Manuel; Egger, Herbert; Scharfetter, Hermann
2010-11-01
Fluorescence optical tomography is a non-invasive imaging modality that employs the absorption and re-emission of light by fluorescent dyes. The aim is to reconstruct the fluorophore distribution in a body from measurements of light intensities at the boundary. Due to the diffusive nature of light propagation in tissue, fluorescence tomography is a nonlinear and severely ill-posed problem, and some sort of regularization is required for a stable solution. In this paper we investigate reconstruction methods based on Tikhonov regularization with nonlinear penalty terms, namely total-variation regularization and a levelset-type method using a nonlinear parameterization of the unknown function. Moreover, we use the full threedimensional nonlinear forward model, which arises from the governing system of partial differential equations. We discuss the numerical realization of the regularization schemes by Newtontype iterations, present some details of the discretization by finite element methods, and outline the efficient implementation of sensitivity systems via adjoint methods. As we will demonstrate in numerical tests, the proposed nonlinear methods provide better reconstructions than standard methods based on linearized forward models and linear penalty terms. We will additionally illustrate, that the careful discretization of the methods derived on the continuous level allows to obtain reliable, mesh independent reconstruction algorithms.
Nonlinear dynamics in atom optics
Energy Technology Data Exchange (ETDEWEB)
Chen Wenyu; Dyrting, S.; Milburn, G.J. [Queensland Univ., St. Lucia, QLD (Australia). Dept. of Physics
1996-12-31
In this paper theoretical work on classical and quantum nonlinear dynamics of cold atoms is reported. The basic concepts in nonlinear dynamics are reviewed and then applied to the motion of atoms in time-dependent standing waves and to the atomic bouncer. The quantum dynamics for the cases of regular and chaotic classical dynamics is described. The effect of spontaneous emission and external noise is also discussed. 104 refs., 1 tab., 21 figs.
Inverse problem for multi-body interaction of nonlinear waves.
Marruzzo, Alessia; Tyagi, Payal; Antenucci, Fabrizio; Pagnani, Andrea; Leuzzi, Luca
2017-06-14
The inverse problem is studied in multi-body systems with nonlinear dynamics representing, e.g., phase-locked wave systems, standard multimode and random lasers. Using a general model for four-body interacting complex-valued variables we test two methods based on pseudolikelihood, respectively with regularization and with decimation, to determine the coupling constants from sets of measured configurations. We test statistical inference predictions for increasing number of sampled configurations and for an externally tunable temperature-like parameter mimicing real data noise and helping minimization procedures. Analyzed models with phasors and rotors are generalizations of problems of real-valued spherical problems (e.g., density fluctuations), discrete spins (Ising and vectorial Potts) or finite number of states (standard Potts): inference methods presented here can, then, be straightforward applied to a large class of inverse problems. The high versatility of the exposed techniques also concerns the number of expected interactions: results are presented for different graph topologies, ranging from sparse to dense graphs.
HOMOTOPY SOLUTION OF THE INVERSE GENERALIZED EIGENVALUE PROBLEMS IN STRUCTURAL DYNAMICS
Institute of Scientific and Technical Information of China (English)
李书; 王波; 胡继忠
2004-01-01
The structural dynamics problems, such as structural design, parameter identification and model correction, are considered as a kind of the inverse generalized eigenvalue problems mathematically. The inverse eigenvalue problems are nonlinear. In general, they could be transformed into nonlinear equations to solve. The structural dynamics inverse problems were treated as quasi multiplicative inverse eigenalue problems which were solved by homotopy method for nonlinear equations. This method had no requirements for initial value essentially because of the homotopy path to solution. Numerical examples were presented to illustrate the homotopy method.
Inverse Problems for Nonlinear Delay Systems
2011-03-15
Ba82]. For nonlinear delay systems such as those discussed here, approximation in the context of a linear semigroup framework as presented [BBu1, BBu2...linear part generates a linear semigroup as in [BBu1, BBu2, BKap]. One then uses the linear semigroup in a vari- ation of parameters implicit...BBu2, BKap] (for the linear semigroup ) plus a Gronwall inequality. An alternative (and more general) approach given in [Ba82] eschews use of the Trotter
Inverse Coefficient Problems for Nonlinear Parabolic Differential Equations
Institute of Scientific and Technical Information of China (English)
Yun Hua OU; Alemdar HASANOV; Zhen Hai LIU
2008-01-01
This paper is devoted to a class of inverse problems for a nonlinear parabolic differential equation.The unknown coefficient of the equation depends on the gradient of the solution and belongs to a set of admissible coefficients.It is proved that the convergence of solutions for the corresponding direct problems continuously depends on the coefficient convergence.Based on this result the existence of a quasisolution of the inverse problem is obtained in the appropriate class of admissible coefficients.
Nonlinear magnetization dynamics in nanosystems
Mayergoyz, Isaak D; Serpico, Claudio
2014-01-01
As data transfer rates increase within the magnetic recording industry, improvements in device performance and reliability crucially depend on the thorough understanding of nonlinear magnetization dynamics at a sub-nanoscale level. This book offers a modern, stimulating approach to the subject of nonlinear magnetization dynamics by discussing important aspects such as the Landau-Lifshitz-Gilbert (LLG) equation, analytical solutions, and the connection between the general topological and structural aspects of dynamics. An advanced reference for the study and understanding of non
Neurodynamics: nonlinear dynamics and neurobiology.
Abarbanel, H D; Rabinovich, M I
2001-08-01
The use of methods from contemporary nonlinear dynamics in studying neurobiology has been rather limited.Yet, nonlinear dynamics has become a practical tool for analyzing data and verifying models. This has led to productive coupling of nonlinear dynamics with experiments in neurobiology in which the neural circuits are forced with constant stimuli, with slowly varying stimuli, with periodic stimuli, and with more complex information-bearing stimuli. Analysis of these more complex stimuli of neural circuits goes to the heart of how one is to understand the encoding and transmission of information by nervous systems.
Nonlinear Dynamic Phenomena in Mechanics
Warminski, Jerzy; Cartmell, Matthew P
2012-01-01
Nonlinear phenomena should play a crucial role in the design and control of engineering systems and structures as they can drastically change the prevailing dynamical responses. This book covers theoretical and applications-based problems of nonlinear dynamics concerned with both discrete and continuous systems of interest in civil and mechanical engineering. They include pendulum-like systems, slender footbridges, shape memory alloys, sagged elastic cables and non-smooth problems. Pendulums can be used as a dynamic absorber mounted in high buildings, bridges or chimneys. Geometrical nonlinear
Nonlinear Approach in Nuclear Dynamics
Gridnev, K. A.; Kartavenko, V. G.; Greiner, W.
2002-11-01
Attention is focused on the various approaches that use the concept of nonlinear dispersive waves (solitons) in nonrelativistic nuclear physics. The problem of dynamical instability and clustering (stable fragments formation) in a breakup of excited nuclear systems are considered from the points of view of the soliton concept. It is shown that the volume (spinodal) instability can be associated with nonlinear terms, and the surface (Rayleigh-Taylor type) instability, with the dispersion terms in the evolution equations. The both instabilities may compensate each other and lead to stable solutions (solitons). A static scission configuration in cold ternary fission is considered in the framework of mean field approach. We suggest to use the inverse mean field method to solve single-particle Schrödinger equation, instead of constrained selfconsistent Hartree-Fock equations. It is shown, that it is possible to simulate one-dimensional three-center system in the approximation of reflectless single-particle potentials. The soliton-like solutions of the Korteweg-de Vries equation are using to describe collective excitations of nuclei observed in inelastic alpha-particle and proton scattering. The analogy between fragmentation into parts of nuclei and buckyballs has led us to the idea of light nuclei as quasi-crystals. We establish that the quasi-crystalline structure can be formed when the distance between the alpha-particles is comparable with the length of the De Broglia wave of the alpha-particle. Applying this model to the scattering of alpha-particles we obtain that the form factor of the clusterized nucleus can be factorized into the formfactor of the cluster and the density of clusters in the nucleus. It gives possibility to study the distribution of clusters in nuclei and to resolve what kind of distribution we are dealing with: a surface or volume one.
A nonlinear approach of elastic reflection waveform inversion
Guo, Qiang
2016-09-06
Elastic full waveform inversion (EFWI) embodies the original intention of waveform inversion at its inception as it is a better representation of the mostly solid Earth. However, compared with the acoustic P-wave assumption, EFWI for P- and S-wave velocities using multi-component data admitted mixed results. Full waveform inversion (FWI) is a highly nonlinear problem and this nonlinearity only increases under the elastic assumption. Reflection waveform inversion (RWI) can mitigate the nonlinearity by relying on transmissions from reflections focused on inverting low wavenumber components of the model. In our elastic endeavor, we split the P- and S-wave velocities into low wavenumber and perturbation components and propose a nonlinear approach to invert for both of them. The new optimization problem is built on an objective function that depends on both background and perturbation models. We utilize an equivalent stress source based on the model perturbation to generate reflection instead of demigrating from an image, which is applied in conventional RWI. Application on a slice of an ocean-bottom data shows that our method can efficiently update the low wavenumber parts of the model, but more so, obtain perturbations that can be added to the low wavenumbers for a high resolution output.
The inverse maximum dynamic flow problem
Institute of Scientific and Technical Information of China (English)
BAGHERIAN; Mehri
2010-01-01
We consider the inverse maximum dynamic flow (IMDF) problem.IMDF problem can be described as: how to change the capacity vector of a dynamic network as little as possible so that a given feasible dynamic flow becomes a maximum dynamic flow.After discussing some characteristics of this problem,it is converted to a constrained minimum dynamic cut problem.Then an efficient algorithm which uses two maximum dynamic flow algorithms is proposed to solve the problem.
Nonlinear dynamics: Challenges and perspectives
Indian Academy of Sciences (India)
M Lakshmanan
2005-04-01
The study of nonlinear dynamics has been an active area of research since 1960s, after certain path-breaking discoveries, leading to the concepts of solitons, integrability, bifurcations, chaos and spatio-temporal patterns, to name a few. Several new techniques and methods have been developed to understand nonlinear systems at different levels. Along with these, a multitude of potential applications of nonlinear dynamics have also been enunciated. In spite of these developments, several challenges, some of them fundamental and others on the efficacy of these methods in developing cutting edge technologies, remain to be tackled. In this article, a brief personal perspective of these issues is presented.
Nonlinear dynamics in biological systems
Carballido-Landeira, Jorge
2016-01-01
This book presents recent research results relating to applications of nonlinear dynamics, focusing specifically on four topics of wide interest: heart dynamics, DNA/RNA, cell mobility, and proteins. The book derives from the First BCAM Workshop on Nonlinear Dynamics in Biological Systems, held in June 2014 at the Basque Center of Applied Mathematics (BCAM). At this international meeting, researchers from different but complementary backgrounds, including molecular dynamics, physical chemistry, bio-informatics and biophysics, presented their most recent results and discussed the future direction of their studies using theoretical, mathematical modeling and experimental approaches. Such was the level of interest stimulated that the decision was taken to produce this publication, with the organizers of the event acting as editors. All of the contributing authors are researchers working on diverse biological problems that can be approached using nonlinear dynamics. The book will appeal especially to applied math...
Sparse nonlinear inverse imaging for shot count reduction in inverse lithography.
Wu, Xiaofei; Liu, Shiyuan; Lv, Wen; Lam, Edmund Y
2015-10-19
Inverse lithography technique (ILT) is significant to reduce the feature size of ArF optical lithography due to its strong ability to overcome the optical proximity effect. A critical issue for inverse lithography is the complex curvilinear patterns produced, which are very costly to write due to the large number of shots needed with the current variable shape beam (VSB) writers. In this paper, we devise an inverse lithography method to reduce the shot count by incorporating a model-based fracturing (MBF) in the optimization. The MBF is formulated as a sparse nonlinear inverse imaging problem based on representing the mask as a linear combination of shots followed by a threshold function. The problem is approached with a Gauss-Newton algorithm, which is adapted to promote sparsity of the solution, corresponding to the reduction of the shot count. Simulations of inverse lithography are performed on several test cases, and results demonstrate reduced shot count of the resulting mask.
A Recursive Born Approach to Nonlinear Inverse Scattering
Kamilov, Ulugbek S; Mansour, Hassan; Boufounos, Petros T
2016-01-01
The Iterative Born Approximation (IBA) is a well-known method for describing waves scattered by semi-transparent objects. In this paper, we present a novel nonlinear inverse scattering method that combines IBA with an edge-preserving total variation (TV) regularizer. The proposed method is obtained by relating iterations of IBA to layers of a feedforward neural network and developing a corresponding error backpropagation algorithm for efficiently estimating the permittivity of the object. Simulations illustrate that, by accounting for multiple scattering, the method successfully recovers the permittivity distribution where the traditional linear inverse scattering fails.
Device Applications of Nonlinear Dynamics
Baglio, Salvatore
2006-01-01
This edited book is devoted specifically to the applications of complex nonlinear dynamic phenomena to real systems and device applications. While in the past decades there has been significant progress in the theory of nonlinear phenomena under an assortment of system boundary conditions and preparations, there exist comparatively few devices that actually take this rich behavior into account. "Device Applications of Nonlinear Dynamics" applies and exploits this knowledge to make devices which operate more efficiently and cheaply, while affording the promise of much better performance. Given the current explosion of ideas in areas as diverse as molecular motors, nonlinear filtering theory, noise-enhanced propagation, stochastic resonance and networked systems, the time is right to integrate the progress of complex systems research into real devices.
Iterative total variation schemes for nonlinear inverse problems
Bachmayr, Markus; Burger, Martin
2009-10-01
In this paper we discuss the construction, analysis and implementation of iterative schemes for the solution of inverse problems based on total variation regularization. Via different approximations of the nonlinearity we derive three different schemes resembling three well-known methods for nonlinear inverse problems in Hilbert spaces, namely iterated Tikhonov, Levenberg-Marquardt and Landweber. These methods can be set up such that all arising subproblems are convex optimization problems, analogous to those appearing in image denoising or deblurring. We provide a detailed convergence analysis and appropriate stopping rules in the presence of data noise. Moreover, we discuss the implementation of the schemes and the application to distributed parameter estimation in elliptic partial differential equations.
Practical compensation for nonlinear dynamic thrust measurement system
Directory of Open Access Journals (Sweden)
Chen Lin
2015-04-01
Full Text Available The real dynamic thrust measurement system usually tends to be nonlinear due to the complex characteristics of the rig, pipes connection, etc. For a real dynamic measuring system, the nonlinearity must be eliminated by some adequate methods. In this paper, a nonlinear model of dynamic thrust measurement system is established by using radial basis function neural network (RBF-NN, where a novel multi-step force generator is designed to stimulate the nonlinearity of the system, and a practical compensation method for the measurement system using left inverse model is proposed. Left inverse model can be considered as a perfect dynamic compensation of the dynamic thrust measurement system, and in practice, it can be approximated by RBF-NN based on least mean square (LMS algorithms. Different weights are set for producing the multi-step force, which is the ideal input signal of the nonlinear dynamic thrust measurement system. The validity of the compensation method depends on the engine’s performance and the tolerance error 0.5%, which is commonly demanded in engineering. Results from simulations and experiments show that the practical compensation using left inverse model based on RBF-NN in dynamic thrust measuring system can yield high tracking accuracy than the conventional methods.
Review of the Study of Nonlinear Atmospheric Dynamics in China (1999-2002)
Institute of Scientific and Technical Information of China (English)
刁一娜; 封国林; 刘式达; 刘式适; 罗德海; 黄思训; 陆维松; 丑纪范
2004-01-01
Researches on nonlinear atmospheric dynamics in China (1999-2002) are briefly surveyed. This review includes the major achievements in the following branches of nonlinear dynamics: nonlinear stability theory,nonlinear blocking dynamics, 3D spiral structure in the atmosphere, traveling wave solution of the nonlinear evolution equation, numerical predictability in a chaotic system, and global analysis of climate dynamics.Some applications of nonlinear methods such as hierarchy structure of climate and scaling invariance, the spatial-temporal series predictive method, the nonlinear inverse problem, and a new difference scheme with multi-time levels are also introduced.
Inverse problems in stochastic computational dynamics
Capiez-Lernout, Evangéline; Soize, Christian
2008-01-01
International audience; This paper deals with robust updating of dynamical systems using stochastic computational models for which model and parameter uncertainties are taken into account by the nonparametric probabilistic approach. Such a problem is formulated as an inverse problem consisting in identifying the parameters of the mean computational model and the parameters of the probabilistic model of uncertainties. This inverse problem leads us to solve an optimization problem for which the...
An inverse problem in analytical dynamics
Institute of Scientific and Technical Information of China (English)
Li Guang-Cheng; Mei-Feng-Xiang
2006-01-01
This paper presents an inverse problem in analytical dynamics.The inverse problem is to construct the Lagrangian when the integrals of a system are given.Firstly,the differential equations are obtained by using the time derivative of the integrals.Secondly,the differential equations can be written in the Lagrange equations under certain conditions and the Lagrangian can be obtained.Finally,two examples are given to illustrate the application of the result.
Nonlinear Deformable-body Dynamics
Luo, Albert C J
2010-01-01
"Nonlinear Deformable-body Dynamics" mainly consists in a mathematical treatise of approximate theories for thin deformable bodies, including cables, beams, rods, webs, membranes, plates, and shells. The intent of the book is to stimulate more research in the area of nonlinear deformable-body dynamics not only because of the unsolved theoretical puzzles it presents but also because of its wide spectrum of applications. For instance, the theories for soft webs and rod-reinforced soft structures can be applied to biomechanics for DNA and living tissues, and the nonlinear theory of deformable bodies, based on the Kirchhoff assumptions, is a special case discussed. This book can serve as a reference work for researchers and a textbook for senior and postgraduate students in physics, mathematics, engineering and biophysics. Dr. Albert C.J. Luo is a Professor of Mechanical Engineering at Southern Illinois University, Edwardsville, IL, USA. Professor Luo is an internationally recognized scientist in the field of non...
Meyer, G.; Cicolani, L.
1981-01-01
A practical method for the design of automatic flight control systems for aircraft with complex characteristics and operational requirements, such as the powered lift STOL and V/STOL configurations, is presented. The method is effective for a large class of dynamic systems requiring multi-axis control which have highly coupled nonlinearities, redundant controls, and complex multidimensional operational envelopes. It exploits the concept of inverse dynamic systems, and an algorithm for the construction of inverse is given. A hierarchic structure for the total control logic with inverses is presented. The method is illustrated with an application to the Augmentor Wing Jet STOL Research Aircraft equipped with a digital flight control system. Results of flight evaluation of the control concept on this aircraft are presented.
Zero Dynamics Analysis for Inverse Decoupling Control of Asynchronous Traction Motor
Directory of Open Access Journals (Sweden)
Haiying Dong
2013-07-01
Full Text Available Considering the problem for inverse system method in EMU AC induction traction motor linear decoupling, the zero dynamics subsystem will be separated from the original dynamic system through coordinate transformation. Firstly, a getting method for zero dynamics of the multiple input multiple output nonlinear system is discussed when γ＜n. Second, the zero dynamics analysis for five order nonlinear model of asynchronous traction motor which base on the stationary coordinate system is given by using inverse decoupling method. The analysis results show that if the stability of the zero dynamics can be ensured, then the entire linearization of original nonlinear system is not necessary, need only partial linearization which effect on the external dynamic portion. The inverse decoupling process of asynchronous traction motor can be simplified by this conclusion.
Elastic reflection based waveform inversion with a nonlinear approach
Guo, Qiang
2017-08-16
Full waveform inversion (FWI) is a highly nonlinear problem due to the complex reflectivity of the Earth, and this nonlinearity only increases under the more expensive elastic assumption. In elastic media, we need a good initial P-wave velocity and even a better initial S-wave velocity models with accurate representation of the low model wavenumbers for FWI to converge. However, inverting for the low wavenumber components of P- and S-wave velocities using reflection waveform inversion (RWI) with an objective to fit the reflection shape, rather than produce reflections, may mitigate the limitations of FWI. Because FWI, performing as a migration operator, is in preference of the high wavenumber updates along reflectors. We propose a nonlinear elastic RWI that inverts for both the low wavenumber and perturbation components of the P- and S-wave velocities. To generate the full elastic reflection wavefields, we derive an equivalent stress source made up by the inverted model perturbations and incident wavefields. We update both the perturbation and propagation parts of the velocity models in a nested fashion. Applications on synthetic isotropic models and field data show that our method can efficiently update the low and high wavenumber parts of the models.
Zhang, Kun; Yan, Jiayong; Lü, Qingtian; Zhao, Jinhua; Hu, Hao
2017-04-01
A new inversion method using marine magnetotellurics is proposed based on previous studies using the nonlinear conjugate gradient method. A numerical example is used to verify the inversion algorithm and program. The inversion model and response resemble the synthetic model. Some technologies have been added to the inversion algorithm: parallel structure, terrain inversion and static shift correction.
Inverse Dynamics of Flexible Manipulators
Moberg, Stig; Hanssen, Sven
2010-01-01
High performance robot manipulators, in terms of cycle time and accuracy, require well designed control methods, based on accurate dynamic models. Robot manipulators are traditionally described by the ﬂexible joint model or the ﬂexible link model. These models only consider elasticity in the rotational direction. When these models are used for control or simulation, the accuracy can be limited due to the model simpliﬁcations, since a real manipulator has a distributed ﬂexibility inall directi...
Dynamic decoupling nonlinear control method for aircraft gust alleviation
Lv, Yang; Wan, Xiaopeng; Li, Aijun
2008-10-01
A dynamic decoupling nonlinear control method for MIMO system is presented in this paper. The dynamic inversion method is used to decouple the multivariable system. The nonlinear control method is used to overcome the poor decoupling effect when the system model is inaccurate. The nonlinear control method has correcting function and is expressed in analytic form, it is easy to adjust the parameters of the controller and optimize the design of the control system. The method is used to design vertical transition mode of active control aircraft for gust alleviation. Simulation results show that the designed vertical transition mode improves the gust alleviation effect about 34% comparing with the normal aircraft.
Edge detection by nonlinear dynamics
Energy Technology Data Exchange (ETDEWEB)
Wong, Yiu-fai
1994-07-01
We demonstrate how the formulation of a nonlinear scale-space filter can be used for edge detection and junction analysis. By casting edge-preserving filtering in terms of maximizing information content subject to an average cost function, the computed cost at each pixel location becomes a local measure of edgeness. This computation depends on a single scale parameter and the given image data. Unlike previous approaches which require careful tuning of the filter kernels for various types of edges, our scheme is general enough to be able to handle different edges, such as lines, step-edges, corners and junctions. Anisotropy in the data is handled automatically by the nonlinear dynamics.
Inverse problem of HIV cell dynamics using Genetic Algorithms
González, J. A.; Guzmán, F. S.
2017-01-01
In order to describe the cell dynamics of T-cells in a patient infected with HIV, we use a flavour of Perelson's model. This is a non-linear system of Ordinary Differential Equations that describes the evolution of healthy, latently infected, infected T-cell concentrations and the free viral cells. Different parameters in the equations give different dynamics. Considering the concentration of these types of cells is known for a particular patient, the inverse problem consists in estimating the parameters in the model. We solve this inverse problem using a Genetic Algorithm (GA) that minimizes the error between the solutions of the model and the data from the patient. These errors depend on the parameters of the GA, like mutation rate and population, although a detailed analysis of this dependence will be described elsewhere.
Dynamic inverse models in human-cyber-physical systems
Robinson, Ryan M.; Scobee, Dexter R. R.; Burden, Samuel A.; Sastry, S. Shankar
2016-05-01
Human interaction with the physical world is increasingly mediated by automation. This interaction is characterized by dynamic coupling between robotic (i.e. cyber) and neuromechanical (i.e. human) decision-making agents. Guaranteeing performance of such human-cyber-physical systems will require predictive mathematical models of this dynamic coupling. Toward this end, we propose a rapprochement between robotics and neuromechanics premised on the existence of internal forward and inverse models in the human agent. We hypothesize that, in tele-robotic applications of interest, a human operator learns to invert automation dynamics, directly translating from desired task to required control input. By formulating the model inversion problem in the context of a tracking task for a nonlinear control system in control-a_ne form, we derive criteria for exponential tracking and show that the resulting dynamic inverse model generally renders a portion of the physical system state (i.e., the internal dynamics) unobservable from the human operator's perspective. Under stability conditions, we show that the human can achieve exponential tracking without formulating an estimate of the system's state so long as they possess an accurate model of the system's dynamics. These theoretical results are illustrated using a planar quadrotor example. We then demonstrate that the automation can intervene to improve performance of the tracking task by solving an optimal control problem. Performance is guaranteed to improve under the assumption that the human learns and inverts the dynamic model of the altered system. We conclude with a discussion of practical limitations that may hinder exact dynamic model inversion.
Handling of impact forces in inverse dynamics
Bisseling, Rob W.; Hof, At L.
2006-01-01
In the standard inverse dynamic method, joint moments are assessed from ground reaction force data and position data, where segmental accelerations are calculated by numerical differentiation of position data after low-pass filtering. This method falls short in analyzing the impact phase, e.g.
Crestel, Benjamin; Alexanderian, Alen; Stadler, Georg; Ghattas, Omar
2017-07-01
The computational cost of solving an inverse problem governed by PDEs, using multiple experiments, increases linearly with the number of experiments. A recently proposed method to decrease this cost uses only a small number of random linear combinations of all experiments for solving the inverse problem. This approach applies to inverse problems where the PDE solution depends linearly on the right-hand side function that models the experiment. As this method is stochastic in essence, the quality of the obtained reconstructions can vary, in particular when only a small number of combinations are used. We develop a Bayesian formulation for the definition and computation of encoding weights that lead to a parameter reconstruction with the least uncertainty. We call these weights A-optimal encoding weights. Our framework applies to inverse problems where the governing PDE is nonlinear with respect to the inversion parameter field. We formulate the problem in infinite dimensions and follow the optimize-then-discretize approach, devoting special attention to the discretization and the choice of numerical methods in order to achieve a computational cost that is independent of the parameter discretization. We elaborate our method for a Helmholtz inverse problem, and derive the adjoint-based expressions for the gradient of the objective function of the optimization problem for finding the A-optimal encoding weights. The proposed method is potentially attractive for real-time monitoring applications, where one can invest the effort to compute optimal weights offline, to later solve an inverse problem repeatedly, over time, at a fraction of the initial cost.
A nonlinear inversion for the velocity background and perturbation models
Wu, Zedong
2015-08-19
Reflected waveform inversion (RWI) provides a method to reduce the nonlinearity of the standard full waveform inversion (FWI) by inverting for the single scattered wavefield obtained using an image. However, current RWI methods usually neglect diving waves, which is an important source of information for extracting the long wavelength components of the velocity model. Thus, we propose a new optimization problem through breaking the velocity model into the background and the perturbation in the wave equation directly. In this case, the perturbed model is no longer the single scattering model, but includes all scattering. We optimize both components simultaneously, and thus, the objective function is nonlinear with respect to both the background and perturbation. The new introduced w can absorb the non-smooth update of background naturally. Application to the Marmousi model with frequencies that start at 5 Hz shows that this method can converge to the accurate velocity starting from a linearly increasing initial velocity. Application to the SEG2014 demonstrates the versatility of the approach.
Linear inverse problem of the reactor dynamics
Volkov, N. P.
2017-01-01
The aim of this work is the study transient processes in nuclear reactors. The mathematical model of the reactor dynamics excluding reverse thermal coupling is investigated. This model is described by a system of integral-differential equations, consisting of a non-stationary anisotropic multispeed kinetic transport equation and a delayed neutron balance equation. An inverse problem was formulated to determine the stationary part of the function source along with the solution of the direct problem. The author obtained sufficient conditions for the existence and uniqueness of a generalized solution of this inverse problem.
Inverse design of nonlinearity in energy harvesters for optimum damping
Ghandchi Tehrani, Maryam; Elliott, S. J.
2016-09-01
This paper presents the inverse design method for the nonlinearity in an energy harvester in order to achieve an optimum damping. A single degree-of-freedom electromechanical oscillator is considered as an energy harvester, which is subjected to a harmonic base excitation. The harvester has a limited throw due to the physical constraint of the device, which means that the amplitude of the relative displacement between the mass of the harvester and the base cannot exceed a threshold when the device is driven at resonance and beyond a particular amplitude. This physical constraint requires the damping of the harvester to be adjusted for different excitation amplitudes, such that the relative displacement is controlled and maintained below the limit. For example, the damping can be increased to reduce the amplitude of the relative displacement. For high excitation amplitudes, the optimum damping is, therefore, dependent on the amplitude of the base excitation, and can be synthesised by a nonlinear function. In this paper, a nonlinear function in the form of a bilinear is considered to represent the damping model of the device. A numerical optimisation using Matlab is carried out to fit a curve to the amplitude-dependent damping in order to determine the optimum bilinear model. The nonlinear damping is then used in the time-domain simulations and the relative displacement and the average harvested power are obtained. It is demonstrated that the proposed nonlinear damping can maintain the relative displacement of the harvester at its maximum level for a wide range of excitation, therefore providing the optimum condition for power harvesting.
Statistical methods in nonlinear dynamics
Indian Academy of Sciences (India)
K P N Murthy; R Harish; S V M Satyanarayana
2005-03-01
Sensitivity to initial conditions in nonlinear dynamical systems leads to exponential divergence of trajectories that are initially arbitrarily close, and hence to unpredictability. Statistical methods have been found to be helpful in extracting useful information about such systems. In this paper, we review briefly some statistical methods employed in the study of deterministic and stochastic dynamical systems. These include power spectral analysis and aliasing, extreme value statistics and order statistics, recurrence time statistics, the characterization of intermittency in the Sinai disorder problem, random walk analysis of diffusion in the chaotic pendulum, and long-range correlations in stochastic sequences of symbols.
Nonlinear system guidance in the presence of transmission zero dynamics
Meyer, G.; Hunt, L. R.; Su, R.
1995-01-01
An iterative procedure is proposed for computing the commanded state trajectories and controls that guide a possibly multiaxis, time-varying, nonlinear system with transmission zero dynamics through a given arbitrary sequence of control points. The procedure is initialized by the system inverse with the transmission zero effects nulled out. Then the 'steady state' solution of the perturbation model with the transmission zero dynamics intact is computed and used to correct the initial zero-free solution. Both time domain and frequency domain methods are presented for computing the steady state solutions of the possibly nonminimum phase transmission zero dynamics. The procedure is illustrated by means of linear and nonlinear examples.
Biped control via nonlinear dynamics
Hmam, Hatem M.
1992-09-01
This thesis applies nonlinear techniques to actuate a biped system and provides a rigorous analysis of the resulting motion. From observation of human locomotion, it is believed that the 'complex' dynamics developed by the aggregation of multiple muscle systems can be generated by a reduced order system which captures the rough details of the locomotion process. The investigation is begun with a simple model of a biped system. Since the locomotion process is cyclic in nature, we focus on applying the topologically similar concept of limit cycles to the simple model in order to generate the desired gaits. A rigorous analysis of the biped dynamics shows that the controlled motion is robust against dynamical disturbances. In addition, different biped gaits are generated by merely adjusting some of the limit cycle parameters. More dynamical and actuation complexities are then added for realism. First, two small foot components are added and the overall biped motion under the same control actuation is analyzed. Due to the physical constraints on the feet, it is shown using singular perturbation theory how the gross behavior of the biped dynamics are dictated by those of the reduced model. Next, an analysis of the biped dynamics under added nonlinear elasticities in the legs is carried out. Moreover, using a slightly modified model, forward motion is generated in the sagittal plane. At each step, a small amount of energy is consistently derived from the vertical plane and converted into a forward motion. Stability of the forward dynamics is guaranteed by appropriate foot placement. Finally, the robustness of the controlled biped dynamics is rigorously analyzed and illustrated through extensive computer simulations.
Humanoid Walking Robot: Modeling, Inverse Dynamics, and Gain Scheduling Control
Directory of Open Access Journals (Sweden)
Elvedin Kljuno
2010-01-01
Full Text Available This article presents reference-model-based control design for a 10 degree-of-freedom bipedal walking robot, using nonlinear gain scheduling. The main goal is to show concentrated mass models can be used for prediction of the required joint torques for a bipedal walking robot. Relatively complicated architecture, high DOF, and balancing requirements make the control task of these robots difficult. Although linear control techniques can be used to control bipedal robots, nonlinear control is necessary for better performance. The emphasis of this work is to show that the reference model can be a bipedal walking model with concentrated mass at the center of gravity, which removes the problems related to design of a pseudo-inverse system. Another significance of this approach is the reduced calculation requirements due to the simplified procedure of nominal joint torques calculation. Kinematic and dynamic analysis is discussed including results for joint torques and ground force necessary to implement a prescribed walking motion. This analysis is accompanied by a comparison with experimental data. An inverse plant and a tracking error linearization-based controller design approach is described. We propose a novel combination of a nonlinear gain scheduling with a concentrated mass model for the MIMO bipedal robot system.
Nonlinear dynamics of cardiovascular ageing
Energy Technology Data Exchange (ETDEWEB)
Shiogai, Y. [Physics Department, Lancaster University, Lancaster LA1 4YB (United Kingdom); Stefanovska, A. [Physics Department, Lancaster University, Lancaster LA1 4YB (United Kingdom); Faculty of Electrical Engineering, University of Ljubljana, Ljubljana (Slovenia); McClintock, P.V.E. [Physics Department, Lancaster University, Lancaster LA1 4YB (United Kingdom)], E-mail: p.v.e.mcclintock@lancaster.ac.uk
2010-03-15
The application of methods drawn from nonlinear and stochastic dynamics to the analysis of cardiovascular time series is reviewed, with particular reference to the identification of changes associated with ageing. The natural variability of the heart rate (HRV) is considered in detail, including the respiratory sinus arrhythmia (RSA) corresponding to modulation of the instantaneous cardiac frequency by the rhythm of respiration. HRV has been intensively studied using traditional spectral analyses, e.g. by Fourier transform or autoregressive methods, and, because of its complexity, has been used as a paradigm for testing several proposed new methods of complexity analysis. These methods are reviewed. The application of time-frequency methods to HRV is considered, including in particular the wavelet transform which can resolve the time-dependent spectral content of HRV. Attention is focused on the cardio-respiratory interaction by introduction of the respiratory frequency variability signal (RFV), which can be acquired simultaneously with HRV by use of a respiratory effort transducer. Current methods for the analysis of interacting oscillators are reviewed and applied to cardio-respiratory data, including those for the quantification of synchronization and direction of coupling. These reveal the effect of ageing on the cardio-respiratory interaction through changes in the mutual modulation of the instantaneous cardiac and respiratory frequencies. Analyses of blood flow signals recorded with laser Doppler flowmetry are reviewed and related to the current understanding of how endothelial-dependent oscillations evolve with age: the inner lining of the vessels (the endothelium) is shown to be of crucial importance to the emerging picture. It is concluded that analyses of the complex and nonlinear dynamics of the cardiovascular system can illuminate the mechanisms of blood circulation, and that the heart, the lungs and the vascular system function as a single entity in
International Conference on Applications in Nonlinear Dynamics
Longhini, Patrick; Palacios, Antonio
2017-01-01
This book presents collaborative research works carried out by experimentalists and theorists around the world in the field of nonlinear dynamical systems. It provides a forum for applications of nonlinear systems while solving practical problems in science and engineering. Topics include: Applied Nonlinear Optics, Sensor, Radar & Communication Signal Processing, Nano Devices, Nonlinear Biomedical Applications, Circuits & Systems, Coupled Nonlinear Oscillator, Precision Timing Devices, Networks, and other contemporary topics in the general field of Nonlinear Science. This book provides a comprehensive report of the various research projects presented at the International Conference on Applications in Nonlinear Dynamics (ICAND 2016) held in Denver, Colorado, 2016. It can be a valuable tool for scientists and engineering interested in connecting ideas and methods in nonlinear dynamics with actual design, fabrication and implementation of engineering applications or devices.
The Dynamics of Nonlinear Inference
Kadakia, Nirag
The determination of the hidden states of coupled nonlinear systems is frustrated by the presence of high-dimensionality, chaos, and sparse observability. This problem resides naturally in a Bayesian context: an underlying physical process produces a data stream, which - though noisy and incomplete - can in principle be inverted to express the likelihood of the underlying process itself. A large class of well-developed methods treat this problem in a sequential predict-and-correct manner that alternates information from the presumed dynamical model with information from the data. One might instead formulate this problem in a temporally global, non-sequential manner, which suggests new avenues of approach within an optimization context, but also poses new challenges in numerical implementation. The variational annealing (VA) technique is proposed to address these problems by leveraging an inherent separability between the convex and nonconvex contributions of the resulting functional forms. VA is shown to reliably track unobservable states in sparsely observed chaotic systems, as well as in minimally-observed biophysical neural models. Second, this problem can be formally cast in continuous time as a Wiener path integral, which then suggests classical solutions derived from Hamilton's principle. These solutions come with their own difficulties in that they comprise an unstable boundary-value problem. Accordingly, a further technique called Hamiltonian variational annealing is proposed, which again exploits an existing separability of convexity and nonlinearity, this time in a an enlarged manifold constrained by underlying symmetries. A running theme in this thesis is that the optimal estimate of a nonlinear system is itself a dynamical system that lives in an unstable, symplectic manifold. When this system is recast in a variational context, instability is manifested as nonconvexity, the central idea being that when this nonconvexity is incorporated in a systematic
Double inverse stochastic resonance with dynamic synapses
Uzuntarla, Muhammet; Torres, Joaquin J.; So, Paul; Ozer, Mahmut; Barreto, Ernest
2017-01-01
We investigate the behavior of a model neuron that receives a biophysically realistic noisy postsynaptic current based on uncorrelated spiking activity from a large number of afferents. We show that, with static synapses, such noise can give rise to inverse stochastic resonance (ISR) as a function of the presynaptic firing rate. We compare this to the case with dynamic synapses that feature short-term synaptic plasticity and show that the interval of presynaptic firing rate over which ISR exists can be extended or diminished. We consider both short-term depression and facilitation. Interestingly, we find that a double inverse stochastic resonance (DISR), with two distinct wells centered at different presynaptic firing rates, can appear.
Dynamic computer-generated nonlinear-optical holograms
Liu, Haigang; Li, Jun; Fang, Xiangling; Zhao, Xiaohui; Zheng, Yuanlin; Chen, Xianfeng
2017-08-01
We propose and experimentally demonstrate dynamic nonlinear optical holograms by introducing the concept of computer-generated holograms for second-harmonic generation of a structured fundamental wave with a specially designed wave front. The generation of Laguerre-Gaussian second-harmonic beams is investigated in our experiment. Such a method, which only dynamically controls the wave front of the fundamental wave by a spatial light modulator, does not need domain inversion in nonlinear crystals and hence is a more flexible way to achieve the off-axis nonlinear second-harmonic beams. It can also be adopted in other schemes and has potential applications in nonlinear frequency conversion, optical signal processing, and real-time hologram, etc.
Explanation of the inverse Doppler effect observed in nonlinear transmission lines.
Kozyrev, Alexander B; van der Weide, Daniel W
2005-05-27
The theory of the inverse Doppler effect recently observed in magnetic nonlinear transmission lines is developed. We explain the crucial role of the backward spatial harmonic in the occurrence of an inverse Doppler effect and draw analogies of the magnetic nonlinear transmission line to the backward wave oscillator.
Inverse Eigenvalue Problem in Structural Dynamics Design
Institute of Scientific and Technical Information of China (English)
Huiqing Xie; Hua Dai
2006-01-01
A kind of inverse eigenvalue problem in structural dynamics design is considered. The problem is formulated as an optimization problem. The properties of this problem are analyzed, and the existence of the optimum solution is proved. The directional derivative of the objective function is obtained and a necessary condition for a point to be a local minimum point is given. Then a numerical algorithm for solving the problem is presented and a plane-truss problem is discussed to show the applications of the theories and the algorithm.
Nonlinear inversion for arbitrarily-oriented anisotropic models II: Inversion techniques
Bremner, P. M.; Panning, M. P.
2011-12-01
We present output models from inversion of a synthetic surface wave dataset. We implement new 3-D finite-frequency kernels, based on the Born approximation, to invert for upper mantle structure beneath western North America. The kernels are formulated based on a hexagonal symmetry with an arbitrary orientation. Numerical tests were performed to achieve a robust inversion scheme. Four synthetic input models were created, to include: isotropic, constant strength anisotropic, variable strength anisotropic, and both anisotropic and isotropic together. The reference model was a simplified version of PREM (dubbed PREM LIGHT) in which the crust and 220 km discontinuity have been removed. Output models from inversions of calculated synthetic data are compared against these input models to test for accurate reproduction of input model features, and the resolution of those features. The object of this phase of the study was to determine appropriate nonlinear inversion schemes that adequately recover the input models. The synthetic dataset consists of collected seismic waveforms of 126 earthquake mechanisms, of magnitude 6-7 from Dec 2006 to Feb 2009, from the IRIS database. Events were selected to correlate with USArray deployments, and to have as complete an azimuthal coverage as possible. The events occurred within a circular region of radius 150o centered about 44o lat, -110o lon (an arbitrary location within USArray coverage). Synthetic data were calculated utilizing a spectral element code (SEM) coupled to a normal mode solution. The mesh consists of a 3-D heterogeneous outer shell, representing the upper mantle above 450 km depth, coupled to a spherically symmetric inner sphere. From the synthetic dataset, multi-taper fundamental mode surface wave phase delay measurements are taken. The orthogonal 2.5π -prolate spheroidal wave function eigentapers (Slepian tapers) reduce noise biasing, and can provide error estimates in phase delay measurements. This study is a
Rayleigh scattering and nonlinear inversion of elastic waves
Energy Technology Data Exchange (ETDEWEB)
Gritto, R.
1995-12-01
Rayleigh scattering of elastic waves by an inclusion is investigated and the limitations determined. In the near field of the inhomogeneity, the scattered waves are up to a factor of 300 stronger than in the far field, excluding the application of the far field Rayleigh approximation for this range. The investigation of the relative error as a function of parameter perturbation shows a range of applicability broader than previously assumed, with errors of 37% and 17% for perturbations of {minus}100% and +100%, respectively. The validity range for the Rayleigh limit is controlled by large inequalities, and therefore, the exact limit is determined as a function of various parameter configurations, resulting in surprisingly high values of up to k{sub p}R = 0.9. The nonlinear scattering problem can be solved by inverting for equivalent source terms (moments) of the scatterer, before the elastic parameters are determined. The nonlinear dependence between the moments and the elastic parameters reveals a strong asymmetry around the origin, which will produce different results for weak scattering approximations depending on the sign of the anomaly. Numerical modeling of cross hole situations shows that near field terms are important to yield correct estimates of the inhomogeneities in the vicinity of the receivers, while a few well positioned sources and receivers considerably increase the angular coverage, and thus the model resolution of the inversion parameters. The pattern of scattered energy by an inhomogeneity is complicated and varies depending on the object, the wavelength of the incident wave, and the elastic parameters involved. Therefore, it is necessary to investigate the direction of scattered amplitudes to determine the best survey geometry.
MINIMAL INVERSION AND ITS ALGORITHMS OF DISCRETE-TIME NONLINEAR SYSTEMS
Institute of Scientific and Technical Information of China (English)
ZHENG Yufan
2005-01-01
The left-inverse system with minimal order and its algorithms of discrete-time nonlinear systems are studied in a linear algebraic framework. The general structure of left-inverse system is described and computed in symbolic algorithm. Two algorithms are given for constructing left-inverse systems with minimal order.
RESEARCH ON NONLINEAR PROBLEMS IN STRUCTURAL DYNAMICS.
Research on nonlinear problems structural dynamics is briefly summarized. Panel flutter was investigated to make a critical comparison between theory...panel flutter in aerospace vehicles, plausible simplifying assumptions are examined in the light of experimental results. Structural dynamics research
Nonlinear inverse modeling of sensor based on back-propagation fuzzy logical system
Institute of Scientific and Technical Information of China (English)
Li Jun; Liu Junhua
2007-01-01
Objective To correct the nonlinear error of sensor output, a new approach to sensor inverse modeling based on Back-Propagation Fuzzy Logical System (BP FS) is presented. Methods The BP FS is a computationally efficient nonlinear universal approximator, which is capable of implementing complex nonlinear mapping from its input pattern space to the output with fast convergence speed. Results The neuro-fuzzy hybrid system, i.e. BP FS, is then applied to construct nonlinear inverse model of pressure sensor. The experimental results show that the proposed inverse modeling method automatically compensates the associated nonlinear error in pressure estimation, and thus the performance of pressure sensor is significantly improved. Conclusion The proposed method can be widely used in nonlinearity correction of various kinds of sensors to compensate the effects of nonlinearity and temperature on sensor output.
An inverse problem of determining a nonlinear term in an ordinary differential equation
Kamimura, Yutaka
1998-01-01
An inverse problem for a nonlinear ordinary differential equation is discussed. We prove an existence theorem of a nonlinear term with which a boundary value problem admits a solution. This is an improvement of earlier work by A. Lorenzi. We also prove a uniqueness theorem of the nonlinear term.
Nonlinear dynamics in human behavior
Energy Technology Data Exchange (ETDEWEB)
Huys, Raoul [Centre National de la Recherche Scientifique (CNRS), 13 - Marseille (France); Marseille Univ. (France). Movement Science Inst.; Jirsa, Viktor K. (eds.) [Centre National de la Recherche Scientifique (CNRS), 13 - Marseille (France); Marseille Univ. (France). Movement Science Inst.; Florida Atlantic Univ., Boca Raton, FL (United States). Center for Complex Systems and Brain Sciences
2010-07-01
Humans engage in a seemingly endless variety of different behaviors, of which some are found across species, while others are conceived of as typically human. Most generally, behavior comes about through the interplay of various constraints - informational, mechanical, neural, metabolic, and so on - operating at multiple scales in space and time. Over the years, consensus has grown in the research community that, rather than investigating behavior only from bottom up, it may be also well understood in terms of concepts and laws on the phenomenological level. Such top down approach is rooted in theories of synergetics and self-organization using tools from nonlinear dynamics. The present compendium brings together scientists from all over the world that have contributed to the development of their respective fields departing from this background. It provides an introduction to deterministic as well as stochastic dynamical systems and contains applications to motor control and coordination, visual perception and illusion, as well as auditory perception in the context of speech and music. (orig.)
Nonlinear Dynamical Analysis of Fibrillation
Kerin, John A.; Sporrer, Justin M.; Egolf, David A.
2013-03-01
The development of spatiotemporal chaotic behavior in heart tissue, termed fibrillation, is a devastating, life-threatening condition. The chaotic behavior of electrochemical signals, in the form of spiral waves, causes the muscles of the heart to contract in an incoherent manner, hindering the heart's ability to pump blood. We have applied the mathematical tools of nonlinear dynamics to large-scale simulations of a model of fibrillating heart tissue to uncover the dynamical modes driving this chaos. By studying the evolution of Lyapunov vectors and exponents over short times, we have found that the fibrillating tissue is sensitive to electrical perturbations only in narrow regions immediately in front of the leading edges of spiral waves, especially when these waves collide, break apart, or hit the edges of the tissue sample. Using this knowledge, we have applied small stimuli to areas of varying sensitivity. By studying the evolution of the effects of these perturbations, we have made progress toward controlling the electrochemical patterns associated with heart fibrillation. This work was supported by the U.S. National Science Foundation (DMR-0094178) and Research Corporation.
Nonlinear Chemical Dynamics and Synchronization
Li, Ning
Alan Turing's work on morphogenesis, more than half a century ago, continues to motivate and inspire theoretical and experimental biologists even today. That said, there are very few experimental systems for which Turing's theory is applicable. In this thesis we present an experimental reaction-diffusion system ideally suited for testing Turing's ideas in synthetic "cells" consisting of microfluidically produced surfactant-stabilized emulsions in which droplets containing the Belousov-Zhabotinsky (BZ) oscillatory chemical reactants are dispersed in oil. The BZ reaction has become the prototype of nonlinear dynamics in chemistry and a preferred system for exploring the behavior of coupled nonlinear oscillators. Our system consists of a surfactant stabilized monodisperse emulsion of drops of aqueous BZ solution dispersed in a continuous phase of oil. In contrast to biology, here the chemistry is understood, rate constants are measured and interdrop coupling is purely diffusive. We explore a large set of parameters through control of rate constants, drop size, spacing, and spatial arrangement of the drops in lines and rings in one-dimension (1D) and hexagonal arrays in two-dimensions (2D). The Turing model is regarded as a metaphor for morphogenesis in biology but not for prediction. Here, we develop a quantitative and falsifiable reaction-diffusion model that we experimentally test with synthetic cells. We quantitatively establish the extent to which the Turing model in 1D describes both stationary pattern formation and temporal synchronization of chemical oscillators via reaction-diffusion and in 2D demonstrate that chemical morphogenesis drives physical differentiation in synthetic cells.
Inverse solution technique of steady-state responses for local nonlinear structures
Wang, Xing; Guan, Xin; Zheng, Gangtie
2016-03-01
An inverse solution technique with the ability of obtaining complete steady-state primary harmonic responses of local nonlinear structures in the frequency domain is proposed in the present paper. In this method, the nonlinear dynamic equations of motion is first condensed from many to only one algebraic amplitude-frequency equation of relative motion. Then this equation is transformed into a polynomial form, and with its frequency as the unknown variable, the polynomial equation is solved by tracing all the solutions of frequency with the increase of amplitude. With this solution technique, some complicated dynamic behaviors such as sharp tuning, anomalous jumps, breaks in responses and detached resonance curves could be obtained. The proposed method is demonstrated and validated through a finite element beam under force excitations and a lumped parameter model with a local nonlinear element under base excitations. The phenomenon of detached resonance curves in the frequency response and its coupling effects with multiple linear modes in the latter example are observed.
Dynamics and vibrations progress in nonlinear analysis
Kachapi, Seyed Habibollah Hashemi
2014-01-01
Dynamical and vibratory systems are basically an application of mathematics and applied sciences to the solution of real world problems. Before being able to solve real world problems, it is necessary to carefully study dynamical and vibratory systems and solve all available problems in case of linear and nonlinear equations using analytical and numerical methods. It is of great importance to study nonlinearity in dynamics and vibration; because almost all applied processes act nonlinearly, and on the other hand, nonlinear analysis of complex systems is one of the most important and complicated tasks, especially in engineering and applied sciences problems. There are probably a handful of books on nonlinear dynamics and vibrations analysis. Some of these books are written at a fundamental level that may not meet ambitious engineering program requirements. Others are specialized in certain fields of oscillatory systems, including modeling and simulations. In this book, we attempt to strike a balance between th...
Inverse Dynamics and the Immeasurable Motions
DEFF Research Database (Denmark)
Rasmussen, John; Andersen, Michael Skipper; Damsgaard, Michael
, typically gait, and a well-conducted experiment with a good-quality motion capture system will register this degree-of-freedom with sufficient accuracy for most applications. However, it is known from bone pin studies (Benoit et al. 2006) that the knee has significant movements additional to flexion...... complications of this scheme is that a large part of the acting forces are due to muscle contractions, which in this case also must be simulated. The ability to predict muscle contraction in complex movements has improved significantly in recent years, but the simultaneous prediction of movement and force...... in a reformulation of the underdeterminate inverse dynamics-type equilibrium equations to allow certain degrees of freedom to be governed by elastic equilibrium rather than measured movements. We briefly outline the method and compare predicted movements during overground gait on a treadmill measured using...
Nonlinear tuning of microresonators for dynamic range enhancement.
Saghafi, M; Dankowicz, H; Lacarbonara, W
2015-07-08
This paper investigates the development of a novel framework and its implementation for the nonlinear tuning of nano/microresonators. Using geometrically exact mechanical formulations, a nonlinear model is obtained that governs the transverse and longitudinal dynamics of multilayer microbeams, and also takes into account rotary inertia effects. The partial differential equations of motion are discretized, according to the Galerkin method, after being reformulated into a mixed form. A zeroth-order shift as well as a hardening effect are observed in the frequency response of the beam. These results are confirmed by a higher order perturbation analysis using the method of multiple scales. An inverse problem is then proposed for the continuation of the critical amplitude at which the transition to nonlinear response characteristics occurs. Path-following techniques are employed to explore the dependence on the system parameters, as well as on the geometry of bilayer microbeams, of the magnitude of the dynamic range in nano/microresonators.
Nonlinear tuning of microresonators for dynamic range enhancement
Saghafi, M.; Dankowicz, H.; Lacarbonara, W.
2015-01-01
This paper investigates the development of a novel framework and its implementation for the nonlinear tuning of nano/microresonators. Using geometrically exact mechanical formulations, a nonlinear model is obtained that governs the transverse and longitudinal dynamics of multilayer microbeams, and also takes into account rotary inertia effects. The partial differential equations of motion are discretized, according to the Galerkin method, after being reformulated into a mixed form. A zeroth-order shift as well as a hardening effect are observed in the frequency response of the beam. These results are confirmed by a higher order perturbation analysis using the method of multiple scales. An inverse problem is then proposed for the continuation of the critical amplitude at which the transition to nonlinear response characteristics occurs. Path-following techniques are employed to explore the dependence on the system parameters, as well as on the geometry of bilayer microbeams, of the magnitude of the dynamic range in nano/microresonators. PMID:26345078
Research on Nonlinear Dynamical Systems.
1983-01-10
investigated fundamental aspects of functional differential equations, including qualitative questions (stability, nonlinear oscillations ), in 142,45,47,52...Bifurcation in the Duffing equation with several parameters, II. Proc. of the Royal Society of Edinburgh, Series A, 79A (1977), pp.317-326. 1I.J (with ;Ibtoas...Lecture Notes in Mathematics, Vol. 730 (1979). [54] Nonlinear oscillations in equations with delays. Proc. at A.M.S. 10th Summer Seminar on Nonlinear
Nonlinear and nonequilibrium dynamics in geomaterials.
TenCate, James A; Pasqualini, Donatella; Habib, Salman; Heitmann, Katrin; Higdon, David; Johnson, Paul A
2004-08-01
The transition from linear to nonlinear dynamical elasticity in rocks is of considerable interest in seismic wave propagation as well as in understanding the basic dynamical processes in consolidated granular materials. We have carried out a careful experimental investigation of this transition for Berea and Fontainebleau sandstones. Below a well-characterized strain, the materials behave linearly, transitioning beyond that point to a nonlinear behavior which can be accurately captured by a simple macroscopic dynamical model. At even higher strains, effects due to a driven nonequilibrium state, and relaxation from it, complicate the characterization of the nonlinear behavior.
Quantum Dynamics of Nonlinear Cavity Systems
Nation, Paul D.
2010-01-01
We investigate the quantum dynamics of three different configurations of nonlinear cavity systems. To begin, we carry out a quantum analysis of a dc superconducting quantum interference device (SQUID) mechanical displacement detector comprised of a SQUID with a mechanically compliant loop segment. The SQUID is approximated by a nonlinear current-dependent inductor, inducing a flux tunable nonlinear Duffing term in the cavity equation of motion. Expressions are derived for the detector signal ...
Nonlinear Dynamic Model Explains The Solar Dynamic
Kuman, Maria
Nonlinear mathematical model in torus representation describes the solar dynamic. Its graphic presentation shows that without perturbing force the orbits of the planets would be circles; only perturbing force could elongate the circular orbits into ellipses. Since the Hubble telescope found that the planetary orbits of other stars in the Milky Way are also ellipses, powerful perturbing force must be present in our galaxy. Such perturbing force is the Sagittarius Dwarf Galaxy with its heavy Black Hole and leftover stars, which we see orbiting around the center of our galaxy. Since observations of NASA's SDO found that magnetic fields rule the solar activity, we can expect when the planets align and their magnetic moments sum up, the already perturbed stars to reverse their magnetic parity (represented graphically as periodic looping through the hole of the torus). We predict that planets aligned on both sides of the Sun, when their magnetic moments sum-up, would induce more flares in the turbulent equatorial zone, which would bulge. When planets align only on one side of the Sun, the strong magnetic gradient of their asymmetric pull would flip the magnetic poles of the Sun. The Sun would elongate pole-to-pole, emit some energy through the poles, and the solar activity would cease. Similar reshaping and emission was observed in stars called magnetars and experimentally observed in super-liquid fast-spinning Helium nanodroplets. We are certain that NASA's SDO will confirm our predictions.
Nonlinear dynamics of the left ventricle.
Munteanu, Ligia; Chiroiu, Calin; Chiroiu, Veturia
2002-05-01
The cnoidal method is applied to solve the set of nonlinear dynamic equations of the left ventricle. By using the theta-function representation of the solutions and a genetic algorithm, the ventricular motion can be described as a linear superposition of cnoidal pulses and additional terms, which include nonlinear interactions among them.
Nonlinear instability and dynamic bifurcation of a planeinterface during solidification
Institute of Scientific and Technical Information of China (English)
吴金平; 侯安新; 黄定华; 鲍征宇; 高志农; 屈松生
2001-01-01
By taking average over the curvature, the temperature and its gradient, the solute con-centration and its gradient at the flange of planar interface perturbed by sinusoidal ripple during solidifi-cation, the nonlinear dynamic equations of the sinusoidal perturbation wave have been set up. Analysisof the nonlinear instability and the behaviors of dynamic bifurcation of the solutions of these equationsshows that (i) the way of dynamic bifurcation of the flat-to-cellular interface transition vades with differ-ent thermal gradients. The quasi-subcritical-lag bifurcation occurs in the small interface thermal gradientscope, the supercritical-lag bifurcation in the medium thermal gradient scope and the supercritical bifur-cation in the large thermal gradient scope. (ii) The transition of cellular-to-flat interface is realizedthrough supercritical inverse bifurcation in the rapid solidification area.
Alkhalifah, Tariq Ali
2012-09-25
Traveltime inversion focuses on the geometrical features of the waveform (traveltimes), which is generally smooth, and thus, tends to provide averaged (smoothed) information of the model. On other hand, general waveform inversion uses additional elements of the wavefield including amplitudes to extract higher resolution information, but this comes at the cost of introducing non-linearity to the inversion operator, complicating the convergence process. We use unwrapped phase-based objective functions in waveform inversion as a link between the two general types of inversions in a domain in which such contributions to the inversion process can be easily identified and controlled. The instantaneous traveltime is a measure of the average traveltime of the energy in a trace as a function of frequency. It unwraps the phase of wavefields yielding far less non-linearity in the objective function than that experienced with conventional wavefields, yet it still holds most of the critical wavefield information in its frequency dependency. However, it suffers from non-linearity introduced by the model (or reflectivity), as reflections from independent events in our model interact with each other. Unwrapping the phase of such a model can mitigate this non-linearity as well. Specifically, a simple modification to the inverted domain (or model), can reduce the effect of the model-induced non-linearity and, thus, make the inversion more convergent. Simple numerical examples demonstrate these assertions.
NONLINEAR DYNAMIC ANALYSIS OF FLEXIBLE MULTIBODY SYSTEM
Institute of Scientific and Technical Information of China (English)
A.Y.T.Leung; WuGuorong; ZhongWeifang
2004-01-01
The nonlinear dynamic equations of a multibody system composed of flexible beams are derived by using the Lagrange multiplier method. The nonlinear Euler beam theory with inclusion of axial deformation effect is employed and its deformation field is described by exact vibration modes. A numerical procedure for solving the dynamic equations is presented based on the Newmark direct integration method combined with Newton-Raphson iterative method. The results of numerical examples prove the correctness and efficiency of the method proposed.
Dissipative Nonlinear Dynamics in Holography
Basu, Pallab
2013-01-01
We look at the response of a nonlinearly coupled scalar field in an asymptotically AdS black brane geometry and find a behaviour very similar to that of known dissipative nonlinear systems like the chaotic pendulum. Transition to chaos proceeds through a series of period-doubling bifurcations. The presence of dissipation, crucial to this behaviour, arises naturally in a black hole background from the ingoing conditions imposed at the horizon. AdS/CFT translates our solution to a chaotic response of the operator dual to the scalar field. Our setup can also be used to study quench-like behaviour in strongly coupled nonlinear systems.
Equivalence Between Approximate Dynamic Inversion and Proportional-Integral Control
2008-09-29
Hovakimyan, E. Lavretsky, and C. Cao, “Dynamic inversion of multi- input nonaffine systems via time-scale separation,” in Proceedings of the American Control Conference , Minneapolis...Adaptive dynamic inversion for nonaffine-in-control systems via time-scale separation: Part II,” in Proceedings of the American Control Conference , Portland
Nonlinear dynamics as an engine of computation.
Kia, Behnam; Lindner, John F; Ditto, William L
2017-03-06
Control of chaos teaches that control theory can tame the complex, random-like behaviour of chaotic systems. This alliance between control methods and physics-cybernetical physics-opens the door to many applications, including dynamics-based computing. In this article, we introduce nonlinear dynamics and its rich, sometimes chaotic behaviour as an engine of computation. We review our work that has demonstrated how to compute using nonlinear dynamics. Furthermore, we investigate the interrelationship between invariant measures of a dynamical system and its computing power to strengthen the bridge between physics and computation.This article is part of the themed issue 'Horizons of cybernetical physics'.
Nonlinear dynamics as an engine of computation
Kia, Behnam; Lindner, John F.; Ditto, William L.
2017-03-01
Control of chaos teaches that control theory can tame the complex, random-like behaviour of chaotic systems. This alliance between control methods and physics-cybernetical physics-opens the door to many applications, including dynamics-based computing. In this article, we introduce nonlinear dynamics and its rich, sometimes chaotic behaviour as an engine of computation. We review our work that has demonstrated how to compute using nonlinear dynamics. Furthermore, we investigate the interrelationship between invariant measures of a dynamical system and its computing power to strengthen the bridge between physics and computation. This article is part of the themed issue 'Horizons of cybernetical physics'.
Teaching nonlinear dynamics through elastic cords
Energy Technology Data Exchange (ETDEWEB)
Chacon, R; Galan, C A; Sanchez-Bajo, F, E-mail: rchacon@unex.e [Departamento de Fisica Aplicada, Escuela de IngenierIas Industriales, Universidad de Extremadura, Apartado Postal 382, E-06071 Badajoz (Spain)
2011-01-15
We experimentally studied the restoring force of a length of stretched elastic cord. A simple analytical expression for the restoring force was found to fit all the experimental results for different elastic materials. Remarkably, this analytical expression depends upon an elastic-cord characteristic parameter which exhibits two limiting values corresponding to two nonlinear springs with different Hooke's elastic constants. Additionally, the simplest model of elastic cord dynamics is capable of exhibiting a great diversity of nonlinear phenomena, including bifurcations and chaos, thus providing a suitable alternative model system for discussing the basic essentials of nonlinear dynamics in the context of intermediate physics courses at university level.
MEMS linear and nonlinear statics and dynamics
Younis, Mohammad I
2011-01-01
MEMS Linear and Nonlinear Statics and Dynamics presents the necessary analytical and computational tools for MEMS designers to model and simulate most known MEMS devices, structures, and phenomena. This book also provides an in-depth analysis and treatment of the most common static and dynamic phenomena in MEMS that are encountered by engineers. Coverage also includes nonlinear modeling approaches to modeling various MEMS phenomena of a nonlinear nature, such as those due to electrostatic forces, squeeze-film damping, and large deflection of structures. The book also: Includes examples of nume
Mathematical modeling and applications in nonlinear dynamics
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...
Geodynamic inversion to constrain the nonlinear rheology of the lithosphere
Baumann, Tobias; Kaus, Boris
2015-04-01
A common method to determine the strength of the lithosphere is through estimating its effective elastic thickness from the coherence between gravity and topography. This method assumes a priori that the lithosphere is a thin elastic plate floating on a viscous mantle. Whereas this seems to work well with oceanic plates, it has given controversial results in continental collision zones. Usually, continental collisions zones are well-studied areas for which additional geophysical datasets such as receiver functions and seismic tomography exist that constrain the geometry of the lithosphere and often show that it is rather complex. Yet, lithospheric geometry by itself is insufficient to understand the dynamics of the lithosphere, as this also requires knowledge of the rheology of the lithosphere. Experimental results show significant variability between various rock types and there are large uncertainties in extrapolating laboratory values to nature, which leaves room for speculation. An independent approach is thus required to better understand the rheology and dynamics of the lithosphere in collision zones. Our method combines numerical thermo-mechanical forward models of the present-day lithosphere with a massively parallel Bayesian inversion approach. The geometry of the forward models is part of the a priori knowledge and is constructed from seismological data. We jointly invert topography, gravity, horizontal and vertical surface velocities to constrain the unknown rheological material parameters of the forward models in a probabilistic sense. The model rheology is described with experimentally determined viscous creep laws and other parameters describing the plastic behaviour. As viscosity is temperature dependent, the temperature structure of the forward models is parameterised as well. We apply the method to cross-sections of the India-Asia collision system. In this case, we deal with 17 to 20 model parameters, which requires solving up to 2 × 106 forward
Nonlinear Dynamics of Structures with Material Degradation
Soltani, P.; Wagg, D. J.; Pinna, C.; Whear, R.; Briody, C.
2016-09-01
Structures usually experience deterioration during their working life. Oxidation, corrosion, UV exposure, and thermo-mechanical fatigue are some of the most well-known mechanisms that cause degradation. The phenomenon gradually changes structural properties and dynamic behaviour over their lifetime, and can be more problematic and challenging in the presence of nonlinearity. In this paper, we study how the dynamic behaviour of a nonlinear system changes as the thermal environment causes certain parameters to vary. To this end, a nonlinear lumped mass modal model is considered and defined under harmonic external force. Temperature dependent material functions, formulated from empirical test data, are added into the model. Using these functions, bifurcation parameters are defined and the corresponding nonlinear responses are observed by numerical continuation. A comparison between the results gives a preliminary insight into how temperature induced properties affects the dynamic response and highlights changes in stability conditions of the structure.
Nonlinear dynamics and chaotic phenomena an introduction
Shivamoggi, Bhimsen K
2014-01-01
This book starts with a discussion of nonlinear ordinary differential equations, bifurcation theory and Hamiltonian dynamics. It then embarks on a systematic discussion of the traditional topics of modern nonlinear dynamics -- integrable systems, Poincaré maps, chaos, fractals and strange attractors. The Baker’s transformation, the logistic map and Lorenz system are discussed in detail in view of their central place in the subject. There is a detailed discussion of solitons centered around the Korteweg-deVries equation in view of its central place in integrable systems. Then, there is a discussion of the Painlevé property of nonlinear differential equations which seems to provide a test of integrability. Finally, there is a detailed discussion of the application of fractals and multi-fractals to fully-developed turbulence -- a problem whose understanding has been considerably enriched by the application of the concepts and methods of modern nonlinear dynamics. On the application side, there is a special...
Nonlinear inverse synthesis for high spectral efficiency transmission in optical fibers
Le, Son Thai; Turitsyn, Sergei K
2014-01-01
In linear communication channels, spectral components (modes) defined by the Fourier transform of the signal propagate without interactions with each other. In certain nonlinear channels, such as the one modelled by the classical nonlinear Schr\\"odinger equation, there are nonlinear modes (nonlinear signal spectrum) that also propagate without interacting with each other and without corresponding nonlinear cross talk; effectively, in a linear manner. Here, we describe in a constructive way how to introduce such nonlinear modes for a given input signal. We investigate the performance of the nonlinear inverse synthesis (NIS) method, in which the information is encoded directly onto the continuous part of the nonlinear signal spectrum. This transmission technique, combined with the appropriate distributed Raman amplification, can provide an effective eigenvalue division multiplexing with high spectral efficiency, thanks to highly suppressed channel cross talk. The proposed NIS approach can be integrated with any...
Theory and application of nonlinear river dynamics
Institute of Scientific and Technical Information of China (English)
Yu-chuan BAI; Zhao-yin WANG
2014-01-01
A theoretical model for river evolution including riverbed formation and meandering pattern formation is presented in this paper. Based on nonlinear mathematic theory, the nonlinear river dynamic theory is set up for river dynamic process. Its core content includes the stability and tropism characteristics of flow motion in river and river selves’ evolution. The stability of river dynamic process depends on the response of river selves to the external disturbance, if the disturbance and the resulting response will eventually attenuate, and the river dynamics process can be restored to new equilibrium state, the river dynamic process is known as stable;otherwise, the river dynamic process is unstable. The river dynamic process tropism refers to that the evolution tendency of river morphology after the disturbance. As an application of this theory, the dynamical stability of the constant curvature river bend is calculated for its coherent vortex disturbance and response. In addition, this paper discusses the nonlinear evolution of the river peristaltic process under a large-scale disturbance, showing the nonlinear tendency of river dynamic processes, such as river filtering and butterfly effect.
Inverse Learning Control of Nonlinear Systems Using Support Vector Machines
Institute of Scientific and Technical Information of China (English)
HU Zhong-hui; LI Yuan-gui; CAI Yun-ze; XU Xiao-ming
2005-01-01
An inverse learning control scheme using the support vector machine (SVM) for regression was proposed. The inverse learning approach is originally researched in the neural networks. Compared with neural networks, SVMs overcome the problems of local minimum and curse of dimensionality. Additionally, the good generalization performance of SVMs increases the robustness of control system. The method of designing SVM inverselearning controller was presented. The proposed method is demonstrated on tracking problems and the performance is satisfactory.
Heeding the waveform inversion nonlinearity by unwrapping the model and data
Alkhalifah, Tariq Ali
2012-01-01
Unlike traveltime inversion, waveform inversion provides relatively higher-resolution inverted models. This feature, however, comes at the cost of introducing complex nonlinearity to the inversion operator complicating the convergence process. We use unwrapped-phase-based objective functions to reduce such nonlinearity in a domain in which the high-frequency component is given by the traveltime inversion. Such information is packaged in a frequency-dependent attribute (or traveltime) that can be easily manipulated at different frequencies. It unwraps the phase of the wavefield yielding far less nonlinearity in the objective function than those experienced with the conventional misfit objective function, and yet it still holds most of the critical waveform information in its frequency dependency. However, it suffers from nonlinearity introduced by the model (or reflectivity), as events interact with each other (something like cross talk). This stems from the sinusoidal nature of the band-limited reflectivity model. Unwrapping the phase for such a model can mitigate this nonlinearity as well. Specifically, a simple modification to the inverted domain (or model), can reduce the effect of the model-induced nonlinearity and, thus, make the inversion more convergent. Simple examples are used to highlight such features.
Fast Inverse Nonlinear Fourier Transforms for Fiber Bragg Grating Design and Related Problems
Wahls, Sander
2016-01-01
The problem of constructing a fiber Bragg grating profile numerically such that the reflection coefficient of the grating matches a given specification is considered. The well-known analytic solution to this problem is given by a suitable inverse nonlinear Fourier transform (also known as inverse scattering transform) of the specificed reflection coefficient. Many different algorithms have been proposed to compute this inverse nonlinear Fourier transform numerically. The most efficient ones require $\\mathcal{O}(D^{2})$ floating point operations (flops) to generate $D$ samples of the grating profile. In this paper, two new fast inverse nonlinear Fourier transform algorithms that require only $\\mathcal{O}(D\\log^{2}D)$ flops are proposed. The merits of our algorithms are demonstrated in numerical examples, in which they are compared to a conventional layer peeling method, the Toeplitz inner bordering method and integral layer peeling. One of our two algorithms also extends to the design problem for fiber-assiste...
Nonlinear dynamics new directions models and applications
Ugalde, Edgardo
2015-01-01
This book, along with its companion volume, Nonlinear Dynamics New Directions: Theoretical Aspects, covers topics ranging from fractal analysis to very specific applications of the theory of dynamical systems to biology. This second volume contains mostly new applications of the theory of dynamical systems to both engineering and biology. The first volume is devoted to fundamental aspects and includes a number of important new contributions as well as some review articles that emphasize new development prospects. The topics addressed in the two volumes include a rigorous treatment of fluctuations in dynamical systems, topics in fractal analysis, studies of the transient dynamics in biological networks, synchronization in lasers, and control of chaotic systems, among others. This book also: · Develops applications of nonlinear dynamics on a diversity of topics such as patterns of synchrony in neuronal networks, laser synchronization, control of chaotic systems, and the study of transient dynam...
Dynamic disturbance decoupling for nonlinear systems
Huijberts, H.J.C.; Nijmeijer, H.; Wegen, van der L.L.M.
1992-01-01
In analogy with the dynamic input-output decoupling problem the dynamic disturbance decoupling problem for nonlinear systems is introduced. A local solution of this problem is obtained in the case that the system under consideration is invertible. The solution is given in algebraic as well as in geo
Nonlinear-dynamical arrhythmia control in humans.
Christini, D J; Stein, K M; Markowitz, S M; Mittal, S; Slotwiner, D J; Scheiner, M A; Iwai, S; Lerman, B B
2001-05-08
Nonlinear-dynamical control techniques, also known as chaos control, have been used with great success to control a wide range of physical systems. Such techniques have been used to control the behavior of in vitro excitable biological tissue, suggesting their potential for clinical utility. However, the feasibility of using such techniques to control physiological processes has not been demonstrated in humans. Here we show that nonlinear-dynamical control can modulate human cardiac electrophysiological dynamics by rapidly stabilizing an unstable target rhythm. Specifically, in 52/54 control attempts in five patients, we successfully terminated pacing-induced period-2 atrioventricular-nodal conduction alternans by stabilizing the underlying unstable steady-state conduction. This proof-of-concept demonstration shows that nonlinear-dynamical control techniques are clinically feasible and provides a foundation for developing such techniques for more complex forms of clinical arrhythmia.
Nonlinear Dynamics Inversion Optimal Control for Hypersonic Vehicle%针对高超声速飞行器的非线性动态逆最优控制
Institute of Scientific and Technical Information of China (English)
谭毅伦; 闫杰
2011-01-01
高超声速飞行器具有高度非线性,并且输入输出之间存有耦合.传统控制方案中的线性化处理方法有严重的局限性.采用状态反馈线性化方法对高超声速飞行器纵向模型输入输出线性化,并结合最优控制理论设计控制系统,以求提供满意的非线性解耦控制能力,维持良好的纵向稳定性能.基于某常用的高超声速飞行器模型的仿真研究表明该方案能够使飞行器有效跟踪参考轨迹,满足系统需要.%Hypersonic aircrafts have a highly nonlinear dynamics and input/output coupling. Conventional control scheme of linearization method has serious limitations. In order to provide satisfactory nonlinear dacoupling ability and maintain good longitudinal stability, a kind of condition feedback linearization method is adopted in this paper to linearize the input and output of a hypersonic longitudinal vehicle model and optimal control theory is considered in the controller designing. Simulation based on an existing hypersonic vehicle model shows that the controller successfully tracks the reference trajectories and meets the system need.
Nonlinear amplitude dynamics in flagellar beating
Oriola, David; Casademunt, Jaume
2016-01-01
The physical basis of flagellar and ciliary beating is a major problem in biology which is still far from completely understood. The fundamental cytoskeleton structure of cilia and flagella is the axoneme, a cylindrical array of microtubule doublets connected by passive crosslinkers and dynein motor proteins. The complex interplay of these elements leads to the generation of self-organized bending waves. Although many mathematical models have been proposed to understand this process, few attempts have been made to assess the role of dyneins on the nonlinear nature of the axoneme. Here, we investigate the nonlinear dynamics of flagella by considering an axonemal sliding control mechanism for dynein activity. This approach unveils the nonlinear selection of the oscillation amplitudes, which are typically either missed or prescribed in mathematical models. The explicit set of nonlinear equations are derived and solved numerically. Our analysis reveals the spatiotemporal dynamics of dynein populations and flagell...
Nonlinear Dynamics and Control of Flexible Structures
1991-03-01
Freedom," Ph.D. Thesis, Department of Theoretical and Applied Mechanics, Cornell University, in preparation. 5I I URI Reorts Islam , Saiful and Mircea...Theoretical and Applied Mechanics I S. Islam Civil and Environmental Engineering I 2! I 3 URI Accomplishments 3 -Nonlinear Dynamics and Chaos in Flexible...Structures with Symmetry," 31 (1991) 265-285. Islam , S. and M. Grigoriu, "Nonlinear Random Vibration of Pin-Jointed Trusses with Imperfections," in
Dynamical Imaging using Spatial Nonlinearity
2014-01-29
Imin )/ (Imax + Imin ) = 0.15 for detection of the bars (from maxima to central dip). For our experimental measurements, the best linear visibility is...Statistical theory for incoherent light propagation in nonlinear media, Physical Review E, 65 (2002) 035602. [52] M.J. Bastiaans, Application of the...1238. [53] M.E. Testorf, B.M. Hennelly, J. Ojeda-Castañeda, Phase-space optics : fundamentals and applications , McGraw-Hill, New York, 2010. [54] K.H
Nonlinear dynamic vibration absorbers with a saturation
Febbo, M.; Machado, S. P.
2013-03-01
The behavior of a new type of nonlinear dynamic vibration absorber is studied. A distinctive characteristic of the proposed absorber is the impossibility to extend the system to infinity. The mathematical formulation is based on a finite extensibility nonlinear elastic potential to model the saturable nonlinearity. The absorber is attached to a single degree-of-freedom linear/nonlinear oscillator subjected to a periodic external excitation. In order to solve the equations of motion and to analyze the frequency-response curves, the method of averaging is used. The performance of the FENE absorber is evaluated considering a variation of the nonlinearity of the primary system, the damping and the linearized frequency of the absorber and the mass ratio. The numerical results show that the proposed absorber has a very good efficiency when the nonlinearity of the primary system increases. When compared with a cubic nonlinear absorber, for a large nonlinearity of the primary system, the FENE absorber shows a better effectiveness for the whole studied frequency range. A complete absence of quasi-periodic oscillations is also found for an appropriate selection of the parameters of the absorber. Finally, direct integrations of the equations of motion are performed to verify the accuracy of the proposed method.
Structural optimization for nonlinear dynamic response.
Dou, Suguang; Strachan, B Scott; Shaw, Steven W; Jensen, Jakob S
2015-09-28
Much is known about the nonlinear resonant response of mechanical systems, but methods for the systematic design of structures that optimize aspects of these responses have received little attention. Progress in this area is particularly important in the area of micro-systems, where nonlinear resonant behaviour is being used for a variety of applications in sensing and signal conditioning. In this work, we describe a computational method that provides a systematic means for manipulating and optimizing features of nonlinear resonant responses of mechanical structures that are described by a single vibrating mode, or by a pair of internally resonant modes. The approach combines techniques from nonlinear dynamics, computational mechanics and optimization, and it allows one to relate the geometric and material properties of structural elements to terms in the normal form for a given resonance condition, thereby providing a means for tailoring its nonlinear response. The method is applied to the fundamental nonlinear resonance of a clamped-clamped beam and to the coupled mode response of a frame structure, and the results show that one can modify essential normal form coefficients by an order of magnitude by relatively simple changes in the shape of these elements. We expect the proposed approach, and its extensions, to be useful for the design of systems used for fundamental studies of nonlinear behaviour as well as for the development of commercial devices that exploit nonlinear behaviour.
Directory of Open Access Journals (Sweden)
Syed Zaki Hassan Kazmi
Full Text Available The dynamical fluctuations in the rhythms of biological systems provide valuable information about the underlying functioning of these systems. During the past few decades analysis of cardiac function based on the heart rate variability (HRV; variation in R wave to R wave intervals has attracted great attention, resulting in more than 17000-publications (PubMed list. However, it is still controversial about the underling mechanisms of HRV. In this study, we performed both linear (time domain and frequency domain and nonlinear analysis of HRV data acquired from humans and animals to identify the relationship between HRV and heart rate (HR. The HRV data consists of the following groups: (a human normal sinus rhythm (n = 72; (b human congestive heart failure (n = 44; (c rabbit sinoatrial node cells (SANC; n = 67; (d conscious rat (n = 11. In both human and animal data at variant pathological conditions, both linear and nonlinear analysis techniques showed an inverse correlation between HRV and HR, supporting the concept that HRV is dependent on HR, and therefore, HRV cannot be used in an ordinary manner to analyse autonomic nerve activity of a heart.
Non-linear magnetorheological behaviour of an inverse ferrofluid
de Gans, B.J.; Hoekstra, Hans; Mellema, J.
1999-01-01
The non-linear magnetorheological behaviour is studied of a model system consisting of monodisperse silica particles suspended in a ferrofluid. The stress/strain curve as well as the flow curve was measured as a function of volume fraction silica particles and field strength, using a home-made
Linear and Nonlinear Dynamical Chaos
Chirikov, B V
1997-01-01
Interrelations between dynamical and statistical laws in physics, on the one hand, and between the classical and quantum mechanics, on the other hand, are discussed with emphasis on the new phenomenon of dynamical chaos. The principal results of the studies into chaos in classical mechanics are presented in some detail, including the strong local instability and robustness of the motion, continuity of both the phase space as well as the motion spectrum, and time reversibility but nonrecurrency of statistical evolution, within the general picture of chaos as a specific case of dynamical behavior. Analysis of the apparently very deep and challenging contradictions of this picture with the quantum principles is given. The quantum view of dynamical chaos, as an attempt to resolve these contradictions guided by the correspondence principle and based upon the characteristic time scales of quantum evolution, is explained. The picture of the quantum chaos as a new generic dynamical phenomenon is outlined together wit...
Hein, Matthias
2010-01-01
Many problems in machine learning and statistics can be formulated as (generalized) eigenproblems. In terms of the associated optimization problem, computing linear eigenvectors amounts to finding critical points of a quadratic function subject to quadratic constraints. In this paper we show that a certain class of constrained optimization problems with nonquadratic objective and constraints can be understood as nonlinear eigenproblems. We derive a generalization of the inverse power method which is guaranteed to converge to a nonlinear eigenvector. We apply the inverse power method to 1-spectral clustering and sparse PCA which can naturally be formulated as nonlinear eigenproblems. In both applications we achieve state-of-the-art results in terms of solution quality and runtime. Moving beyond the standard eigenproblem should be useful also in many other applications and our inverse power method can be easily adapted to new problems.
Nonlinear dynamics of cell orientation
Safran, S. A.; de, Rumi
2009-12-01
The nonlinear dependence of cellular orientation on an external, time-varying stress field determines the distribution of orientations in the presence of noise and the characteristic time, τc , for the cell to reach its steady-state orientation. The short, local cytoskeletal relaxation time distinguishes between high-frequency (nearly perpendicular) and low-frequency (random or parallel) orientations. However, τc is determined by the much longer, orientational relaxation time. This behavior is related to experiments for which we predict the angle and characteristic time as a function of frequency.
An ICPSO-RBFNN nonlinear inversion for electrical resistivity imaging
Institute of Scientific and Technical Information of China (English)
江沸菠; 戴前伟; 董莉
2016-01-01
To improve the global search ability and imaging quality of electrical resistivity imaging(ERI) inversion, a two-stage learning ICPSO algorithm of radial basis function neural network (RBFNN) based on information criterion (IC) and particle swarm optimization (PSO) is presented. In the proposed method, IC is applied to obtain the hidden layer structure by calculating the optimal IC value automatically and PSO algorithm is used to optimize the centers and widths of the radial basis functions in the hidden layer. Meanwhile, impacts of different information criteria to the inversion results are compared, and an implementation of the proposed ICPSO algorithm is given. The optimized neural network has one hidden layer with 261 nodes selected by AKAIKE’s information criterion (AIC) and it is trained on 32 data sets and tested on another 8 synthetic data sets. Two complex synthetic examples are used to verify the feasibility and effectiveness of the proposed method with two learning stages. The results show that the proposed method has better performance and higher imaging quality than three-layer and four-layer back propagation neural networks (BPNNs) and traditional least square(LS) inversion.
Multi-task Gaussian Process Learning of Robot Inverse Dynamics
Chai, Kian Ming; Williams, Christopher K. I.; Klanke, Stefan; Vijayakumar, Sethu
2008-01-01
The inverse dynamics problem for a robotic manipulator is to compute the torques needed at the joints to drive it along a given trajectory; it is beneficial to be able to learn this function for adaptive control. A robotic manipulator will often need to be controlled while holding different loads in its end effector, giving rise to a multi-task learning problem. By placing independent Gaussian process priors over the latent functions of the inverse dynamics, we obtain a multi-t...
Nonlinear inversion of potential-field data using a hybrid-encoding genetic algorithm
Chen, C.; Xia, J.; Liu, J.; Feng, G.
2006-01-01
Using a genetic algorithm to solve an inverse problem of complex nonlinear geophysical equations is advantageous because it does not require computer gradients of models or "good" initial models. The multi-point search of a genetic algorithm makes it easier to find the globally optimal solution while avoiding falling into a local extremum. As is the case in other optimization approaches, the search efficiency for a genetic algorithm is vital in finding desired solutions successfully in a multi-dimensional model space. A binary-encoding genetic algorithm is hardly ever used to resolve an optimization problem such as a simple geophysical inversion with only three unknowns. The encoding mechanism, genetic operators, and population size of the genetic algorithm greatly affect search processes in the evolution. It is clear that improved operators and proper population size promote the convergence. Nevertheless, not all genetic operations perform perfectly while searching under either a uniform binary or a decimal encoding system. With the binary encoding mechanism, the crossover scheme may produce more new individuals than with the decimal encoding. On the other hand, the mutation scheme in a decimal encoding system will create new genes larger in scope than those in the binary encoding. This paper discusses approaches of exploiting the search potential of genetic operations in the two encoding systems and presents an approach with a hybrid-encoding mechanism, multi-point crossover, and dynamic population size for geophysical inversion. We present a method that is based on the routine in which the mutation operation is conducted in the decimal code and multi-point crossover operation in the binary code. The mix-encoding algorithm is called the hybrid-encoding genetic algorithm (HEGA). HEGA provides better genes with a higher probability by a mutation operator and improves genetic algorithms in resolving complicated geophysical inverse problems. Another significant
Adaptive Neural Network Dynamic Inversion with Prescribed Performance for Aircraft Flight Control
Wendong Gai; Honglun Wang; Jing Zhang; Yuxia Li
2013-01-01
An adaptive neural network dynamic inversion with prescribed performance method is proposed for aircraft flight control. The aircraft nonlinear attitude angle model is analyzed. And we propose a new attitude angle controller design method based on prescribed performance which describes the convergence rate and overshoot of the tracking error. Then the model error is compensated by the adaptive neural network. Subsequently, the system stability is analyzed in detail. Finally, the proposed meth...
Imaging of discontinuities in nonlinear 3-D seismic inversion
Energy Technology Data Exchange (ETDEWEB)
Carrion, P.M.; Cerveny, V. (PPPG/UFBA, Salvador (Brazil))
1990-09-01
The authors present a nonlinear approach for reconstruction of discontinuities in geological environment (earth's crust, say). The advantage of the proposed method is that it is not limited to a Born approximation (small angles of propagation and weak scatterers). One can expect significantly better images since larger apertures including wide angle reflection arrivals can be incorporated into the imaging operator. In this paper, they treat only compressional body waves: shear and surface waves are considered as noise.
Structural optimization for nonlinear dynamic response
DEFF Research Database (Denmark)
Dou, Suguang; Strachan, B. Scott; Shaw, Steven W.
2015-01-01
condition, thereby providing a means for tailoring its nonlinear response. The method is applied to the fundamental nonlinear resonance of a clamped–clamped beam and to the coupled mode response of a frame structure, and the results show that one can modify essential normal form coefficients by an order...... resonant behaviour is being used for a variety of applications in sensing and signal conditioning. In this work, we describe a computational method that provides a systematic means for manipulating and optimizing features of nonlinear resonant responses of mechanical structures that are described...... by a single vibrating mode, or by a pair of internally resonant modes. The approach combines techniques from nonlinear dynamics, computational mechanics and optimization, and it allows one to relate the geometric and material properties of structural elements to terms in the normal form for a given resonance...
Dynamics of Nonlinear Waves on Bounded Domains
Maliborski, Maciej
2016-01-01
This thesis is concerned with dynamics of conservative nonlinear waves on bounded domains. In general, there are two scenarios of evolution. Either the solution behaves in an oscillatory, quasiperiodic manner or the nonlinear effects cause the energy to concentrate on smaller scales leading to a turbulent behaviour. Which of these two possibilities occurs depends on a model and the initial conditions. In the quasiperiodic scenario there exist very special time-periodic solutions. They result for a delicate balance between dispersion and nonlinear interaction. The main body of this dissertation is concerned with construction (by means of perturbative and numerical methods) of time-periodic solutions for various nonlinear wave equations on bounded domains. While turbulence is mainly associated with hydrodynamics, recent research in General Relativity has also revealed turbulent phenomena. Numerical studies of a self-gravitating massless scalar field in spherical symmetry gave evidence that anti-de Sitter space ...
Adaptive Neural Network Dynamic Inversion with Prescribed Performance for Aircraft Flight Control
Directory of Open Access Journals (Sweden)
Wendong Gai
2013-01-01
Full Text Available An adaptive neural network dynamic inversion with prescribed performance method is proposed for aircraft flight control. The aircraft nonlinear attitude angle model is analyzed. And we propose a new attitude angle controller design method based on prescribed performance which describes the convergence rate and overshoot of the tracking error. Then the model error is compensated by the adaptive neural network. Subsequently, the system stability is analyzed in detail. Finally, the proposed method is applied to the aircraft attitude tracking control system. The nonlinear simulation demonstrates that this method can guarantee the stability and tracking performance in the transient and steady behavior.
Decoupling of Double Extraction Turbo-Unit by Nonlinear Multivariable Inverse System Method
Institute of Scientific and Technical Information of China (English)
黎浩荣; 李立勤; 李东海; 宋兆星; 王伟
2001-01-01
A multivariable inverse nonlinear control scheme is developed to decouple the strongly nonlinear double extraction steam turbo-unit, improving the transient stability of the power and heating system. Computer simulation tests show that not only does the control scheme achieve satisfactory decoupling of the high and low pressure turbines and the electric power, remarkably improving the transient stability, but also the design is very intuitive and concise.
Nonlinear dynamics in the study of birdsong
Mindlin, Gabriel B.
2017-09-01
Birdsong, a rich and complex behavior, is a stellar model to understand a variety of biological problems, from motor control to learning. It also enables us to study how behavior emerges when a nervous system, a biomechanical device and the environment interact. In this review, I will show that many questions in the field can benefit from the approach of nonlinear dynamics, and how birdsong can inspire new directions for research in dynamics.
Nonlinear dynamics in particle accelerators
Dilão, Rui
1996-01-01
This book is an introductory course to accelerator physics at the level of graduate students. It has been written for a large audience which includes users of accelerator facilities, accelerator physicists and engineers, and undergraduates aiming to learn the basic principles of construction, operation and applications of accelerators.The new concepts of dynamical systems developed in the last twenty years give the theoretical setting to analyse the stability of particle beams in accelerator. In this book a common language to both accelerator physics and dynamical systems is integrated and dev
Ontology of Earth's nonlinear dynamic complex systems
Babaie, Hassan; Davarpanah, Armita
2017-04-01
As a complex system, Earth and its major integrated and dynamically interacting subsystems (e.g., hydrosphere, atmosphere) display nonlinear behavior in response to internal and external influences. The Earth Nonlinear Dynamic Complex Systems (ENDCS) ontology formally represents the semantics of the knowledge about the nonlinear system element (agent) behavior, function, and structure, inter-agent and agent-environment feedback loops, and the emergent collective properties of the whole complex system as the result of interaction of the agents with other agents and their environment. It also models nonlinear concepts such as aperiodic, random chaotic behavior, sensitivity to initial conditions, bifurcation of dynamic processes, levels of organization, self-organization, aggregated and isolated functionality, and emergence of collective complex behavior at the system level. By incorporating several existing ontologies, the ENDCS ontology represents the dynamic system variables and the rules of transformation of their state, emergent state, and other features of complex systems such as the trajectories in state (phase) space (attractor and strange attractor), basins of attractions, basin divide (separatrix), fractal dimension, and system's interface to its environment. The ontology also defines different object properties that change the system behavior, function, and structure and trigger instability. ENDCS will help to integrate the data and knowledge related to the five complex subsystems of Earth by annotating common data types, unifying the semantics of shared terminology, and facilitating interoperability among different fields of Earth science.
Some Nonlinear Dynamic Inequalities on Time Scales
Indian Academy of Sciences (India)
Wei Nian Li; Weihong Sheng
2007-11-01
The aim of this paper is to investigate some nonlinear dynamic inequalities on time scales, which provide explicit bounds on unknown functions. The inequalities given here unify and extend some inequalities in (B G Pachpatte, On some new inequalities related to a certain inequality arising in the theory of differential equation, J. Math. Anal. Appl. 251 (2000) 736--751).
Estimating the uncertainty in underresolved nonlinear dynamics
Energy Technology Data Exchange (ETDEWEB)
Chorin, Alelxandre; Hald, Ole
2013-06-12
The Mori-Zwanzig formalism of statistical mechanics is used to estimate the uncertainty caused by underresolution in the solution of a nonlinear dynamical system. A general approach is outlined and applied to a simple example. The noise term that describes the uncertainty turns out to be neither Markovian nor Gaussian. It is argued that this is the general situation.
Nonlinear dynamics and quantitative EEG analysis.
Jansen, B H
1996-01-01
Quantitative, computerized electroencephalogram (EEG) analysis appears to be based on a phenomenological approach to EEG interpretation, and is primarily rooted in linear systems theory. A fundamentally different approach to computerized EEG analysis, however, is making its way into the laboratories. The basic idea, inspired by recent advances in the area of nonlinear dynamics and chaos theory, is to view an EEG as the output of a deterministic system of relatively simple complexity, but containing nonlinearities. This suggests that studying the geometrical dynamics of EEGs, and the development of neurophysiologically realistic models of EEG generation may produce more successful automated EEG analysis techniques than the classical, stochastic methods. A review of the fundamentals of chaos theory is provided. Evidence supporting the nonlinear dynamics paradigm to EEG interpretation is presented, and the kind of new information that can be extracted from the EEG is discussed. A case is made that a nonlinear dynamic systems viewpoint to EEG generation will profoundly affect the way EEG interpretation is currently done.
A Projected Non-linear Conjugate Gradient Method for Interactive Inverse Kinematics
DEFF Research Database (Denmark)
Engell-Nørregård, Morten; Erleben, Kenny
2009-01-01
Inverse kinematics is the problem of posing an articulated figure to obtain a wanted goal, without regarding inertia and forces. Joint limits are modeled as bounds on individual degrees of freedom, leading to a box-constrained optimization problem. We present A projected Non-linear Conjugate...... Gradient optimization method suitable for box-constrained optimization problems for inverse kinematics. We show application on inverse kinematics positioning of a human figure. Performance is measured and compared to a traditional Jacobian Transpose method. Visual quality of the developed method...
Generation and Nonlinear Dynamical Analyses of Fractional-Order Memristor-Based Lorenz Systems
Directory of Open Access Journals (Sweden)
Huiling Xi
2014-11-01
Full Text Available In this paper, four fractional-order memristor-based Lorenz systems with the flux-controlled memristor characterized by a monotone-increasing piecewise linear function, a quadratic nonlinearity, a smooth continuous cubic nonlinearity and a quartic nonlinearity are presented, respectively. The nonlinear dynamics are analyzed by using numerical simulation methods, including phase portraits, bifurcation diagrams, the largest Lyapunov exponent and power spectrum diagrams. Some interesting phenomena, such as inverse period-doubling bifurcation and intermittent chaos, are found to exist in the proposed systems.
Energy Technology Data Exchange (ETDEWEB)
Alvarez-Estrada, R.F.
1979-08-01
A comprehensive review of the inverse scattering solution of certain non-linear evolution equations of physical interest in one space dimension is presented. We explain in some detail the interrelated techniques which allow to linearize exactly the following equations: (1) the Korteweg and de Vries equation; (2) the non-linear Schrodinger equation; (3) the modified Korteweg and de Vries equation; (4) the Sine-Gordon equation. We concentrate in discussing the pairs of linear operators which accomplish such an exact linearization and the solution of the associated initial value problem. The application of the method to other non-linear evolution equations is reviewed very briefly.
Depict noise-driven nonlinear dynamic networks from output data by using high-order correlations
Chen, Yang; Chen, Tianyu; Wang, Shihong; Hu, Gang
2016-01-01
Many practical systems can be described by dynamic networks, for which modern technique can measure their output signals, and accumulate extremely rich data. Nevertheless, the network structures producing these data are often deeply hidden in these data. Depicting network structures by analysing the available data turns to be significant inverse problems. On one hand, dynamics are often driven by various unknown facts, called noises. On the other hand, network structures of practical systems are commonly nonlinear, and different nonlinearities can provide rich dynamic features and meaningful functions of realistic networks. So far, no method, both theoretically or numerically, has been found to systematically treat the both difficulties together. Here we propose to use high-order correlation computations (HOCC) to treat nonlinear dynamics; use two-time correlations to treat noise effects; and use suitable basis and correlator vectors to unifiedly depict all dynamic nonlinearities and topological interaction l...
Dynamical effects of overparametrization in nonlinear models
Aguirre, Luis Antonio; Billings, S. A.
1995-01-01
This paper is concemed with dynamical reconstruction for nonlinear systems. The effects of the driving function and of the complexity of a given representation on the bifurcation patter are investigated. It is shown that the use of different driving functions to excite the system may yield models with different bifurcation patterns. The complexity of the reconstructions considered is quantified by the embedding dimension and the number of estimated parameters. In this respect it appears that models which reproduce the original bifurcation behaviour are of limited complexity and that excessively complex models tend to induce ghost bifurcations and spurious dynamical regimes. Moreover, some results suggest that the effects of overparametrization on the global dynamical behaviour of a nonlinear model may be more deleterious than the presence of moderate noise levels. In order to precisely quantify the complexity of the reconstructions, global polynomials are used although the results are believed to apply to a much wider class of representations including neural networks.
Nonlinear dynamics of a double bilipid membrane.
Sample, C; Golovin, A A
2007-09-01
The nonlinear dynamics of a biological double membrane that consists of two coupled lipid bilayers, typical of some intracellular organelles such as mitochondria or nuclei, is studied. A phenomenological free-energy functional is formulated in which the curvatures of the two parts of the double membrane and the distance between them are coupled to the lipid chemical composition. The derived nonlinear evolution equations for the double-membrane dynamics are studied analytically and numerically. A linear stability analysis is performed, and the domains of parameters are found in which the double membrane is stable. For the parameter values corresponding to an unstable membrane, numerical simulations are performed that reveal various types of complex dynamics, including the formation of stationary, spatially periodic patterns.
Nonlinear dynamics and quantum chaos an introduction
Wimberger, Sandro
2014-01-01
The field of nonlinear dynamics and chaos has grown very much over the last few decades and is becoming more and more relevant in different disciplines. This book presents a clear and concise introduction to the field of nonlinear dynamics and chaos, suitable for graduate students in mathematics, physics, chemistry, engineering, and in natural sciences in general. It provides a thorough and modern introduction to the concepts of Hamiltonian dynamical systems' theory combining in a comprehensive way classical and quantum mechanical description. It covers a wide range of topics usually not found in similar books. Motivations of the respective subjects and a clear presentation eases the understanding. The book is based on lectures on classical and quantum chaos held by the author at Heidelberg University. It contains exercises and worked examples, which makes it ideal for an introductory course for students as well as for researchers starting to work in the field.
Nonlinear adhesion dynamics of confined lipid membranes
To, Tung; Le Goff, Thomas; Pierre-Louis, Olivier
Lipid membranes, which are ubiquitous objects in biological environments are often confined. For example, they can be sandwiched between a substrate and the cytoskeleton between cell adhesion, or between other membranes in stacks, or in the Golgi apparatus. We present a study of the nonlinear dynamics of membranes in a model system, where the membrane is confined between two flat walls. The dynamics derived from the lubrication approximation is highly nonlinear and nonlocal. The solution of this model in one dimension exhibits frozen states due to oscillatory interactions between membranes caused by the bending rigidity. We develope a kink model for these phenomena based on the historical work of Kawasaki and Otha. In two dimensions, the dynamics is more complex, and depends strongly on the amount of excess area in the system. We discuss the relevance of our findings for experiments on model membranes, and for biological systems. Supported by the grand ANR Biolub.
Superworldvolume dynamics of superbranes from nonlinear realizations
Energy Technology Data Exchange (ETDEWEB)
Bellucci, S. [Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali di Frascati, Frascati, RM (Italy); Ivanov, E. [Paris Univ., Paris (France). Lab. de Physique Theorique et des Hautes Energies]|[Bogoliubov Laboratory of Theoretical Physics, Dubna, Moscow (USSR); Krivonos, S. [Bogoliubov Laboratory of Theoretical Physics, Dubna, Moscow (USSR)
2000-07-01
Based on the concept of the partial breaking of global supersymmetry (PBGS), it has been derived the worldvolume 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.
Nonlinear Dynamics on Interconnected Networks
Arenas, Alex; De Domenico, Manlio
2016-06-01
Networks of dynamical interacting units can represent many complex systems, from the human brain to transportation systems and societies. The study of these complex networks, when accounting for different types of interactions has become a subject of interest in the last few years, especially because its representational power in the description of users' interactions in diverse online social platforms (Facebook, Twitter, Instagram, etc.) [1], or in representing different transportation modes in urban networks [2,3]. The general name coined for these networks is multilayer networks, where each layer accounts for a type of interaction (see Fig. 1).
Nonlinear dynamics of interacting populations
Bazykin, Alexander D
1998-01-01
This book contains a systematic study of ecological communities of two or three interacting populations. Starting from the Lotka-Volterra system, various regulating factors are considered, such as rates of birth and death, predation and competition. The different factors can have a stabilizing or a destabilizing effect on the community, and their interplay leads to increasingly complicated behavior. Studying and understanding this path to greater dynamical complexity of ecological systems constitutes the backbone of this book. On the mathematical side, the tool of choice is the qualitative the
THE APPLICATION OF GENETIC ALGORITHM IN NON-LINEAR INVERSION OF ROCK MECHANICS PARAMETERS
Institute of Scientific and Technical Information of China (English)
赵晓东
1998-01-01
The non-linear inversion of rock mechanics parameters based on genetic algorithm ispresented. The principle and step of genetic algorithm is also given. A brief discussion of thismethod and an application example is presented at the end of this paper. From the satisfied re-sult, quick, convenient and practical new approach is developed to solve this kind of problems.
Ascent guidance for air-breathing hypersonic vehicles based on dynamic inversion
Directory of Open Access Journals (Sweden)
Xing Liu
2017-05-01
Full Text Available This article presents an adaptive ascent guidance strategy based on dynamic inversion for air-breathing hypersonic vehicles. Since dynamic inversion is effective to deal with nonlinear problems, this method is employed here to design the ascent guidance command. Compared with conventional dynamic inversion, an adaptive scheme is added into the guidance strategy, which significantly improves the robust performance of this method. And the stability analysis is given to prove the convergence of the nonlinear system. Besides, considering the real-world dynamic motions of the vehicle should be aware to calculate the guidance command instead of referring to the nominal model, the least squares algorithm with forgetting factor is adopted in this article to estimate the real thrust acceleration. And the reference trajectory generated online by polynomial fitting shows better adaptation to the change of flight environment and less computation time than other trajectory generation methods. Results of simulation are provided to demonstrate the feasibility and effectiveness of this approach.
McMC-based nonlinear EIVAZ inversion driven by rock physics
Pan, Xinpeng; Zhang, Guangzhi; Chen, Huaizhen; Yin, Xingyao
2017-03-01
A single set of vertically aligned fractures embedded in a purely isotropic background medium may be considered as a long-wavelength effective transversely isotropic medium with a horizontal symmetry axis (HTI). The estimation of fracture weaknesses is essential for characterizing the anisotropy in HTI media. Using the fractured anisotropic rock-physics models and the wide-azimuth seismic data, elastic impedance inversion variation with incident angle and azimuth, or simply ‘EIVAZ’ for short, can be carried out for the estimation of the normal and tangential fracture weaknesses with the nonlinear Markov chain Monte Carlo (McMC) strategy. Firstly, an inversion method of nonlinear anisotropic elastic impedance (AEI) with the McMC algorithm was proposed, which is used for the inversion of nonlinear AEI information with different angles of incidence and azimuth. Then we extracted the normal and tangential fracture weaknesses directly using the ratio differences of inverted nonlinear AEI data. So we can eliminate the influence of the isotropic background elastic impedance on the anisotropic perturbation elastic impedance and obtain the normal and tangential fracture weaknesses more stably. A test on a 2D over-thrust model shows that the fracture weaknesses are still estimated reasonably with moderate noise. A test on a real data set demonstrates that the estimated results are in good agreement with the results of the well log interpretation, and our McMC-based nonlinear AEI approach appears to be a stable method for predicting fracture weaknesses.
A Quadratic precision generalized nonlinear global optimization migration velocity inversion method
Institute of Scientific and Technical Information of China (English)
Zhao Taiyin; Hu Guangmin; He Zhenhua; Huang Deji
2009-01-01
An important research topic for prospecting seismology is to provide a fast accurate velocity model from pre-stack depth migration. Aiming at such a problem, we propose a quadratic precision generalized nonlinear global optimization migration velocity inversion. First we discard the assumption that there is a linear relationship between residual depth and residual velocity and propose a velocity model correction equation with quadratic precision which enables the velocity model from each iteration to approach the real model as quickly as possible. Second, we use a generalized nonlinear inversion to get the global optimal velocity perturbation model to all traces. This method can expedite the convergence speed and also can decrease the probability of falling into a local minimum during inversion. The synthetic data and Marmousi data examples show that our method has a higher precision and needs only a few iterations and consequently enhances the practicability and accuracy of migration velocity analysis (MVA) in complex areas.
Solution of the nonlinear inverse scattering problem by T -matrix completion. II. Simulations
Levinson, Howard W.; Markel, Vadim A.
2016-10-01
This is Part II of the paper series on data-compatible T -matrix completion (DCTMC), which is a method for solving nonlinear inverse problems. Part I of the series [H. W. Levinson and V. A. Markel, Phys. Rev. E 94, 043317 (2016), 10.1103/PhysRevE.94.043317] contains theory and here we present simulations for inverse scattering of scalar waves. The underlying mathematical model is the scalar wave equation and the object function that is reconstructed is the medium susceptibility. The simulations are relevant to ultrasound tomographic imaging and seismic tomography. It is shown that DCTMC is a viable method for solving strongly nonlinear inverse problems with large data sets. It provides not only the overall shape of the object, but the quantitative contrast, which can correspond, for instance, to the variable speed of sound in the imaged medium.
Bubble nonlinear dynamics and stimulated scattering process
Jie, Shi; De-Sen, Yang; Sheng-Guo, Shi; Bo, Hu; Hao-Yang, Zhang; Shi-Yong, Hu
2016-02-01
A complete understanding of the bubble dynamics is deemed necessary in order to achieve their full potential applications in industry and medicine. For this purpose it is first needed to expand our knowledge of a single bubble behavior under different possible conditions including the frequency and pressure variations of the sound field. In addition, stimulated scattering of sound on a bubble is a special effect in sound field, and its characteristics are associated with bubble oscillation mode. A bubble in liquid can be considered as a representative example of nonlinear dynamical system theory with its resonance, and its dynamics characteristics can be described by the Keller-Miksis equation. The nonlinear dynamics of an acoustically excited gas bubble in water is investigated by using theoretical and numerical analysis methods. Our results show its strongly nonlinear behavior with respect to the pressure amplitude and excitation frequency as the control parameters, and give an intuitive insight into stimulated sound scattering on a bubble. It is seen that the stimulated sound scattering is different from common dynamical behaviors, such as bifurcation and chaos, which is the result of the nonlinear resonance of a bubble under the excitation of a high amplitude acoustic sound wave essentially. The numerical analysis results show that the threshold of stimulated sound scattering is smaller than those of bifurcation and chaos in the common condition. Project supported by the Program for Changjiang Scholars and Innovative Research Team in University, China (Grant No. IRT1228) and the Young Scientists Fund of the National Natural Science Foundation of China (Grant Nos. 11204050 and 11204049).
Nonlinear Dynamics of Coiling in Viscoelastic Jets
Majmudar, Trushant; Hartt, William; McKinley, Gareth
2010-01-01
Instabilities in free surface continuous jets of non-Newtonian fluids, although relevant for many industrial processes, remain less well understood in terms of fundamental fluid dynamics. Inviscid, and viscous Newtonian jets have been studied in great detail; buckling instability in viscous jets leads to regular periodic coiling of the jet that exhibits a non-trivial frequency dependence with the height of the fall. Very few experimental or theoretical studies exist for continuous viscoelastic jets beyond the onset of the first instability. Here, we present a systematic study of the effects of viscoelasticity on the dynamics of free surface continuous jets of surfactant solutions that form worm-like micelles. We observe complex nonlinear spatio-temporal dynamics of the jet and uncover a transition from periodic to doubly-periodic or quasi-periodic to a multi-frequency, possibly chaotic dynamics. Beyond this regime, the jet dynamics smoothly crosses over to exhibit the "leaping shampoo effect" or the Kaye effe...
Nonlinear Dynamics and Chaos: Applications in Atmospheric Sciences
Selvam, A M
2010-01-01
Atmospheric flows, an example of turbulent fluid flows, exhibit fractal fluctuations of all space-time scales ranging from turbulence scale of mm - sec to climate scales of thousands of kilometers - years and may be visualized as a nested continuum of weather cycles or periodicities, the smaller cycles existing as intrinsic fine structure of the larger cycles. The power spectra of fractal fluctuations exhibit inverse power law form signifying long - range correlations identified as self - organized criticality and are ubiquitous to dynamical systems in nature and is manifested as sensitive dependence on initial condition or 'deterministic chaos' in finite precision computer realizations of nonlinear mathematical models of real world dynamical systems such as atmospheric flows. Though the self-similar nature of atmospheric flows have been widely documented and discussed during the last three to four decades, the exact physical mechanism is not yet identified. There now exists an urgent need to develop and inco...
CISM course on exploiting nonlinear behaviour in structural dynamics
Virgin, Lawrence; Exploiting Nonlinear Behavior in Structural Dynamics
2012-01-01
The articles in this volume give an overview and introduction to nonlinear phenomena in structural dynamics. Topics treated are approximate methods for analyzing nonlinear systems (where the level of nonlinearity is assumed to be relatively small), vibration isolation, the mitigation of undesirable torsional vibration in rotating systems utilizing specifically nonlinear features in the dynamics, the vibration of nonlinear structures in which the motion is sufficiently large amplitude and structural systems with control.
Cluster-based control of nonlinear dynamics
Kaiser, Eurika; Spohn, Andreas; Cattafesta, Louis N; Morzynski, Marek
2016-01-01
The ability to manipulate and control fluid flows is of great importance in many scientific and engineering applications. Here, a cluster-based control framework is proposed to determine optimal control laws with respect to a cost function for unsteady flows. The proposed methodology frames high-dimensional, nonlinear dynamics into low-dimensional, probabilistic, linear dynamics which considerably simplifies the optimal control problem while preserving nonlinear actuation mechanisms. The data-driven approach builds upon a state space discretization using a clustering algorithm which groups kinematically similar flow states into a low number of clusters. The temporal evolution of the probability distribution on this set of clusters is then described by a Markov model. The Markov model can be used as predictor for the ergodic probability distribution for a particular control law. This probability distribution approximates the long-term behavior of the original system on which basis the optimal control law is de...
Non-Linear Dynamics and Fundamental Interactions
Khanna, Faqir
2006-01-01
The book is directed to researchers and graduate students pursuing an advanced degree. It provides details of techniques directed towards solving problems in non-linear dynamics and chos that are, in general, not amenable to a perturbative treatment. The consideration of fundamental interactions is a prime example where non-perturbative techniques are needed. Extension of these techniques to finite temperature problems is considered. At present these ideas are primarily used in a perturbative context. However, non-perturbative techniques have been considered in some specific cases. Experts in the field on non-linear dynamics and chaos and fundamental interactions elaborate the techniques and provide a critical look at the present status and explore future directions that may be fruitful. The text of the main talks will be very useful to young graduate students who are starting their studies in these areas.
Nonlinear Dynamics in Double Square Well Potential
Khomeriki, Ramaz; Ruffo, Stefano; Wimberger, Sandro; 10.1007/s11232-007-0096-y
2009-01-01
Considering the coherent nonlinear dynamics in double square well potential we find the example of coexistence of Josephson oscillations with a self-trapping regime. This macroscopic bistability is explained by proving analytically the simultaneous existence of symmetric, antisymmetric and asymmetric stationary solutions of the associated Gross-Pitaevskii equation. The effect is illustrated and confirmed by numerical simulations. This property allows to make suggestions on possible experiments using Bose-Einstein condensates in engineered optical lattices or weakly coupled optical waveguide arrays.
Geometrodynamics: The Nonlinear Dynamics of Curved Spacetime
Scheel, Mark A.; Thorne, Kip S.
2017-01-01
We review discoveries in the nonlinear dynamics of curved spacetime, largely made possible by numerical solutions of Einstein's equations. We discuss critical phenomena and self-similarity in gravitational collapse, the behavior of spacetime curvature near singularities, the instability of black strings in 5 spacetime dimensions, and the collision of four-dimensional black holes. We also discuss the prospects for further discoveries in geometrodynamics via observation of gravitational waves.
Time Series Forecasting: A Nonlinear Dynamics Approach
Sello, Stefano
1999-01-01
The problem of prediction of a given time series is examined on the basis of recent nonlinear dynamics theories. Particular attention is devoted to forecast the amplitude and phase of one of the most common solar indicator activity, the international monthly smoothed sunspot number. It is well known that the solar cycle is very difficult to predict due to the intrinsic complexity of the related time behaviour and to the lack of a succesful quantitative theoretical model of the Sun magnetic cy...
Control of a high beta maneuvering reentry vehicle using dynamic inversion.
Energy Technology Data Exchange (ETDEWEB)
Watts, Alfred Chapman
2005-05-01
The design of flight control systems for high performance maneuvering reentry vehicles presents a significant challenge to the control systems designer. These vehicles typically have a much higher ballistic coefficient than crewed vehicles like as the Space Shuttle or proposed crew return vehicles such as the X-38. Moreover, the missions of high performance vehicles usually require a steeper reentry flight path angle, followed by a pull-out into level flight. These vehicles then must transit the entire atmosphere and robustly perform the maneuvers required for the mission. The vehicles must also be flown with small static margins in order to perform the required maneuvers, which can result in highly nonlinear aerodynamic characteristics that frequently transition from being aerodynamically stable to unstable as angle of attack increases. The control system design technique of dynamic inversion has been applied successfully to both high performance aircraft and low beta reentry vehicles. The objective of this study was to explore the application of this technique to high performance maneuvering reentry vehicles, including the basic derivation of the dynamic inversion technique, followed by the extension of that technique to the use of tabular trim aerodynamic models in the controller. The dynamic inversion equations are developed for high performance vehicles and augmented to allow the selection of a desired response for the control system. A six degree of freedom simulation is used to evaluate the performance of the dynamic inversion approach, and results for both nominal and off nominal aerodynamic characteristics are presented.
INVERSE DYNAMIC FORMULATION OF A NOVEL HYBRID MACHINE TOOL
Institute of Scientific and Technical Information of China (English)
无
2003-01-01
In recent years, hybrid devices have increasingly received more research.However, few of researchers studied the dynamic analysis.The inverse dynamic analysis of a novel hybrid machine tool designed in Tsinghua University is presented.The hybrid machine tool under consideration consists of parallel and serial structures, which is based on a new 2-DOF parallel platform and serial orientations.The kinematics and the dynamic equations are studied first for the parallel structure through Newton-Euler approach.And then, the dynamic analysis for serial structures is conducted.Finally, a closed-form inverse dynamic formulation is derived by using some elimination techniques.Some simulation results are also given.
DYNAMIC BIFURCATION OF NONLINEAR EVOLUTION EQUATIONS
Institute of Scientific and Technical Information of China (English)
MA TIAN; WANG SHOUHONG
2005-01-01
The authors introduce a notion of dynamic bifurcation for nonlinear evolution equations, which can be called attractor bifurcation. It is proved that as the control parameter crosses certain critical value, the system bifurcates from a trivial steady state solution to an attractor with dimension between m and m + 1, where m + 1 is the number of eigenvalues crossing the imaginary axis. The attractor bifurcation theory presented in this article generalizes the existing steady state bifurcations and the Hopf bifurcations. It provides a unified point of view on dynamic bifurcation and can be applied to many problems in physics and mechanics.
Dynamic Associations in Nonlinear Computing Arrays
Huberman, B. A.; Hogg, T.
1985-10-01
We experimentally show that nonlinear parallel arrays can be made to compute with attractors. This leads to fast adaptive behavior in which dynamical associations can be made between different inputs which initially produce sharply distinct outputs. We first define a set of simple local procedures which allow a general computing structure to change its state in time so as to produce classical Pavlovian conditioning. We then examine the dynamics of coalescence and dissociation of attractors with a number of quantitative experiments. We also show how such arrays exhibit generalization and differentiation of inputs in their behavior.
Nonlinear dynamic analysis of sandwich panels
Lush, A. M.
1984-01-01
Two analytical techniques applicable to large deflection dynamic response calculations for pressure loaded composite sandwich panels are demonstrated. One technique utilizes finite element modeling with a single equivalent layer representing the face sheets and core. The other technique utilizes the modal analysis computer code DEPROP which was recently modified to include transverse shear deformation in a core layer. The example problem consists of a simply supported rectangular sandwich panel. Included are comparisons of linear and nonlinear static response calculations, in addition to dynamic response calculations.
Nonlinear inversion of electrical resistivity imaging using pruning Bayesian neural networks
Jiang, Fei-Bo; Dai, Qian-Wei; Dong, Li
2016-06-01
Conventional artificial neural networks used to solve electrical resistivity imaging (ERI) inversion problem suffer from overfitting and local minima. To solve these problems, we propose to use a pruning Bayesian neural network (PBNN) nonlinear inversion method and a sample design method based on the K-medoids clustering algorithm. In the sample design method, the training samples of the neural network are designed according to the prior information provided by the K-medoids clustering results; thus, the training process of the neural network is well guided. The proposed PBNN, based on Bayesian regularization, is used to select the hidden layer structure by assessing the effect of each hidden neuron to the inversion results. Then, the hyperparameter α k , which is based on the generalized mean, is chosen to guide the pruning process according to the prior distribution of the training samples under the small-sample condition. The proposed algorithm is more efficient than other common adaptive regularization methods in geophysics. The inversion of synthetic data and field data suggests that the proposed method suppresses the noise in the neural network training stage and enhances the generalization. The inversion results with the proposed method are better than those of the BPNN, RBFNN, and RRBFNN inversion methods as well as the conventional least squares inversion.
Inverse optimal sliding mode control of spacecraft with coupled translation and attitude dynamics
Pukdeboon, Chutiphon
2015-10-01
This paper proposes two robust inverse optimal control schemes for spacecraft with coupled translation and attitude dynamics in the presence of external disturbances. For the first controller, an inverse optimal control law is designed based on Sontag-type formula and the control Lyapunov function. Then a robust inverse optimal position and attitude controller is designed by using a new second-order integral sliding mode control method to combine a sliding mode control with the derived inverse optimal control. The global asymptotic stability of the proposed control law is proved by using the second method of Lyapunov. For the other control law, a nonlinear H∞ inverse optimal controller for spacecraft position and attitude tracking motion is developed to achieve the design conditions of controller gains that the control law becomes suboptimal H∞ state feedback control. The ultimate boundedness of system state is proved by using the Lyapunov stability theory. Both developed robust inverse optimal controllers can minimise a performance index and ensure the stability of the closed-loop system and external disturbance attenuation. An example of position and attitude tracking manoeuvres is presented and simulation results are included to show the performance of the proposed controllers.
Nonlinear dynamics non-integrable systems and chaotic dynamics
Borisov, Alexander
2017-01-01
This monograph reviews advanced topics in the area of nonlinear dynamics. Starting with theory of integrable systems – including methods to find and verify integrability – the remainder of the book is devoted to non-integrable systems with an emphasis on dynamical chaos. Topics include structural stability, mechanisms of emergence of irreversible behaviour in deterministic systems as well as chaotisation occurring in dissipative systems.
Short- and long-term variations in non-linear dynamics of heart rate variability
DEFF Research Database (Denmark)
Kanters, J K; Højgaard, M V; Agner, E;
1996-01-01
OBJECTIVES: The purpose of the study was to investigate the short- and long-term variations in the non-linear dynamics of heart rate variability, and to determine the relationships between conventional time and frequency domain methods and the newer non-linear methods of characterizing heart rate...... variability. METHODS: Twelve healthy subjects were investigated by 3-h ambulatory ECG recordings repeated on 3 separate days. Correlation dimension, non-linear predictability, mean heart rate, and heart rate variability in the time and frequency domains were measured and compared with the results from...... corresponding surrogate time series. RESULTS: A small significant amount of non-linear dynamics exists in heart rate variability. Correlation dimensions and non-linear predictability are relatively specific parameters for each individual examined. The correlation dimension is inversely correlated to the heart...
Linearized versus non-linear inverse methods for seismic localization of underground sources
DEFF Research Database (Denmark)
Oh, Geok Lian; Jacobsen, Finn
2013-01-01
The problem of localization of underground sources from seismic measurements detected by several geophones located on the ground surface is addressed. Two main approaches to the solution of the problem are considered: a beamforming approach that is derived from the linearized inversion problem...... Difference elastic wave-field numerical method. In this paper, the accuracy and performance of the linear beamformer and nonlinear inverse methods to localize a underground seismic source are checked and compared using computer generated synthetic experimental data. © 2013 Acoustical Society of America....
On the use of nonlinear regularization in inverse method for the tachocline profile determination
Corbard, T; Provost, J P; Blanc-Féraud, L
1998-01-01
Inversions of rotational splittings have shown that the surface layers and the so-called solar tachocline at the base of the convection zone are regions in which high radial gradients of the rotation rate occur. The usual regularization methods tend to smooth out every high gradients in the solution and may not be appropriate for the study of a zone like the tachocline. In this paper we use nonlinear regularization methods that are developed for edge-preserving regularization in computed imaging (e.g. Blanc-Féraud et al. 1995) and we apply them in the helioseismic context of rotational inversions.
Chen, Xiang-Jun; Lam, Wa Kun
2004-06-01
An inverse scattering transform for the derivative nonlinear Schrödinger equation with nonvanishing boundary conditions is derived by introducing an affine parameter to avoid constructing Riemann sheets. A one-soliton solution simpler than that in the literature is obtained, which is a breather and degenerates to a bright or dark soliton as the discrete eigenvalue becomes purely imaginary. The solution is mapped to that of the modified nonlinear Schrödinger equation by a gaugelike transformation, predicting some sub-picosecond solitons in optical fibers.
Nonlinear and stochastic dynamics in the heart
Energy Technology Data Exchange (ETDEWEB)
Qu, Zhilin, E-mail: zqu@mednet.ucla.edu [Department of Medicine (Cardiology), David Geffen School of Medicine, University of California, Los Angeles, CA 90095 (United States); Hu, Gang [Department of Physics, Beijing Normal University, Beijing 100875 (China); Garfinkel, Alan [Department of Medicine (Cardiology), David Geffen School of Medicine, University of California, Los Angeles, CA 90095 (United States); Department of Integrative Biology and Physiology, University of California, Los Angeles, CA 90095 (United States); Weiss, James N. [Department of Medicine (Cardiology), David Geffen School of Medicine, University of California, Los Angeles, CA 90095 (United States); Department of Physiology, David Geffen School of Medicine, University of California, Los Angeles, CA 90095 (United States)
2014-10-10
In a normal human life span, the heart beats about 2–3 billion times. Under diseased conditions, a heart may lose its normal rhythm and degenerate suddenly into much faster and irregular rhythms, called arrhythmias, which may lead to sudden death. The transition from a normal rhythm to an arrhythmia is a transition from regular electrical wave conduction to irregular or turbulent wave conduction in the heart, and thus this medical problem is also a problem of physics and mathematics. In the last century, clinical, experimental, and theoretical studies have shown that dynamical theories play fundamental roles in understanding the mechanisms of the genesis of the normal heart rhythm as well as lethal arrhythmias. In this article, we summarize in detail the nonlinear and stochastic dynamics occurring in the heart and their links to normal cardiac functions and arrhythmias, providing a holistic view through integrating dynamics from the molecular (microscopic) scale, to the organelle (mesoscopic) scale, to the cellular, tissue, and organ (macroscopic) scales. We discuss what existing problems and challenges are waiting to be solved and how multi-scale mathematical modeling and nonlinear dynamics may be helpful for solving these problems.
Nonlinear dynamics analysis of a new autonomous chaotic system
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
In this paper, a new nonlinear autonomous system introduced by Chlouverakis and Sprott is studied further, to present very rich and complex nonlinear dynamical behaviors. Some basic dynamical properties are studied either analytically or nuchaotic system with very high Lyapunov dimensions is constructed and investigated. Two new nonlinear autonomous systems can be changed into one another by adding or omitting some constant coefficients.
Gradient-based optimization in nonlinear structural dynamics
DEFF Research Database (Denmark)
Dou, Suguang
The intrinsic nonlinearity of mechanical structures can give rise to rich nonlinear dynamics. Recently, nonlinear dynamics of micro-mechanical structures have contributed to developing new Micro-Electro-Mechanical Systems (MEMS), for example, atomic force microscope, passive frequency divider, fr...
Nonlinear dynamics of neural delayed feedback
Energy Technology Data Exchange (ETDEWEB)
Longtin, A.
1990-01-01
Neural delayed feedback is a property shared by many circuits in the central and peripheral nervous systems. The evolution of the neural activity in these circuits depends on their present state as well as on their past states, due to finite propagation time of neural activity along the feedback loop. These systems are often seen to undergo a change from a quiescent state characterized by low level fluctuations to an oscillatory state. We discuss the problem of analyzing this transition using techniques from nonlinear dynamics and stochastic processes. Our main goal is to characterize the nonlinearities which enable autonomous oscillations to occur and to uncover the properties of the noise sources these circuits interact with. The concepts are illustrated on the human pupil light reflex (PLR) which has been studied both theoretically and experimentally using this approach. 5 refs., 3 figs.
Digital Communications Using Chaos and Nonlinear Dynamics
Larson, Lawrence E; Liu, Jia-Ming
2006-01-01
This book introduces readers to a new and exciting cross-disciplinary field of digital communications with chaos. This field was born around 15 years ago, when it was first demonstrated that nonlinear systems which produce complex non-periodic noise-like chaotic signals, can be synchronized and modulated to carry useful information. Thus, chaotic signals can be used instead of pseudo-random digital sequences for spread-spectrum and private communication applications. This deceptively simple idea spun hundreds of research papers, and many novel communication schemes based on chaotic signals have been proposed. However, only very recently researchers have begun to make a transition from academic studies toward practical implementation issues, and many "promising" schemes had to be discarded or re-formulated. This book describes the state of the art (both theoretical and experimental) of this novel field. The book is written by leading experts in the fields of Nonlinear Dynamics and Electrical Engineering who pa...
Rossler Nonlinear Dynamical Machine for Cryptography Applications
Pandey, Sunil; Shrivastava, Dr S C
2009-01-01
In many of the cryptography applications like password or IP address encryption schemes, symmetric cryptography is useful. In these relatively simpler applications of cryptography, asymmetric cryptography is difficult to justify on account of the computational and implementation complexities associated with asymmetric cryptography. Symmetric schemes make use of a single shared key known only between the two communicating hosts. This shared key is used both for the encryption as well as the decryption of data. This key has to be small in size besides being a subset of a potentially large keyspace making it convenient for the communicating hosts while at the same time making cryptanalysis difficult for the potential attackers. In the present work, an abstract Rossler nonlinear dynamical machine has been described first. The Rossler system exhibits chaotic dynamics for certain values of system parameters and initial conditions. The chaotic dynamics of the Rossler system with its apparently erratic and irregular ...
Shimelevich, M. I.; Obornev, E. A.; Obornev, I. E.; Rodionov, E. A.
2017-07-01
The iterative approximation neural network method for solving conditionally well-posed nonlinear inverse problems of geophysics is presented. The method is based on the neural network approximation of the inverse operator. The inverse problem is solved in the class of grid (block) models of the medium on a regularized parameterization grid. The construction principle of this grid relies on using the calculated values of the continuity modulus of the inverse operator and its modifications determining the degree of ambiguity of the solutions. The method provides approximate solutions of inverse problems with the maximal degree of detail given the specified degree of ambiguity with the total number of the sought parameters n × 103 of the medium. The a priori and a posteriori estimates of the degree of ambiguity of the approximated solutions are calculated. The work of the method is illustrated by the example of the three-dimensional (3D) inversion of the synthesized 2D areal geoelectrical (audio magnetotelluric sounding, AMTS) data corresponding to the schematic model of a kimberlite pipe.
Three-Dimensional Induced Polarization Parallel Inversion Using Nonlinear Conjugate Gradients Method
Directory of Open Access Journals (Sweden)
Huan Ma
2015-01-01
Full Text Available Four kinds of array of induced polarization (IP methods (surface, borehole-surface, surface-borehole, and borehole-borehole are widely used in resource exploration. However, due to the presence of large amounts of the sources, it will take much time to complete the inversion. In the paper, a new parallel algorithm is described which uses message passing interface (MPI and graphics processing unit (GPU to accelerate 3D inversion of these four methods. The forward finite differential equation is solved by ILU0 preconditioner and the conjugate gradient (CG solver. The inverse problem is solved by nonlinear conjugate gradients (NLCG iteration which is used to calculate one forward and two “pseudo-forward” modelings and update the direction, space, and model in turn. Because each source is independent in forward and “pseudo-forward” modelings, multiprocess modes are opened by calling MPI library. The iterative matrix solver within CULA is called in each process. Some tables and synthetic data examples illustrate that this parallel inversion algorithm is effective. Furthermore, we demonstrate that the joint inversion of surface and borehole data produces resistivity and chargeability results are superior to those obtained from inversions of individual surface data.
Nonlinear dynamics of hydrostatic internal gravity waves
Energy Technology Data Exchange (ETDEWEB)
Stechmann, Samuel N.; Majda, Andrew J. [New York University, Courant Institute of Mathematical Sciences, NY (United States); Khouider, Boualem [University of Victoria, Department of Mathematics and Statistics, Victoria, BC (Canada)
2008-11-15
Stratified hydrostatic fluids have linear internal gravity waves with different phase speeds and vertical profiles. Here a simplified set of partial differential equations (PDE) is derived to represent the nonlinear dynamics of waves with different vertical profiles. The equations are derived by projecting the full nonlinear equations onto the vertical modes of two gravity waves, and the resulting equations are thus referred to here as the two-mode shallow water equations (2MSWE). A key aspect of the nonlinearities of the 2MSWE is that they allow for interactions between a background wind shear and propagating waves. This is important in the tropical atmosphere where horizontally propagating gravity waves interact together with wind shear and have source terms due to convection. It is shown here that the 2MSWE have nonlinear internal bore solutions, and the behavior of the nonlinear waves is investigated for different background wind shears. When a background shear is included, there is an asymmetry between the east- and westward propagating waves. This could be an important effect for the large-scale organization of tropical convection, since the convection is often not isotropic but organized on large scales by waves. An idealized illustration of this asymmetry is given for a background shear from the westerly wind burst phase of the Madden-Julian oscillation; the potential for organized convection is increased to the west of the existing convection by the propagating nonlinear gravity waves, which agrees qualitatively with actual observations. The ideas here should be useful for other physical applications as well. Moreover, the 2MSWE have several interesting mathematical properties: they are a system of nonconservative PDE with a conserved energy, they are conditionally hyperbolic, and they are neither genuinely nonlinear nor linearly degenerate over all of state space. Theory and numerics are developed to illustrate these features, and these features are
Nonlinear dynamical triggering of slow slip
Energy Technology Data Exchange (ETDEWEB)
Johnson, Paul A [Los Alamos National Laboratory; Knuth, Matthew W [WISCONSIN; Kaproth, Bryan M [PENN STATE; Carpenter, Brett [PENN STATE; Guyer, Robert A [Los Alamos National Laboratory; Le Bas, Pierre - Yves [Los Alamos National Laboratory; Daub, Eric G [Los Alamos National Laboratory; Marone, Chris [PENN STATE
2010-12-10
Among the most fascinating, recent discoveries in seismology have been the phenomena of triggered slip, including triggered earthquakes and triggered-tremor, as well as triggered slow, silent-slip during which no seismic energy is radiated. Because fault nucleation depths cannot be probed directly, the physical regimes in which these phenomena occur are poorly understood. Thus determining physical properties that control diverse types of triggered fault sliding and what frictional constitutive laws govern triggered faulting variability is challenging. We are characterizing the physical controls of triggered faulting with the goal of developing constitutive relations by conducting laboratory and numerical modeling experiments in sheared granular media at varying load conditions. In order to simulate granular fault zone gouge in the laboratory, glass beads are sheared in a double-direct configuration under constant normal stress, while subject to transient perturbation by acoustic waves. We find that triggered, slow, silent-slip occurs at very small confining loads ({approx}1-3 MPa) that are smaller than those where dynamic earthquake triggering takes place (4-7 MPa), and that triggered slow-slip is associated with bursts of LFE-like acoustic emission. Experimental evidence suggests that the nonlinear dynamical response of the gouge material induced by dynamic waves may be responsible for the triggered slip behavior: the slip-duration, stress-drop and along-strike slip displacement are proportional to the triggering wave amplitude. Further, we observe a shear-modulus decrease corresponding to dynamic-wave triggering relative to the shear modulus of stick-slips. Modulus decrease in response to dynamical wave amplitudes of roughly a microstrain and above is a hallmark of elastic nonlinear behavior. We believe that the dynamical waves increase the material non-affine elastic deformation during shearing, simultaneously leading to instability and slow-slip. The inferred
Nonlinear dynamics new directions theoretical aspects
Ugalde, Edgardo
2015-01-01
This book, along with its companion volume, Nonlinear Dynamics New Directions: Models and Applications, covers topics ranging from fractal analysis to very specific applications of the theory of dynamical systems to biology. This first volume is devoted to fundamental aspects and includes a number of important new contributions as well as some review articles that emphasize new development prospects. The second volume contains mostly new applications of the theory of dynamical systems to both engineering and biology. The topics addressed in the two volumes include a rigorous treatment of fluctuations in dynamical systems, topics in fractal analysis, studies of the transient dynamics in biological networks, synchronization in lasers, and control of chaotic systems, among others. This book also: · Presents a rigorous treatment of fluctuations in dynamical systems and explores a range of topics in fractal analysis, among other fundamental topics · Features recent developments on...
Nonlinear damping calculation in cylindrical gear dynamic modeling
Guilbault, Raynald; Lalonde, Sébastien; Thomas, Marc
2012-04-01
The nonlinear dynamic problem posed by cylindrical gear systems has been extensively covered in the literature. Nonetheless, a significant proportion of the mechanisms involved in damping generation remains to be investigated and described. The main objective of this study is to contribute to this task. Overall, damping is assumed to consist of three sources: surrounding element contribution, hysteresis of the teeth, and oil squeeze damping. The first two contributions are considered to be commensurate with the supported load; for its part however, squeeze damping is formulated using expressions developed from the Reynolds equation. A lubricated impact analysis between the teeth is introduced in this study for the minimum film thickness calculation during contact losses. The dynamic transmission error (DTE) obtained from the final model showed close agreement with experimental measurements available in the literature. The nonlinear damping ratio calculated at different mesh frequencies and torque amplitudes presented average values between 5.3 percent and 8 percent, which is comparable to the constant 8 percent ratio used in published numerical simulations of an equivalent gear pair. A close analysis of the oil squeeze damping evidenced the inverse relationship between this damping effect and the applied load.
Modified Nonlinear Inverse Synthesis for Optical Links with Distributed Raman Amplification
Le, Son T; Rosa, Pawel; Ania-Castanon, Juan D; Turitsyn, Sergei K
2015-01-01
Nonlinear Fourier transform (NFT) and eigenvalue communication with the use of nonlinear signal spectrum (both discrete and continuous), have been recently discussed as a promising transmission method to combat fiber nonlinearity impairments. However, because the NFT-based transmission method employs the integrability property of the lossless nonlinear Schr\\"odinger equation (NLSE), the original approach can only be applied directly to optical links with ideal distributed Raman amplification. In this paper, we investigate in details the impact of a non-ideal Raman gain profile on the performance of the nonlinear inverse synthesis (NIS) scheme, in which the transmitted information is encoded directly onto the continuous part of the nonlinear signal spectrum. We propose the lossless path-averaged (LPA) model for fiber links with non-ideal Raman gain profile by taking into account the average effect of the Raman gain. We show that the NIS scheme employing the LPA model can offer a performance gain of 3 dB regard...
Adaptive explicit Magnus numerical method for nonlinear dynamical systems
Institute of Scientific and Technical Information of China (English)
LI Wen-cheng; DENG Zi-chen
2008-01-01
Based on the new explicit Magnus expansion developed for nonlinear equations defined on a matrix Lie group,an efficient numerical method is proposed for nonlinear dynamical systems.To improve computational efficiency,the integration step size can be adaptively controlled.Validity and effectiveness of the method are shown by application to several nonlinear dynamical systems including the Duffing system,the van der Pol system with strong stiffness,and the nonlinear Hamiltonian pendulum system.
Giant dynamical Zeeman split in inverse spin valves
Wang, X. R.
2008-01-01
The inversion of a spin valve device is proposed. Opposite to a conventional spin valve of a non-magnetic spacer sandwiched between two ferromagnetic metals, an inverse spin valve is a ferromagnet sandwiched between two non-magnetic metals. It is predicted that, under a bias, the chemical potentials of spin-up and spin-down electrons in the metals split at metal-ferromagnet interfaces, a dynamical Zeeman effect. This split is of the order of an applied bias. Thus, there should be no problem o...
Inverse and forward dynamics: models of multi-body systems.
Otten, E
2003-01-01
Connected multi-body systems exhibit notoriously complex behaviour when driven by external and internal forces and torques. The problem of reconstructing the internal forces and/or torques from the movements and known external forces is called the 'inverse dynamics problem', whereas calculating motion from known internal forces and/or torques and resulting reaction forces is called the 'forward dynamics problem'. When stepping forward to cross the street, people use muscle forces that generate angular accelerations of their body segments and, by virtue of reaction forces from the street, a forward acceleration of the centre of mass of their body. Inverse dynamics calculations applied to a set of motion data from such an event can teach us how temporal patterns of joint torques were responsible for the observed motion. In forward dynamics calculations we may attempt to create motion from such temporal patterns, which is extremely difficult, because of the complex mechanical linkage along the chains forming the multi-body system. To understand, predict and sometimes control multi-body systems, we may want to have mathematical expressions for them. The Newton-Euler, Lagrangian and Featherstone approaches have their advantages and disadvantages. The simulation of collisions and the inclusion of muscle forces or other internal forces are discussed. Also, the possibility to perform a mixed inverse and forward dynamics calculation are dealt with. The use and limitations of these approaches form the conclusion. PMID:14561340
Nonlinear dynamics from lasers to butterflies
Ball, R
2003-01-01
This book is an inspirational introduction to modern research directions and scholarship in nonlinear dynamics, and will also be a valuable reference for researchers in the field. With the scholarly level aimed at the beginning graduate student, the book will have broad appeal to those with an undergraduate background in mathematical or physical sciences.In addition to pedagogical and new material, each chapter reviews the current state of the area and discusses classic and open problems in engaging, surprisingly non-technical ways. The contributors are Brian Davies (bifurcations in maps), Nal
Beam stability & nonlinear dynamics. Formal report
Energy Technology Data Exchange (ETDEWEB)
Parsa, Z. [ed.
1996-12-31
his Report includes copies of transparencies and notes from the presentations made at the Symposium on Beam Stability and Nonlinear Dynamics, December 3-5, 1996 at the Institute for Theoretical Physics, University of California, Santa Barbara California, that was made available by the authors. Editing, reduction and changes to the authors contributions were made only to fulfill the printing and publication requirements. We would like to take this opportunity and thank the speakers for their informative presentations and for providing copies of their transparencies and notes for inclusion in this Report.
Research on nonlinear stochastic dynamical price model
Energy Technology Data Exchange (ETDEWEB)
Li Jiaorui [Department of Applied Mathematics, Northwestern Polytechnical University, Xi' an 710072 (China); School of Statistics, Xi' an University of Finance and Economics, Xi' an 710061 (China)], E-mail: jiaoruili@mail.nwpu.edu.cn; Xu Wei; Xie Wenxian; Ren Zhengzheng [Department of Applied Mathematics, Northwestern Polytechnical University, Xi' an 710072 (China)
2008-09-15
In consideration of many uncertain factors existing in economic system, nonlinear stochastic dynamical price model which is subjected to Gaussian white noise excitation is proposed based on deterministic model. One-dimensional averaged Ito stochastic differential equation for the model is derived by using the stochastic averaging method, and applied to investigate the stability of the trivial solution and the first-passage failure of the stochastic price model. The stochastic price model and the methods presented in this paper are verified by numerical studies.
Nonlinear dynamic macromodeling techniques for audio systems
Ogrodzki, Jan; Bieńkowski, Piotr
2015-09-01
This paper develops a modelling method and a models identification technique for the nonlinear dynamic audio systems. Identification is performed by means of a behavioral approach based on a polynomial approximation. This approach makes use of Discrete Fourier Transform and Harmonic Balance Method. A model of an audio system is first created and identified and then it is simulated in real time using an algorithm of low computational complexity. The algorithm consists in real time emulation of the system response rather than in simulation of the system itself. The proposed software is written in Python language using object oriented programming techniques. The code is optimized for a multithreads environment.
Franck, I M
2014-01-01
This paper presents an efficient Bayesian framework for solving nonlinear, high-dimensional model calibration problems. It is based on Variational Bayesian formulation that aims at approximating the exact posterior by means of solving an optimization problem in an appropriately selected family of distributions. The goal is two-fold. Firstly, to find lower-dimensional representations of the unknown parameter vector that capture as much as possible of the associated posterior density, and secondly to enable the computation of the approximate posterior density with as few forward calls as possible. We discuss how these objectives can be achieved by using a fully Bayesian argumentation and employing the marginal likelihood or evidence as the ultimate model validation metric for any proposed dimensionality reduction. We demonstrate the performance of the proposed methodology to problems in nonlinear elastography where the identification of the mechanical properties of biological materials can inform non-invasive, ...
Fast Inverse Nonlinear Fourier Transform For Generating Multi-Solitons In Optical Fiber
Wahls, Sander
2015-01-01
The achievable data rates of current fiber-optic wavelength-division-multiplexing (WDM) systems are limited by nonlinear interactions between different subchannels. Recently, it was thus proposed to replace the conventional Fourier transform in WDM systems with an appropriately defined nonlinear Fourier transform (NFT). The computational complexity of NFTs is a topic of current research. In this paper, a fast inverse NFT algorithm for the important special case of multi-solitonic signals is presented. The algorithm requires only $\\mathcal{O}(D\\log^{2}D)$ floating point operations to compute $D$ samples of a multi-soliton. To the best of our knowledge, this is the first algorithm for this problem with $\\log^{2}$-linear complexity. The paper also includes a many samples analysis of the generated nonlinear Fourier spectra.
Nonlinear Dynamics of Electrostatically Actuated MEMS Arches
Al Hennawi, Qais M.
2015-05-01
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 a multi- mode Galarkin Reduced Order Model (ROM). We investigate the static response of the arch experimentally where we show several jumps due to the snap-through instability. Experimentally, a case study of in-plane silicon micromachined arch is studied and its mechanical behavior is measured using optical techniques. We develop an algorithm to extract various parameters that are needed to model the arch, such as the induced axial force, the modulus of elasticity, and the initially induced initial rise. After that, we excite the arch by a DC electrostatic force superimposed to an AC harmonic load. A softening spring behavior is observed when the excitation is close to the first resonance frequency due to the quadratic nonlinearity coming from the arch geometry and the electrostatic force. Also, a hardening spring behavior is observed when the excitation is close to the third (second symmetric) resonance frequency due to the cubic nonlinearity coming from mid-plane stretching. Then, we excite the arch by an electric load of two AC frequency components, where we report a combination resonance of the summed type. Agreement is reported among the theoretical and experimental work.
Nonlinear dynamical characteristics of bed load motion
Institute of Scientific and Technical Information of China (English)
BAI; Yuchuan; XU; Haijue; XU; Dong
2006-01-01
Bed forms of various kinds that evolve naturally on the bottom of sandy coasts and rivers are a result of the kinematics of bed load transport. Based on the group motion of particles in the bed load within the bottom layer, a study on the nonlinear dynamics of bed load transport is presented in this paper. It is found that some development stages, such as the initiation, the equilibrium sediment transport, and the transition from a smooth bed to sand dunes, can be accounted for by different states in the nonlinear system of the bed load transport. It is verified by comparison with experimental data reported by Laboratoire Nationae D'Hydraulique, Chatou, France, that the evolution from a smooth bed to sand dunes is determined by mutation in the bed load transport. This paper presents results that may offer theoretical explanations to the experimental observations. It is also an attempt to apply the state-of-the-art nonlinear science to the classical sediment transport mechanics.
Sparse Identification of Nonlinear Dynamics (SINDy)
Brunton, Steven; Proctor, Joshua; Kutz, Nathan
2016-11-01
This work develops a general new framework to discover the governing equations underlying a dynamical system simply from data measurements, leveraging advances in sparsity techniques and machine learning. The so-called sparse identification of nonlinear dynamics (SINDy) method results in models that are parsimonious, balancing model complexity with descriptive ability while avoiding over fitting. The only assumption about the structure of the model is that there are only a few important terms that govern the dynamics, so that the equations are sparse in the space of possible functions; this assumption holds for many physical systems in an appropriate basis. We demonstrate the algorithm on a wide range of problems, from simple canonical systems, including the chaotic Lorenz system, to the canonical fluid vortex shedding behind an circular cylinder at Re=100. We also show that this method generalizes to parameterized systems and systems that are time-varying or have external forcing. With abundant data and elusive laws, data-driven discovery of dynamics will continue to play an increasingly important role in the characterization and control of fluid dynamics.
Nonlinear Dynamic Characteristics of the Railway Vehicle
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
Dynamics of Nonlinear Time-Delay Systems
Lakshmanan, Muthusamy
2010-01-01
Synchronization of chaotic systems, a patently nonlinear phenomenon, has emerged as a highly active interdisciplinary research topic at the interface of physics, biology, applied mathematics and engineering sciences. In this connection, time-delay systems described by delay differential equations have developed as particularly suitable tools for modeling specific dynamical systems. Indeed, time-delay is ubiquitous in many physical systems, for example due to finite switching speeds of amplifiers in electronic circuits, finite lengths of vehicles in traffic flows, finite signal propagation times in biological networks and circuits, and quite generally whenever memory effects are relevant. This monograph presents the basics of chaotic time-delay systems and their synchronization with an emphasis on the effects of time-delay feedback which give rise to new collective dynamics. Special attention is devoted to scalar chaotic/hyperchaotic time-delay systems, and some higher order models, occurring in different bran...
Chaotic Discrimination and Non-Linear Dynamics
Directory of Open Access Journals (Sweden)
Partha Gangopadhyay
2005-01-01
Full Text Available This study examines a particular form of price discrimination, known as chaotic discrimination, which has the following features: sellers quote a common price but, in reality, they engage in secret and apparently unsystematic price discounts. It is widely held that such forms of price discrimination are seriously inconsistent with profit maximization by sellers.. However, there is no theoretical salience to support this kind of price discrimination. By straining the logic of non-linear dynamics this study explains why such secret discounts are chaotic in the sense that sellers fail to adopt profit-maximising price discounts. A model is developed to argue that such forms of discrimination may derive from the regions of instability of a dynamic model of price discounts.
Synchronization of Nonlinear Oscillators Over Networks with Dynamic Links
De Persis, Claudio
2015-01-01
In this paper we investigate the problem of synchronization of homogeneous nonlinear oscillators coupled by dynamic links. The output of the nonlinear oscillators is the input to the dynamic links, while the output of these dynamics links is the quantity available to the distributed controllers at t
Neuromechanical tuning of nonlinear postural control dynamics
Ting, Lena H.; van Antwerp, Keith W.; Scrivens, Jevin E.; McKay, J. Lucas; Welch, Torrence D. J.; Bingham, Jeffrey T.; DeWeerth, Stephen P.
2009-06-01
Postural control may be an ideal physiological motor task for elucidating general questions about the organization, diversity, flexibility, and variability of biological motor behaviors using nonlinear dynamical analysis techniques. Rather than presenting "problems" to the nervous system, the redundancy of biological systems and variability in their behaviors may actually be exploited to allow for the flexible achievement of multiple and concurrent task-level goals associated with movement. Such variability may reflect the constant "tuning" of neuromechanical elements and their interactions for movement control. The problem faced by researchers is that there is no one-to-one mapping between the task goal and the coordination of the underlying elements. We review recent and ongoing research in postural control with the goal of identifying common mechanisms underlying variability in postural control, coordination of multiple postural strategies, and transitions between them. We present a delayed-feedback model used to characterize the variability observed in muscle coordination patterns during postural responses to perturbation. We emphasize the significance of delays in physiological postural systems, requiring the modulation and coordination of both the instantaneous, "passive" response to perturbations as well as the delayed, "active" responses to perturbations. The challenge for future research lies in understanding the mechanisms and principles underlying neuromechanical tuning of and transitions between the diversity of postural behaviors. Here we describe some of our recent and ongoing studies aimed at understanding variability in postural control using physical robotic systems, human experiments, dimensional analysis, and computational models that could be enhanced from a nonlinear dynamics approach.
Bubble and Drop Nonlinear Dynamics (BDND)
Trinh, E. H.; Leal, L. Gary; Thomas, D. A.; Crouch, R. K.
1998-01-01
Free drops and bubbles are weakly nonlinear mechanical systems that are relatively simple to characterize experimentally in 1-G as well as in microgravity. The understanding of the details of their motion contributes to the fundamental study of nonlinear phenomena and to the measurement of the thermophysical properties of freely levitated melts. The goal of this Glovebox-based experimental investigation is the low-gravity assessment of the capabilities of a modular apparatus based on ultrasonic resonators and on the pseudo- extinction optical method. The required experimental task is the accurate measurements of the large-amplitude dynamics of free drops and bubbles in the absence of large biasing influences such as gravity and levitation fields. A single-axis levitator used for the positioning of drops in air, and an ultrasonic water-filled resonator for the trapping of air bubbles have been evaluated in low-gravity and in 1-G. The basic feasibility of drop positioning and shape oscillations measurements has been verified by using a laptop-interfaced automated data acquisition and the optical extinction technique. The major purpose of the investigation was to identify the salient technical issues associated with the development of a full-scale Microgravity experiment on single drop and bubble dynamics.
Time Series Forecasting A Nonlinear Dynamics Approach
Sello, S
1999-01-01
The problem of prediction of a given time series is examined on the basis of recent nonlinear dynamics theories. Particular attention is devoted to forecast the amplitude and phase of one of the most common solar indicator activity, the international monthly smoothed sunspot number. It is well known that the solar cycle is very difficult to predict due to the intrinsic complexity of the related time behaviour and to the lack of a succesful quantitative theoretical model of the Sun magnetic cycle. Starting from a previous recent work, we checked the reliability and accuracy of a forecasting model based on concepts of nonlinear dynamical systems applied to experimental time series, such as embedding phase space,Lyapunov spectrum,chaotic behaviour. The model is based on a locally hypothesis of the behaviour on the embedding space, utilizing an optimal number k of neighbour vectors to predict the future evolution of the current point with the set of characteristic parameters determined by several previous paramet...
Directory of Open Access Journals (Sweden)
G. Forget
2015-10-01
Full Text Available This paper presents the ECCO v4 non-linear inverse modeling framework and its baseline solution for the evolving ocean state over the period 1992–2011. Both components are publicly available and subjected to regular, automated regression tests. The modeling framework includes sets of global conformal grids, a global model setup, implementations of data constraints and control parameters, an interface to algorithmic differentiation, as well as a grid-independent, fully capable Matlab toolbox. The baseline ECCO v4 solution is a dynamically consistent ocean state estimate without unidentified sources of heat and buoyancy, which any interested user will be able to reproduce accurately. The solution is an acceptable fit to most data and has been found to be physically plausible in many respects, as documented here and in related publications. Users are being provided with capabilities to assess model–data misfits for themselves. The synergy between modeling and data synthesis is asserted through the joint presentation of the modeling framework and the state estimate. In particular, the inverse estimate of parameterized physics was instrumental in improving the fit to the observed hydrography, and becomes an integral part of the ocean model setup available for general use. More generally, a first assessment of the relative importance of external, parametric and structural model errors is presented. Parametric and external model uncertainties appear to be of comparable importance and dominate over structural model uncertainty. The results generally underline the importance of including turbulent transport parameters in the inverse problem.
Non-Linear Dynamics of Saturn's Rings
Esposito, L. W.
2015-12-01
Non-linear processes can explain why Saturn's rings are so active and dynamic. Some of this non-linearity is captured in a simple Predator-Prey Model: Periodic forcing from the moon causes streamline crowding; This damps the relative velocity, and allows aggregates to grow. About a quarter phase later, the aggregates stir the system to higher relative velocity and the limit cycle repeats each orbit, with relative velocity ranging from nearly zero to a multiple of the orbit average: 2-10x is possible. Summary of Halo Results: A predator-prey model for ring dynamics produces transient structures like 'straw' that can explain the halo structure and spectroscopy: Cyclic velocity changes cause perturbed regions to reach higher collision speeds at some orbital phases, which preferentially removes small regolith particles; Surrounding particles diffuse back too slowly to erase the effect: this gives the halo morphology; This requires energetic collisions (v ≈ 10m/sec, with throw distances about 200km, implying objects of scale R ≈ 20km); We propose 'straw', as observed ny Cassini cameras. Transform to Duffing Eqn : With the coordinate transformation, z = M2/3, the Predator-Prey equations can be combined to form a single second-order differential equation with harmonic resonance forcing. Ring dynamics and history implications: Moon-triggered clumping at perturbed regions in Saturn's rings creates both high velocity dispersion and large aggregates at these distances, explaining both small and large particles observed there. This confirms the triple architecture of ring particles: a broad size distribution of particles; these aggregate into temporary rubble piles; coated by a regolith of dust. We calculate the stationary size distribution using a cell-to-cell mapping procedure that converts the phase-plane trajectories to a Markov chain. Approximating the Markov chain as an asymmetric random walk with reflecting boundaries allows us to determine the power law index from
Inversion of geothermal heat flux in a thermomechanically coupled nonlinear Stokes ice sheet model
Zhu, Hongyu; Petra, Noemi; Stadler, Georg; Isaac, Tobin; Hughes, Thomas J. R.; Ghattas, Omar
2016-07-01
We address the inverse problem of inferring the basal geothermal heat flux from surface velocity observations using a steady-state thermomechanically coupled nonlinear Stokes ice flow model. This is a challenging inverse problem since the map from basal heat flux to surface velocity observables is indirect: the heat flux is a boundary condition for the thermal advection-diffusion equation, which couples to the nonlinear Stokes ice flow equations; together they determine the surface ice flow velocity. This multiphysics inverse problem is formulated as a nonlinear least-squares optimization problem with a cost functional that includes the data misfit between surface velocity observations and model predictions. A Tikhonov regularization term is added to render the problem well posed. We derive adjoint-based gradient and Hessian expressions for the resulting partial differential equation (PDE)-constrained optimization problem and propose an inexact Newton method for its solution. As a consequence of the Petrov-Galerkin discretization of the energy equation, we show that discretization and differentiation do not commute; that is, the order in which we discretize the cost functional and differentiate it affects the correctness of the gradient. Using two- and three-dimensional model problems, we study the prospects for and limitations of the inference of the geothermal heat flux field from surface velocity observations. The results show that the reconstruction improves as the noise level in the observations decreases and that short-wavelength variations in the geothermal heat flux are difficult to recover. We analyze the ill-posedness of the inverse problem as a function of the number of observations by examining the spectrum of the Hessian of the cost functional. Motivated by the popularity of operator-split or staggered solvers for forward multiphysics problems - i.e., those that drop two-way coupling terms to yield a one-way coupled forward Jacobian - we study the
Forward and Inverse Dynamics of the Biped PASIBOT
Directory of Open Access Journals (Sweden)
Eduardo Corral
2014-07-01
Full Text Available This article addresses the supporting foot slippage of the biped robot PASIBOT and develops its forward and inverse dynamics for simple and double support phases. To address the slippage phenomenon, we consider an additional degree of freedom at the supporting foot and also distinguish between static and kinetic friction conditions. The inverse and forward dynamics, accounting for support foot slippage, are encoded in MATLAB. The algorithm predicts the motion of the biped from the torque function given by the biped’s sole motor. Thus, the algorithm becomes an indispensable tool for studying transient states of the biped (for example, the torques required for starting and braking, as well as defining the conditions that prevent or control slippage. Since the developed code is parametric, its output can greatly assist in the design, optimization and control of PASIBOT and similar biped robots. The topology, kinematics and inverse dynamics of the one-degree-of-freedom biped PASIBOT have been previously described, but without regard to slippage between the supporting foot and the ground.
Consensus tracking for multiagent systems with nonlinear dynamics.
Dong, Runsha
2014-01-01
This paper concerns the problem of consensus tracking for multiagent systems with a dynamical leader. In particular, it proposes the corresponding explicit control laws for multiple first-order nonlinear systems, second-order nonlinear systems, and quite general nonlinear systems based on the leader-follower and the tree shaped network topologies. Several numerical simulations are given to verify the theoretical results.
GARCH modelling of covariance in dynamical estimation of inverse solutions
Energy Technology Data Exchange (ETDEWEB)
Galka, Andreas [Institute of Experimental and Applied Physics, University of Kiel, 24098 Kiel (Germany) and Institute of Statistical Mathematics (ISM), Minami-Azabu 4-6-7, Tokyo 106-8569 (Japan)]. E-mail: galka@physik.uni-kiel.de; Yamashita, Okito [ATR Computational Neuroscience Laboratories, Hikaridai 2-2-2, Kyoto 619-0288 (Japan); Ozaki, Tohru [Institute of Statistical Mathematics (ISM), Minami-Azabu 4-6-7, Tokyo 106-8569 (Japan)
2004-12-06
The problem of estimating unobserved states of spatially extended dynamical systems poses an inverse problem, which can be solved approximately by a recently developed variant of Kalman filtering; in order to provide the model of the dynamics with more flexibility with respect to space and time, we suggest to combine the concept of GARCH modelling of covariance, well known in econometrics, with Kalman filtering. We formulate this algorithm for spatiotemporal systems governed by stochastic diffusion equations and demonstrate its feasibility by presenting a numerical simulation designed to imitate the situation of the generation of electroencephalographic recordings by the human cortex.
Nonlinear Dynamics and Optimization of Spur Gears
Pellicano, Francesco; Bonori, Giorgio; Faggioni, Marcello; Scagliarini, Giorgio
In the present study a single degree of freedom oscillator with clearance type non-linearity is considered. Such oscillator represents the simplest model able to analyze a single teeth gear pair, neglecting: bearings and shafts stiffness and multi mesh interactions. One of the test cases considered in the present work represents an actual gear pair that is part of a gear box of an agricultural vehicle; such gear pair gave rise to noise problems. The main gear pair characteristics (mesh stiffness and inertia) are evaluated after an accurate geometrical modelling. The meshing stiffness of the gear pair is piecewise linear and time varying (in particular periodic); it is evaluated numerically using nonlinear finite element analysis (with contact mechanics) for different positions along one mesh cycle, then it is expanded in Fourier series. A direct numerical integration approach and a smoothing technique have been considered to obtain the dynamic scenario. Bifurcation diagrams of Poincaré maps are plotted according to some sample case study from literature. Optimization procedures are proposed, in order to find optimal involute modifications that reduce gears vibration.
On the Theory of Nonlinear Dynamics and its Applications in Vehicle Systems Dynamics
DEFF Research Database (Denmark)
True, Hans
1999-01-01
We present a brief outline of nonlinear dynamics and its applications to vehicle systems dynamics problems. The concept of a phase space is introduced in order to illustrate the dynamics of nonlinear systems in a way that is easy to perceive. Various equilibrium states are defined...... of nonlinear dynamics in vehicle simulations is discussed, and it is argued that it is necessary to know the equilibrium states of the full nonlinear system before the simulation calculations are performed....
Nonlinear inversion-based output tracking control of a boiler-turbine unit
Institute of Scientific and Technical Information of China (English)
Fang FANG; Jizhen LIU; Wen TAN
2005-01-01
The capability to perform fast load-following has been an important issue in the power industry. An output tracking control system of a boiler-turbine unit is developed. The system is composed of stable inversion and feedback controller.The stable inversion is implemented as a feedforward controller to improve the load-following capability, and the feedback controller is utilized to guarantee the stability and robustness of the whole system. Loop-shaping H∞ method is used to design the feedback controller and the final controller is reduced to a multivariable PI form. The output tracking control system takes account of the multivariable, nonlinear and coupling behavior of boiler-turbine system, and the simulation tests show that the control system works well and can be widely applied.
Nonlinear Inversion of Potential-Field Data Using an Improved Genetic Algorithm
Institute of Scientific and Technical Information of China (English)
Feng Gangding; Chen Chao
2004-01-01
The genetic algorithm is useful for solving an inversion of complex nonlinear geophysical equations. The multi-point search of the genetic algorithm makes it easier to find a globally optimal solution and avoid falling into a local extremum. The search efficiency of the genetic algorithm is a key to producing successful solutions in a huge multi-parameter model space. The encoding mechanism of the genetic algorithm affects the searching processes in the evolution. Not all genetic operations perform perfectly in a search under either a binary or decimal encoding system. As such, a standard genetic algorithm (SGA) is sometimes unable to resolve an optimization problem such as a simple geophysical inversion. With the binary encoding system the operation of the crossover may produce more new individuals. The decimal encoding system, on the other hand, makes the mutation generate more new genes. This paper discusses approaches of exploiting the search potentials of genetic operations with different encoding systems and presents a hybrid-encoding mechanism for the genetic algorithm. This is referred to as the hybrid-encoding genetic algorithm (HEGA). The method is based on the routine in which the mutation operation is executed in decimal code and other operations in binary code. HEGA guarantees the birth of better genes by mutation processing with a high probability, so that it is beneficial for resolving the inversions of complicated problems. Synthetic and real-world examples demonstrate the advantages of using HEGA in the inversion of potential-field data.
Nonlinear dynamics of electron-positron clusters
Manfredi, Giovanni; Haas, Fernando; 10.1088/1367-2630/14/7/075012
2012-01-01
Electron-positron clusters are studied using a quantum hydrodynamic model that includes Coulomb and exchange interactions. A variational Lagrangian method is used to determine their stationary and dynamical properties. The cluster static features are validated against existing Hartree-Fock calculations. In the linear response regime, we investigate both dipole and monopole (breathing) modes. The dipole mode is reminiscent of the surface plasmon mode usually observed in metal clusters. The nonlinear regime is explored by means of numerical simulations. We show that, by exciting the cluster with a chirped laser pulse with slowly varying frequency (autoresonance), it is possible to efficiently separate the electron and positron populations on a timescale of a few tens of femtoseconds.
Chua's Nonlinear Dynamics Perspective of Cellular Automata
Pazienza, Giovanni E.
2013-01-01
Chua's `Nonlinear Dynamics Perspective of Cellular Automata' represents a genuine breakthrough in this area and it has had a major impact on the recent scientific literature. His results have been accurately described in a series of fourteen papers appeared over the course of eight years but there is no compendious introduction to his work. Therefore, here for the first time, we present Chua's main ideas as well as a few unpublished results that have not been included in his previous papers. This overview illustrates the essence of Chua's work by using a clear terminology and a consistent notation, and it is aimed at those who want to approach this subject through a concise but thorough exposition.
Directory of Open Access Journals (Sweden)
Morteza Ebrahimi
2012-01-01
Full Text Available The purpose of the present study is to provide a fast and accurate algorithm for identifying the medium temperature and the unknown radiation term from an overspecified condition on the boundary in an inverse problem of linear heat equation with nonlinear boundary condition. The design of the paper is to employ Taylor’s series expansion for linearize nonlinear term and then finite-difference approximation to discretize the problem domain. Owing to the application of the finite difference scheme, a large sparse system of linear algebraic equations is obtained. An approach of Monte Carlo method is employed to solve the linear system and estimate unknown radiation term. The Monte Carlo optimization is adopted to modify the estimated values. Results show that a good estimation on the radiation term can be obtained within a couple of minutes CPU time at pentium IV-2.4 GHz PC.
Murio, Diego A.
1991-01-01
An explicit and unconditionally stable finite difference method for the solution of the transient inverse heat conduction problem in a semi-infinite or finite slab mediums subject to nonlinear radiation boundary conditions is presented. After measuring two interior temperature histories, the mollification method is used to determine the surface transient heat source if the energy radiation law is known. Alternatively, if the active surface is heated by a source at a rate proportional to a given function, the nonlinear surface radiation law is then recovered as a function of the interface temperature when the problem is feasible. Two typical examples corresponding to Newton cooling law and Stefan-Boltzmann radiation law respectively are illustrated. In all cases, the method predicts the surface conditions with an accuracy suitable for many practical purposes.
Buried Object Detection by an Inexact Newton Method Applied to Nonlinear Inverse Scattering
Directory of Open Access Journals (Sweden)
Matteo Pastorino
2012-01-01
Full Text Available An approach to reconstruct buried objects is proposed. It is based on the integral equations of the electromagnetic inverse scattering problem, written in terms of the Green’s function for half-space geometries. The full nonlinearity of the problem is exploited in order to inspect strong scatterers. After discretization of the continuous model, the resulting equations are solved in a regularization sense by means of a two-step inexact Newton algorithm. The capabilities and limitations of the method are evaluated by means of some numerical simulations.
Directory of Open Access Journals (Sweden)
Slavica M. Perovich
2011-06-01
Full Text Available The subject of the theoretical analysis presented in this paper is an analytical approach to the temperature estimation, as an inverse problem, for different thermistors – linear resistances structures: series and parallel ones, by the STFT - Special Trans Functions Theory (S.M. Perovich. The mathematical formulae genesis of both cases is given. Some numerical and graphical simulations in MATHEMATICA program have been realized. The estimated temperature intervals for strongly determined values of the equivalent resistances of the nonlinear structures are given, as well.
Nonlinear Dynamics: Integrability, Chaos and Patterns
Energy Technology Data Exchange (ETDEWEB)
Grammaticos, B [GMPIB, Universite Paris VII, Tour 24--14, 5e etage, Case 7021, 75251 Paris (France)
2004-02-06
When the editorial office of Journal of Physics A: Mathematical and General of the Institute of Physics Publishing asked me to review a book on nonlinear dynamics I experienced an undeniable apprehension. Indeed, the domain is a rapidly expanding one and writing a book aiming at a certain degree of completeness looks like an almost impossible task. My uneasiness abated somewhat when I saw the names of the authors, two well-known specialists of the nonlinear domain, but it was only when I held the book in my hands that I felt really reassured. The book is not just a review of the recent (and less so) findings on nonlinear systems. It is also a textbook. The authors set out to provide a detailed, step by step, introduction to the domain of nonlinearity and its various subdomains: chaos, integrability and pattern formation (although this last topic is treated with far less detail than the other two). The public they have in mind is obviously that of university students, graduate or undergraduate, who are interested in nonlinear phenomena. I suspect that a non-negligible portion of readers will be people who have to teach topics which figure among those included in the book: they will find this monograph an excellent companion to their course. The book is written in a pedagogical way, with a profusion of examples, detailed explanations and clear diagrams. The point of view is that of a physicist, which to my eyes is a major advantage. The mathematical formulation remains simple and perfectly intelligible. Thus the reader is not bogged down by fancy mathematical formalism, which would have discouraged the less experienced ones. A host of exercises accompanies every chapter. This will give the novice the occasion to develop his/her problem-solving skills and acquire competence in the use of nonlinear techniques. Some exercises are quite straightforward, like 'verify the relation 14.81'. Others are less so, such as 'prepare a write-up on a) frequency
Gamma ray vortices from nonlinear inverse Compton scattering of circularly polarized light
Taira, Yoshitaka; Katoh, Masahiro
2016-01-01
Inverse Compton scattering (ICS) is an elemental radiation process that produces high-energy photons both in nature and in the laboratory. Non-linear ICS is a process in which multiple photons are converted to a single high-energy photon. Here, we theoretically show that the photon produced by non-linear ICS of circularly polarized photons is a vortex, which means that it possesses a helical wave front and carries orbital angular momentum. Our work explains a recent experimental result regarding non-linear Compton scattering that clearly shows an annular intensity distribution as a remarkable feature of a vortex beam. Our work implies that gamma ray vortices should be produced in various situations in astrophysics in which high-energy electrons and intense circularly polarized light fields coexist. They should play a critical role in stellar nucleosynthesis. Non-linear ICS is the most promising radiation process for realizing a gamma ray vortex source based on currently available laser and accelerator technol...
Surfactant and nonlinear drop dynamics in microgravity
Jankovsky, Joseph Charles
2000-11-01
Large amplitude drop dynamics in microgravity were conducted during the second United States Microgravity Laboratory mission carried onboard the Space Shuttle Columbia (20 October-5 November 1995). Centimeter- sized drops were statically deformed by acoustic radiation pressure and released to oscillate freely about a spherical equilibrium. Initial aspect ratios of up to 2.0 were achieved. Experiments using pure water and varying aqueous concentrations of Triton-X 100 and bovine serum albumin (BSA) were performed. The axisymmetric drop shape oscillations were fit using the degenerate spherical shape modes. The frequency and decay values of the fundamental quadrupole and fourth order shape mode were analyzed. Several large amplitude nonlinear oscillation dynamics were observed. Shape entrainment of the higher modes by the fundamental quadrupole mode occurred. Amplitude- dependent effects were observed. The nonlinear frequency shift, where the oscillation frequency is found to decrease with larger amplitudes, was largely unaffected by the presence of surfactants. The percentage of time spent in the prolate shape over one oscillation cycle was found to increase with oscillation amplitude. This prolate shape bias was also unaffected by the addition of surfactants. These amplitude-dependent effects indicate that the nonlinearities are a function of the bulk properties and not the surface properties. BSA was found to greatly enhance the surface viscoelastic properties by increasing the total damping of the oscillation, while Triton had only a small influence on damping. The surface concentration of BSA was found to be diffusion-controlled over the time of the experiments, while the Triton diffusion rate was very rapid. Using the experimental frequency and decay values, the suface viscoelastic properties of surface dilatational viscosity ( ks ) and surface shear viscosity ( ms ) were found for varying surfactant concentrations using the transcendental equation of Lu
XXIII International Conference on Nonlinear Dynamics of Electronic Systems
Stoop, Ruedi; Stramaglia, Sebastiano
2017-01-01
This book collects contributions to the XXIII international conference “Nonlinear dynamics of electronic systems”. Topics range from non-linearity in electronic circuits to synchronisation effects in complex networks to biological systems, neural dynamics and the complex organisation of the brain. Resting on a solid mathematical basis, these investigations address highly interdisciplinary problems in physics, engineering, biology and biochemistry.
A NEW SOLUTION MODEL OF NONLINEAR DYNAMIC LEAST SQUARE ADJUSTMENT
Institute of Scientific and Technical Information of China (English)
陶华学; 郭金运
2000-01-01
The nonlinear least square adjustment is a head object studied in technology fields. The paper studies on the non-derivative solution to the nonlinear dynamic least square adjustment and puts forward a new algorithm model and its solution model. The method has little calculation load and is simple. This opens up a theoretical method to solve the linear dynamic least square adjustment.
Method and system for training dynamic nonlinear adaptive filters which have embedded memory
Rabinowitz, Matthew (Inventor)
2002-01-01
Described herein is a method and system for training nonlinear adaptive filters (or neural networks) which have embedded memory. Such memory can arise in a multi-layer finite impulse response (FIR) architecture, or an infinite impulse response (IIR) architecture. We focus on filter architectures with separate linear dynamic components and static nonlinear components. Such filters can be structured so as to restrict their degrees of computational freedom based on a priori knowledge about the dynamic operation to be emulated. The method is detailed for an FIR architecture which consists of linear FIR filters together with nonlinear generalized single layer subnets. For the IIR case, we extend the methodology to a general nonlinear architecture which uses feedback. For these dynamic architectures, we describe how one can apply optimization techniques which make updates closer to the Newton direction than those of a steepest descent method, such as backpropagation. We detail a novel adaptive modified Gauss-Newton optimization technique, which uses an adaptive learning rate to determine both the magnitude and direction of update steps. For a wide range of adaptive filtering applications, the new training algorithm converges faster and to a smaller value of cost than both steepest-descent methods such as backpropagation-through-time, and standard quasi-Newton methods. We apply the algorithm to modeling the inverse of a nonlinear dynamic tracking system 5, as well as a nonlinear amplifier 6.
Interactions between nonlinear spur gear dynamics and surface wear
Ding, Huali; Kahraman, Ahmet
2007-11-01
In this study, two different dynamic models, a finite elements-based deformable-body model and a simplified discrete model, and a surface wear model are combined to study the interaction between gear surface wear and gear dynamic response. The proposed dynamic gear wear model includes the influence of worn surface profiles on dynamic tooth forces and transmission error as well as the influence of dynamic tooth forces on wear profiles. This paper first introduces the nonlinear dynamic models that include gear backlash and time-varying gear mesh stiffness, and a wear model separately. It presents a comparison to experiments for validation of the dynamic models. The dynamic models are combined with the wear model to study the interaction of surface wear and dynamic behavior in both linear and nonlinear response regimes. At the end, several sets of simulation results are used to demonstrate the two-way relationship between nonlinear gear dynamics and surface wear.
Dynamic data integration and stochastic inversion of a confined aquifer
Wang, D.; Zhang, Y.; Irsa, J.; Huang, H.; Wang, L.
2013-12-01
Much work has been done in developing and applying inverse methods to aquifer modeling. The scope of this paper is to investigate the applicability of a new direct method for large inversion problems and to incorporate uncertainty measures in the inversion outcomes (Wang et al., 2013). The problem considered is a two-dimensional inverse model (50×50 grid) of steady-state flow for a heterogeneous ground truth model (500×500 grid) with two hydrofacies. From the ground truth model, decreasing number of wells (12, 6, 3) were sampled for facies types, based on which experimental indicator histograms and directional variograms were computed. These parameters and models were used by Sequential Indicator Simulation to generate 100 realizations of hydrofacies patterns in a 100×100 (geostatistical) grid, which were conditioned to the facies measurements at wells. These realizations were smoothed with Simulated Annealing, coarsened to the 50×50 inverse grid, before they were conditioned with the direct method to the dynamic data, i.e., observed heads and groundwater fluxes at the same sampled wells. A set of realizations of estimated hydraulic conductivities (Ks), flow fields, and boundary conditions were created, which centered on the 'true' solutions from solving the ground truth model. Both hydrofacies conductivities were computed with an estimation accuracy of ×10% (12 wells), ×20% (6 wells), ×35% (3 wells) of the true values. For boundary condition estimation, the accuracy was within × 15% (12 wells), 30% (6 wells), and 50% (3 wells) of the true values. The inversion system of equations was solved with LSQR (Paige et al, 1982), for which coordinate transform and matrix scaling preprocessor were used to improve the condition number (CN) of the coefficient matrix. However, when the inverse grid was refined to 100×100, Gaussian Noise Perturbation was used to limit the growth of the CN before the matrix solve. To scale the inverse problem up (i.e., without smoothing
Directory of Open Access Journals (Sweden)
Merboldt Klaus-Dietmar
2010-07-01
Full Text Available Abstract Background Functional assessments of the heart by dynamic cardiovascular magnetic resonance (CMR commonly rely on (i electrocardiographic (ECG gating yielding pseudo real-time cine representations, (ii balanced gradient-echo sequences referred to as steady-state free precession (SSFP, and (iii breath holding or respiratory gating. Problems may therefore be due to the need for a robust ECG signal, the occurrence of arrhythmia and beat to beat variations, technical instabilities (e.g., SSFP "banding" artefacts, and limited patient compliance and comfort. Here we describe a new approach providing true real-time CMR with image acquisition times as short as 20 to 30 ms or rates of 30 to 50 frames per second. Methods The approach relies on a previously developed real-time MR method, which combines a strongly undersampled radial FLASH CMR sequence with image reconstruction by regularized nonlinear inversion. While iterative reconstructions are currently performed offline due to limited computer speed, online monitoring during scanning is accomplished using gridding reconstructions with a sliding window at the same frame rate but with lower image quality. Results Scans of healthy young subjects were performed at 3 T without ECG gating and during free breathing. The resulting images yield T1 contrast (depending on flip angle with an opposed-phase or in-phase condition for water and fat signals (depending on echo time. They completely avoid (i susceptibility-induced artefacts due to the very short echo times, (ii radiofrequency power limitations due to excitations with flip angles of 10° or less, and (iii the risk of peripheral nerve stimulation due to the use of normal gradient switching modes. For a section thickness of 8 mm, real-time images offer a spatial resolution and total acquisition time of 1.5 mm at 30 ms and 2.0 mm at 22 ms, respectively. Conclusions Though awaiting thorough clinical evaluation, this work describes a robust and
A limited memory BFGS method for a nonlinear inverse problem in digital breast tomosynthesis
Landi, G.; Loli Piccolomini, E.; Nagy, J. G.
2017-09-01
Digital breast tomosynthesis (DBT) is an imaging technique that allows the reconstruction of a pseudo three-dimensional image of the breast from a finite number of low-dose two-dimensional projections obtained by different x-ray tube angles. An issue that is often ignored in DBT is the fact that an x-ray beam is polyenergetic, i.e. it is composed of photons with different levels of energy. The polyenergetic model requires solving a large-scale, nonlinear inverse problem, which is more expensive than the typically used simplified, linear monoenergetic model. However, the polyenergetic model is much less susceptible to beam hardening artifacts, which show up as dark streaks and cupping (i.e. background nonuniformities) in the reconstructed image. In addition, it has been shown that the polyenergetic model can be exploited to obtain additional quantitative information about the material of the object being imaged. In this paper we consider the multimaterial polyenergetic DBT model, and solve the nonlinear inverse problem with a limited memory BFGS quasi-Newton method. Regularization is enforced at each iteration using a diagonally modified approximation of the Hessian matrix, and by truncating the iterations.
COMPARISON OF NONLINEAR DYNAMICS OPTIMIZATION METHODS FOR APS-U
Energy Technology Data Exchange (ETDEWEB)
Sun, Y.; Borland, Michael
2017-06-25
Many different objectives and genetic algorithms have been proposed for storage ring nonlinear dynamics performance optimization. These optimization objectives include nonlinear chromaticities and driving/detuning terms, on-momentum and off-momentum dynamic acceptance, chromatic detuning, local momentum acceptance, variation of transverse invariant, Touschek lifetime, etc. In this paper, the effectiveness of several different optimization methods and objectives are compared for the nonlinear beam dynamics optimization of the Advanced Photon Source upgrade (APS-U) lattice. The optimized solutions from these different methods are preliminarily compared in terms of the dynamic acceptance, local momentum acceptance, chromatic detuning, and other performance measures.
Experimental mastering of nonlinear dynamics in circuits by sporadic pulses
Energy Technology Data Exchange (ETDEWEB)
Ruiz, P. [Instituto de Fisica de Cantabria IFCA (CSIC-UC), Santander (Spain); Gutierrez, J.M. [Department of Applied Mathematics and Computer Science, University of Cantabria, 39005 Santander (Spain)], E-mail: gutierjm@unican.es; Gueemez, J. [Department of Applied Physics, Universidad de Cantabria (Spain)
2008-05-15
We present some experimental evidence of mastering chaos (control and anticontrol) in nonlinear circuits using a simple impulsive method which does not require any knowledge about the system's dynamics. The method works by introducing instantaneous pulses in some system variables-in this paper the pulses are applied to a capacitor voltage-and, hence, is an additional plug-in that does not modify the system itself. When varying the mastering parameters (amplitude and frequency of pulses) we obtain a bifurcation structure similar to the one obtained when varying some system's parameters. Therefore, this device allows us investigating the dynamics of a given circuit providing us with a versatile component for performing both control or anticontrol of chaos. In particular, we show how a double-scroll chaotic system is stabilized in period three, single-scroll, period-4, period-2, period-1, fixed point, following an inverse bifurcation route as a function of the pulses amplitude (chaos control). It is also shown how a periodic Chua's circuit is driven to chaotic behavior (chaos anticontrol)
Inverse optimal control for speed-varying path following of marine vessels with actuator dynamics
Qu, Yang; Xu, Haixiang; Yu, Wenzhao; Feng, Hui; Han, Xin
2017-06-01
A controller which is locally optimal near the origin and globally inverse optimal for the nonlinear system is proposed for path following of over actuated marine crafts with actuator dynamics. The motivation is the existence of undesired signals sent to the actuators, which can result in bad behavior in path following. To attenuate the oscillation of the control signal and obtain smooth thrust outputs, the actuator dynamics are added into the ship maneuvering model. Instead of modifying the Line-of-Sight (LOS) guidance law, this proposed controller can easily adjust the vessel speed to minimize the large cross-track error caused by the high vessel speed when it is turning. Numerical simulations demonstrate the validity of this proposed controller.
Uieda, Leonardo; Barbosa, Valéria C. F.
2016-10-01
Estimating the relief of the Moho from gravity data is a computationally intensive non-linear inverse problem. What is more, the modeling must take the Earths curvature into account when the study area is of regional scale or greater. We present a regularized non-linear gravity inversion method that has a low computational footprint and employs a spherical Earth approximation. To achieve this, we combine the highly efficient Bott's method with smoothness regularization and a discretization of the anomalous Moho into tesseroids (spherical prisms). The computational efficiency of our method is attained by harnessing the fact that all matrices involved are sparse. The inversion results are controlled by three hyper-parameters: the regularization parameter, the anomalous Moho density-contrast, and the reference Moho depth. We estimate the regularization parameter using the method of hold-out cross-validation. Additionally, we estimate the density-contrast and the reference depth using knowledge of the Moho depth at certain points. We apply the proposed method to estimate the Moho depth for the South American continent using satellite gravity data and seismological data. The final Moho model is in accordance with previous gravity-derived models and seismological data. The misfit to the gravity and seismological data is worse in the Andes and best in oceanic areas, central Brazil and Patagonia, and along the Atlantic coast. Similarly to previous results, the model suggests a thinner crust of 30-35 km under the Andean foreland basins. Discrepancies with the seismological data are greatest in the Guyana Shield, the central Solimões and Amazonas Basins, the Paraná Basins, and the Borborema province. These differences suggest the existence of crustal or mantle density anomalies that were unaccounted for during gravity data processing.
Uieda, Leonardo; Barbosa, Valéria C. F.
2017-01-01
Estimating the relief of the Moho from gravity data is a computationally intensive nonlinear inverse problem. What is more, the modelling must take the Earths curvature into account when the study area is of regional scale or greater. We present a regularized nonlinear gravity inversion method that has a low computational footprint and employs a spherical Earth approximation. To achieve this, we combine the highly efficient Bott's method with smoothness regularization and a discretization of the anomalous Moho into tesseroids (spherical prisms). The computational efficiency of our method is attained by harnessing the fact that all matrices involved are sparse. The inversion results are controlled by three hyperparameters: the regularization parameter, the anomalous Moho density-contrast, and the reference Moho depth. We estimate the regularization parameter using the method of hold-out cross-validation. Additionally, we estimate the density-contrast and the reference depth using knowledge of the Moho depth at certain points. We apply the proposed method to estimate the Moho depth for the South American continent using satellite gravity data and seismological data. The final Moho model is in accordance with previous gravity-derived models and seismological data. The misfit to the gravity and seismological data is worse in the Andes and best in oceanic areas, central Brazil and Patagonia, and along the Atlantic coast. Similarly to previous results, the model suggests a thinner crust of 30-35 km under the Andean foreland basins. Discrepancies with the seismological data are greatest in the Guyana Shield, the central Solimões and Amazonas Basins, the Paraná Basin, and the Borborema province. These differences suggest the existence of crustal or mantle density anomalies that were unaccounted for during gravity data processing.
Sparse-grid, reduced-basis Bayesian inversion: Nonaffine-parametric nonlinear equations
Chen, Peng; Schwab, Christoph
2016-07-01
We extend the reduced basis (RB) accelerated Bayesian inversion methods for affine-parametric, linear operator equations which are considered in [16,17] to non-affine, nonlinear parametric operator equations. We generalize the analysis of sparsity of parametric forward solution maps in [20] and of Bayesian inversion in [48,49] to the fully discrete setting, including Petrov-Galerkin high-fidelity (;HiFi;) discretization of the forward maps. We develop adaptive, stochastic collocation based reduction methods for the efficient computation of reduced bases on the parametric solution manifold. The nonaffinity and nonlinearity with respect to (w.r.t.) the distributed, uncertain parameters and the unknown solution is collocated; specifically, by the so-called Empirical Interpolation Method (EIM). For the corresponding Bayesian inversion problems, computational efficiency is enhanced in two ways: first, expectations w.r.t. the posterior are computed by adaptive quadratures with dimension-independent convergence rates proposed in [49]; the present work generalizes [49] to account for the impact of the PG discretization in the forward maps on the convergence rates of the Quantities of Interest (QoI for short). Second, we propose to perform the Bayesian estimation only w.r.t. a parsimonious, RB approximation of the posterior density. Based on the approximation results in [49], the infinite-dimensional parametric, deterministic forward map and operator admit N-term RB and EIM approximations which converge at rates which depend only on the sparsity of the parametric forward map. In several numerical experiments, the proposed algorithms exhibit dimension-independent convergence rates which equal, at least, the currently known rate estimates for N-term approximation. We propose to accelerate Bayesian estimation by first offline construction of reduced basis surrogates of the Bayesian posterior density. The parsimonious surrogates can then be employed for online data assimilation
Sparse-grid, reduced-basis Bayesian inversion: Nonaffine-parametric nonlinear equations
Energy Technology Data Exchange (ETDEWEB)
Chen, Peng, E-mail: peng@ices.utexas.edu [The Institute for Computational Engineering and Sciences, The University of Texas at Austin, 201 East 24th Street, Stop C0200, Austin, TX 78712-1229 (United States); Schwab, Christoph, E-mail: christoph.schwab@sam.math.ethz.ch [Seminar für Angewandte Mathematik, Eidgenössische Technische Hochschule, Römistrasse 101, CH-8092 Zürich (Switzerland)
2016-07-01
We extend the reduced basis (RB) accelerated Bayesian inversion methods for affine-parametric, linear operator equations which are considered in [16,17] to non-affine, nonlinear parametric operator equations. We generalize the analysis of sparsity of parametric forward solution maps in [20] and of Bayesian inversion in [48,49] to the fully discrete setting, including Petrov–Galerkin high-fidelity (“HiFi”) discretization of the forward maps. We develop adaptive, stochastic collocation based reduction methods for the efficient computation of reduced bases on the parametric solution manifold. The nonaffinity and nonlinearity with respect to (w.r.t.) the distributed, uncertain parameters and the unknown solution is collocated; specifically, by the so-called Empirical Interpolation Method (EIM). For the corresponding Bayesian inversion problems, computational efficiency is enhanced in two ways: first, expectations w.r.t. the posterior are computed by adaptive quadratures with dimension-independent convergence rates proposed in [49]; the present work generalizes [49] to account for the impact of the PG discretization in the forward maps on the convergence rates of the Quantities of Interest (QoI for short). Second, we propose to perform the Bayesian estimation only w.r.t. a parsimonious, RB approximation of the posterior density. Based on the approximation results in [49], the infinite-dimensional parametric, deterministic forward map and operator admit N-term RB and EIM approximations which converge at rates which depend only on the sparsity of the parametric forward map. In several numerical experiments, the proposed algorithms exhibit dimension-independent convergence rates which equal, at least, the currently known rate estimates for N-term approximation. We propose to accelerate Bayesian estimation by first offline construction of reduced basis surrogates of the Bayesian posterior density. The parsimonious surrogates can then be employed for online data
A general nonlinear inverse transport algorithm using forward and adjoint flux computations
Energy Technology Data Exchange (ETDEWEB)
Norton, S.J. [Oak Ridge National Lab., TN (United States)
1997-04-01
Iterative approaches to the nonlinear inverse transport problem are described, which give rise to the structure that best predicts a set of transport observations. Such methods are based on minimizing a global error functional measuring the discrepancy between predicted and observed transport data. Required for this minimization is the functional gradient (Frechet derivative) of the global error evaluated with respect to a set of unknown material parameters (specifying boundary locations, scattering cross sections, etc.) which are to be determined. It is shown how this functional gradient is obtained from numerical solutions to the forward and adjoint transport problems computed once per iteration. This approach is not only far more efficient, but also more accurate, than a finite-difference method for computing the gradient of the global error. The general technique can be applied to inverse-transport problems of all descriptions, provided only that solutions to the forward and adjoint problems can be found numerically. As an illustration, two inverse problems are treated: the reconstruction of an anisotropic scattering function in a one-dimensional homogeneous slab and the two-dimensional imaging of a spatially-varying scattering cross section.
Nonlinear Bubble Dynamics And The Effects On Propagation Through Near-Surface Bubble Layers
Leighton, Timothy G.
2004-11-01
Nonlinear bubble dynamics are often viewed as the unfortunate consequence of having to use high acoustic pressure amplitudes when the void fraction in the near-surface oceanic bubble layer is great enough to cause severe attenuation (e.g. >50 dB/m). This is seen as unfortunate since existing models for acoustic propagation in bubbly liquids are based on linear bubble dynamics. However, the development of nonlinear models does more than just allow quantification of the errors associated with the use of linear models. It also offers the possibility of propagation modeling and acoustic inversions which appropriately incorporate the bubble nonlinearity. Furthermore, it allows exploration and quantification of possible nonlinear effects which may be exploited. As a result, high acoustic pressure amplitudes may be desirable even in low void fractions, because they offer opportunities to gain information about the bubble cloud from the nonlinearities, and options to exploit the nonlinearities to enhance communication and sonar in bubbly waters. This paper presents a method for calculating the nonlinear acoustic cross-sections, scatter, attenuations and sound speeds from bubble clouds which may be inhomogeneous. The method allows prediction of the time dependency of these quantities, both because the cloud may vary and because the incident acoustic pulse may have finite and arbitrary time history. The method can be readily adapted for bubbles in other environments (e.g. clouds of interacting bubbles, sediments, structures, in vivo, reverberant conditions etc.). The possible exploitation of bubble acoustics by marine mammals, and for sonar enhancement, is explored.
Energy flow theory of nonlinear dynamical systems with applications
Xing, Jing Tang
2015-01-01
This monograph develops a generalised energy flow theory to investigate non-linear dynamical systems governed by ordinary differential equations in phase space and often met in various science and engineering fields. Important nonlinear phenomena such as, stabilities, periodical orbits, bifurcations and chaos are tack-led and the corresponding energy flow behaviors are revealed using the proposed energy flow approach. As examples, the common interested nonlinear dynamical systems, such as, Duffing’s oscillator, Van der Pol’s equation, Lorenz attractor, Rössler one and SD oscillator, etc, are discussed. This monograph lights a new energy flow research direction for nonlinear dynamics. A generalised Matlab code with User Manuel is provided for readers to conduct the energy flow analysis of their nonlinear dynamical systems. Throughout the monograph the author continuously returns to some examples in each chapter to illustrate the applications of the discussed theory and approaches. The book can be used as ...
Light dynamics in nonlinear trimers ans twisted multicore fibers
Castro-Castro, Claudia; Srinivasan, Gowri; Aceves, Alejandro B; Kevrekidis, Panayotis G
2016-01-01
Novel photonic structures such as multi-core fibers and graphene based arrays present unique opportunities to manipulate and control the propagation of light. Here we discuss nonlinear dynamics for structures with a few (2 to 6) elements for which linear and nonlinear properties can be tuned. Specifically we show how nonlinearity, coupling, and parity-time PT symmetric gain/loss relate to existence, stability and in general, dynamical properties of nonlinear optical modes. The main emphasis of our presentation will be on systems with few degrees of freedom, most notably couplers, trimers and generalizations thereof to systems with 6 nodes.
Applications of Nonlinear Dynamics Model and Design of Complex Systems
In, Visarath; Palacios, Antonio
2009-01-01
This edited book is aimed at interdisciplinary, device-oriented, applications of nonlinear science theory and methods in complex systems. In particular, applications directed to nonlinear phenomena with space and time characteristics. Examples include: complex networks of magnetic sensor systems, coupled nano-mechanical oscillators, nano-detectors, microscale devices, stochastic resonance in multi-dimensional chaotic systems, biosensors, and stochastic signal quantization. "applications of nonlinear dynamics: model and design of complex systems" brings together the work of scientists and engineers that are applying ideas and methods from nonlinear dynamics to design and fabricate complex systems.
Energy Technology Data Exchange (ETDEWEB)
Xie, G.; Li, J.; Majer, E.; Zuo, D.
1998-07-01
This paper describes a new 3D parallel GILD electromagnetic (EM) modeling and nonlinear inversion algorithm. The algorithm consists of: (a) a new magnetic integral equation instead of the electric integral equation to solve the electromagnetic forward modeling and inverse problem; (b) a collocation finite element method for solving the magnetic integral and a Galerkin finite element method for the magnetic differential equations; (c) a nonlinear regularizing optimization method to make the inversion stable and of high resolution; and (d) a new parallel 3D modeling and inversion using a global integral and local differential domain decomposition technique (GILD). The new 3D nonlinear electromagnetic inversion has been tested with synthetic data and field data. The authors obtained very good imaging for the synthetic data and reasonable subsurface EM imaging for the field data. The parallel algorithm has high parallel efficiency over 90% and can be a parallel solver for elliptic, parabolic, and hyperbolic modeling and inversion. The parallel GILD algorithm can be extended to develop a high resolution and large scale seismic and hydrology modeling and inversion in the massively parallel computer.
Real-time inverse kinematics and inverse dynamics for lower limb applications using OpenSim.
Pizzolato, C; Reggiani, M; Modenese, L; Lloyd, D G
2017-03-01
Real-time estimation of joint angles and moments can be used for rapid evaluation in clinical, sport, and rehabilitation contexts. However, real-time calculation of kinematics and kinetics is currently based on approximate solutions or generic anatomical models. We present a real-time system based on OpenSim solving inverse kinematics and dynamics without simplifications at 2000 frame per seconds with less than 31.5 ms of delay. We describe the software architecture, sensitivity analyses to minimise delays and errors, and compare offline and real-time results. This system has the potential to strongly impact current rehabilitation practices enabling the use of personalised musculoskeletal models in real-time.
Algebraic dynamics solution to and algebraic dynamics algorithm for nonlinear advection equation
Institute of Scientific and Technical Information of China (English)
2008-01-01
Algebraic dynamics approach and algebraic dynamics algorithm for the solution of nonlinear partial differential equations are applied to the nonlinear advection equa-tion. The results show that the approach is effective for the exact analytical solu-tion and the algorithm has higher precision than other existing algorithms in nu-merical computation for the nonlinear advection equation.
Chaotic behavior in nonlinear polarization dynamics
Energy Technology Data Exchange (ETDEWEB)
David, D.; Holm, D.D.; Tratnik, M.V. (Los Alamos National Lab., NM (USA))
1989-01-01
We analyze the problem of two counterpropagating optical laser beams in a slightly nonlinear medium from the point of view of Hamiltonian systems; the one-beam subproblem is also investigated as a special case. We are interested in these systems as integrable dynamical systems which undergo chaotic behavior under various types of perturbations. The phase space for the two-beam problem is C{sup 2} {times} C{sup 2} when we restricted the the regime of travelling-wave solutions. We use the method of reduction for Hamiltonian systems invariant under one-parameter symmetry groups to demonstrate that the phase space reduces to the two-sphere S{sup 2} and is therefore completely integrable. The phase portraits of the system are classified and we also determine the bifurcations that modify these portraits; some new degenerate bifurcations are presented in this context. Finally, we introduce various physically relevant perturbations and use the Melnikov method to prove that horseshoe chaos and Arnold diffusion occur as consequences of these perturbations. 10 refs., 7 figs., 1 tab.
Directory of Open Access Journals (Sweden)
G. Forget
2015-05-01
Full Text Available This paper presents the ECCO v4 non-linear inverse modeling framework and its baseline solution for the evolving ocean state over the period 1992–2011. Both components are publicly available and highly integrated with the MITgcm. They are both subjected to regular, automated regression tests. The modeling framework includes sets of global conformal grids, a global model setup, implementations of model-data constraints and adjustable control parameters, an interface to algorithmic differentiation, as well as a grid-independent, fully capable Matlab toolbox. The reference ECCO v4 solution is a dynamically consistent ocean state estimate (ECCO-Production, release 1 without un-identified sources of heat and buoyancy, which any interested user will be able to reproduce accurately. The solution is an acceptable fit to most data and has been found physically plausible in many respects, as documented here and in related publications. Users are being provided with capabilities to assess model-data misfits for themselves. The synergy between modeling and data synthesis is asserted through the joint presentation of the modeling framework and the state estimate. In particular, the inverse estimate of parameterized physics was instrumental in improving the fit to the observed hydrography, and becomes an integral part of the ocean model setup available for general use. More generally, a first assessment of the relative importance of external, parametric and structural model errors is presented. Parametric and external model uncertainties appear to be of comparable importance and dominate over structural model uncertainty. The results generally underline the importance of including turbulent transport parameters in the inverse problem.
Nonlinear dynamical model of an automotive dual mass flywheel
Directory of Open Access Journals (Sweden)
Lei Chen
2015-06-01
Full Text Available The hysteresis, stick–slip, and rotational speed-dependent characteristics in a basic dual mass flywheel are obtained from a static and a dynamic experiments. Based on the experimental results, a nonlinear model of the transferred torque in this dual mass flywheel is developed, with the overlying form of nonlinear elastic torque and frictional torque. The nonlinearities of stiffness are investigated, deriving a nonlinear model to describe the rotational speed-dependent stiffness. In addition, Bouc–Wen model is used to model the hysteretic frictional torque. Thus, the nonlinear 2-degree-of-freedom system of this dual mass flywheel is set up. Then, the Levenberg–Marquardt method is adopted for the parameter estimation of the frictional torque. Finally, taking the nonlinear stiffness in this model into account, the parameters of Bouc–Wen model are estimated based on the dynamic test data.
Transistor-based metamaterials with dynamically tunable nonlinear susceptibility
Barrett, John P.; Katko, Alexander R.; Cummer, Steven A.
2016-08-01
We present the design, analysis, and experimental demonstration of an electromagnetic metamaterial with a dynamically tunable effective nonlinear susceptibility. Split-ring resonators loaded with transistors are shown theoretically and experimentally to act as metamaterials with a second-order nonlinear susceptibility that can be adjusted through the use of a bias voltage. Measurements confirm that this allows for the design of a nonlinear metamaterial with adjustable mixing efficiency.
Chaotic Dynamics and Application of LCR Oscillators Sharing Common Nonlinearity
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.
The numerical dynamic for highly nonlinear partial differential equations
Lafon, A.; Yee, H. C.
1992-01-01
Problems associated with the numerical computation of highly nonlinear equations in computational fluid dynamics are set forth and analyzed in terms of the potential ranges of spurious behaviors. A reaction-convection equation with a nonlinear source term is employed to evaluate the effects related to spatial and temporal discretizations. The discretization of the source term is described according to several methods, and the various techniques are shown to have a significant effect on the stability of the spurious solutions. Traditional linearized stability analyses cannot provide the level of confidence required for accurate fluid dynamics computations, and the incorporation of nonlinear analysis is proposed. Nonlinear analysis based on nonlinear dynamical systems complements the conventional linear approach and is valuable in the analysis of hypersonic aerodynamics and combustion phenomena.
Nonlinear switching dynamics in a photonic-crystal nanocavity
DEFF Research Database (Denmark)
Yu, Yi; Palushani, Evarist; Heuck, Mikkel;
2014-01-01
the cavity is perturbed by strong pulses, we observe several nonlinear effects, i.e., saturation of the switching contrast, broadening of the switching window, and even initial reduction of the transmission. The effects are analyzed by comparison with nonlinear coupled mode theory and explained in terms......We report the experimental observation of nonlinear switching dynamics in an InP photonic crystal nanocavity. Usually, the regime of relatively small cavity perturbations is explored, where the signal transmitted through the cavity follows the temporal variation of the cavity resonance. When...... of large dynamical variations of the cavity resonance in combination with nonlinear losses. The results provide insight into the nonlinear optical processes that govern the dynamics of nanocavities and are important for applications in optical signal processing, where one wants to optimize the switching...
Nonlinear dynamics of zigzag molecular chains (in Russian)
DEFF Research Database (Denmark)
Savin, A. V.; Manevitsch, L. I.; Christiansen, Peter Leth;
1999-01-01
Nonlinear, collective, soliton type excitations in zigzag molecular chains are analyzed. It is shown that the nonlinear dynamics of a chain dramatically changes in passing from the one-dimensional linear chain to the more realistic planar zigzag model-due, in particular, to the geometry-dependent...
Non-linear wave packet dynamics of coherent states
Indian Academy of Sciences (India)
J Banerji
2001-02-01
We have compared the non-linear wave packet dynamics of coherent states of various symmetry groups and found that certain generic features of non-linear evolution are present in each case. Thus the initial coherent structures are quickly destroyed but are followed by Schrödinger cat formation and revival. We also report important differences in their evolution.
Weng, Su-Ming; Sheng, Zheng-Ming; Zhang, Jie
2009-11-01
Inverse bremsstrahlung (IB) absorption and evolution of the electron distribution function (EDF) in a wide laser intensity range (10;{12}-10;{17} W/cm;{2}) have been studied systematically by a two velocity-dimension Fokker-Planck code. It is found that Langdon's IB operator overestimates the absorption rate at high laser intensity, consequently with an overdistorted non-Maxwellian EDF. According to the small anisotropy of EDF in the oscillation frame, we introduce an IB operator which is similar to Langdon's but without the low laser intensity limit. This operator is appropriate for self-consistently tackling the nonlinear effects of high laser intensity as well as non-Maxwellian EDF. Particularly, our operator is capable of treating IB absorption properly in the indirect and direct-drive inertial confinement fusion schemes with the National Ignition Facility and Laser MegaJoule laser parameters at focused laser intensity beyond 10;{15} W/cm;{2} .
Nonlinear Inverse Problem for an Ion-Exchange Filter Model: Numerical Recovery of Parameters
Directory of Open Access Journals (Sweden)
Balgaisha Mukanova
2015-01-01
Full Text Available This paper considers the problem of identifying unknown parameters for a mathematical model of an ion-exchange filter via measurement at the outlet of the filter. The proposed mathematical model consists of a material balance equation, an equation describing the kinetics of ion-exchange for the nonequilibrium case, and an equation for the ion-exchange isotherm. The material balance equation includes a nonlinear term that depends on the kinetics of ion-exchange and several parameters. First, a numerical solution of the direct problem, the calculation of the impurities concentration at the outlet of the filter, is provided. Then, the inverse problem, finding the parameters of the ion-exchange process in nonequilibrium conditions, is formulated. A method for determining the approximate values of these parameters from the impurities concentration measured at the outlet of the filter is proposed.
Doyuran, Adnan; Joshi, Chandrashekhar; Lim, Jae; Rosenzweig, James E; Tochitsky, Sergei Ya; Travish, Gil; Williams, Oliver
2005-01-01
An Inverse Compton Scattering (ICS) experiment investigating the polarized harmonic production in the nonlinear regime has begun which will utilize the existing terawatt CO2 laser system and 15 MeV photoinjector in the Neptune Laboratory at UCLA. A major motivation for a source of high brightness polarized x-rays is the production of polarized positrons for use in future linear collider experiments. Analytical calculations have been performed to predict the angular and frequency spectrums for various polarizations and different scattering angles. Currently, the experiment is running and we report the set-up and initial results. The advantages and limitations of using a high laser vector potential, ao, in an ICS-based polarized positron source are expected to be revealed with further measurement of the harmonic spectrum and angular characteristics.
Energy Technology Data Exchange (ETDEWEB)
Belendez, A; Gimeno, E; Mendez, D I; Alvarez, M L [Departamento de Fisica, IngenierIa de Sistemas y TeorIa de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Fernandez, E [Departamento de Optica, FarmacologIa y AnatomIa, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)], E-mail: a.belendez@ua.es
2008-06-15
A modified generalized, rational harmonic balance method is used to construct approximate frequency-amplitude relations for a conservative nonlinear singular oscillator in which the restoring force is inversely proportional to the dependent variable. The procedure is used to solve the nonlinear differential equation approximately. The approximate frequency obtained using this procedure is more accurate than those obtained using other approximate methods and the discrepancy between the approximate frequency and the exact one is lower than 0.40%.
Jiang, Yi; Li, Guoyang; Qian, Lin-Xue; Liang, Si; Destrade, Michel; Cao, Yanping
2015-10-01
We use supersonic shear wave imaging (SSI) technique to measure not only the linear but also the nonlinear elastic properties of brain matter. Here, we tested six porcine brains ex vivo and measured the velocities of the plane shear waves induced by acoustic radiation force at different states of pre-deformation when the ultrasonic probe is pushed into the soft tissue. We relied on an inverse method based on the theory governing the propagation of small-amplitude acoustic waves in deformed solids to interpret the experimental data. We found that, depending on the subjects, the resulting initial shear modulus [Formula: see text] varies from 1.8 to 3.2 kPa, the stiffening parameter [Formula: see text] of the hyperelastic Demiray-Fung model from 0.13 to 0.73, and the third- [Formula: see text] and fourth-order [Formula: see text] constants of weakly nonlinear elasticity from [Formula: see text]1.3 to [Formula: see text]20.6 kPa and from 3.1 to 8.7 kPa, respectively. Paired [Formula: see text] test performed on the experimental results of the left and right lobes of the brain shows no significant difference. These values are in line with those reported in the literature on brain tissue, indicating that the SSI method, combined to the inverse analysis, is an efficient and powerful tool for the mechanical characterization of brain tissue, which is of great importance for computer simulation of traumatic brain injury and virtual neurosurgery.
Sliding mode identifier for parameter uncertain nonlinear dynamic systems with nonlinear input
Institute of Scientific and Technical Information of China (English)
张克勤; 庄开宇; 苏宏业; 褚健; 高红
2002-01-01
This paper presents a sliding mode(SM) based identifier to deal with the parameter idenfification problem for a class of parameter uncertain nonlinear dynamic systems with input nonlinearity. A sliding mode controller (SMC) is used to ensure the global reaching condition of the sliding mode for the nonlinear system;an identifier is designed to identify the uncertain parameter of the nonlinear system. A numerical example is studied to show the feasibility of the SM controller and the asymptotical convergence of the identifier.
Bifurcation methods of dynamical systems for handling nonlinear wave equations
Indian Academy of Sciences (India)
Dahe Feng; Jibin Li
2007-05-01
By using the bifurcation theory and methods of dynamical systems to construct the exact travelling wave solutions for nonlinear wave equations, some new soliton solutions, kink (anti-kink) solutions and periodic solutions with double period are obtained.
NONLINEAR STOCHASTIC DYNAMICS: A SURVEY OF RECENT DEVELOPMENTS
Institute of Scientific and Technical Information of China (English)
朱位秋; 蔡国强
2002-01-01
This paper provides an overview of significant advances in nonlinearstochastic dynamics during the past two decades, including random response, stochas-tic stability, stochastic bifurcation, first passage problem and nonlinear stochasticcontrol. Topics for future research are also suggested.
Unified Nonlinear Flight Dynamics and Aeroelastic Simulator Tool Project
National Aeronautics and Space Administration — ZONA Technology, Inc. (ZONA) proposes a R&D effort to develop a Unified Nonlinear Flight Dynamics and Aeroelastic Simulator (UNFDAS) Tool that will combine...
The fractional-nonlinear robotic manipulator: Modeling and dynamic simulations
David, S. A.; Balthazar, J. M.; Julio, B. H. S.; Oliveira, C.
2012-11-01
In this paper, we applied the Riemann-Liouville approach and the fractional Euler-Lagrange equations in order to obtain the fractional-order nonlinear dynamics equations of a two link robotic manipulator. The aformentioned equations have been simulated for several cases involving: integer and non-integer order analysis, with and without external forcing acting and some different initial conditions. The fractional nonlinear governing equations of motion are coupled and the time evolution of the angular positions and the phase diagrams have been plotted to visualize the effect of fractional order approach. The new contribution of this work arises from the fact that the dynamics equations of a two link robotic manipulator have been modeled with the fractional Euler-Lagrange dynamics approach. The results reveal that the fractional-nonlinear robotic manipulator can exhibit different and curious behavior from those obtained with the standard dynamical system and can be useful for a better understanding and control of such nonlinear systems.
Nonlinear Dynamics of the Perceived Pitch of Complex Sounds
Cartwright, J H E; Piro, O; Cartwright, Julyan H. E.; Gonzalez, Diego L.; Piro, Oreste
1999-01-01
We apply results from nonlinear dynamics to an old problem in acoustical physics: the mechanism of the perception of the pitch of sounds, especially the sounds known as complex tones that are important for music and speech intelligibility.
Robust adaptive dynamic programming and feedback stabilization of nonlinear systems.
Jiang, Yu; Jiang, Zhong-Ping
2014-05-01
This paper studies the robust optimal control design for a class of uncertain nonlinear systems from a perspective of robust adaptive dynamic programming (RADP). The objective is to fill up a gap in the past literature of adaptive dynamic programming (ADP) where dynamic uncertainties or unmodeled dynamics are not addressed. A key strategy is to integrate tools from modern nonlinear control theory, such as the robust redesign and the backstepping techniques as well as the nonlinear small-gain theorem, with the theory of ADP. The proposed RADP methodology can be viewed as an extension of ADP to uncertain nonlinear systems. Practical learning algorithms are developed in this paper, and have been applied to the controller design problems for a jet engine and a one-machine power system.
Nonlinear dynamics of DNA - Riccati generalized solitary wave solutions
Energy Technology Data Exchange (ETDEWEB)
Alka, W.; Goyal, Amit [Department of Physics, Panjab University, Chandigarh-160014 (India); Nagaraja Kumar, C., E-mail: cnkumar@pu.ac.i [Department of Physics, Panjab University, Chandigarh-160014 (India)
2011-01-17
We study the nonlinear dynamics of DNA, for longitudinal and transverse motions, in the framework of the microscopic model of Peyrard and Bishop. The coupled nonlinear partial differential equations for dynamics of DNA model, which consists of two long elastic homogeneous strands connected with each other by an elastic membrane, have been solved for solitary wave solution which is further generalized using Riccati parameterized factorization method.
Nonlinear dynamics of DNA - Riccati generalized solitary wave solutions
Alka, W.; Goyal, Amit; Nagaraja Kumar, C.
2011-01-01
We study the nonlinear dynamics of DNA, for longitudinal and transverse motions, in the framework of the microscopic model of Peyrard and Bishop. The coupled nonlinear partial differential equations for dynamics of DNA model, which consists of two long elastic homogeneous strands connected with each other by an elastic membrane, have been solved for solitary wave solution which is further generalized using Riccati parameterized factorization method.
Directory of Open Access Journals (Sweden)
Y. Sakai
2017-06-01
Full Text Available Inverse Compton scattering (ICS is a unique mechanism for producing fast pulses—picosecond and below—of bright photons, ranging from x to γ rays. These nominally narrow spectral bandwidth electromagnetic radiation pulses are efficiently produced in the interaction between intense, well-focused electron and laser beams. The spectral characteristics of such sources are affected by many experimental parameters, with intense laser effects often dominant. A laser field capable of inducing relativistic oscillatory motion may give rise to harmonic generation and, importantly for the present work, nonlinear redshifting, both of which dilute the spectral brightness of the radiation. As the applications enabled by this source often depend sensitively on its spectra, it is critical to resolve the details of the wavelength and angular distribution obtained from ICS collisions. With this motivation, we present an experimental study that greatly improves on previous spectral measurement methods based on x-ray K-edge filters, by implementing a multilayer bent-crystal x-ray spectrometer. In tandem with a collimating slit, this method reveals a projection of the double differential angular-wavelength spectrum of the ICS radiation in a single shot. The measurements enabled by this diagnostic illustrate the combined off-axis and nonlinear-field-induced redshifting in the ICS emission process. The spectra obtained illustrate in detail the strength of the normalized laser vector potential, and provide a nondestructive measure of the temporal and spatial electron-laser beam overlap.
Sakai, Y.; Gadjev, I.; Hoang, P.; Majernik, N.; Nause, A.; Fukasawa, A.; Williams, O.; Fedurin, M.; Malone, B.; Swinson, C.; Kusche, K.; Polyanskiy, M.; Babzien, M.; Montemagno, M.; Zhong, Z.; Siddons, P.; Pogorelsky, I.; Yakimenko, V.; Kumita, T.; Kamiya, Y.; Rosenzweig, J. B.
2017-06-01
Inverse Compton scattering (ICS) is a unique mechanism for producing fast pulses—picosecond and below—of bright photons, ranging from x to γ rays. These nominally narrow spectral bandwidth electromagnetic radiation pulses are efficiently produced in the interaction between intense, well-focused electron and laser beams. The spectral characteristics of such sources are affected by many experimental parameters, with intense laser effects often dominant. A laser field capable of inducing relativistic oscillatory motion may give rise to harmonic generation and, importantly for the present work, nonlinear redshifting, both of which dilute the spectral brightness of the radiation. As the applications enabled by this source often depend sensitively on its spectra, it is critical to resolve the details of the wavelength and angular distribution obtained from ICS collisions. With this motivation, we present an experimental study that greatly improves on previous spectral measurement methods based on x-ray K -edge filters, by implementing a multilayer bent-crystal x-ray spectrometer. In tandem with a collimating slit, this method reveals a projection of the double differential angular-wavelength spectrum of the ICS radiation in a single shot. The measurements enabled by this diagnostic illustrate the combined off-axis and nonlinear-field-induced redshifting in the ICS emission process. The spectra obtained illustrate in detail the strength of the normalized laser vector potential, and provide a nondestructive measure of the temporal and spatial electron-laser beam overlap.
Vibrational mechanics nonlinear dynamic effects, general approach, applications
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
Directory of Open Access Journals (Sweden)
M. Hong
2013-02-01
Full Text Available Based on time series data of 500 hPa potential field from NCEP/NCAR (National Center for Environmental Forecast of American/National Center for Atmospheric Research, a novel consideration of empirical orthogonal function (EOF time–space separation and dynamic system reconstruction for time series is introduced. This method consists of two parts: first, the dynamical model inversion and model parameter optimization are carried out on the EOF time coefficient series using the genetic algorithm (GA, and, second, a nonlinear dynamic model representing the subtropical high (SH activity and its abnormality is established. The SH activity and its abnormal mechanism is studied using the developed dynamical model. Results show that the configuration and diversification of the SH equilibriums have good correspondence with the actual short–medium term abnormal activity of the SH. Change of SH potential field brought by the combination of equilibriums is more complex than that by mutation, and their exhibition patterns are different. The mutation behavior from high-value to low-value equilibriums of the SH in summer corresponds with the southward drop of the SH in the observed weather process. The combination behavior of the two steady equilibriums corresponds with disappearance of the "double-ridge" phenomenon of the SH. Dynamical mechanisms of these phenomena are explained.
Nonlinear dynamics of resistive electrostatic drift waves
DEFF Research Database (Denmark)
Korsholm, Søren Bang; Michelsen, Poul; Pécseli, H.L.
1999-01-01
The evolution of weakly nonlinear electrostatic drift waves in an externally imposed strong homogeneous magnetic field is investigated numerically in three spatial dimensions. The analysis is based on a set of coupled, nonlinear equations, which are solved for an initial condition which is pertur......The evolution of weakly nonlinear electrostatic drift waves in an externally imposed strong homogeneous magnetic field is investigated numerically in three spatial dimensions. The analysis is based on a set of coupled, nonlinear equations, which are solved for an initial condition which...... is perturbed by a small amplitude incoherent wave-field. The initial evolution is exponential, following the growth of perturbations predicted by linear stability theory. The fluctuations saturate at relatively high amplitudes, by forming a pair of magnetic field aligned vortex-like structures of opposite...
Non-linear dynamics in pulse combustor: A review
Indian Academy of Sciences (India)
Sirshendu Mondal; Achintya Kukhopadhyay; Swarnendu Sen
2015-03-01
The state of the art of non-linear dynamics applied to pulse combustor theoretically and experimentally is reviewed. Pulse combustors are a class of air-breathing engines in which pulsations in combustion are utilized to improve the performance. As no analytical solution can be obtained for most of the nonlinear systems, the whole set of solutions can be investigated with the help of dynamical system theory. Many studies have been carried out on pulse combustors whose dynamics include limit cycle behaviour, Hopf bifurcation and period-doubling bifurcation. The dynamic signature has also been used for early prediction of extinction.
Employment of CB models for non-linear dynamic analysis
Klein, M. R. M.; Deloo, P.; Fournier-Sicre, A.
1990-01-01
The non-linear dynamic analysis of large structures is always very time, effort and CPU consuming. Whenever possible the reduction of the size of the mathematical model involved is of main importance to speed up the computational procedures. Such reduction can be performed for the part of the structure which perform linearly. Most of the time, the classical Guyan reduction process is used. For non-linear dynamic process where the non-linearity is present at interfaces between different structures, Craig-Bampton models can provide a very rich information, and allow easy selection of the relevant modes with respect to the phenomenon driving the non-linearity. The paper presents the employment of Craig-Bampton models combined with Newmark direct integration for solving non-linear friction problems appearing at the interface between the Hubble Space Telescope and its solar arrays during in-orbit maneuvers. Theory, implementation in the FEM code ASKA, and practical results are shown.
Research on Nonlinear Dynamics with Defense Applications
2006-04-01
numerical verifications, we have experimentally realized the scheme by using a Duffing -type of nonlinear electronic oscillator (originally developed by C...circuits In defense applications it may be desirable to induce chaos in nonlinear oscillators operating in a stable regime. Examples of such oscillators ...evolutions of the target Duffing circuit and deliver resonant perturbations to generate robust chaotic attractors. A brief account of the work has been
Nonlinear modeling of an aerospace object dynamics
Davydov, I. E.; Davydov, E. I.
2017-01-01
Here are presented the scientific results, obtained by motion modeling of complicated technical systems of aerospace equipment with consideration of nonlinearities. Computerized panel that allows to measure mutual influence of the system's motion and stabilization device with consideration of its real characteristics has been developed. Analysis of motion stability of a system in general has been carried out and time relationships of the system's motion taking in account nonlinearities are presented.
A Modal Model to Simulate Typical Structural Dynamic Nonlinearity
Energy Technology Data Exchange (ETDEWEB)
Pacini, Benjamin Robert [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Mayes, Randall L. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Roettgen, Daniel R [Univ. of Wisconsin, Madison, WI (United States)
2015-10-01
Some initial investigations have been published which simulate nonlinear response with almost traditional modal models: instead of connecting the modal mass to ground through the traditional spring and damper, a nonlinear Iwan element was added. This assumes that the mode shapes do not change with amplitude and there are no interactions between modal degrees of freedom. This work expands on these previous studies. An impact experiment is performed on a structure which exhibits typical structural dynamic nonlinear response, i.e. weak frequency dependence and strong damping dependence on the amplitude of vibration. Use of low level modal test results in combination with high level impacts are processed using various combinations of modal filtering, the Hilbert Transform and band-pass filtering to develop response data that are then fit with various nonlinear elements to create a nonlinear pseudo-modal model. Simulations of forced response are compared with high level experimental data for various nonlinear element assumptions.
Double symbolic joint entropy in nonlinear dynamic complexity analysis
Yao, Wenpo; Wang, Jun
2017-07-01
Symbolizations, the base of symbolic dynamic analysis, are classified as global static and local dynamic approaches which are combined by joint entropy in our works for nonlinear dynamic complexity analysis. Two global static methods, symbolic transformations of Wessel N. symbolic entropy and base-scale entropy, and two local ones, namely symbolizations of permutation and differential entropy, constitute four double symbolic joint entropies that have accurate complexity detections in chaotic models, logistic and Henon map series. In nonlinear dynamical analysis of different kinds of heart rate variability, heartbeats of healthy young have higher complexity than those of the healthy elderly, and congestive heart failure (CHF) patients are lowest in heartbeats' joint entropy values. Each individual symbolic entropy is improved by double symbolic joint entropy among which the combination of base-scale and differential symbolizations have best complexity analysis. Test results prove that double symbolic joint entropy is feasible in nonlinear dynamic complexity analysis.
Rigatos, Gerasimos G; Rigatou, Efthymia G; Djida, Jean Daniel
2015-10-01
A method for early diagnosis of parametric changes in intracellular protein synthesis models (e.g. the p53 protein - mdm2 inhibitor model) is developed with the use of a nonlinear Kalman Filtering approach (Derivative-free nonlinear Kalman Filter) and of statistical change detection methods. The intracellular protein synthesis dynamic model is described by a set of coupled nonlinear differential equations. It is shown that such a dynamical system satisfies differential flatness properties and this allows to transform it, through a change of variables (diffeomorphism), to the so-called linear canonical form. For the linearized equivalent of the dynamical system, state estimation can be performed using the Kalman Filter recursion. Moreover, by applying an inverse transformation based on the previous diffeomorphism it becomes also possible to obtain estimates of the state variables of the initial nonlinear model. By comparing the output of the Kalman Filter (which is assumed to correspond to the undistorted dynamical model) with measurements obtained from the monitored protein synthesis system, a sequence of differences (residuals) is obtained. The statistical processing of the residuals with the use of x2 change detection tests, can provide indication within specific confidence intervals about parametric changes in the considered biological system and consequently indications about the appearance of specific diseases (e.g. malignancies).
Nonlinear dynamic analysis of traveling wave-type ultrasonic motors.
Nakagawa, Yosuke; Saito, Akira; Maeno, Takashi
2008-03-01
In this paper, nonlinear dynamic response of a traveling wave-type ultrasonic motor was investigated. In particular, understanding the transient dynamics of a bar-type ultrasonic motor, such as starting up and stopping, is of primary interest. First, the transient response of the bar-type ultrasonic motor at starting up and stopping was measured using a laser Doppler velocimeter, and its driving characteristics are discussed in detail. The motor is shown to possess amplitude-dependent nonlinearity that greatly influences the transient dynamics of the motor. Second, a dynamical model of the motor was constructed as a second-order nonlinear oscillator, which represents the dynamics of the piezoelectric ceramic, stator, and rotor. The model features nonlinearities caused by the frictional interface between the stator and the rotor, and cubic nonlinearity in the dynamics of the stator. Coulomb's friction model was employed for the interface model, and a stick-slip phenomenon is considered. Lastly, it was shown that the model is capable of representing the transient dynamics of the motor accurately. The critical parameters in the model were identified from measured results, and numerical simulations were conducted using the model with the identified parameters. Good agreement between the results of measurements and numerical simulations is observed.
Adaptive Fuzzy Dynamic Surface Control for Uncertain Nonlinear Systems
Institute of Scientific and Technical Information of China (English)
Xiao-Yuan Luo; Zhi-Hao Zhu; Xin-Ping Guan
2009-01-01
In this paper, a robust adaptive fuzzy dynamic surface control for a class of uncertain nonlinear systems is proposed. A novel adaptive fuzzy dynamic surface model is built to approximate the uncertain nonlinear functions by only one fuzzy logic system. The approximation capability of this model is proved and the model is implemented to solve the problem that too many approximators are used in the controller design of uncertain nonlinear systems. The shortage of "explosion of complexity" in backstepping design procedure is overcome by using the proposed dynamic surface control method. It is proved by constructing appropriate Lyapunov candidates that all signals of closed-loop systems are semi-globaily uniformly ultimate bounded. Also, this novel controller stabilizes the states of uncertain nonlinear systems faster than the adaptive sliding mode controller (SMC). Two simulation examples are provided to illustrate the effectiveness of the control approach proposed in this paper.
International Conference on Structural Nonlinear Dynamics and Diagnosis
CSNDD 2012; CSNDD 2014
2015-01-01
This book, which presents the peer-reviewed post-proceedings of CSNDD 2012 and CSNDD 2014, addresses the important role that relevant concepts and tools from nonlinear and complex dynamics could play in present and future engineering applications. It includes 22 chapters contributed by outstanding researchers and covering various aspects of applications, including: structural health monitoring, diagnosis and damage detection, experimental methodologies, active vibration control and smart structures, passive control of structures using nonlinear energy sinks, vibro-impact dynamic MEMS/NEMS/AFM, energy-harvesting materials and structures, and time-delayed feedback control, as well as aspects of deterministic versus stochastic dynamics and control of nonlinear phenomena in physics. Researchers and engineers interested in the challenges posed and opportunities offered by nonlinearities in the development of passive and active control strategies, energy harvesting, novel design criteria, modeling and characteriz...
Nonlinear Dynamics and Strong Cavity Cooling of Levitated Nanoparticles
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 Dynamic Characteristics of Combustion Wave in SHS Process
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
The characteristic of combustion wave and its change were analyzed by numerical value calculation and computer simulation,based on the combustion dynamical model of SHS process. It is shown that with the change of condition parameters in SHS process various time-space order combustion waves appear.It is concluded from non-liner dynamical mechanism analysis that the strong coupling of two non-linear dynamical processes is the dynamical mechanism causing the time-space order dissipation structures.
Adaptive fuzzy control with smooth inverse for nonlinear systems preceded by non-symmetric dead-zone
Wang, Xingjian; Wang, Shaoping
2016-07-01
In this study, the adaptive output feedback control problem of a class of nonlinear systems preceded by non-symmetric dead-zone is considered. To cope with the possible control signal chattering phenomenon which is caused by non-smooth dead-zone inverse, a new smooth inverse is proposed for non-symmetric dead-zone compensation. For the systematic design procedure of the adaptive fuzzy control algorithm, we combine the backstepping technique and small-gain approach. The Takagi-Sugeno fuzzy logic systems are used to approximate unknown system nonlinearities. The closed-loop stability is studied by using small gain theorem and the closed-loop system is proved to be semi-globally uniformly ultimately bounded. Simulation results indicate that, compared to the algorithm with the non-smooth inverse, the proposed control strategy can achieve better tracking performance and the chattering phenomenon can be avoided effectively.
Dynamic Analysis of Vibrating Systems with Nonlinearities
M. Kalami, Yazdi; Ahmadian, H.; Mirzabeigy, A.; Yildirim, A.
2012-02-01
The max-min approach is applied to mathematical models of some nonlinear oscillations. The models are regarding to three different forms that are governed by nonlinear ordinary differential equations. In this context, the strongly nonlinear Duffing oscillator with third, fifth, and seventh powers of the amplitude, the pendulum attached to a rotating rigid frame and the cubic Duffing oscillator with discontinuity are taken into consideration. The obtained results via the approach are compared with ones achieved utilizing other techniques. The results indicate that the approach has a good agreement with other well-known methods. He's max-min approach is a promising technique and can be successfully exerted to a lot of practical engineering and physical problems.
Nonlinear and stochastic dynamics of coherent structures
DEFF Research Database (Denmark)
Rasmussen, Kim
1997-01-01
system described by a tight-binding Hamiltonian and a harmonic lattice coupled b y a deformation-type potential. This derivation results in a two-dimensional nonline ar Schrödinger model, and considering the harmonic lattice to be in thermal contact with a heat bath w e show that the nonlinear...... phenomenon. We find numerically and analytically that the collapse can be delayed and ultimatively arrested by the fluctuations. Allowing the system to reach thermal equilibrium we further augment the model by a nonlineardamping term and find that this prohibits collapse in the strict mathematical se nse....... However a collapse like behavior still persists in the presence of the nonlinear damping . Apart from the absence of the collapse in the strict mathematical sense we find that the nonlinear damping term has rather weak influence on the interplay between fluctuations and self-focusing. The study...
Incremental approximate dynamic programming for nonlinear flight control design
Zhou, Y.; Van Kampen, E.J.; Chu, Q.P.
2015-01-01
A self-learning adaptive flight control design for non-linear systems allows reliable and effective operation of flight vehicles in a dynamic environment. Approximate dynamic programming (ADP) provides a model-free and computationally effective process for designing adaptive linear optimal
Nonlinear dynamics of a microelectromechanical oscillator with delayed feedback
Van Leeuwen, R.; Karabacak, D.M.; Van der Zant, H.S.J.; Venstra, W.J.
2013-01-01
We study the dynamics of a nonlinear electromechanical oscillator with delayed feedback. Compared to their linear counterparts, we find that the dynamics is dramatically different. The well-known Barkhausen stability criterion ceases to exist, and two modes of operation emerge: one characterized by
Nonlinear Dynamics in the Ultradian Rhythm of Desmodium motorium
Chen, Jyh-Phen; Engelmann, Wolfgang; Baier, Gerold
1995-12-01
The dynamics of the lateral leaflet movement of Desmodium motorium is studied. Simple periodic, quasiperiodic and aperiodic time series are observed. The long-scale dynamics may either be uniform or composed of several prototypic oscillations (one of them reminiscent of homoclinic chaos). Diffusively coupled nonlinear oscillators may account for the variety of ultradian rhythms.
Reconstructing the Nonlinear Dynamical Systems by Evolutionary Computation Techniques
Institute of Scientific and Technical Information of China (English)
LIU Minzhong; KANG Lishan
2006-01-01
We introduce a new dynamical evolutionary algorithm(DEA) based on the theory of statistical mechanics and investigate the reconstruction problem for the nonlinear dynamical systems using observation data. The convergence of the algorithm is discussed. We make the numerical experiments and test our model using the two famous chaotic systems (mainly the Lorenz and Chen systems ). The results show the relatively accurate reconstruction of these chaotic systems based on observational data can be obtained. Therefore we may conclude that there are broad prospects using our method to model the nonlinear dynamical systems.
NONLINEAR DYNAMICS OF CARBON NANOTUBES UNDER LARGE ELECTROSTATIC FORCE
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.
Jiang, Yi; Li, Guo-Yang; Qian, Lin-Xue; Hu, Xiang-Dong; Liu, Dong; Liang, Si; Cao, Yanping
2015-02-01
Dynamic elastography has become a new clinical tool in recent years to characterize the elastic properties of soft tissues in vivo, which are important for the disease diagnosis, e.g., the detection of breast and thyroid cancer and liver fibrosis. This paper investigates the supersonic shear imaging (SSI) method commercialized in recent years with the purpose to determine the nonlinear elastic properties based on this promising technique. Particularly, we explore the propagation of the shear wave induced by the acoustic radiation force in a stressed hyperelastic soft tissue described via the Demiray-Fung model. Based on the elastodynamics theory, an analytical solution correlating the wave speed with the hyperelastic parameters of soft tissues is first derived. Then an inverse approach is established to determine the hyperelastic parameters of biological soft tissues based on the measured wave speeds at different stretch ratios. The property of the inverse method, e.g., the existence, uniqueness and stability of the solution, has been investigated. Numerical experiments based on finite element simulations and the experiments conducted on the phantom and pig livers have been employed to validate the new method. Experiments performed on the human breast tissue and human heel fat pads have demonstrated the capability of the proposed method for measuring the in vivo nonlinear elastic properties of soft tissues. Generalization of the inverse analysis to other material models and the implication of the results reported here for clinical diagnosis have been discussed. Copyright © 2014 Elsevier B.V. All rights reserved.
Nonlinear dynamics based digital logic and circuits.
Kia, Behnam; Lindner, John F; Ditto, William L
2015-01-01
We discuss the role and importance of dynamics in the brain and biological neural networks and argue that dynamics is one of the main missing elements in conventional Boolean logic and circuits. We summarize a simple dynamics based computing method, and categorize different techniques that we have introduced to realize logic, functionality, and programmability. We discuss the role and importance of coupled dynamics in networks of biological excitable cells, and then review our simple coupled dynamics based method for computing. In this paper, for the first time, we show how dynamics can be used and programmed to implement computation in any given base, including but not limited to base two.
Nonlinear ship waves and computational fluid dynamics
National Research Council Canada - National Science Library
MIYATA, Hideaki; ORIHARA, Hideo; SATO, Yohei
2014-01-01
.... Finding of the occurrence of nonlinear waves (named Free-Surface Shock Waves) in the vicinity of a ship advancing at constant speed provided the start-line for the progress of innovative technologies in the ship hull-form design...
Nonlinear Kinetic Dynamics of Magnetized Weibel Instability
Palodhi, L; Pegoraro, F
2010-01-01
Kinetic numerical simulations of the evolution of the Weibel instability during the full nonlinear regime are presented. The formation of strong distortions in the electron distribution function resulting in formation of strong peaks in it and their influence on the resulting electrostatic waves are shown.
High Dynamic Performance Nonlinear Source Emulator
DEFF Research Database (Denmark)
Nguyen-Duy, Khiem; Knott, Arnold; Andersen, Michael A. E.
2016-01-01
As research and development of renewable and clean energy based systems is advancing rapidly, the nonlinear source emulator (NSE) is becoming very essential for testing of maximum power point trackers or downstream converters. Renewable and clean energy sources play important roles in both terres...
Llibre, Jaume; Ramírez, Rafael; Ramírez, Valentín
2017-09-01
We consider polynomial vector fields X with a linear type and with homogenous nonlinearities. It is well-known that X has a center at the origin if and only if X has an analytic first integral of the form H =1/2 (x2 +y2) + ∑ j = 3 ∞Hj, where Hj =Hj (x , y) is a homogenous polynomial of degree j. The classical center-focus problem already studied by H. Poincaré consists in distinguishing when the origin of X is either a center or a focus. In this paper we study the inverse center-focus problem. In particular for a given analytic function H defined in a neighborhood of the origin we want to determine the homogenous polynomials in such a way that H is a first integral of X and consequently the origin of X will be a center. We study the particular case of centers which have a local analytic first integral of the form H =1/2 (x2 +y2) (1 + ∑ j = 1 ∞ϒj) , in a neighborhood of the origin, where ϒj is a convenient homogenous polynomial of degree j, for j ≥ 1. These centers are called weak centers, they contain the class of center studied by Alwash and Lloyd, the uniform isochronous centers and the isochronous holomorphic centers, but they do not coincide with the class of isochronous centers. We give a classification of the weak centers for quadratic and cubic vector fields with homogenous nonlinearities.
Photonic Nonlinear Transient Computing with Multiple-Delay Wavelength Dynamics
Martinenghi, Romain; Rybalko, Sergei; Jacquot, Maxime; Chembo, Yanne K.; Larger, Laurent
2012-06-01
We report on the experimental demonstration of a hybrid optoelectronic neuromorphic computer based on a complex nonlinear wavelength dynamics including multiple delayed feedbacks with randomly defined weights. This neuromorphic approach is based on a new paradigm of a brain-inspired computational unit, intrinsically differing from Turing machines. This recent paradigm consists in expanding the input information to be processed into a higher dimensional phase space, through the nonlinear transient response of a complex dynamics excited by the input information. The computed output is then extracted via a linear separation of the transient trajectory in the complex phase space. The hyperplane separation is derived from a learning phase consisting of the resolution of a regression problem. The processing capability originates from the nonlinear transient, resulting in nonlinear transient computing. The computational performance is successfully evaluated on a standard benchmark test, namely, a spoken digit recognition task.
Residual Minimizing Model Reduction for Parameterized Nonlinear Dynamical Systems
Constantine, Paul G
2010-01-01
We present a method for approximating the solution of a parameterized, nonlinear dynamical (or static) system using an affine combination of solutions computed at other points in the input parameter space. The coefficients of the affine combination are computed with a nonlinear least squares procedure that minimizes the residual of the dynamical system. The approximation properties of this residual minimizing scheme are comparable to existing reduced basis and POD-Galerkin model reduction methods, but its implementation requires only independent evaluations of the nonlinear forcing function. We prove some interesting characteristics of the scheme including uniqueness and an interpolatory property, and we present heuristics for mitigating the effects of the ill-conditioning and reducing the overall cost of the method. We apply the method to representative numerical examples from kinetics - a three state system with one parameter controlling the stiffness - and groundwater modeling - a nonlinear parabolic PDE w...
NONLINEAR THEORY OF DYNAMIC STABILITY FOR LAMINATED COMPOSITE CYLINDRICAL SHELLS
Institute of Scientific and Technical Information of China (English)
周承倜; 王列东
2001-01-01
Hamilton Principle was uaed to derive the general governing equations of nonlinear dynamic stability for laminated cylindrical shells in which, factors of nonlinear large deflection, transverse shear and longitudinal inertia force were concluded. Equations were solved by variational method. Analysis reveals that under the action of dynamic load,laminated cylindrical shells will fall into a state of parametric resonance and enter into the dynamic unstable region that causes dynamic instability of shells. Laminated shells of three typical composites were computed: i.e. T300/5 208 graphite epoxy E-glass epoxy, and ARALL shells. Results show that all factors will induce important influence for dynamic stability of laminated shells. So, in research of dynamic stability for laminated shells, to consider these factors is important.
Energy Technology Data Exchange (ETDEWEB)
Nguyen, Ba Phi [Central University of Construction, Tuy Hoa (Viet Nam); Kim, Ki Hong [Ajou University, Suwon (Korea, Republic of)
2014-02-15
We study numerically the dynamics of an initially localized wave packet in one-dimensional nonlinear Schroedinger lattices with both local and nonlocal nonlinearities. Using the discrete nonlinear Schroedinger equation generalized by including a nonlocal nonlinear term, we calculate four different physical quantities as a function of time, which are the return probability to the initial excitation site, the participation number, the root-mean-square displacement from the excitation site and the spatial probability distribution. We investigate the influence of the nonlocal nonlinearity on the delocalization to self-trapping transition induced by the local nonlinearity. In the non-self-trapping region, we find that the nonlocal nonlinearity compresses the soliton width and slows down the spreading of the wave packet. In the vicinity of the delocalization to self-trapping transition point and inside the self-trapping region, we find that a new kind of self-trapping phenomenon, which we call partial self-trapping, takes place when the nonlocal nonlinearity is sufficiently strong.
Non-linear Flight Dynamics at High Angles of Attack
DEFF Research Database (Denmark)
Granasy, P.; Sørensen, C.B.; Mosekilde, Erik
1998-01-01
The methods of nonlinear dynamics are applied to the longitudinal motion of a vectored thrust aircraft, in particular the behavior at high angles of attack. Our model contains analytic nonlinear aerodynamical coefficients based on NASA windtunnel experiments on the F-18 high-alpha research vehicle...... (HARV). When the aircraft is forced with small thrust deflections whilst in poststall equilibrium, chaotic motion is observed at certain frequencies. At other frequencies, several limiting states coexist....
Nonlinear Dynamic Analysis of the Whole Vehicle on Bumpy Road
Institute of Scientific and Technical Information of China (English)
王威; 李瑰贤; 宋玉玲
2010-01-01
Through the research into the characteristics of 7-DoF high dimensional nonlinear dynamics of a vehicle on bumpy road, the periodic movement and chaotic behavior of the vehicle were found.The methods of nonlinear frequency response analysis, global bifurcation, frequency chart and Poincaré maps were used simultaneously to derive strange super chaotic attractor.According to Lyapunov exponents calculated by Gram-Schmidt method, the unstable region was compartmentalized and the super chaotic characteristic of ...
Estimating nonlinear dynamic equilibrium economies: a likelihood approach
2004-01-01
This paper presents a framework to undertake likelihood-based inference in nonlinear dynamic equilibrium economies. The authors develop a sequential Monte Carlo algorithm that delivers an estimate of the likelihood function of the model using simulation methods. This likelihood can be used for parameter estimation and for model comparison. The algorithm can deal both with nonlinearities of the economy and with the presence of non-normal shocks. The authors show consistency of the estimate and...
Nonlinear laser dynamics from quantum dots to cryptography
Lüdge, Kathy
2012-01-01
A distinctive discussion of the nonlinear dynamical phenomena of semiconductor lasers. The book combines recent results of quantum dot laser modeling with mathematical details and an analytic understanding of nonlinear phenomena in semiconductor lasers and points out possible applications of lasers in cryptography and chaos control. This interdisciplinary approach makes it a unique and powerful source of knowledge for anyone intending to contribute to this field of research.By presenting both experimental and theoretical results, the distinguished authors consider solitary lase
Inverse Force Determination on a Small Scale Launch Vehicle Model Using a Dynamic Balance
Ngo, Christina L.; Powell, Jessica M.; Ross, James C.
2017-01-01
A launch vehicle can experience large unsteady aerodynamic forces in the transonic regime that, while usually only lasting for tens of seconds during launch, could be devastating if structural components and electronic hardware are not designed to account for them. These aerodynamic loads are difficult to experimentally measure and even harder to computationally estimate. The current method for estimating buffet loads is through the use of a few hundred unsteady pressure transducers and wind tunnel test. Even with a large number of point measurements, the computed integrated load is not an accurate enough representation of the total load caused by buffeting. This paper discusses an attempt at using a dynamic balance to experimentally determine buffet loads on a generic scale hammer head launch vehicle model tested at NASA Ames Research Center's 11' x 11' transonic wind tunnel. To use a dynamic balance, the structural characteristics of the model needed to be identified so that the natural modal response could be and removed from the aerodynamic forces. A finite element model was created on a simplified version of the model to evaluate the natural modes of the balance flexures, assist in model design, and to compare to experimental data. Several modal tests were conducted on the model in two different configurations to check for non-linearity, and to estimate the dynamic characteristics of the model. The experimental results were used in an inverse force determination technique with a psuedo inverse frequency response function. Due to the non linearity, the model not being axisymmetric, and inconsistent data between the two shake tests from different mounting configuration, it was difficult to create a frequency response matrix that satisfied all input and output conditions for wind tunnel configuration to accurately predict unsteady aerodynamic loads.
Nonlinear Galerkin Optimal Truncated Low—dimensional Dynamical Systems
Institute of Scientific and Technical Information of China (English)
ChuijieWU
1996-01-01
In this paper,a new theory of constructing nonlinear Galerkin optimal truncated Low-Dimensional Dynamical Systems(LDDSs) directly from partial differential equations has been developed.Applying the new theory to the nonlinear Burgers' equation,it is shown that a nearly perfect LDDS can be gotten,and the initial-boundary conditions are automatically included in the optimal bases.The nonlinear Galerkin method does not have advantages within the optimization process,but it can significantly improve the results,after the Galerkin optimal bases have been gotten.
NONLINEAR DYNAMICAL CHARACTERISTICS OF PILES UNDER HORIZONTAL VIBRATION
Institute of Scientific and Technical Information of China (English)
HU Yu-jia; CHENG Chang-jun; YANG Xiao
2005-01-01
The pile-soil system is regarded as a visco-elastic half-space embedded pile. Based on the method of continuum mechanics, a nonlinear mathematical model of pilesoil interaction was established-a coupling nonlinear boundary value problem. Under the case of horizontal vibration, the nonlinearly dynamical characteristics of pile applying the axis force were studied in horizontal direction in frequency domain. The effects of parameters, especially the axis force on the stiffness were studied in detail. The numerical results suggest that it is possible that the pile applying an axis force will lose its stability. So, the effect of the axis force on the pile is considered.
Chaos and Nonlinear Dynamics in a Quantum Artificial Economy
Gonçalves, Carlos Pedro
2012-01-01
Chaos and nonlinear economic dynamics are addressed for a quantum coupled map lattice model of an artificial economy, with quantized supply and demand equilibrium conditions. The measure theoretic properties and the patterns that emerge in both the economic business volume dynamics' diagrams as well as in the quantum mean field averages are addressed and conclusions are drawn in regards to the application of quantum chaos theory to address signatures of chaotic dynamics in relevant discrete economic state variables.
CHAOS-REGULARIZATION HYBRID ALGORITHM FOR NONLINEAR TWO-DIMENSIONAL INVERSE HEAT CONDUCTION PROBLEM
Institute of Scientific and Technical Information of China (English)
王登刚; 刘迎曦; 李守巨
2002-01-01
A numerical model of nonlinear two-dimensional steady inverse heat conduction problem was established considering the thermal conductivity changing with temperature.Combining the chaos optimization algorithm with the gradient regularization method, a chaos-regularization hybrid algorithm was proposed to solve the established numerical model.The hybrid algorithm can give attention to both the advantages of chaotic optimization algorithm and those of gradient regularization method. The chaos optimization algorithm was used to help the gradient regalarization method to escape from local optima in the hybrid algorithm. Under the assumption of temperature-dependent thermal conductivity changing with temperature in linear rule, the thermal conductivity and the linear rule were estimated by using the present method with the aid of boundary temperature measurements. Numerical simulation results show that good estimation on the thermal conductivity and the linear function can be obtained with arbitrary initial guess values, and that the present hybrid algorithm is much more efficient than conventional genetic algorithm and chaos optimization algorithm.
Electron dynamics with radiation and nonlinear wigglers
Energy Technology Data Exchange (ETDEWEB)
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.
Robust adaptive control of nonlinearly parameterized systems with unmodeled dynamics
Institute of Scientific and Technical Information of China (English)
LIU Yu-sheng; CHEN Jiang; LI Xing-yuan
2006-01-01
Many physical systems such as biochemical processes and machines with friction are of nonlinearly parameterized systems with uncertainties.How to control such systems effectively is one of the most challenging problems.This paper presents a robust adaptive controller for a significant class of nonlinearly parameterized systems.The controller can be used in cases where there exist parameter and nonlinear uncertainties,unmodeled dynamics and unknown bounded disturbances.The design of the controller is based on the control Lyapunov function method.A dynamic signal is introduced and adaptive nonlinear damping terms are used to restrain the effects of unmodeled dynamics,nonlinear uncertainties and unknown bounded disturbances.The backstepping procedure is employed to overcome the complexity in the design.With the proposed method,the estimation of the unknown parameters of the system is not required and there is only one adaptive parameter no matter how high the order of the system is and how many unknown parameters.there are.It is proved theoretically that the proposed robust adaptive control scheme guarantees the stability of nonlinearly parameterized system.Furthermore,all the states approach the equilibrium in arbitrary precision by choosing some design constants appropriately.Simulation results illustrate the effectiveness of the proposed robust adaptive controller.
Unmodeled Dynamics in Robust Nonlinear Control
2000-08-01
IEEE Transactions on Automatic Control , vol. 44, pp. 1975–1981, 1999. [6] D. Bestle...systems,” IEEE Transactions on Automatic Control , vol. 41, pp. 876–880, 1996. 95 [9] C.I. Byrnes and A. Isidori, “New results and examples in...Output-feedback stochastic nonlinear stabilization,” IEEE Transactions on Automatic Control , vol. 44, pp. 328–333, 1999. [14] J. Eker and K.J.
Power Spectral Density Conversions and Nonlinear Dynamics
Directory of Open Access Journals (Sweden)
Mostafa Rassaian
1994-01-01
Full Text Available To predict the vibration environment of a payload carried by a ground or air transporter, mathematical models are required from which a transfer function to a prescribed input can be calculated. For sensitive payloads these models typically include linear shock isolation system stiffness and damping elements relying on the assumption that the isolation system has a predetermined characteristic frequency and damping ratio independent of excitation magnitude. In order to achieve a practical spectral analysis method, the nonlinear system has to be linearized when the input transportation and handling vibration environment is in the form of an acceleration power spectral density. Test data from commercial isolators show that when nonlinear stiffness and damping effects exist the level of vibration input causes a variation in isolator resonant frequency. This phenomenon, described by the stationary response of the Duffing oscillator to narrow-band Gaussian random excitation, requires an alternative approach for calculation of power spectral density acceleration response at a shock isolated payload under random vibration. This article details the development of a plausible alternative approach for analyzing the spectral response of a nonlinear system subject to random Gaussian excitations.
Theoretical and software considerations for nonlinear dynamic analysis
Schmidt, R. J.; Dodds, R. H., Jr.
1983-01-01
In the finite element method for structural analysis, it is generally necessary to discretize the structural model into a very large number of elements to accurately evaluate displacements, strains, and stresses. As the complexity of the model increases, the number of degrees of freedom can easily exceed the capacity of present-day software system. Improvements of structural analysis software including more efficient use of existing hardware and improved structural modeling techniques are discussed. One modeling technique that is used successfully in static linear and nonlinear analysis is multilevel substructuring. This research extends the use of multilevel substructure modeling to include dynamic analysis and defines the requirements for a general purpose software system capable of efficient nonlinear dynamic analysis. The multilevel substructuring technique is presented, the analytical formulations and computational procedures for dynamic analysis and nonlinear mechanics are reviewed, and an approach to the design and implementation of a general purpose structural software system is presented.
Nonlinear dynamics and quantum entanglement in optomechanical systems.
Wang, Guanglei; Huang, Liang; Lai, Ying-Cheng; Grebogi, Celso
2014-03-21
To search for and exploit quantum manifestations of classical nonlinear dynamics is one of the most fundamental problems in physics. Using optomechanical systems as a paradigm, we address this problem from the perspective of quantum entanglement. We uncover strong fingerprints in the quantum entanglement of two common types of classical nonlinear dynamical behaviors: periodic oscillations and quasiperiodic motion. There is a transition from the former to the latter as an experimentally adjustable parameter is changed through a critical value. Accompanying this process, except for a small region about the critical value, the degree of quantum entanglement shows a trend of continuous increase. The time evolution of the entanglement measure, e.g., logarithmic negativity, exhibits a strong dependence on the nature of classical nonlinear dynamics, constituting its signature.
Nonlinear Dynamic Characteristics of Oil-in-Water Emulsions
Yin, Zhaoqi; Han, Yunfeng; Ren, Yingyu; Yang, Qiuyi; Jin, Ningde
2016-08-01
In this article, the nonlinear dynamic characteristics of oil-in-water emulsions under the addition of surfactant were experimentally investigated. Firstly, based on the vertical upward oil-water two-phase flow experiment in 20 mm inner diameter (ID) testing pipe, dynamic response signals of oil-in-water emulsions were recorded using vertical multiple electrode array (VMEA) sensor. Afterwards, the recurrence plot (RP) algorithm and multi-scale weighted complexity entropy causality plane (MS-WCECP) were employed to analyse the nonlinear characteristics of the signals. The results show that the certainty is decreasing and the randomness is increasing with the increment of surfactant concentration. This article provides a novel method for revealing the nonlinear dynamic characteristics, complexity, and randomness of oil-in-water emulsions with experimental measurement signals.
Newtonian Nonlinear Dynamics for Complex Linear and Optimization Problems
Vázquez, Luis
2013-01-01
Newtonian Nonlinear Dynamics for Complex Linear and Optimization Problems explores how Newton's equation for the motion of one particle in classical mechanics combined with finite difference methods allows creation of a mechanical scenario to solve basic problems in linear algebra and programming. The authors present a novel, unified numerical and mechanical approach and an important analysis method of optimization. This book also: Presents mechanical method for determining matrix singularity or non-independence of dimension and complexity Illustrates novel mathematical applications of classical Newton’s law Offers a new approach and insight to basic, standard problems Includes numerous examples and applications Newtonian Nonlinear Dynamics for Complex Linear and Optimization Problems is an ideal book for undergraduate and graduate students as well as researchers interested in linear problems and optimization, and nonlinear dynamics.
Nonlinear electronic circuit with neuron like bursting and spiking dynamics.
Savino, Guillermo V; Formigli, Carlos M
2009-07-01
It is difficult to design electronic nonlinear devices capable of reproducing complex oscillations because of the lack of general constructive rules, and because of stability problems related to the dynamical robustness of the circuits. This is particularly true for current analog electronic circuits that implement mathematical models of bursting and spiking neurons. Here we describe a novel, four-dimensional and dynamically robust nonlinear analog electronic circuit that is intrinsic excitable, and that displays frequency adaptation bursting and spiking oscillations. Despite differences from the classical Hodgkin-Huxley (HH) neuron model, its bifurcation sequences and dynamical properties are preserved, validating the circuit as a neuron model. The circuit's performance is based on a nonlinear interaction of fast-slow circuit blocks that can be clearly dissected, elucidating burst's starting, sustaining and stopping mechanisms, which may also operate in real neurons. Our analog circuit unit is easily linked and may be useful in building networks that perform in real-time.
Nonlinear dynamics of zigzag molecular chains (in Russian)
DEFF Research Database (Denmark)
Savin, A. V.; Manevitsch, L. I.; Christiansen, Peter Leth
1999-01-01
Nonlinear, collective, soliton type excitations in zigzag molecular chains are analyzed. It is shown that the nonlinear dynamics of a chain dramatically changes in passing from the one-dimensional linear chain to the more realistic planar zigzag model-due, in particular, to the geometry......-dependent anharmonism that comes into the picture. The existence or otherwise of solitons is determined in this case by the interplay between the geometrical anharmonism and the physical anharmonism of the interstitial interaction, of opposite signs. The nonlinear dynamic analysis of the three most typical zigzag...... models (two-dimensional alpha-spiral, polyethylene transzigzag backbone, and the zigzag chain of hydrogen bonds) shows that the zigzag structure essentially limits the soliton dynamics to finite, relatively narrow, supersonic soliton velocity intervals and may also result in that several acoustic soliton...
A Cumulant-based Analysis of Nonlinear Magnetospheric Dynamics
Energy Technology Data Exchange (ETDEWEB)
Jay R. Johnson; Simon Wing
2004-01-28
Understanding magnetospheric dynamics and predicting future behavior of the magnetosphere is of great practical interest because it could potentially help to avert catastrophic loss of power and communications. In order to build good predictive models it is necessary to understand the most critical nonlinear dependencies among observed plasma and electromagnetic field variables in the coupled solar wind/magnetosphere system. In this work, we apply a cumulant-based information dynamical measure to characterize the nonlinear dynamics underlying the time evolution of the Dst and Kp geomagnetic indices, given solar wind magnetic field and plasma input. We examine the underlying dynamics of the system, the temporal statistical dependencies, the degree of nonlinearity, and the rate of information loss. We find a significant solar cycle dependence in the underlying dynamics of the system with greater nonlinearity for solar minimum. The cumulant-based approach also has the advantage that it is reliable even in the case of small data sets and therefore it is possible to avoid the assumption of stationarity, which allows for a measure of predictability even when the underlying system dynamics may change character. Evaluations of several leading Kp prediction models indicate that their performances are sub-optimal during active times. We discuss possible improvements of these models based on this nonparametric approach.
Analysis of Nonlinear Dynamics by Square Matrix Method
Energy Technology Data Exchange (ETDEWEB)
Yu, Li Hua [Brookhaven National Lab. (BNL), Upton, NY (United States). Energy and Photon Sciences Directorate. National Synchrotron Light Source II
2016-07-25
The nonlinear dynamics of a system with periodic structure can be analyzed using a square matrix. In this paper, we show that because the special property of the square matrix constructed for nonlinear dynamics, we can reduce the dimension of the matrix from the original large number for high order calculation to low dimension in the first step of the analysis. Then a stable Jordan decomposition is obtained with much lower dimension. The transformation to Jordan form provides an excellent action-angle approximation to the solution of the nonlinear dynamics, in good agreement with trajectories and tune obtained from tracking. And more importantly, the deviation from constancy of the new action-angle variable provides a measure of the stability of the phase space trajectories and their tunes. Thus the square matrix provides a novel method to optimize the nonlinear dynamic system. The method is illustrated by many examples of comparison between theory and numerical simulation. Finally, in particular, we show that the square matrix method can be used for optimization to reduce the nonlinearity of a system.
Dynamic Source Inversion of Intermediate Depth Earthquakes in Mexico
Yuto Sho Mirwald, Aron; Cruz-Atienza, Victor Manuel; Krishna Singh-Singh, Shri
2017-04-01
The source mechanisms of earthquakes at intermediate depth (50-300 km) are still under debate. Due to the high confining pressure at depths below 50 km, rocks ought to deform by ductile flow rather than brittle failure, which is the mechanism originating most earthquakes. Several source mechanisms have been proposed, but for neither of them conclusive evidence has been found. One of two viable mechanisms is Dehydration Embrittlement, where liberation of water lowers the effective pressure and enables brittle fracture. The other is Thermal Runaway, a highly localized ductile deformation (Prieto et. al., Tecto., 2012). In the Mexican subduction zone, intermediate depth earthquakes represent a real hazard in central Mexico due to their proximity to highly populated areas and the large accelerations induced on ground motion (Iglesias et. al., BSSA, 2002). To improve our understanding of these rupture processes, we use a recently introduced inversion method (Diaz-Mojica et. al., JGR, 2014) to analyze several intermediate depth earthquakes in Mexico. The method inverts strong motion seismograms to determine the dynamic source parameters based on a genetic algorithm. It has been successfully used for the M6.5 Zumpango earthquake that occurred at a depth of 62 km in the state of Guerrero, Mexico. For this event, high radiated energy, low radiation efficiency and low rupture velocity were determined. This indicates a highly dissipative rupture process, suggesting that Thermal Runaway could probably be the dominant source process. In this work we improved the inversion method by introducing a theoretical consideration for the nucleation process that minimizes the effects of rupture initiation and guarantees self-sustained rupture propagation (Galis et. al., GJInt., 2014). Preliminary results indicate that intermediate depth earthquakes in central Mexico may vary in their rupture process. For instance, for a M5.9 normal-faulting earthquake at 55 km depth that produced very
Spatial heterogeneity, nonlinear dynamics and chaos in infectious diseases.
Grenfell, B T; Kleczkowski, A; Gilligan, C A; Bolker, B M
1995-06-01
There is currently considerable interest in the role of nonlinear phenomena in the population dynamics of infectious diseases. Childhood diseases such as measles are particularly well documented dynamically, and have recently been the subject of analyses (of both models and notification data) to establish whether the pattern of epidemics is chaotic. Though the spatial dynamics of measles have also been extensively studied, spatial and nonlinear dynamics have only recently been brought together. The present review concentrates mainly on describing this synthesis. We begin with a general review of the nonlinear dynamics of measles models, in a spatially homogeneous environment. Simple compartmental models (specifically the SEIR model) can behave chaotically, under the influence of strong seasonal 'forcing' of infection rate associated with patterns of schooling. However, adding observed heterogeneities such as age structure can simplify the deterministic dynamics back to limit cycles. By contrast all current strongly seasonally forced stochastic models show large amplitude irregular fluctuations, with many more 'fadeouts' of infection that is observed in real communities of similar size. This indicates that (social and/or geographical) spatial heterogeneity is needed in the models. We review the exploration of this problem with nonlinear spatiotemporal models. The few studies to date indicate that spatial heterogeneity can help to increase the realism of models. However, a review of nonlinear analyses of spatially subdivided measles data show that more refinements of the models (particularly in representing the impact of human demographic changes on infection dynamics) are required. We conclude with a discussion of the implication of these results for the dynamics of infectious diseases in general and, in particular, the possibilities of cross fertilization between human disease epidemiology and the study of plant and animal diseases.
Application of dynamic recurrent neural networks in nonlinear system identification
Du, Yun; Wu, Xueli; Sun, Huiqin; Zhang, Suying; Tian, Qiang
2006-11-01
An adaptive identification method of simple dynamic recurrent neural network (SRNN) for nonlinear dynamic systems is presented in this paper. This method based on the theory that by using the inner-states feed-back of dynamic network to describe the nonlinear kinetic characteristics of system can reflect the dynamic characteristics more directly, deduces the recursive prediction error (RPE) learning algorithm of SRNN, and improves the algorithm by studying topological structure on recursion layer without the weight values. The simulation results indicate that this kind of neural network can be used in real-time control, due to its less weight values, simpler learning algorithm, higher identification speed, and higher precision of model. It solves the problems of intricate in training algorithm and slow rate in convergence caused by the complicate topological structure in usual dynamic recurrent neural network.
Structure-based control of complex networks with nonlinear dynamics
Zañudo, Jorge G T; Albert, Réka
2016-01-01
Given the network of interactions underlying a complex system, what can we learn about controlling such a system solely from its structure? Over a century of research in control theory has given us tools to answer this question, which were widely applied in science and engineering. Yet the current tools do not always consider the inherently nonlinear dynamics of real systems and the naturally occurring system states in their definition of "control", a term whose interpretation varies across disciplines. Here we use a new mathematical framework for structure-based control of networks governed by a broad class of nonlinear dynamics that includes the major dynamic models of biological, technological, and social processes. This framework provides realizable node overrides that steer a system towards any of its natural long term dynamic behaviors and which are guaranteed to be effective regardless of the dynamic details and parameters of the underlying system. We use this framework on several real networks, compar...
Nonlinear dynamic phenomena in the beer model
DEFF Research Database (Denmark)
Mosekilde, Erik; Laugesen, Jakob Lund
2007-01-01
The production-distribution system or "beer game" is one of the most well-known system dynamics models. Notorious for the complex dynamics it produces, the beer game has been used for nearly five decades to illustrate how structure generates behavior and to explore human decision making. Here we...
Directory of Open Access Journals (Sweden)
S. L. Han
2012-01-01
Full Text Available The nonlinear responses of ship rolling motion characterized by a roll damping moment are of great interest to naval architects and ocean engineers. Modeling and identification of the nonlinear damping moment are essential to incorporate the inherent nonlinearity in design, analysis, and control of a ship. A stochastic nonparametric approach for identification of nonlinear damping in the general mechanical system has been presented in the literature (Han and Kinoshits 2012. The method has been also applied to identification of the nonlinear damping moment of a ship at zero-forward speed (Han and Kinoshits 2013. In the presence of forward speed, however, the characteristic of roll damping moment of a ship is significantly changed due to the lift effect. In this paper, the stochastic inverse method is applied to identification of the nonlinear damping moment of a ship moving at nonzero-forward speed. The workability and validity of the method are verified with laboratory tests under controlled conditions. In experimental trials, two different types of ship rolling motion are considered: time-dependent transient motion and frequency-dependent periodic motion. It is shown that this method enables the inherent nonlinearity in damping moment to be estimated, including its reliability analysis.
Nonlinear dynamics of the mammalian inner ear
Szalai, Robert; Homer, Martin
2015-01-01
A simple nonlinear transmission-line model of the cochlea with longitudinal coupling is introduced that can reproduce Basilar membrane response and neural tuning in the chinchilla. It is found that the middle ear has little effect on cochlear resonances, and hence conclude that the theory of coherent reflections is not applicable to the model. The model also provides an explanation of the emergence of spontaneous otoacoustic emissions (SOAEs). It is argued that SOAEs arise from Hopf bifurcations of the transmission-line model and not from localized instabilities. The paper shows that emissions can become chaotic, intermittent and fragile to perturbations.
Nonlinear Dynamical Friction in a Gaseous Medium
Kim, Hyosun
2009-01-01
Using high-resolution, two-dimensional hydrodynamic simulations, we investigate nonlinear gravitational responses of gas to, and the resulting drag force on, a very massive perturber M_p moving at velocity V_p through a uniform gaseous medium of adiabatic sound speed a_0. We model the perturber as a Plummer potential with softening radius r_s, and run various models with differing A=GM_p/(a_0^2 r_s) and M=V_p/a_0 by imposing cylindrical symmetry with respect to the line of perturber motion. For supersonic cases, a massive perturber quickly develops nonlinear flows that produce a detached bow shock and a vortex ring, which is unlike in the linear cases where Mach cones are bounded by low-amplitude Mach waves. The flows behind the shock are initially non-steady, displaying quasi-periodic, overstable oscillations of the vortex ring and the shock. The vortex ring is eventually shed downstream and the flows evolve toward a quasi-steady state where the density wake near the perturber is in near hydrostatic equilibr...
Guidance of Nonlinear Nonminimum-Phase Dynamic Systems
Devasia, Santosh
1997-01-01
The first two years research work has advanced the inversion-based guidance theory for: (1) systems with non-hyperbolic internal dynamics; (2) systems with parameter jumps; (3) systems where a redesign of the output trajectory is desired; and (4) the generation of recovery guidance maneuvers.
Nonlinear dynamics and millikelvin cavity-cooling of levitated nanoparticles
Fonseca, P Z G; Millen, J; Monteiro, T S; Barker, P F
2015-01-01
Optomechanical systems explore and exploit the coupling between light and the mechanical motion of matter. A nonlinear coupling offers access to rich new physics, in both the quantum and classical regimes. We investigate a dynamic, as opposed to the usually studied static, nonlinear optomechanical system, comprising of a nanosphere levitated and cooled 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 to millikelvin temperatures for indefinite periods of time in high vacuum. We observe cooling of the linear and non-linear motion, leading to a $10^5$ fold reduction in phonon number $n_p$, attaining final occupancies of $n_p = 100-1000$. This work puts cavity cooling of a levitated object to the quantum ground-state firmly within reach.
Geodynamic inversion to constrain the non-linear rheology of the lithosphere
Baumann, T. S.; Kaus, Boris J. P.
2015-08-01
One of the main methods to determine the strength of the lithosphere is by estimating it's effective elastic thickness. This method assumes that the lithosphere is a thin elastic plate that floats on the mantle and uses both topography and gravity anomalies to estimate the plate thickness. Whereas this seems to work well for oceanic plates, it has given controversial results in continental collision zones. For most of these locations, additional geophysical data sets such as receiver functions and seismic tomography exist that constrain the geometry of the lithosphere and often show that it is rather complex. Yet, lithospheric geometry by itself is insufficient to understand the dynamics of the lithosphere as this also requires knowledge of the rheology of the lithosphere. Laboratory experiments suggest that rocks deform in a viscous manner if temperatures are high and stresses low, or in a plastic/brittle manner if the yield stress is exceeded. Yet, the experimental results show significant variability between various rock types and there are large uncertainties in extrapolating laboratory values to nature, which leaves room for speculation. An independent method is thus required to better understand the rheology and dynamics of the lithosphere in collision zones. The goal of this paper is to discuss such an approach. Our method relies on performing numerical thermomechanical forward models of the present-day lithosphere with an initial geometry that is constructed from geophysical data sets. We employ experimentally determined creep-laws for the various parts of the lithosphere, but assume that the parameters of these creep-laws as well as the temperature structure of the lithosphere are uncertain. This is used as a priori information to formulate a Bayesian inverse problem that employs topography, gravity, horizontal and vertical surface velocities to invert for the unknown material parameters and temperature structure. In order to test the general methodology
Elizondo, D.; Cappelaere, B.; Faure, Ch.
2002-04-01
Emerging tools for automatic differentiation (AD) of computer programs should be of great benefit for the implementation of many derivative-based numerical methods such as those used for inverse modeling. The Odyssée software, one such tool for Fortran 77 codes, has been tested on a sample model that solves a 2D non-linear diffusion-type equation. Odyssée offers both the forward and the reverse differentiation modes, that produce the tangent and the cotangent models, respectively. The two modes have been implemented on the sample application. A comparison is made with a manually-produced differentiated code for this model (MD), obtained by solving the adjoint equations associated with the model's discrete state equations. Following a presentation of the methods and tools and of their relative advantages and drawbacks, the performances of the codes produced by the manual and automatic methods are compared, in terms of accuracy and of computing efficiency (CPU and memory needs). The perturbation method (finite-difference approximation of derivatives) is also used as a reference. Based on the test of Taylor, the accuracy of the two AD modes proves to be excellent and as high as machine precision permits, a good indication of Odyssée's capability to produce error-free codes. In comparison, the manually-produced derivatives (MD) sometimes appear to be slightly biased, which is likely due to the fact that a theoretical model (state equations) and a practical model (computer program) do not exactly coincide, while the accuracy of the perturbation method is very uncertain. The MD code largely outperforms all other methods in computing efficiency, a subject of current research for the improvement of AD tools. Yet these tools can already be of considerable help for the computer implementation of many numerical methods, avoiding the tedious task of hand-coding the differentiation of complex algorithms.
Santaren, D.; Peylin, P.; Viovy, N.; Ciais, P.
2003-04-01
Global model of Carbone, water, and energy exchanges between the biosphere and the atmosphere are usually validated and calibrated with intensive measurement made over specific ecosystem like those of the fluxnet networks.However the nonlinear dependance between fluxes and model parameters generally complicate the optimization of the major parameters.In this study, we estimate few key parameters of the ORCHIDEE french model,using diurnal variation measurements of latent heat,sensible heat and net CO2 fluxes for 3 weeks over pine forest (Landes, France).The model is forced with the observed climatic forcing: Temperature, income solar radiations,wind velocity norm, air humidity, pressure and precipitations. We will first present the inverse methodology and the problem linkedto the non linearity. The result of the optimization shows correlations within the initial ensemble of parameters which allow us to choose only five parameters determined independently from the observations. Directly related to the net CO2 flux, the maximum rate of carboxylation,Vcmax,and the stomatal conductance, gs, are significantly changed from their apriori estimate for that period. The aerodynamic resistance, the albedo and a parameter linked to maintenance respiration were also modified within their physical range.Overall the model fit to the data was largely improved. Note however that some discrepancies remain for sensible heat flux which would probably require some model improvements for the stocking of energy in the soil. Such work is currently extended in time to account for parameter variations between the season. The application to other ecosystems and with the supplementary data of the Leaf Area Index will be also discussed.
Nonlinear dynamics of giant resonances in atomic nuclei
Vretenar, D; Ring, P; Lalazissis, G A
1999-01-01
The dynamics of monopole giant resonances in nuclei is analyzed in the time-dependent relativistic mean-field model. The phase spaces of isoscalar and isovector collective oscillations are reconstructed from the time-series of dynamical variables that characterize the proton and neutron density distributions. The analysis of the resulting recurrence plots and correlation dimensions indicate regular motion for the isoscalar mode, and chaotic dynamics for the isovector oscillations. Information-theoretic functionals identify and quantify the nonlinear dynamics of giant resonances in quantum systems that have spatial as well as temporal structure.
High Dynamic Performance Nonlinear Source Emulator
DEFF Research Database (Denmark)
Nguyen-Duy, Khiem; Knott, Arnold; Andersen, Michael A. E.
2016-01-01
As research and development of renewable and clean energy based systems is advancing rapidly, the nonlinear source emulator (NSE) is becoming very essential for testing of maximum power point trackers or downstream converters. Renewable and clean energy sources play important roles in both...... terrestrial and nonterrestrial applications. However, most existing NSEs have only been concerned with simulating energy sources in terrestrial applications, which may not be fast enough for testing of nonterrestrial applications. In this paper, a high-bandwidth NSE is developed that is able to simulate...... change in the input source but also to a load step between nominal and open circuit. Moreover, all of these operation modes have a very fast settling time of only 10 μs, which is hundreds of times faster than that of existing works. This attribute allows for higher speed and a more efficient maximum...
Institute of Scientific and Technical Information of China (English)
2008-01-01
Using functional derivative technique in quantum field theory, the algebraic dy-namics approach for solution of ordinary differential evolution equations was gen-eralized to treat partial differential evolution equations. The partial differential evo-lution equations were lifted to the corresponding functional partial differential equations in functional space by introducing the time translation operator. The functional partial differential evolution equations were solved by algebraic dynam-ics. The algebraic dynamics solutions are analytical in Taylor series in terms of both initial functions and time. Based on the exact analytical solutions, a new nu-merical algorithm—algebraic dynamics algorithm was proposed for partial differ-ential evolution equations. The difficulty of and the way out for the algorithm were discussed. The application of the approach to and computer numerical experi-ments on the nonlinear Burgers equation and meteorological advection equation indicate that the algebraic dynamics approach and algebraic dynamics algorithm are effective to the solution of nonlinear partial differential evolution equations both analytically and numerically.
ANALYSIS OF NONLINEAR DYNAMIC STABILITY OF LIQUID-CONVEYING PIPES
Institute of Scientific and Technical Information of China (English)
张立翔; 黄文虎
2002-01-01
Nonlinearly dynamic stability of flexible liquid-conveying pipe in fluid structure interaction was analyzed by using modal disassembling technique. The effects of Poisson,Junction and Friction couplings in the wave-flowing-vibration system on the pipe dynamic stability were included in the analytical model constituted by four nonlinear differential equations. An analyzing example of cantilevered pipe was done to illustrate the dynamic stability characteristics of the pipe in the full coupling mechanisms, and the phase curves related to the first four modal motions were drawn. The results show that the dynamic stable characteristics of the pipe are very complicated in the complete coupling mechanisms, and the kinds of the singularity points corresponding to the various modal motions are different.
Report of the working group on single-particle nonlinear dynamics
Energy Technology Data Exchange (ETDEWEB)
Bazzani, A.; Bongini, L.; Corbett, J.; Dome, G.; Fedorova, A.; Freguglia, P.; Ng, K.; Ohmi, K.; Owen, H.; Papaphilippou, Y.; Robin, D.; Safranek, J.; Scandale, W.; Terebilo, A.; Turchetti, G.; Todesco, E.; Warnock, R.; Zeitlin, M. (Office of Energy Research, Office of Basic Energy Sciences, Materials Sciences Division, U.S. Department of Energy (United States))
1999-04-01
The Working Group on single-particle nonlinear dynamics has developed a set of tools to study nonlinear dynamics in a particle accelerator. The design of rings with large dynamic apertures is still far from automatic. The Working Group has concluded that nonlinear single-particle dynamics limits the performance of acclerators. (AIP) [copyright] [ital 1999] [ital American Institute of Physics
Report of the working group on single-particle nonlinear dynamics
Bazzani, A.; Bongini, L.; Corbett, J.; Dome, G.; Fedorova, A.; Freguglia, P.; Ng, K.; Ohmi, K.; Owen, H.; Papaphilippou, Y.; Robin, D.; Safranek, J.; Scandale, W.; Terebilo, A.; Turchetti, G.; Todesco, E.; Warnock, R.; Zeitlin, M.
1999-04-01
The Working Group on single-particle nonlinear dynamics has developed a set of tools to study nonlinear dynamics in a particle accelerator. The design of rings with large dynamic apertures is still far from automatic. The Working Group has concluded that nonlinear single-particle dynamics limits the performance of acclerators. (AIP)
Nonlinear dynamical system identification using unscented Kalman filter
Rehman, M. Javvad ur; Dass, Sarat Chandra; Asirvadam, Vijanth Sagayan
2016-11-01
Kalman Filter is the most suitable choice for linear state space and Gaussian error distribution from decades. In general practical systems are not linear and Gaussian so these assumptions give inconsistent results. System Identification for nonlinear dynamical systems is a difficult task to perform. Usually, Extended Kalman Filter (EKF) is used to deal with non-linearity in which Jacobian method is used for linearizing the system dynamics, But it has been observed that in highly non-linear environment performance of EKF is poor. Unscented Kalman Filter (UKF) is proposed here as a better option because instead of analytical linearization of state space, UKF performs statistical linearization by using sigma point calculated from deterministic samples. Formation of the posterior distribution is based on the propagation of mean and covariance through sigma points.
Nonlinear Analyses of the Dynamic Properties of Hydrostatic Bearing Systems
Institute of Scientific and Technical Information of China (English)
LIU Wei(刘伟); WU Xiujiang(吴秀江); V.A. Prokopenko
2003-01-01
Nonlinear analyses of hydrostatic bearing systems are necessary to adequately model the fluid-solid interaction. The dynamic properties of linear and nonlinear analytical models of hydrostatic bearings are compared in this paper. The analyses were based on the determination of the aperiodic border of transient processes with external step loads. The results show that the dynamic properties can be most effectively improved by increasing the hydrostatic bearing crosspiece width and additional pocket volume in a bearing can extend the load range for which the transient process is aperiodic, but an additional restrictor and capacitor (RC) chain must be introduced for increasing damping. The nonlinear analyses can also be used to predict typical design parameters for a hydrostatic bearing.
Nonlinear Dynamics, Chaotic and Complex Systems
Infeld, E.; Zelazny, R.; Galkowski, A.
2011-04-01
Part I. Dynamic Systems Bifurcation Theory and Chaos: 1. Chaos in random dynamical systems V. M. Gunldach; 2. Controlling chaos using embedded unstable periodic orbits: the problem of optimal periodic orbits B. R. Hunt and E. Ott; 3. Chaotic tracer dynamics in open hydrodynamical flows G. Karolyi, A. Pentek, T. Tel and Z. Toroczkai; 4. Homoclinic chaos L. P. Shilnikov; Part II. Spatially Extended Systems: 5. Hydrodynamics of relativistic probability flows I. Bialynicki-Birula; 6. Waves in ionic reaction-diffusion-migration systems P. Hasal, V. Nevoral, I. Schreiber, H. Sevcikova, D. Snita, and M. Marek; 7. Anomalous scaling in turbulence: a field theoretical approach V. Lvov and I. Procaccia; 8. Abelian sandpile cellular automata M. Markosova; 9. Transport in an incompletely chaotic magnetic field F. Spineanu; Part III. Dynamical Chaos Quantum Physics and Foundations Of Statistical Mechanics: 10. Non-equilibrium statistical mechanics and ergodic theory L. A. Bunimovich; 11. Pseudochaos in statistical physics B. Chirikov; 12. Foundations of non-equilibrium statistical mechanics J. P. Dougherty; 13. Thermomechanical particle simulations W. G. Hoover, H. A. Posch, C. H. Dellago, O. Kum, C. G. Hoover, A. J. De Groot and B. L. Holian; 14. Quantum dynamics on a Markov background and irreversibility B. Pavlov; 15. Time chaos and the laws of nature I. Prigogine and D. J. Driebe; 16. Evolutionary Q and cognitive systems: dynamic entropies and predictability of evolutionary processes W. Ebeling; 17. Spatiotemporal chaos information processing in neural networks H. Szu; 18. Phase transitions and learning in neural networks C. Van den Broeck; 19. Synthesis of chaos A. Vanecek and S. Celikovsky; 20. Computational complexity of continuous problems H. Wozniakowski; Part IV. Complex Systems As An Interface Between Natural Sciences and Environmental Social and Economic Sciences: 21. Stochastic differential geometry in finance studies V. G. Makhankov; Part V. Conference Banquet
Nonlinear dynamics mathematical models for rigid bodies with a liquid
Lukovsky, Ivan A
2015-01-01
This book is devoted to analytically approximate methods in the nonlinear dynamics of a rigid body with cavities partly filled by liquid. It combines several methods and compares the results with experimental data. It is useful for experienced and early-stage readers interested in analytical approaches to fluid-structure interaction problems, the fundamental mathematical background and modeling the dynamics of such complex mechanical systems.
Numerical investigation of bubble nonlinear dynamics characteristics
Energy Technology Data Exchange (ETDEWEB)
Shi, Jie, E-mail: shijie@hrbeu.edu.cn; Yang, Desen; Shi, Shengguo; Hu, Bo [Acoustic Science and Technology Laboratory, Harbin Engineering University, Harbin 150001 (China); College of Underwater Acoustic Engineering, Harbin Engineering University, Harbin 150001 (China); Zhang, Haoyang; Jiang, Wei [College of Underwater Acoustic Engineering, Harbin Engineering University, Harbin 150001 (China)
2015-10-28
The complicated dynamical behaviors of bubble oscillation driven by acoustic wave can provide favorable conditions for many engineering applications. On the basis of Keller-Miksis model, the influences of control parameters, including acoustic frequency, acoustic pressure and radius of gas bubble, are discussed by utilizing various numerical analysis methods, Furthermore, the law of power spectral variation is studied. It is shown that the complicated dynamic behaviors of bubble oscillation driven by acoustic wave, such as bifurcation and chaos, further the stimulated scattering processes are revealed.
Consensus in Directed Networks of Agents With Nonlinear Dynamics
Yu, Wenwu; Chen, Guanrong; Cao, Ming; Qu, Z.
2011-01-01
This technical note studies the consensus problem for cooperative agents with nonlinear dynamics in a directed network. Both local and global consensus are defined and investigated. Techniques for studying the synchronization in such complex networks are exploited to establish various sufficient con
Nonlinear dynamics of near-extremal black holes
Green, Stephen; Gralla, Samuel; Zimmerman, Peter
2017-01-01
Near-extremal black holes possess a family of long lived quasinormal modes associated to the near-horizon throat geometry. For long lived modes, nonlinear interactions between the modes can potentially dominate over dissipation. We develop a framework for treating these interactions, and we study their dynamics.
Nonlinear dynamics of incommensurately contacting surfaces : a model study
Consoli, Luca
2002-01-01
This PhD thesis is about the nonlinear dynamics of contacting surfaces. More specifically, it deals with the problem of modelling at the microscopic level some of the contributions that lead to the macroscopic effect of dry sliding friction. In chapter 1, we try to give an overview of the physical q
Major open problems in chaos theory and nonlinear dynamics
Li, Y Charles
2013-01-01
Nowadays, chaos theory and nonlinear dynamics lack research focuses. Here we mention a few major open problems: 1. an effective description of chaos and turbulence, 2. rough dependence on initial data, 3. arrow of time, 4. the paradox of enrichment, 5. the paradox of pesticides, 6. the paradox of plankton.
A toolkit for analyzing nonlinear dynamic stochastic models easily
Uhlig, H.F.H.V.S.
1995-01-01
Often, researchers wish to analyze nonlinear dynamic discrete-time stochastic models. This paper provides a toolkit for solving such models easily, building on log-linearizing the necessary equations characterizing the equilibrium and solving for the recursive equilibrium law of motion with the meth
A toolkit for analyzing nonlinear dynamic stochastic models easily
Uhlig, H.F.H.V.S.
1995-01-01
Often, researchers wish to analyze nonlinear dynamic discrete-time stochastic models. This paper provides a toolkit for solving such models easily, building on log-linearizing the necessary equations characterizing the equilibrium and solving for the recursive equilibrium law of motion with the meth
CLASSIFICATION OF BIFURCATIONS FOR NONLINEAR DYNAMICAL PROBLEMS WITH CONSTRAINTS
Institute of Scientific and Technical Information of China (English)
吴志强; 陈予恕
2002-01-01
Bifurcation of periodic solutions widely existed in nonlinear dynamical systems isa kind of constrained one in intrinsic quality because its amplitude is always non-negative.Classification of the bifurcations with the type of constraint was discussed. All its six typesof transition sets are derived, in which three types are newly found and a method isproposed for analyzing the constrained bifurcation.
Applied Nonlinear Dynamics Analytical, Computational, and Experimental Methods
Nayfeh, Ali H
1995-01-01
A unified and coherent treatment of analytical, computational and experimental techniques of nonlinear dynamics with numerous illustrative applications. Features a discourse on geometric concepts such as Poincaré maps. Discusses chaos, stability and bifurcation analysis for systems of differential and algebraic equations. Includes scores of examples to facilitate understanding.
Variational Bayesian identification and prediction of stochastic nonlinear dynamic causal models
Daunizeau, J.; Friston, K. J.; Kiebel, S. J.
2009-11-01
In this paper, we describe a general variational Bayesian approach for approximate inference on nonlinear stochastic dynamic models. This scheme extends established approximate inference on hidden-states to cover: (i) nonlinear evolution and observation functions, (ii) unknown parameters and (precision) hyperparameters and (iii) model comparison and prediction under uncertainty. Model identification or inversion entails the estimation of the marginal likelihood or evidence of a model. This difficult integration problem can be finessed by optimising a free-energy bound on the evidence using results from variational calculus. This yields a deterministic update scheme that optimises an approximation to the posterior density on the unknown model variables. We derive such a variational Bayesian scheme in the context of nonlinear stochastic dynamic hierarchical models, for both model identification and time-series prediction. The computational complexity of the scheme is comparable to that of an extended Kalman filter, which is critical when inverting high dimensional models or long time-series. Using Monte-Carlo simulations, we assess the estimation efficiency of this variational Bayesian approach using three stochastic variants of chaotic dynamic systems. We also demonstrate the model comparison capabilities of the method, its self-consistency and its predictive power.
Nonlinear dynamics of a vectored thrust aircraft
DEFF Research Database (Denmark)
Sørensen, C.B; Mosekilde, Erik
1996-01-01
With realistic relations for the aerodynamic coefficients, numerical simulations are applied to study the longitudional dynamics of a thrust vectored aircraft. As function of the thrust magnitude and the thrust vectoring angle the equilibrium state exhibits two saddle-node bifurcations and three...
Nonlinear dynamics of a vectored thrust aircraft
DEFF Research Database (Denmark)
Sørensen, C.B; Mosekilde, Erik
1996-01-01
With realistic relations for the aerodynamic coefficients, numerical simulations are applied to study the longitudional dynamics of a thrust vectored aircraft. As function of the thrust magnitude and the thrust vectoring angle the equilibrium state exhibits two saddle-node bifurcations and three ...
Bayo, Eduardo; Ledesma, Ragnar
1993-01-01
A technique is presented for solving the inverse dynamics of flexible planar multibody systems. This technique yields the non-causal joint efforts (inverse dynamics) as well as the internal states (inverse kinematics) that produce a prescribed nominal trajectory of the end effector. A non-recursive global Lagrangian approach is used in formulating the equations for motion as well as in solving the inverse dynamics equations. Contrary to the recursive method previously presented, the proposed method solves the inverse problem in a systematic and direct manner for both open-chain as well as closed-chain configurations. Numerical simulation shows that the proposed procedure provides an excellent tracking of the desired end effector trajectory.
Institute of Scientific and Technical Information of China (English)
WANG Shundin; ZHANG Hua
2008-01-01
Using functional derivative technique In quantum field theory,the algebraic dy-namics approach for solution of ordinary differential evolution equations was gen-eralized to treat partial differential evolution equations.The partial differential evo-lution equations were lifted to the corresponding functional partial differential equations in functional space by Introducing the time translation operator.The functional partial differential evolution equations were solved by algebraic dynam-ics.The algebraic dynamics solutions are analytical In Taylor series In terms of both initial functions and time.Based on the exact analytical solutions,a new nu-merical algorithm-algebraic dynamics algorithm was proposed for partial differ-ential evolution equations.The difficulty of and the way out for the algorithm were discussed.The application of the approach to and computer numerical experi-ments on the nonlinear Burgers equation and meteorological advection equation indicate that the algebraic dynamics approach and algebraic dynamics algorithm are effective to the solution of nonlinear partial differential evolution equations both analytically and numerically.
Humanoid Walking Robot: Modeling, Inverse Dynamics, and Gain Scheduling Control
Elvedin Kljuno; Williams, Robert L.
2010-01-01
This article presents reference-model-based control design for a 10 degree-of-freedom bipedal walking robot, using nonlinear gain scheduling. The main goal is to show concentrated mass models can be used for prediction of the required joint torques for a bipedal walking robot. Relatively complicated architecture, high DOF, and balancing requirements make the control task of these robots difficult. Although linear control techniques can be used to control bipedal robots, nonlinear control is n...
Sliding mode identifier for parameter uncertain nonlinear dynamic systems with nonlinear input
Institute of Scientific and Technical Information of China (English)
张克勤; 庄开宇; 苏宏业; 褚健; 高红
2002-01-01
This paper presents a sliding mode (SM) based identifier to deal wit h the parameter identification problem for a class of parameter uncertain nonlin ear dynamic systems with input nonlinearity. A sliding mode controller (SMC) is used to ensure the global reaching condition of the sliding mode for the nonline ar system; an identifier is designed to identify the uncertain parameter of the nonlinear system. A numerical example is studied to show the feasibility of the SM controller and the asymptotical convergence of the identifier.
Nonlinear Dynamics and Chaos: Advances and Perspectives
Thiel, Marco; Romano, M. Carmen; Károlyi, György; Moura, Alessandro
2010-01-01
This book is a collection of contributions on various aspects of active frontier research in the field of dynamical systems and chaos. Each chapter examines a specific research topic and, in addition to reviewing recent results, also discusses future perspectives. The result is an invaluable snapshot of the state of the field by some of its most important researchers. The first contribution in this book, "How did you get into Chaos?", is actually a collection of personal accounts by a number of distinguished scientists on how they entered the field of chaos and dynamical systems, featuring comments and recollections by James Yorke, Harry Swinney, Floris Takens, Peter Grassberger, Edward Ott, Lou Pecora, Itamar Procaccia, Michael Berry, Giulio Casati, Valentin Afraimovich, Robert MacKay, and last but not least, Celso Grebogi, to whom this volume is dedicated.
Nonlinear Dynamics of A Damped Magnetic Oscillator
Kim, S Y
1999-01-01
We consider a damped magnetic oscillator, consisting of a permanent magnet in a periodically oscillating magnetic field. A detailed investigation of the dynamics of this dissipative magnetic system is made by varying the field amplitude $A$. As $A$ is increased, the damped magnetic oscillator, albeit simple looking, exhibits rich dynamical behaviors such as symmetry-breaking pitchfork bifurcations, period-doubling transitions to chaos, symmetry-restoring attractor-merging crises, and saddle-node bifurcations giving rise to new periodic attractors. Besides these familiar behaviors, a cascade of ``resurrections'' (i.e., an infinite sequence of alternating restabilizations and destabilizations) of the stationary points also occurs. It is found that the stationary points restabilize (destabilize) through alternating subcritical (supercritical) period-doubling and pitchfork bifurcations. We also discuss the critical behaviors in the period-doubling cascades.
Process and meaning: nonlinear dynamics and psychology in visual art.
Zausner, Tobi
2007-01-01
Creating and viewing visual art are both nonlinear experiences. Creating a work of art is an irreversible process involving increasing levels of complexity and unpredictable events. Viewing art is also creative with collective responses forming autopoietic structures that shape cultural history. Artists work largely from the chaos of the unconscious and visual art contains elements of chaos. Works of art by the author are discussed in reference to nonlinear dynamics. "Travelogues" demonstrates continued emerging interpretations and a deterministic chaos. "Advice to the Imperfect" signifies the resolution of paradox in the nonlinear tension of opposites. "Quanah" shows the nonlinear tension of opposites as an ongoing personal evolution. "The Mother of All Things" depicts seemingly separate phenomena arising from undifferentiated chaos. "Memories" refers to emotional fixations as limit cycles. "Compassionate Heart," "Wind on the Lake," and "Le Mal du Pays" are a series of works in fractal format focusing on the archetype of the mother and child. "Sameness, Depth of Mystery" addresses the illusion of hierarchy and the dynamics of symbols. In "Chasadim" the origin of worlds and the regeneration of individuals emerge through chaos. References to chaos in visual art mirror the nonlinear complexity of life.
Nonlinear Dynamic Modeling of Langevin-Type Piezoelectric Transducers
Directory of Open Access Journals (Sweden)
Nicolás Peréz Alvarez
2015-11-01
Full Text Available Langevin transducers are employed in several applications, such as power ultrasound systems, naval hydrophones, and high-displacement actuators. Nonlinear effects can influence their performance, especially at high vibration amplitude levels. These nonlinear effects produce variations in the resonant frequency, harmonics of the excitation frequency, in addition to loss of symmetry in the frequency response and “frequency domain hysteresis”. In this context, this paper presents a simplified nonlinear dynamic model of power ultrasound transducers requiring only two parameters for simulating the most relevant nonlinear effects. One parameter reproduces the changes in the resonance frequency and the other introduces the dependence of the frequency response on the history of the system. The piezoelectric constitutive equations are extended by a linear dependence of the elastic constant on the mechanical displacement amplitude. For introducing the frequency hysteresis, the elastic constant is computed by combining the current value of the mechanical amplitude with the previous state amplitude. The model developed in this work is applied for predicting the dynamic responses of a 26 kHz ultrasonic transducer. The comparison of theoretical and experimental responses, obtained at several input voltages around the tuned frequency, shows a good agreement, indicating that the model can accurately describe the transducer nonlinear behavior.
Nearly linear dynamics of nonlinear dispersive waves
Erdogan, M B; Zharnitsky, V
2010-01-01
Dispersive averaging e?ffects are used to show that KdV equation with periodic boundary conditions possesses high frequency solutions which behave nearly linearly. Numerical simulations are presented which indicate high accuracy of this approximation. Furthermore, this result is applied to shallow water wave dynamics in the limit of KdV approximation, which is obtained by asymptotic analysis in combination with numerical simulations of KdV.
Population mixture model for nonlinear telomere dynamics
Itzkovitz, Shalev; Shlush, Liran I.; Gluck, Dan; Skorecki, Karl
2008-12-01
Telomeres are DNA repeats protecting chromosomal ends which shorten with each cell division, eventually leading to cessation of cell growth. We present a population mixture model that predicts an exponential decrease in telomere length with time. We analytically solve the dynamics of the telomere length distribution. The model provides an excellent fit to available telomere data and accounts for the previously unexplained observation of telomere elongation following stress and bone marrow transplantation, thereby providing insight into the nature of the telomere clock.
Self-Organized Biological Dynamics and Nonlinear Control
Walleczek, Jan
2006-04-01
The frontiers and challenges of biodynamics research Jan Walleczek; Part I. Nonlinear Dynamics in Biology and Response to Stimuli: 1. External signals and internal oscillation dynamics - principal aspects and response of stimulated rhythmic processes Friedemann Kaiser; 2. Nonlinear dynamics in biochemical and biophysical systems: from enzyme kinetics to epilepsy Raima Larter, Robert Worth and Brent Speelman; 3. Fractal mechanisms in neural control: human heartbeat and gait dynamics in health and disease Chung-Kang Peng, Jeffrey M. Hausdorff and Ary L. Goldberger; 4. Self-organising dynamics in human coordination and perception Mingzhou Ding, Yanqing Chen, J. A. Scott Kelso and Betty Tuller; 5. Signal processing in biochemical reaction networks Adam P. Arkin; Part II. Nonlinear Sensitivity of Biological Systems to Electromagnetic Stimuli: 6. Electrical signal detection and noise in systems with long-range coherence Paul C. Gailey; 7. Oscillatory signals in migrating neutrophils: effects of time-varying chemical and electrical fields Howard R. Petty; 8. Enzyme kinetics and nonlinear biochemical amplification in response to static and oscillating magnetic fields Jan Walleczek and Clemens F. Eichwald; 9. Magnetic field sensitivity in the hippocampus Stefan Engström, Suzanne Bawin and W. Ross Adey; Part III. Stochastic Noise-Induced Dynamics and Transport in Biological Systems: 10. Stochastic resonance: looking forward Frank Moss; 11. Stochastic resonance and small-amplitude signal transduction in voltage-gated ion channels Sergey M. Bezrukov and Igor Vodyanoy; 12. Ratchets, rectifiers and demons: the constructive role of noise in free energy and signal transduction R. Dean Astumian; 13. Cellular transduction of periodic and stochastic energy signals by electroconformational coupling Tian Y. Tsong; Part IV. Nonlinear Control of Biological and Other Excitable Systems: 14. Controlling chaos in dynamical systems Kenneth Showalter; 15. Electromagnetic fields and biological
Global investigation of the nonlinear dynamics of carbon nanotubes
Xu, Tiantian
2016-11-17
Understanding the complex nonlinear dynamics of carbon nanotubes (CNTs) is essential to enable utilization of these structures in devices and practical applications. We present in this work an investigation of the global nonlinear dynamics of a slacked CNT when actuated by large electrostatic and electrodynamic excitations. The coexistence of several attractors is observed. The CNT is modeled as an Euler–Bernoulli beam. A reduced-order model based on the Galerkin method is developed and utilized to simulate the static and dynamic responses. Critical computational challenges are posed due to the complicated form of the electrostatic force, which describes the interaction between the upper electrode, consisting of the cylindrically shaped CNT, and the lower electrode. Toward this, we approximate the electrostatic force using the Padé expansion. We explore the dynamics near the primary and superharmonic resonances. The nanostructure exhibits several attractors with different characteristics. To achieve deep insight and describe the complexity and richness of the behavior, we analyze the nonlinear response from an attractor-basins point of view. The competition of attractors is highlighted. Compactness and/or fractality of their basins are discussed. Both the effects of varying the excitation frequency and amplitude are examined up to the dynamic pull-in instability.
Boundedness of Formation Configuration for Nonlinear Three-body Dynamics
Institute of Scientific and Technical Information of China (English)
LI Peng; SONG Yongduan
2011-01-01
The configuration boundedness of the three-body model dynamics is studied for Sun-Earth formation flying missions. The three-body formation flying model is built up with considering the lunar gravitational acceleration and solar radiation pressure. Because traditional linearized dynamics based method has relatively lower accuracy, a modified nonlinear formation configuration analysis method is proposed in this paper. Comparative studies are carried out from three aspects, i.e., natural formation configuration with arbitrary departure time, initialization time and formation configuration boundedness, and specific initialization time for bounded formation configuration. Simulations demonstrate the differences between the two schemes,and indicate that the nonlinear dynamic method reduces the error caused by the model linearization and disturbance approximation, and thus provides higher accuracy for boundedness analysis, which is of value to initial parameters selection for natural three-body formation flying.
On the Nonlinear Evolution of Cosmic Web: Lagrangian Dynamics Revisited
Wang, Xin
2014-01-01
We investigate the nonlinear evolution of cosmic morphologies of the large-scale structure by examining the Lagrangian dynamics of various tensors of a cosmic fluid element, including the velocity gradient tensor, the Hessian matrix of the gravitational potential as well as the deformation tensor. Instead of the eigenvalue representation, the first two tensors, which associate with the "kinematic" and "dynamical" cosmic web classification algorithm respectively, are studied in a more convenient parameter space. These parameters are defined as the rotational invariant coefficients of the characteristic equation of the tensor. In the nonlinear local model (NLM) where the magnetic part of Weyl tensor vanishes, these invariants are fully capable of characterizing the dynamics. Unlike the Zeldovich approximation (ZA), where various morphologies do not change before approaching a one-dimensional singularity, the sheets in NLM are unstable for both overdense and underdense perturbations. While it has long been known...
Selected topics in nonlinear dynamics and theoretical electrical engineering
Energy Technology Data Exchange (ETDEWEB)
Kyamakya, Kyandoghere; Chedjou, Jean Camberlain [Kalgenfurt Univ. (Austria); Halang, Wolfgang A.; Li, Zhong [Hagen Fernuniv. (Germany); Mathis, Wolfgang (eds.) [Leibniz Univ. Hannover (Germany). Inst. fuer Theoretische Elektrotechnik
2013-02-01
Post proceedings of Joint Conference INDS 2011 and ISTET 2011. Recent advances in nonlinear Dynamics and Synchronization as well as in Theoretical Electrical Engineering. Written by leading experts in the field. This book contains a collection of recent advanced contributions in the field of nonlinear dynamics and synchronization, including selected applications in the area of theoretical electrical engineering. The present book is divided into twenty-one chapters grouped in five parts. The first part focuses on theoretical issues related to chaos and synchronization and their potential applications in mechanics, transportation, communication and security. The second part handles dynamic systems modelling and simulation with special applications to real physical systems and phenomena. The third part discusses some fundamentals of electromagnetics (EM) and addresses the modelling and simulation in some real physical electromagnetic scenarios. The fourth part mainly addresses stability concerns. Finally, the last part assembles some sample applications in the area of optimization, data mining, pattern recognition and image processing.
A Review of the Nonlinear Dynamics of Intraseasonal Oscillations
Institute of Scientific and Technical Information of China (English)
ZHAO Qiang; CHEN Jian-Zhou
2011-01-01
In recent years, significant progress has been made regarding theories of intraseasonal oscillations （ISOs） （also known as the Madden-Julian oscillation （MJO） in the tropics）. This short review introduces the latest advances in ISO theories with an emphasis particularly on theoretical paradigms involving nonlinear dynamics in the following aspects： （1） the basic ideas and limitations of the previous and current theories and hypotheses regarding the MJO, （2） the new multi-scale theory of the MJO based on the intraseasonal planetary equatorial synoptic dynamics （IPESD） framework, and （3） nonlinear dynamics of ISOs in the extratropics based on the resonant triads of Rossby-Haurwitz waves.
Dynamic nonlinear thermal optical effects in coupled ring resonators
Directory of Open Access Journals (Sweden)
Chenguang Huang
2012-09-01
Full Text Available We investigate the dynamic nonlinear thermal optical effects in a photonic system of two coupled ring resonators. A bus waveguide is used to couple light in and out of one of the coupled resonators. Based on the coupling from the bus to the resonator, the coupling between the resonators and the intrinsic loss of each individual resonator, the system transmission spectrum can be classified by three different categories: coupled-resonator-induced absorption, coupled-resonator-induced transparency and over coupled resonance splitting. Dynamic thermal optical effects due to linear absorption have been analyzed for each category as a function of the input power. The heat power in each resonator determines the thermal dynamics in this coupled resonator system. Multiple “shark fins” and power competition between resonators can be foreseen. Also, the nonlinear absorption induced thermal effects have been discussed.
Convergence of Chahine's nonlinear relaxation inversion method used for limb viewing remote sensing
Chu, W. P.
1985-01-01
The application of Chahine's (1970) inversion technique to remote sensing problems utilizing the limb viewing geometry is discussed. The problem considered here involves occultation-type measurements and limb radiance-type measurements from either spacecraft or balloon platforms. The kernel matrix of the inversion problem is either an upper or lower triangular matrix. It is demonstrated that the Chahine inversion technique always converges, provided the diagonal elements of the kernel matrix are nonzero.
Falcon, N.
2017-07-01
At cosmic scales the dynamics of the Universe are almost exclusively prescribed by the force of gravity; however the assumption of the law of gravitation, depending on the inverse of the distance, leads to the known problems of the rotation curves of galaxies and missing mass (dark matter). The problem of the coupling of gravity to changes in scale and deviations from the law of the inverse square is an old problem (Laplace, 1805; Seeliger 1898), which has motivated alternatives to Newtonian dynamics compatible with observations. The present paper postulates a modified Newtonian dynamics by adding an inverse Yukawa potential: U(r)≡U0(M)(r-r0)e-α/r is the the potential per unit mass (in N/kg) as a function of the barionic mass that causes the field, r0 is of the order of 50h-1 Mpc and alpha is a coupling constant of the order of 2.5 h-1 Mpc. This potential is zero within the solar system, slightly attractive at interstellar distances, very attractive in galactic range and repulsive at cosmic scales. Its origin is the barionic matter, it allows to include the Milgrow MoND theory to explain the rotation curves, it is compatible with the experiments Eovos type, and allows to deduce the law of Hubble to cosmic scales, in the form H0=100h km/s Mpc≍U0(M)/c, where U0(M)≍ 4pi×6.67 10-11m/s2, is obtained from the Laplace's equation, assuming that the gravitational force is the law of the inverse of the square plus a non-linear term type Yukawa inverse. It is concluded that the modification of the law of gravity with nonlinear terms, allows to model the dynamics of the Universe on a large scale and include non-locality without dark matter. (See Falcon et al. 2014, International Journal of Astronomy and Astrophysics, 4, 551-559).
Dynamics of optical rogue waves in inhomogeneous nonlinear waveguides
Institute of Scientific and Technical Information of China (English)
Zhang Jie-Fang; Jin Mei-Zhen; He Ji-Da; Lou Ji-Hui; Dai Chao-Qing
2013-01-01
We propose a unified theory to construct exact rogue wave solutions of the (2+1)-dimensional nonlinear Schr(o)dinger equation with varying coefficients.And then the dynamics of the first-and the second-order optical rogues are investigated.Finally,the controllability of the optical rogue propagating in inhomogeneous nonlinear waveguides is discussed.By properly choosing the distributed coefficients,we demonstrate analytically that rogue waves can be restrained or even be annihilated,or emerge periodically and sustain forever.We also figure out the center-of-mass motion of the rogue waves.
Dynamic magnetic hysteresis and nonlinear susceptibility of antiferromagnetic nanoparticles
Kalmykov, Yuri P.; Ouari, Bachir; Titov, Serguey V.
2016-08-01
The nonlinear ac stationary response of antiferromagnetic nanoparticles subjected to both external ac and dc fields of arbitrary strength and orientation is investigated using Brown's continuous diffusion model. The nonlinear complex susceptibility and dynamic magnetic hysteresis (DMH) loops of an individual antiferromagnetic nanoparticle are evaluated and compared with the linear regime for extensive ranges of the anisotropy, the ac and dc magnetic fields, damping, and the specific antiferromagnetic parameter. It is shown that the shape and area of the DMH loops of antiferromagnetic particles are substantially altered by applying a dc field that permits tuning of the specific magnetic power loss in the nanoparticles.
Nonlinear Boundary Dynamics and Chiral Symmetry in Holographic QCD
Albrecht, Dylan; Wilcox, Ronald J
2011-01-01
In the hard-wall model of holographic QCD we find that nonlinear boundary dynamics are required in order to maintain the correct pattern of explicit and spontaneous chiral symmetry breaking beyond leading order in the pion fields. With the help of a field redefinition, we demonstrate that the requisite nonlinear boundary conditions are consistent with the Sturm-Liouville structure required for the Kaluza-Klein decomposition of bulk fields. Observables insensitive to the chiral limit receive only small corrections in the improved description, and classical calculations in the hard-wall model remain surprisingly accurate.
Stress-enhanced Gelation: A Dynamic Nonlinearity of Elasticity
Yao, Norman Y.; Broedersz, Chase P.; Depken, Martin; Becker, Daniel J.; Pollak, Martin R.; MacKintosh, Frederick C.; Weitz, David A.
2013-01-01
A hallmark of biopolymer networks is their sensitivity to stress, reflected by pronounced nonlinear elastic stiffening. Here, we demonstrate a distinct dynamical nonlinearity in biopolymer networks consisting of F-actin cross-linked by α-actinin-4. Applied stress delays the onset of relaxation and flow, markedly enhancing gelation and extending the regime of solid-like behavior to much lower frequencies. We show that this macroscopic network response can be accounted for at the single molecule level by the increased binding affinity of the cross-linker under load, characteristic of catch-bond-like behavior. PMID:23383843
Nonlinear dynamics of electromagnetic pulses in cold relativistic plasmas
Energy Technology Data Exchange (ETDEWEB)
Bonatto, A.; Pakter, R.; Rizzato, F.B. [Universidade Federal do Rio Grande do Sul, Instituto de Fisica, Rio Grande do Sul (Brazil)
2004-07-01
The propagation of intense electromagnetic pulses in plasmas is a subject of current interest particularly for particle acceleration and laser fusion.In the present analysis we study the self consistent propagation of nonlinear electromagnetic pulses in a one dimensional relativistic electron-ion plasma, from the perspective of nonlinear dynamics. We show how a series of Hamiltonian bifurcations give rise to the electric fields which are of relevance in the subject of particle acceleration. Connections between these bifurcated solutions and results of earlier analysis are made. (authors)
Building better oscillators using nonlinear dynamics and pattern formation
Indian Academy of Sciences (India)
M C Cross; Eyal Kenig; John-Mark A Allen
2015-03-01
Frequency and time references play an essential role in modern technology and in living systems. The precision of self-sustained oscillations is limited by the effects of noise, which becomes evermore important as the sizes of the devices become smaller. In this paper, we review our recent theoretical results on using nonlinear dynamics and pattern formation to reduce the effects of noise and improve the frequency precision of oscillators, with particular reference to ongoing experiments on oscillators based on nanomechanical resonators. We discuss using resonator nonlinearity, novel oscillator architectures and the synchronization of arrays of oscillators, to improve the frequency precision.
NONLINEAR DYNAMICS OF A CRACKED ROTOR IN A MANEUVERING AIRCRAFT
Institute of Scientific and Technical Information of China (English)
LIN Fu-sheng 林富生; MENG Guang 孟光; Eric Hahn
2004-01-01
The nonlinear dynamics of a cracked rotor system in an aircraft maneuvering with constant velocity or acceleration was investigated. The influence of the aircraft climbing angle on the cracked rotor system response is of particular interest and the results show that the climbing angle can markedly affect the parameter range for bifurcation, for quasi-periodic response and for chaotic response as well as for system stability. Aircraft acceleration is also shown to significantly affect the nonlinear behavior of the cracked rotor system, illustrating the possibility for on-line rotor crack fault diagnosis.
Nonlinear analysis and dynamic structure in the energy market
Aghababa, Hajar
This research assesses the dynamic structure of the energy sector of the aggregate economy in the context of nonlinear mechanisms. Earlier studies have focused mainly on the price of the energy products when detecting nonlinearities in time series data of the energy market, and there is little mention of the production side of the market. Moreover, there is a lack of exploration about the implication of high dimensionality and time aggregation when analyzing the market's fundamentals. This research will address these gaps by including the quantity side of the market in addition to the price and by systematically incorporating various frequencies for sample sizes in three essays. The goal of this research is to provide an inclusive and exhaustive examination of the dynamics in the energy markets. The first essay begins with the application of statistical techniques, and it incorporates the most well-known univariate tests for nonlinearity with distinct power functions over alternatives and tests different null hypotheses. It utilizes the daily spot price observations on five major products in the energy market. The results suggest that the time series daily spot prices of the energy products are highly nonlinear in their nature. They demonstrate apparent evidence of general nonlinear serial dependence in each individual series, as well as nonlinearity in the first, second, and third moments of the series. The second essay examines the underlying mechanism of crude oil production and identifies the nonlinear structure of the production market by utilizing various monthly time series observations of crude oil production: the U.S. field, Organization of the Petroleum Exporting Countries (OPEC), non-OPEC, and the world production of crude oil. The finding implies that the time series data of the U.S. field, OPEC, and the world production of crude oil exhibit deep nonlinearity in their structure and are generated by nonlinear mechanisms. However, the dynamics of the non
Nonlinear dynamics of rotating shallow water methods and advances
Zeitlin, Vladimir
2007-01-01
The rotating shallow water (RSW) model is of wide use as a conceptual tool in geophysical fluid dynamics (GFD), because, in spite of its simplicity, it contains all essential ingredients of atmosphere and ocean dynamics at the synoptic scale, especially in its two- (or multi-) layer version. The book describes recent advances in understanding (in the framework of RSW and related models) of some fundamental GFD problems, such as existence of the slow manifold, dynamical splitting of fast (inertia-gravity waves) and slow (vortices, Rossby waves) motions, nonlinear geostrophic adjustment and wa
Adaptive steady-state stabilization for nonlinear dynamical systems
Braun, David J.
2008-07-01
By means of LaSalle’s invariance principle, we propose an adaptive controller with the aim of stabilizing an unstable steady state for a wide class of nonlinear dynamical systems. The control technique does not require analytical knowledge of the system dynamics and operates without any explicit knowledge of the desired steady-state position. The control input is achieved using only system states with no computer analysis of the dynamics. The proposed strategy is tested on Lorentz, van der Pol, and pendulum equations.
Nonlinear dynamics of a flexible portal frame under support excitation
de Paula, Aline Souza; Balthazar, José Manoel; Felix, Jorge Luis Palacios
2012-11-01
This paper presents a nonlinear dynamic analysis of a flexible portal frame subjected to support excitation, which is provided by an electro-dynamical shaker. The problem is reduced to a mathematical model of four degrees of freedom and the equations of motion are derived via Lagrangian formulation. The main goal of this study is to investigate the dynamic interactions between a flexible portal frame and a non-ideal support excitation. The numerical analysis shows a complex behavior of the system, which can be observed by phase spaces, Poincaŕ sections and bifurcation diagrams..
Global dynamics for steep nonlinearities in two dimensions
Gedeon, Tomáš; Harker, Shaun; Kokubu, Hiroshi; Mischaikow, Konstantin; Oka, Hiroe
2017-01-01
This paper discusses a novel approach to obtaining mathematically rigorous results on the global dynamics of ordinary differential equations. We study switching models of regulatory networks. To each switching network we associate a Morse graph, a computable object that describes a Morse decomposition of the dynamics. In this paper we show that all smooth perturbations of the switching system share the same Morse graph and we compute explicit bounds on the size of the allowable perturbation. This shows that computationally tractable switching systems can be used to characterize dynamics of smooth systems with steep nonlinearities.
Chew, Huck Beng
2013-01-01
Determining the tractions along a surface or interface from measurement data in the far-fields of nonlinear materials is a challenging inverse problem which has significant engineering and nanoscience applications. Previously, a field projection method was established to identify the crack-tip cohesive zone constitutive relations in an isotropic elastic solid (Hong and Kim, 2003. J. Mech. Phys. Solids 51, 1267). In this paper, the field projection method is further generalized to extracting the tractions along interfaces bounded by nonlinear materials, both with and without pre-existing cracks. The new formulation is based on Maxwell-Betti's reciprocal theorem with a reciprocity gap associated with nonlinear materials. We express the unknown normal and shear tractions along the interface in terms of the Fourier series, and use specially constructed analytical auxiliary fields in the reciprocal theorem to extract the unknown Fourier coefficients from far-field data; the reciprocity gap in the formulation is iteratively determined with a set of numerical algorithms. Our detailed numerical experiments demonstrate that this nonlinear field projection method (NFPM) is well-suited for extracting the interfacial tractions from the far-field data of any nonlinear elastic or elasto-plastic material with known constitutive laws. Applications of the NFPM to experiments and atomistic simulations are discussed.
Dynamic structural correlation via nonlinear programming techniques
Ting, T.; Ojalvo, I. U.
1988-01-01
A solution to the correlation between structural dynamic test results and finite element analyses of the same components is presented in this paper. Basically, the method can be categorized as a Levenberg-Marquardt type Gauss-Newton method which requires only the differences between FE modal analyses and test results and their first derivatives with respect to preassigned design variables. With proper variable normalization and equation scaling, the method has been made numerically better-conditioned and the inclusion of the Levenberg-Marquardt technique overcomes any remaining difficulty encountered in inverting singular or near-singular matrices. An important feature is that each iteration requires only one function evaluation along with the associated design sensitivity analysis and so the procedure is computationally efficient.
Applications of chaos and nonlinear dynamics in engineering - Vol 1
Rondoni, Lamberto; Banerjee, Santo
2011-01-01
Chaos and nonlinear dynamics initially developed as a new emergent field with its foundation in physics and applied mathematics. The highly generic, interdisciplinary quality of the insights gained in the last few decades has spawned myriad applications in almost all branches of science and technology—and even well beyond. Wherever quantitative modeling and analysis of complex, nonlinear phenomena is required, chaos theory and its methods can play a key role. This volume concentrates on reviewing the most relevant contemporary applications of chaotic nonlinear systems as they apply to the various cutting-edge branches of engineering. The book covers the theory as applied to robotics, electronic and communication engineering (for example chaos synchronization and cryptography) as well as to civil and mechanical engineering, where its use in damage monitoring and control is explored). Featuring contributions from active and leading research groups, this collection is ideal both as a reference and as a ‘r...
Applications of chaos and nonlinear dynamics in science and engineering
Rondoni, Lamberto; Mitra, Mala
Chaos and nonlinear dynamics initially developed as a new emergent field with its foundation in physics and applied mathematics. The highly generic, interdisciplinary quality of the insights gained in the last few decades has spawned myriad applications in almost all branches of science and technology—and even well beyond. Wherever the quantitative modeling and analysis of complex, nonlinear phenomena are required, chaos theory and its methods can play a key role. This second volume concentrates on reviewing further relevant, contemporary applications of chaotic nonlinear systems as they apply to the various cutting-edge branches of engineering. This encompasses, but is not limited to, topics such as the spread of epidemics; electronic circuits; chaos control in mechanical devices; secure communication; and digital watermarking. Featuring contributions from active and leading research groups, this collection is ideal both as a reference work and as a ‘recipe book’ full of tried and tested, successf...
A Girsanov particle filter in nonlinear engineering dynamics
Energy Technology Data Exchange (ETDEWEB)
Saha, Nilanjan [Structures Lab, Department of Civil Engineering, Indian Institute of Science, Bangalore-560012 (India); Roy, D. [Structures Lab, Department of Civil Engineering, Indian Institute of Science, Bangalore-560012 (India)], E-mail: royd@civil.iisc.ernet.in
2009-02-02
In this Letter, we propose a novel variant of the particle filter (PF) for state and parameter estimations of nonlinear engineering dynamical systems, modelled through stochastic differential equations (SDEs). The aim is to address a possible loss of accuracy in the estimates due to the discretization errors, which are inevitable during numerical integration of the SDEs. In particular, we adopt an explicit local linearization of the governing nonlinear SDEs and the resulting linearization errors in the estimates are corrected using Girsanov transformation of measures. Indeed, the linearization scheme via transformation of measures provides a weak framework for computing moments and this fits in well with any stochastic filtering strategy wherein estimates are themselves statistical moments. We presently implement the strategy using a bootstrap PF and numerically illustrate its performance for state and parameter estimations of the Duffing oscillator with linear and nonlinear measurement equations.
Temporal nonlinear beam dynamics in infiltrated photonic crystal fibers
DEFF Research Database (Denmark)
Bennet, Francis; Rosberg, Christian Romer; Neshev, Dragomir N.
of nonlinear beam reshaping occurring on a short time scale before the establishment of a steady state regime. In experiment, a 532nm laser beam can be injected into a single hole of an infiltrated PCF cladding structure, and the temporal dynamics of the nonlinear response is measured by monitoring......Liquid-infiltrated photonic crystal fibers (PCFs) offer a new way of studying light propagation in periodic and discrete systems. A wide range of available fiber structures combined with the ease of infiltration opens up a range of novel experimental opportunities for optical detection and bio......-sensing as well as active devices for all-optical switching at low (mW) laser powers. Commercially available PCFs infiltrated with liquids also provide a versatile and compact tool for exploration of the fundamentals of nonlinear beam propagation in periodic photonic structures. To explore the full scientific...
Nonlinear systems techniques for dynamical analysis and control
Lefeber, Erjen; Arteaga, Ines
2017-01-01
This treatment of modern topics related to the control of nonlinear systems is a collection of contributions celebrating the work of Professor Henk Nijmeijer and honoring his 60th birthday. It addresses several topics that have been the core of Professor Nijmeijer’s work, namely: the control of nonlinear systems, geometric control theory, synchronization, coordinated control, convergent systems and the control of underactuated systems. The book presents recent advances in these areas, contributed by leading international researchers in systems and control. In addition to the theoretical questions treated in the text, particular attention is paid to a number of applications including (mobile) robotics, marine vehicles, neural dynamics and mechanical systems generally. This volume provides a broad picture of the analysis and control of nonlinear systems for scientists and engineers with an interest in the interdisciplinary field of systems and control theory. The reader will benefit from the expert participan...
Nonlinear dynamics of nanoelectromechanical cantilevers based on nanowire piezoresistive detection
Directory of Open Access Journals (Sweden)
Baguet S.
2012-07-01
Full Text Available The nonlinear dynamics of in-plane nanoelectromechanical cantilevers based on silicon nanowire piezoresistive detection is investigated using a comprehensive analytical model that remains valid up to large displacements in the case of electrostatic actuation. This multiphysics model takes into account geometric, inertial and electrostatic nonlinearities as well as the fringing field effects which are significant for thin resonators. The bistability as well as multistability limits are considered in order to provide close-form expressions of the critical amplitudes. Third order nonlinearity cancellation is analytically inspected and set via an optimal DC drive voltage which permits the actuation of the NEMS beyond its critical amplitude. It may result on a large enhancement of the sensor performances by driving optimally the nanocantilever at very large amplitude, while suppressing the hysteresis.
Non-linear dynamic response of a wind turbine blade
Chopra, I.; Dugundji, J.
1979-01-01
The paper outlines the nonlinear dynamic analysis of an isolated three-degree flap-lag-feather wind turbine blade under a gravity field and with shear flow. Lagrangian equations are used to derive the nonlinear equations of motion of blade for arbitrarily large angular deflections. The limit cycle analysis for forced oscillations and the determination of the principal parametric resonance of the blade due to periodic forces from the gravity field and wind shear are performed using the harmonic balance method. Results are obtained first for a two-degree flap-lag blade, then the effect of the third degree of freedom (feather) is studied. The self-excited flutter solutions are obtained for a uniform wind and with gravity forces neglected. The effects of several parameters on the blade stability are examined, including coning angle, structural damping, Lock number, and feather frequency. The limit cycle flutter solution of a typical configuration shows a substantial nonlinear softening spring behavior.
Design of advanced materials for linear and nonlinear dynamics
DEFF Research Database (Denmark)
Frandsen, Niels Morten Marslev
The primary catalyst of this PhD project has been an ambition to design advanced materials and structural systems including, and possibly even exploiting, nonlinear phenomena such as nonlinear modal interaction leading to energy conversion between modes. An important prerequisite for efficient...... design is accurate and somewhat simple analysis tools, as well as a fundamental understanding of the physical phenomena responsible for the relevant effects. The emphasis of this work lies primarily in the investigation of various advanced material models, developing the necessary analytical tools...... to reveal the fundamental dynamic characteristics and thus the relevant design parameters.The thesis is built around the characterization of two one-dimensional, periodic material systems. The first is a nonlinear mass-spring chain with periodically varying material properties, representing a simple...
Nonlinear Dynamical Modeling and Forecast of ENSO Variability
Feigin, Alexander; Mukhin, Dmitry; Gavrilov, Andrey; Seleznev, Aleksey; Loskutov, Evgeny
2017-04-01
New methodology of empirical modeling and forecast of nonlinear dynamical system variability [1] is applied to study of ENSO climate system. The methodology is based on two approaches: (i) nonlinear decomposition of data [2], that provides low-dimensional embedding for further modeling, and (ii) construction of empirical model in the form of low dimensional random dynamical ("stochastic") system [3]. Three monthly data sets are used for ENSO modeling and forecast: global sea surface temperature anomalies, troposphere zonal wind speed, and thermocline depth; all data sets are limited by 30 S, 30 N and have horizontal resolution 10x10 . We compare results of optimal data decomposition as well as prognostic skill of the constructed models for different combinations of involved data sets. We also present comparative analysis of ENSO indices forecasts fulfilled by our models and by IRI/CPC ENSO Predictions Plume. [1] A. Gavrilov, D. Mukhin, E. Loskutov, A. Feigin, 2016: Construction of Optimally Reduced Empirical Model by Spatially Distributed Climate Data. 2016 AGU Fall Meeting, Abstract NG31A-1824. [2] D. Mukhin, A. Gavrilov, E. Loskutov , A.Feigin, J.Kurths, 2015: Principal nonlinear dynamical modes of climate variability, Scientific Reports, rep. 5, 15510; doi: 10.1038/srep15510. [3] Ya. Molkov, D. Mukhin, E. Loskutov, A. Feigin, 2012: Random dynamical models from time series. Phys. Rev. E, Vol. 85, n.3.
A data driven nonlinear stochastic model for blood glucose dynamics.
Zhang, Yan; Holt, Tim A; Khovanova, Natalia
2016-03-01
The development of adequate mathematical models for blood glucose dynamics may improve early diagnosis and control of diabetes mellitus (DM). We have developed a stochastic nonlinear second order differential equation to describe the response of blood glucose concentration to food intake using continuous glucose monitoring (CGM) data. A variational Bayesian learning scheme was applied to define the number and values of the system's parameters by iterative optimisation of free energy. The model has the minimal order and number of parameters to successfully describe blood glucose dynamics in people with and without DM. The model accounts for the nonlinearity and stochasticity of the underlying glucose-insulin dynamic process. Being data-driven, it takes full advantage of available CGM data and, at the same time, reflects the intrinsic characteristics of the glucose-insulin system without detailed knowledge of the physiological mechanisms. We have shown that the dynamics of some postprandial blood glucose excursions can be described by a reduced (linear) model, previously seen in the literature. A comprehensive analysis demonstrates that deterministic system parameters belong to different ranges for diabetes and controls. Implications for clinical practice are discussed. This is the first study introducing a continuous data-driven nonlinear stochastic model capable of describing both DM and non-DM profiles.
Ranjan, Rajiv; Mallick, Ashis; Prasad, Dilip K.
2016-07-01
The performance characteristics and temperature field of conducting-convecting-radiating annular fin are investigated. The nonlinear variation of thermal conductivity, power law dependency of heat transfer coefficient, linear variation of surface emissivity, and heat generation with the temperature are considered in the analysis. A semi-analytical approach, homotopy perturbation method is employed to solve the nonlinear differential equation of heat transfer. The analysis is presented in non-dimensional form, and the effect of various non-dimensional thermal parameters such as conduction-convection parameter, conduction-radiation parameter, linear and nonlinear variable thermal conductivity parameter, emissivity parameter, heat generation number and variable heat generation parameter are studied. For the correctness of the present analytical solution, the results are compared with the results available in the literature. In addition to forward problem, an inverse approach namely differential evolution method is employed for estimating the unknown thermal parameters for a given temperature field. The temperature fields are reconstructed using the inverse parameters and found to be in good agreement with the forward solution.
Ranjan, Rajiv; Mallick, Ashis; Prasad, Dilip K.
2017-03-01
The performance characteristics and temperature field of conducting-convecting-radiating annular fin are investigated. The nonlinear variation of thermal conductivity, power law dependency of heat transfer coefficient, linear variation of surface emissivity, and heat generation with the temperature are considered in the analysis. A semi-analytical approach, homotopy perturbation method is employed to solve the nonlinear differential equation of heat transfer. The analysis is presented in non-dimensional form, and the effect of various non-dimensional thermal parameters such as conduction-convection parameter, conduction-radiation parameter, linear and nonlinear variable thermal conductivity parameter, emissivity parameter, heat generation number and variable heat generation parameter are studied. For the correctness of the present analytical solution, the results are compared with the results available in the literature. In addition to forward problem, an inverse approach namely differential evolution method is employed for estimating the unknown thermal parameters for a given temperature field. The temperature fields are reconstructed using the inverse parameters and found to be in good agreement with the forward solution.
Xu, Wenjun; Chen, Jie; Lau, Henry Y K; Ren, Hongliang
2017-09-01
Accurate motion control of flexible surgical manipulators is crucial in tissue manipulation tasks. The tendon-driven serpentine manipulator (TSM) is one of the most widely adopted flexible mechanisms in minimally invasive surgery because of its enhanced maneuverability in torturous environments. TSM, however, exhibits high nonlinearities and conventional analytical kinematics model is insufficient to achieve high accuracy. To account for the system nonlinearities, we applied a data driven approach to encode the system inverse kinematics. Three regression methods: extreme learning machine (ELM), Gaussian mixture regression (GMR) and K-nearest neighbors regression (KNNR) were implemented to learn a nonlinear mapping from the robot 3D position states to the control inputs. The performance of the three algorithms was evaluated both in simulation and physical trajectory tracking experiments. KNNR performed the best in the tracking experiments, with the lowest RMSE of 2.1275 mm. The proposed inverse kinematics learning methods provide an alternative and efficient way to accurately model the tendon driven flexible manipulator. Copyright © 2016 John Wiley & Sons, Ltd.
Flight Dynamic Simulation with Nonlinear Aeroelastic Interaction using the ROM-ROM Procedure Project
National Aeronautics and Space Administration — ZONA Technology, Inc. proposes to develop an integrated flight dynamics simulation capability with nonlinear aeroelastic interactions by combining a flight dynamics...
Nonlinear dynamic behaviors of ball bearing rotor system
Institute of Scientific and Technical Information of China (English)
WANG Li-qin; CUI Li; ZHENG De-zhi; GU Le
2009-01-01
Nonlinear forces and moments caused by ball bearing were calculated based on relationship of displacement and deflection and quasi-dynamic model of bearing. Five-DOF dynamic equations of rotor supported by ball bearings were estimated. The Newmark-β method and Newton-Laphson method were used to solve the equations. The dynamic characteristics of rotor system were studied through the time response, the phase portrait, the Poincar? maps and the bifurcation diagrams. The results show that the system goes through the quasiperiodic bifurcation route to chaos as rotate speed increases and there are several quasi-periodic regions and chaos regions. The amplitude decreases and the dynamic behaviors change as the axial load of ball bearing increases; the initial contact angle of ball bearing affects dynamic behaviors of the system obviously. The system can avoid non-periodic vibration by choosing structural parameters and operating parameters reasonably.
On time-space of nonlinear phenomena with Gompertzian dynamics.
Waliszewski, Przemyslaw; Konarski, Jerzy
2005-04-01
This paper describes a universal relationship between time and space for a nonlinear process with Gompertzian dynamics, such as growth. Gompertzian dynamics implicates a coupling between time and space. Those two categories are related to each other through a linear function of their logarithms. Moreover, we demonstrate that the spatial fractal dimension is a function of both scalar time and the temporal fractal dimension. The Gompertz function reflects the equilibrium of regular states, that is, states with dynamics that are predictable for any time-point (e.g., sinusoidal glycolytic oscillations) and chaotic states, that is, states with dynamics that are unpredictable in time, but are characterized by certain regularities (e.g., the existence of strange attractor for any biochemical reaction). We conclude that both this equilibrium and volume of the available complementary Euclidean space determine temporal and spatial expansion of a process with Gompertzian dynamics.
Effects of noise on the phase dynamics of nonlinear oscillators
Daffertshofer, A.
1998-07-01
Various properties of human rhythmic movements have been successfully modeled using nonlinear oscillators. However, despite some extensions towards stochastical differential equations, these models do not comprise different statistical features that can be explained by nondynamical statistics. For instance, one observes certain lag one serial correlation functions for consecutive periods during periodic motion. This work aims at an extension of dynamical descriptions in terms of stochastically forced nonlinear oscillators such as ξ¨+ω20ξ=n(ξ,ξ˙)+q(ξ,ξ˙)Ψ(t), where the nonlinear function n(ξ,ξ˙) generates a limit cycle and Ψ(t) denotes colored noise that is multiplied via q(ξ,ξ˙). Nonlinear self-excited systems have been frequently investigated, particularly emphasizing stability properties and amplitude evolution. Thus, one can focus on the effects of noise on the frequency or phase dynamics that can be analyzed by use of time-dependent Fokker-Planck equations. It can be shown that noise multiplied via polynoms of arbitrary finite order cannot generate the desired period correlation but predominantly results in phase diffusion. The system is extended in terms of forced oscillators in order to find a minimal model producing the required error correction.
Nonlinear dynamics in eccentric Taylor-Couette-Poiseuille flow
Pier, Benoît; Caulfield, C. P.
2015-11-01
The flow in the gap between two parallel but eccentric cylinders and driven by an axial pressure gradient and inner cylinder rotation is characterized by two geometrical parameters (radius ratio and eccentricity) and two dynamic parameters (axial and azimuthal Reynolds numbers). Such a theoretical configuration is a model for the flow between drill string and wellbore in the hydrocarbon drilling industry. The linear convective and absolute instability properties have been systematically derived in a recent study [Leclercq, Pier & Scott, J. Fluid Mech. 2013 and 2014]. Here we address the nonlinear dynamics resulting after saturation of exponentially growing small-amplitude perturbations. By using direct numerical simulations, a range of finite-amplitude states are found and characterized: nonlinear traveling waves (an eccentric counterpart of Taylor vortices, associated with constant hydrodynamic loading on the inner cylinder), modulated nonlinear waves (with time-periodic torque and flow rate) and more irregular states. In the nonlinear regime, the hydrodynamic forces are found to depart significantly from those prevailing for the base flow, even in situations of weak linear instability.
Nonlinear Alfvén wave dynamics in plasmas
Energy Technology Data Exchange (ETDEWEB)
Sarkar, Anwesa; Chakrabarti, Nikhil [Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata 700 064 (India); Schamel, Hans [Theoretical Physics, University of Bayreuth, D-95440 Bayreuth (Germany)
2015-07-15
Nonlinear Alfvén wave dynamics is presented using Lagrangian fluid approach in a compressible collisional magnetized plasma. In the framework of two fluid dynamics, finite electron inertia is shown to serve as a dispersive effect acting against the convective nonlinearity. In a moving frame, the Alfvén wave can, therefore, form an arbitrarily strong amplitude solitary wave structure due to the balance between nonlinearity and dispersion. Weak amplitude Alfvén waves are shown to be governed by a modified KdV equation, which extends for finite dissipation to a mKdV-Burgers equation. These equations have well known solutions. Next, we have analyzed the fourth order nonlinear Alfvén wave system of equations both numerically and by approximation method. The results indicate a collapse of the density and magnetic field irrespective of the presence of dispersion. The wave magnetic field, however, appears to be less singular showing collapse only when the dispersive effects are negligible. These results may contribute to our understanding of the generation of strongly localized magnetic fields (and currents) in plasmas and are expected to be of special importance in the astrophysical context of magnetic star formation.
The coupled nonlinear dynamics of a lift system
Crespo, Rafael Sánchez; Kaczmarczyk, Stefan; Picton, Phil; Su, Huijuan
2014-12-01
Coupled lateral and longitudinal vibrations of suspension and compensating ropes in a high-rise lift system are often induced by the building motions due to wind or seismic excitations. When the frequencies of the building become near the natural frequencies of the ropes, large resonance motions of the system may result. This leads to adverse coupled dynamic phenomena involving nonplanar motions of the ropes, impact loads between the ropes and the shaft walls, as well as vertical vibrations of the car, counterweight and compensating sheave. Such an adverse dynamic behaviour of the system endangers the safety of the installation. This paper presents two mathematical models describing the nonlinear responses of a suspension/ compensating rope system coupled with the elevator car / compensating sheave motions. The models accommodate the nonlinear couplings between the lateral and longitudinal modes, with and without longitudinal inertia of the ropes. The partial differential nonlinear equations of motion are derived using Hamilton Principle. Then, the Galerkin method is used to discretise the equations of motion and to develop a nonlinear ordinary differential equation model. Approximate numerical solutions are determined and the behaviour of the system is analysed.
The coupled nonlinear dynamics of a lift system
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.
APPLICATION OF MODIFIED CONVERSION METHOD TO A NONLINEAR DYNAMICAL SYSTEM
Directory of Open Access Journals (Sweden)
G.I. Melnikov
2015-01-01
Full Text Available The paper deals with a mathematical model of dynamical system with single degree of freedom, presented in the form of ordinary differential equations with nonlinear parts in the form of polynomials with constant and periodic coefficients. A modified method for the study of self-oscillations of nonlinear mechanical systems is presented. A refined method of transformation and integration of the equation, based on Poincare-Dulac normalization method has been developed. Refinement of the method lies in consideration of higher order nonlinear terms by Chebyshev economization technique that improves the accuracy of the calculations. Approximation of the higher order remainder terms by homogeneous forms of lower orders is performed; in the present case, it is done by cubic forms. An application of the modified method for the Van-der-Pol equation is considered as an example; the expressions for the amplitude and the phase of the oscillations are obtained in an analytical form. The comparison of the solution of the Van-der-Pol equation obtained by the developed method and the exact solution is performed. The error of the solution obtained by the modified method equals to 1%, which shows applicability of the developed method for analysis of self-oscillations of nonlinear dynamic systems with constant and periodic parameters.
Nonlinear Alfvén wave dynamics in plasmas
Sarkar, Anwesa; Chakrabarti, Nikhil; Schamel, Hans
2015-07-01
Nonlinear Alfvén wave dynamics is presented using Lagrangian fluid approach in a compressible collisional magnetized plasma. In the framework of two fluid dynamics, finite electron inertia is shown to serve as a dispersive effect acting against the convective nonlinearity. In a moving frame, the Alfvén wave can, therefore, form an arbitrarily strong amplitude solitary wave structure due to the balance between nonlinearity and dispersion. Weak amplitude Alfvén waves are shown to be governed by a modified KdV equation, which extends for finite dissipation to a mKdV-Burgers equation. These equations have well known solutions. Next, we have analyzed the fourth order nonlinear Alfvén wave system of equations both numerically and by approximation method. The results indicate a collapse of the density and magnetic field irrespective of the presence of dispersion. The wave magnetic field, however, appears to be less singular showing collapse only when the dispersive effects are negligible. These results may contribute to our understanding of the generation of strongly localized magnetic fields (and currents) in plasmas and are expected to be of special importance in the astrophysical context of magnetic star formation.
Data based identification and prediction of nonlinear and complex dynamical systems
Wang, Wen-Xu; Lai, Ying-Cheng; Grebogi, Celso
2016-07-01
The problem of reconstructing nonlinear and complex dynamical systems from measured data or time series is central to many scientific disciplines including physical, biological, computer, and social sciences, as well as engineering and economics. The classic approach to phase-space reconstruction through the methodology of delay-coordinate embedding has been practiced for more than three decades, but the paradigm is effective mostly for low-dimensional dynamical systems. Often, the methodology yields only a topological correspondence of the original system. There are situations in various fields of science and engineering where the systems of interest are complex and high dimensional with many interacting components. A complex system typically exhibits a rich variety of collective dynamics, and it is of great interest to be able to detect, classify, understand, predict, and control the dynamics using data that are becoming increasingly accessible due to the advances of modern information technology. To accomplish these goals, especially prediction and control, an accurate reconstruction of the original system is required. Nonlinear and complex systems identification aims at inferring, from data, the mathematical equations that govern the dynamical evolution and the complex interaction patterns, or topology, among the various components of the system. With successful reconstruction of the system equations and the connecting topology, it may be possible to address challenging and significant problems such as identification of causal relations among the interacting components and detection of hidden nodes. The "inverse" problem thus presents a grand challenge, requiring new paradigms beyond the traditional delay-coordinate embedding methodology. The past fifteen years have witnessed rapid development of contemporary complex graph theory with broad applications in interdisciplinary science and engineering. The combination of graph, information, and nonlinear dynamical
Without bounds a scientific canvas of nonlinearity and complex dynamics
Ryazantsev, Yuri; Starov, Victor; Huang, Guo-Xiang; Chetverikov, Alexander; Arena, Paolo; Nepomnyashchy, Alex; Ferrus, Alberto; Morozov, Eugene
2013-01-01
Bringing together over fifty contributions on all aspects of nonlinear and complex dynamics, this impressive topical collection is both a scientific and personal tribute, on the occasion of his 70th birthday, by many outstanding colleagues in the broad fields of research pursued by Prof. Manuel G Velarde. The topics selected reflect the research areas covered by the famous Instituto Pluridisciplinar at the Universidad Complutense of Madrid, which he co-founded over two decades ago, and include: fluid physics and related nonlinear phenomena at interfaces and in other geometries, wetting and spreading dynamics, geophysical and astrophysical flows, and novel aspects of electronic transport in anharmonic lattices, as well as topics in neurodynamics and robotics.
Comparison Criteria for Nonlinear Functional Dynamic Equations of Higher Order
Directory of Open Access Journals (Sweden)
Taher S. Hassan
2016-01-01
Full Text Available We will consider the higher order functional dynamic equations with mixed nonlinearities of the form xnt+∑j=0Npjtϕγjxφjt=0, on an above-unbounded time scale T, where n≥2, xi(t≔ri(tϕαixi-1Δ(t, i=1,…,n-1, with x0=x, ϕβ(u≔uβsgnu, and α[i,j]≔αi⋯αj. The function φi:T→T is a rd-continuous function such that limt→∞φi(t=∞ for j=0,1,…,N. The results extend and improve some known results in the literature on higher order nonlinear dynamic equations.
A nonlinear dynamics for the scalar field in Randers spacetime
Silva, J. E. G.; Maluf, R. V.; Almeida, C. A. S.
2017-03-01
We investigate the properties of a real scalar field in the Finslerian Randers spacetime, where the local Lorentz violation is driven by a geometrical background vector. We propose a dynamics for the scalar field by a minimal coupling of the scalar field and the Finsler metric. The coupling is intrinsically defined on the Randers spacetime, and it leads to a non-canonical kinetic term for the scalar field. The nonlinear dynamics can be split into a linear and nonlinear regimes, which depend perturbatively on the even and odd powers of the Lorentz-violating parameter, respectively. We analyze the plane-waves solutions and the modified dispersion relations, and it turns out that the spectrum is free of tachyons up to second-order.
A nonlinear dynamics for the scalar field in Randers spacetime
Directory of Open Access Journals (Sweden)
J.E.G. Silva
2017-03-01
Full Text Available We investigate the properties of a real scalar field in the Finslerian Randers spacetime, where the local Lorentz violation is driven by a geometrical background vector. We propose a dynamics for the scalar field by a minimal coupling of the scalar field and the Finsler metric. The coupling is intrinsically defined on the Randers spacetime, and it leads to a non-canonical kinetic term for the scalar field. The nonlinear dynamics can be split into a linear and nonlinear regimes, which depend perturbatively on the even and odd powers of the Lorentz-violating parameter, respectively. We analyze the plane-waves solutions and the modified dispersion relations, and it turns out that the spectrum is free of tachyons up to second-order.
Genealogical tree of Russian schools on Nonlinear Dynamics
Prants, S V
2015-01-01
One of the most prominent feature of research in Russia and the former Soviet Union is so-called scientific schools. It is a collaboration of researchers with a common scientific background working, as a rule, together in a specific city or even at an institution. The genealogical tree of scientific schools on nonlinear dynamics in Russia and the former Soviet Union is grown. We use these terminology in a broad sense including theory of dynamical systems and chaos and its applications in nonlinear physics. In most cases we connect two persons if one was an advisor of the Doctoral thesis of another one. It is an analogue of the Candidate of Science thesis in Russia. If the person had no official advisor or we don't know exactly who was an advisor, we fix that person who was known to be an informal teacher and has influenced on him/her very much.
Nonlinear dynamical behavior of shallow cylindrical reticulated shells
Institute of Scientific and Technical Information of China (English)
WANG Xin-zhi; LIANG Cong-xing; HAN Ming-jun; YEH Kai-yuan; WANG Gang
2007-01-01
By using the method of quasi-shells , the nonlinear dynamic equations of three-dimensional single-layer shallow cylindrical reticulated shells with equilateral triangle cell are founded. By using the method of the separating variable function, the transverse displacement of the shallow cylindrical reticulated shells is given under the conditions of two edges simple support. The tensile force is solved out from the compatible equations, a nonlinear dynamic differential equation containing second and third order is derived by using the method of Galerkin. The stability near the equilibrium point is discussed by solving the Floquet exponent and the critical condition is obtained by using Melnikov function. The existence of the chaotic motion of the single-layer shallow cylinmapping.
Kostka, Filip; Gallovic, Frantisek
2017-04-01
We perform dynamic finite-extent source inversion to study the source processes of three earthquakes that occurred close to Amatrice and Norcia, Central Italy, in August-October 2016. The events had moment magnitudes of 6.1-6.5 and resulted in >300 fatalities. To that end, we utilize a modified version of dynamic inversion code by Twardzik et al. (2014). The direct problem is solved by 3D fourth-order staggered-grid finite difference method in a box assuming linear slip-weakening friction law on a planar fault (Madariaga et al., 1998). The optimal solution is sought using the Neighborhood Algorithm by Sambridge (1999). We invert displacement waveforms from the 20-30 nearest stations. The distribution and evolution of slip calculated from physical parameters (stress drop, frictional properties) obtained from the dynamic inversion are compared with results of kinematic inversions and discussed in terms of fault mechanics.
Inflationary Dynamics Reconstruction via Inverse-Scattering Theory
Mastache, Jorge; Kosowsky, Arthur
2016-01-01
The evolution of inflationary fluctuations can be recast as an inverse scattering problem. In this context, we employ the Gel'fand-Levitan method from inverse-scattering theory to reconstruct the evolution of both the inflaton field freeze-out horizon and the Hubble parameter during inflation. We demonstrate this reconstruction procedure numerically for a scenario of slow-roll inflation, as well as for a scenario which temporarily departs from slow-roll. The field freeze-out horizon is reconstructed from the accessible primordial scalar power spectrum alone, while the reconstruction of the Hubble parameter requires additional information from the tensor power spectrum. We briefly discuss the application of this technique to more realistic cases incorporating estimates of the primordial power spectra over limited ranges of scales and with specified uncertainties.
Effect of carbonation on the linear and nonlinear dynamic properties of cement-based materials
Eiras, Jesus N.; Kundu, Tribikram; Popovics, John S.; Monzó, José; Borrachero, María V.; Payá, Jordi
2016-01-01
Carbonation causes a physicochemical alteration of cement-based materials, leading to a decrease of porosity and an increase of material hardness and strength. However, carbonation will decrease the pH of the internal pore water solution, which may depassivate the internal reinforcing steel, giving rise to structural durability concerns. Therefore, the proper selection of materials informed by parameters sensitive to the carbonation process is crucial to ensure the durability of concrete structures. The authors investigate the feasibility of using linear and nonlinear dynamic vibration response data to monitor the progression of the carbonation process in cement-based materials. Mortar samples with dimensions of 40×40×160 mm were subjected to an accelerated carbonation process through a carbonation chamber with 55% relative humidity and >95% of CO2 atmosphere. The progress of carbonation in the material was monitored using data obtained with the test setup of the standard resonant frequency test (ASTM C215-14), from a pristine state until an almost fully carbonated state. Linear dynamic modulus, quality factor, and a material nonlinear response, evaluated through the upward resonant frequency shift during the signal ring-down, were investigated. The compressive strength and the depth of carbonation were also measured. Carbonation resulted in a modest increase in the dynamic modulus, but a substantive increase in the quality factor (inverse attenuation) and a decrease in the material nonlinearity parameter. The combined measurement of the vibration quality factor and nonlinear parameter shows potential as a sensitive measure of material changes brought about by carbonation.
Kaulakys, B.; Alaburda, M.; Ruseckas, J.
2016-05-01
A well-known fact in the financial markets is the so-called ‘inverse cubic law’ of the cumulative distributions of the long-range memory fluctuations of market indicators such as a number of events of trades, trading volume and the logarithmic price change. We propose the nonlinear stochastic differential equation (SDE) giving both the power-law behavior of the power spectral density and the long-range dependent inverse cubic law of the cumulative distribution. This is achieved using the suggestion that when the market evolves from calm to violent behavior there is a decrease of the delay time of multiplicative feedback of the system in comparison to the driving noise correlation time. This results in a transition from the Itô to the Stratonovich sense of the SDE and yields a long-range memory process.
Biondini, Gino; Fagerstrom, Emily; Prinari, Barbara
2016-10-01
We formulate the inverse scattering transform (IST) for the defocusing nonlinear Schrödinger (NLS) equation with fully asymmetric non-zero boundary conditions (i.e., when the limiting values of the solution at space infinities have different non-zero moduli). The theory is formulated without making use of Riemann surfaces, and instead by dealing explicitly with the branched nature of the eigenvalues of the associated scattering problem. For the direct problem, we give explicit single-valued definitions of the Jost eigenfunctions and scattering coefficients over the whole complex plane, and we characterize their discontinuous behavior across the branch cut arising from the square root behavior of the corresponding eigenvalues. We pose the inverse problem as a Riemann-Hilbert Problem on an open contour, and we reduce the problem to a standard set of linear integral equations. Finally, for comparison purposes, we present the single-sheet, branch cut formulation of the inverse scattering transform for the initial value problem with symmetric (equimodular) non-zero boundary conditions, as well as for the initial value problem with one-sided non-zero boundary conditions, and we also briefly describe the formulation of the inverse scattering transform when a different choice is made for the location of the branch cuts.
Directory of Open Access Journals (Sweden)
Nemat Dalir
2014-01-01
Full Text Available Singular nonlinear initial-value problems (IVPs in first-order and second-order partial differential equations (PDEs arising in fluid mechanics are semianalytically solved. To achieve this, the modified decomposition method (MDM is used in conjunction with some new inverse differential operators. In other words, new inverse differential operators are developed for the MDM and used with the MDM to solve first- and second-order singular nonlinear PDEs. The results of the solutions by the MDM together with new inverse operators are compared with the existing exact analytical solutions. The comparisons show excellent agreement.
Nonlinear modeling of neural population dynamics for hippocampal prostheses
Song, Dong; Chan, Rosa H.M.; Vasilis Z Marmarelis; Hampson, Robert E.; Deadwyler, Sam A.; Berger, Theodore W.
2009-01-01
Developing a neural prosthesis for the damaged hippocampus requires restoring the transformation of population neural activities performed by the hippocampal circuitry. To bypass a damaged region, output spike trains need to be predicted from the input spike trains and then reinstated through stimulation. We formulate a multiple-input, multiple-output (MIMO) nonlinear dynamic model for the input–output transformation of spike trains. In this approach, a MIMO model comprises a series of physio...
Numerical Analysis of the Dynamics of Nonlinear Solids and Structures
2008-08-01
of the conservation/ dissipation properties in time for the elastoplastic case 64 11.6. Concluding remarks 70 References 71 li...development of stable time-stepping algorithms for nonlinear dynamics. The focus was on inelastic solids, including finite strain elastoplastic and...set of plas- tic/ damage evolution equations (usually of a unilaterally constrained character due to the presence of the so-called yield/ damage
Estimating dynamic equilibrium economies: linear versus nonlinear likelihood
2004-01-01
This paper compares two methods for undertaking likelihood-based inference in dynamic equilibrium economies: a sequential Monte Carlo filter proposed by Fernández-Villaverde and Rubio-Ramírez (2004) and the Kalman filter. The sequential Monte Carlo filter exploits the nonlinear structure of the economy and evaluates the likelihood function of the model by simulation methods. The Kalman filter estimates a linearization of the economy around the steady state. The authors report two main results...
Analyzing the Dynamics of Nonlinear Multivariate Time Series Models
Institute of Scientific and Technical Information of China (English)
DenghuaZhong; ZhengfengZhang; DonghaiLiu; StefanMittnik
2004-01-01
This paper analyzes the dynamics of nonlinear multivariate time series models that is represented by generalized impulse response functions and asymmetric functions. We illustrate the measures of shock persistences and asymmetric effects of shocks derived from the generalized impulse response functions and asymmetric function in bivariate smooth transition regression models. The empirical work investigates a bivariate smooth transition model of US GDP and the unemployment rate.
Institute of Scientific and Technical Information of China (English)
POUZO; Demian
2009-01-01
This paper considers the estimation of an unknown function h that can be characterized as a solution to a nonlinear operator equation mapping between two infinite dimensional Hilbert spaces. The nonlinear operator is unknown but can be consistently estimated, and its inverse is discontinuous, rendering the problem ill-posed. We establish the consistency for the class of estimators that are regularized using general lower semicompact penalty functions. We derive the optimal convergence rates of the estimators under the Hilbert scale norms. We apply our results to two important problems in economics and finance: (1) estimating the parameters of the pricing kernel of defaultable bonds; (2) recovering the volatility surface implied by option prices allowing for measurement error in the option prices and numerical error in the computation of the operator.
Institute of Scientific and Technical Information of China (English)
CHEN XiaoHong; POUZO Demian
2009-01-01
This paper considers the estimation of an unknown function h that can be characterized as a solution to a nonlinear operator equation mapping between two infinite dimensional Hilbert spaces.The nonlinear operator is unknown but can be consistently estimated, and its inverse is discontinuous,rendering the problem ill-posed. We establish the consistency for the class of estimators that are regularized using general lower semicompact penalty functions. We derive the optimal convergence rates of the estimators under the Hilbert scale norms. We apply our results to two important problems in economics and finance: (1) estimating the parameters of the pricing kernel of defaultable bonds; (2)recovering the volatility surface implied by option prices allowing for measurement error in the option prices and numerical error in the computation of the operator.
Analysis of Nonlinear Structural Dynamics and Resonance in Trees
Directory of Open Access Journals (Sweden)
H. Doumiri Ganji
2012-01-01
Full Text Available Wind and gravity both impact trees in storms, but wind loads greatly exceed gravity loads in most situations. Complex behavior of trees in windstorms is gradually turning into a controversial concern among ecological engineers. To better understand the effects of nonlinear behavior of trees, the dynamic forces on tree structures during periods of high winds have been examined as a mass-spring system. In fact, the simulated dynamic forces created by strong winds are studied in order to determine the responses of the trees to such dynamic loads. Many of such nonlinear differential equations are complicated to solve. Therefore, this paper focuses on an accurate and simple solution, Differential Transformation Method (DTM, to solve the derived equation. In this regard, the concept of differential transformation is briefly introduced. The approximate solution to this equation is calculated in the form of a series with easily computable terms. Then, the method has been employed to achieve an acceptable solution to the presented nonlinear differential equation. To verify the accuracy of the proposed method, the obtained results from DTM are compared with those from the numerical solution. The results reveal that this method gives successive approximations of high accuracy solution.
Classical black holes: the nonlinear dynamics of curved spacetime.
Thorne, Kip S
2012-08-03
Numerical simulations have revealed two types of physical structures, made from curved spacetime, that are attached to black holes: tendexes, which stretch or squeeze anything they encounter, and vortexes, which twist adjacent inertial frames relative to each other. When black holes collide, their tendexes and vortexes interact and oscillate (a form of nonlinear dynamics of curved spacetime). These oscillations generate gravitational waves, which can give kicks up to 4000 kilometers per second to the merged black hole. The gravitational waves encode details of the spacetime dynamics and will soon be observed and studied by the Laser Interferometer Gravitational Wave Observatory and its international partners.
Predicting catastrophes in nonlinear dynamical systems by compressive sensing.
Wang, Wen-Xu; Yang, Rui; Lai, Ying-Cheng; Kovanis, Vassilios; Grebogi, Celso
2011-04-15
An extremely challenging problem of significant interest is to predict catastrophes in advance of their occurrences. We present a general approach to predicting catastrophes in nonlinear dynamical systems under the assumption that the system equations are completely unknown and only time series reflecting the evolution of the dynamical variables of the system are available. Our idea is to expand the vector field or map of the underlying system into a suitable function series and then to use the compressive-sensing technique to accurately estimate the various terms in the expansion. Examples using paradigmatic chaotic systems are provided to demonstrate our idea.
Predicting catastrophes in nonlinear dynamical systems by compressive sensing
Wang, Wen-Xu; Lai, Ying-Cheng; Kovanis, Vassilios; Grebogi, Celso
2011-01-01
An extremely challenging problem of significant interest is to predict catastrophes in advance of their occurrences. We present a general approach to predicting catastrophes in nonlinear dynamical systems under the assumption that the system equations are completely unknown and only time series reflecting the evolution of the dynamical variables of the system are available. Our idea is to expand the vector field or map of the underlying system into a suitable function series and then to use the compressive-sensing technique to accurately estimate the various terms in the expansion. Examples using paradigmatic chaotic systems are provided to demonstrate our idea.
Contributions of plasma physics to chaos and nonlinear dynamics
Escande, D. F.
2016-11-01
This topical review focusses on the contributions of plasma physics to chaos and nonlinear dynamics bringing new methods which are or can be used in other scientific domains. It starts with the development of the theory of Hamiltonian chaos, and then deals with order or quasi order, for instance adiabatic and soliton theories. It ends with a shorter account of dissipative and high dimensional Hamiltonian dynamics, and of quantum chaos. Most of these contributions are a spin-off of the research on thermonuclear fusion by magnetic confinement, which started in the fifties. Their presentation is both exhaustive and compact. [15 April 2016
Dynamics in a nonlinear Keynesian good market model
Energy Technology Data Exchange (ETDEWEB)
Naimzada, Ahmad, E-mail: ahmad.naimzada@unimib.it [Department of Economics, Quantitative Methods and Management, University of Milano-Bicocca, U7 Building, Via Bicocca degli Arcimboldi 8, 20126 Milano (Italy); Pireddu, Marina, E-mail: marina.pireddu@unimib.it [Department of Mathematics and Applications, University of Milano-Bicocca, U5 Building, Via Cozzi 55, 20125 Milano (Italy)
2014-03-15
In this paper, we show how a rich variety of dynamical behaviors can emerge in the standard Keynesian income-expenditure model when a nonlinearity is introduced, both in the cases with and without endogenous government spending. A specific sigmoidal functional form is used for the adjustment mechanism of income with respect to the excess demand, in order to bound the income variation. With the aid of analytical and numerical tools, we investigate the stability conditions, bifurcations, as well as periodic and chaotic dynamics. Globally, we study multistability phenomena, i.e., the coexistence of different kinds of attractors.
Nonlinear dynamic susceptibilities of interacting and noninteracting magnetic nanoparticles
Joensson, P; García-Palacios, J L; Svedlindh, P
2000-01-01
The linear and cubic dynamic susceptibilities of solid dispersions of nanosized maghemite gamma-Fe sub 2 O sub 3 particles have been measured for three samples with a volume concentration of magnetic particles ranging from 0.3% to 17%, in order to study the effect of dipole-dipole interactions. Significant differences between the dynamic response of the samples are observed. While the linear and cubic dynamic susceptibilities of the most dilute sample compare reasonably well with the corresponding expressions proposed by Raikher and Stepanov for noninteracting particles, the nonlinear dynamic response of the most concentrated sample exhibits at low temperatures similar features as observed in a Ag(11 at% Mn) spin glass.
Nonlinear Dynamics of Dipoles in Microtubules: Pseudo-Spin Model
Nesterov, Alexander I; Berman, Gennady P; Mavromatos, Nick E
2016-01-01
We perform a theoretical study of the dynamics of the electric field excitations in a microtubule by taking into consideration the realistic cylindrical geometry, dipole-dipole interactions of the tubulin-based protein heterodimers, the radial electric field produced by the solvent, and a possible degeneracy of energy states of individual heterodimers. The consideration is done in the frames of the classical pseudo-spin model. We derive the system of nonlinear dynamical ordinary differential equations of motion for interacting dipoles, and the continuum version of these equations. We obtain the solutions of these equations in the form of snoidal waves, solitons, kinks, and localized spikes. Our results will help to a better understanding of the functional properties of microtubules including the motor protein dynamics and the information transfer processes. Our considerations are based on classical dynamics. Some speculations on the role of possible quantum effects are also made.
Nonlinear dynamics of dipoles in microtubules: Pseudospin model.
Nesterov, Alexander I; Ramírez, Mónica F; Berman, Gennady P; Mavromatos, Nick E
2016-06-01
We perform a theoretical study of the dynamics of the electric field excitations in a microtubule by taking into consideration the realistic cylindrical geometry, dipole-dipole interactions of the tubulin-based protein heterodimers, the radial electric field produced by the solvent, and a possible degeneracy of energy states of individual heterodimers. The consideration is done in the frame of the classical pseudospin model. We derive the system of nonlinear dynamical partial differential equations of motion for interacting dipoles and the continuum version of these equations. We obtain the solutions of these equations in the form of snoidal waves, solitons, kinks, and localized spikes. Our results will help to achieve a better understanding of the functional properties of microtubules including the motor protein dynamics and the information transfer processes. Our considerations are based on classical dynamics. Some speculations on the role of possible quantum effects are also made.
Optical Nonlinearities and Ultrafast Carrier Dynamics in Semiconductor Quantum Dots
Energy Technology Data Exchange (ETDEWEB)
Klimov, V.; McBranch, D.; Schwarz, C.
1998-08-10
Low-dimensional semiconductors have attracted great interest due to the potential for tailoring their linear and nonlinear optical properties over a wide-range. Semiconductor nanocrystals (NC's) represent a class of quasi-zero-dimensional objects or quantum dots. Due to quantum cordhement and a large surface-to-volume ratio, the linear and nonlinear optical properties, and the carrier dynamics in NC's are significantly different horn those in bulk materials. napping at surface states can lead to a fast depopulation of quantized states, accompanied by charge separation and generation of local fields which significantly modifies the nonlinear optical response in NC's. 3D carrier confinement also has a drastic effect on the energy relaxation dynamics. In strongly confined NC's, the energy-level spacing can greatly exceed typical phonon energies. This has been expected to significantly inhibit phonon-related mechanisms for energy losses, an effect referred to as a phonon bottleneck. It has been suggested recently that the phonon bottleneck in 3D-confined systems can be removed due to enhanced role of Auger-type interactions. In this paper we report femtosecond (fs) studies of ultrafast optical nonlinearities, and energy relaxation and trap ping dynamics in three types of quantum-dot systems: semiconductor NC/glass composites made by high temperature precipitation, ion-implanted NC's, and colloidal NC'S. Comparison of ultrafast data for different samples allows us to separate effects being intrinsic to quantum dots from those related to lattice imperfections and interface properties.
Analysis of forward and inverse problems in chemical dynamics and spectroscopy
Energy Technology Data Exchange (ETDEWEB)
Rabitz, H. [Princeton Univ., NJ (United States)
1993-12-01
The overall scope of this research concerns the development and application of forward and inverse analysis tools for problems in chemical dynamics and chemical kinetics. The chemical dynamics work is specifically associated with relating features in potential surfaces and resultant dynamical behavior. The analogous inverse research aims to provide stable algorithms for extracting potential surfaces from laboratory data. In the case of chemical kinetics, the focus is on the development of systematic means to reduce the complexity of chemical kinetic models. Recent progress in these directions is summarized below.
Modelling and Control of Inverse Dynamics for a 5-DOF Parallel Kinematic Polishing Machine
Directory of Open Access Journals (Sweden)
Weiyang Lin
2013-08-01
/ control method is presented and investigated 2∞ in order to track the error control of the inverse dynamic model; the simulation results from different conditions show that the mixed / control method could 2∞ achieve an optimal and robust control performance. This work shows that the presented PKPM has a higher dynamic performance than conventional machine tools.
Precise integration method without inverse matrix calculation for structural dynamic equations
Institute of Scientific and Technical Information of China (English)
Wang Mengfu; F. T. K. Au
2007-01-01
The precise integration method proposed for linear time-invariant homogeneous dynamic systems can provide accurate numerical results that approach an exact solution at integration points. However, difficulties arise when the algorithm is used for non-homogeneous dynamic systems due to the inverse matrix calculation required. In this paper, the structural dynamic equalibrium equations are converted into a special form, the inverse matrix calculation is replaced by the Crout decomposition method to solve the dynamic equilibrium equations, and the precise integration method without the inverse matrix calculation is obtained. The new algorithm enhances the present precise integration method by improving both the computational accuracy and efficiency. Two numerical examples are given to demonstrate the validity and efficiency of the proposed algorithm.
On trajectory generation for flexible space crane: Inverse dynamics analysis by LATDYN
Chen, G.-S.; Housner, J. M.; Wu, S.-C.; Chang, C.-W.
1989-01-01
For future in-space construction facility, one or more space cranes capable of manipulating and positioning large and massive spacecraft components will be needed. Inverse dynamics was extensively studied as a basis for trajectory generation and control of robot manipulators. The focus here is on trajectory generation in the gross-motion phase of space crane operation. Inverse dynamics of the flexible crane body is much more complex and intricate as compared with rigid robot link. To model and solve the space crane's inverse dynamics problem, LATDYN program which employs a three-dimensional finite element formulation for the multibody truss-type structures will be used. The formulation is oriented toward a joint dominated structure which is suitable for the proposed space crane concept. To track a planned trajectory, procedures will be developed to obtain the actuation profile and dynamics envelope which are pertinent to the design and performance requirements of the space crane concept.
Strongly nonlinear dynamics of electrolytes in large ac voltages
DEFF Research Database (Denmark)
Olesen, Laurits Højgaard; Bazant, Martin Z.; Bruus, Henrik
2010-01-01
We study the response of a model microelectrochemical cell to a large ac voltage of frequency comparable to the inverse cell relaxation time. To bring out the basic physics, we consider the simplest possible model of a symmetric binary electrolyte confined between parallel-plate blocking electrodes...... in the electrolyte near the electrodes and, at very large voltage, the breakdown of the quasiequilibrium structure of the double layers. The former leads to the prediction of “ac capacitive desalination” since there is a time-averaged transfer of salt from the bulk to the double layers, via oscillating diffusion...... nonlinear responses to large ac voltages, such as Faradaic reactions, electro-osmotic instabilities, and induced-charge electrokinetic phenomena....
Strongly nonlinear dynamics of electrolytes in large ac voltages
Olesen, Laurits H; Bruus, Henrik
2009-01-01
We study the response of a model micro-electrochemical cell to a large ac voltage of frequency comparable to the inverse cell relaxation time. To bring out the basic physics, we consider the simplest possible model of a symmetric binary electrolyte confined between parallel-plate blocking electrodes, ignoring any transverse instability or fluid flow. We analyze the resulting one-dimensional problem by matched asymptotic expansions in the limit of thin double layers and extend previous work into the strongly nonlinear regime, which is characterized by two novel features - significant salt depletion in the electrolyte near the electrodes and, at very large voltage, the breakdown of the quasi-equilibrium structure of the double layers. The former leads to the prediction of "ac capacitive desalination", since there is a time-averaged transfer of salt from the bulk to the double layers, via oscillating diffusion layers. The latter is associated with transient diffusion limitation, which drives the formation and co...
Investigation of Nonlinear Pupil Dynamics by Recurrence Quantification Analysis
Directory of Open Access Journals (Sweden)
L. Mesin
2013-01-01
Full Text Available Pupil is controlled by the autonomous nervous system (ANS. It shows complex movements and changes of size even in conditions of constant stimulation. The possibility of extracting information on ANS by processing data recorded during a short experiment using a low cost system for pupil investigation is studied. Moreover, the significance of nonlinear information contained in the pupillogram is investigated. We examined 13 healthy subjects in different stationary conditions, considering habitual dental occlusion (HDO as a weak stimulation of the ANS with respect to the maintenance of the rest position (RP of the jaw. Images of pupil captured by infrared cameras were processed to estimate position and size on each frame. From such time series, we extracted linear indexes (e.g., average size, average displacement, and spectral parameters and nonlinear information using recurrence quantification analysis (RQA. Data were classified using multilayer perceptrons and support vector machines trained using different sets of input indexes: the best performance in classification was obtained including nonlinear indexes in the input features. These results indicate that RQA nonlinear indexes provide additional information on pupil dynamics with respect to linear descriptors, allowing the discrimination of even a slight stimulation of the ANS. Their use in the investigation of pathology is suggested.
Linear and nonlinear dynamic systems in financial time series prediction
Directory of Open Access Journals (Sweden)
Salim Lahmiri
2012-10-01
Full Text Available Autoregressive moving average (ARMA process and dynamic neural networks namely the nonlinear autoregressive moving average with exogenous inputs (NARX are compared by evaluating their ability to predict financial time series; for instance the S&P500 returns. Two classes of ARMA are considered. The first one is the standard ARMA model which is a linear static system. The second one uses Kalman filter (KF to estimate and predict ARMA coefficients. This model is a linear dynamic system. The forecasting ability of each system is evaluated by means of mean absolute error (MAE and mean absolute deviation (MAD statistics. Simulation results indicate that the ARMA-KF system performs better than the standard ARMA alone. Thus, introducing dynamics into the ARMA process improves the forecasting accuracy. In addition, the ARMA-KF outperformed the NARX. This result may suggest that the linear component found in the S&P500 return series is more dominant than the nonlinear part. In sum, we conclude that introducing dynamics into the ARMA process provides an effective system for S&P500 time series prediction.
Dark-lines in bifurcation plots of nonlinear dynamic systems
Institute of Scientific and Technical Information of China (English)
Gao Zhi-Ying; Shen Yun-Wen; Liu Meng-Jun
2005-01-01
Based on the regressive character of chaotic motion in nonlinear dynamic systems, a numerical regression algorithm is developed, which can be used to research the dark-lines passing through chaotic regions in bifurcation plots. The dark-lines of the parabolic mapping are obtained by using the numerical regression algorithm, and compared with those that are accurately acquired through dark-line equations. Thus the validity of this algorithm is proved. Furthermore,for the Brussel oscillation system and the piecewise linear dynamic system of a gear pair, the dark-lines are researched by using the regression algorithm. By researching the dark-lines in the bifurcation plots of nonlinear dynamic systems,the periodic windows embedded in chaotic regions can be ascertained by tangential points of dark-lines, and the turning points of chaotic attractors can be also obtained by intersected points. The results show that this algorithm is helpful to analyse dynamic behaviour of systems and control chaotic motion.
Inversion factor in the comparative analysis of dynamical processes in radioecology
Energy Technology Data Exchange (ETDEWEB)
Zarubin, O.; Zarubina, N. [Institute for Nuclear Researh of National Academy of Science of Ukraine (Ukraine)
2014-07-01
We have studied levels of specific activity of radionuclides in fish and fungi of the Kiev region of Ukraine since 1986 till 2013, including 30-km alienation zone of Chernobyl Nuclear Power Plant (ChNPP) after the accident. The radionuclides specific activity dynamics analysis for 10 species of freshwater fishes of different trophic levels and at 7 species of higher fungi was carried out for this period. Multiple research of specific activity of radionuclides in fish was carried out on the Kanevskoe reservoir and cooling-pond of ChNPP, in fungi - on 6 testing areas, which are situated within the range of 2 to 150 km from ChNPP. The basic attention was given to accumulation of {sup 137}Cs. We have established that dynamics of specific activity of {sup 137}Cs within different species of fish in the same reservoir is not identical. Dynamics of specific activity of {sup 137}Cs within various species of fungi of the same testing area is also not identical. Dynamics of specific activity of {sup 137}Cs with the investigated objects of various testing dry-land and water areas also varies. Authors suggest an inversion factor to be used for comparison of dynamics of specific activity of {sup 137}Cs, which in case of biota is a nonlinear process: K{sub inv} = A{sub 0} / A{sub t}, where A{sub 0} stands for the value of specific activity of the radionuclide at time 0; A{sub t} - specific activity of radionuclide at time t. Therefore, K{sub inv} reflects ratio (inversion) of specific activity of radionuclides to its starting value as a function of time, where K{sub inv} > 1 corresponds to increase in radionuclides' specific activity and K{sub inv} < 1 corresponds to its decrease. For example, K{sub inv} of {sup 137}Cs in fish Rutilus rutilus in the Kanevskoe reservoir was equal to 0.57, and 13.33 in the cooling-pond of ChNPP, at Blicca bjoerkna 0.95 and 29.61 accordingly in 1987 - 1996. In 1987 - 2011 K{sub inv} of {sup 137}Cs at R. rutilus in the Kanevskoe reservoir
Nonlinear dynamic behaviors of a floating structure in focused waves
Cao, Fei-feng; Zhao, Xi-zeng
2015-12-01
Floating structures are commonly seen in coastal and offshore engineering. They are often subjected to extreme waves and, therefore, their nonlinear dynamic behaviors are of great concern. In this paper, an in-house CFD code is developed to investigate the accurate prediction of nonlinear dynamic behaviors of a two-dimensional (2-D) box-shaped floating structure in focused waves. Computations are performed by an enhanced Constrained Interpolation Profile (CIP)-based Cartesian grid model, in which a more accurate VOF (Volume of Fluid) method, the THINC/SW scheme (THINC: tangent of hyperbola for interface capturing; SW: Slope Weighting), is used for interface capturing. A focusing wave theory is used for the focused wave generation. The wave component of constant steepness is chosen. Comparisons between predictions and physical measurements show good agreement including body motions and free surface profiles. Although the overall agreement is good, some discrepancies are observed for impact pressure on the superstructure due to water on deck. The effect of grid resolution on the results is checked. With a fine grid, no obvious improvement is seen in the global body motions and impact pressures due to water on deck. It is concluded that highly nonlinear phenomena, such as distorted free surface, large-amplitude body motions, and violent impact flow, have been predicted successfully.
Machine learning control taming nonlinear dynamics and turbulence
Duriez, Thomas; Noack, Bernd R
2017-01-01
This is the first book on a generally applicable control strategy for turbulence and other complex nonlinear systems. The approach of the book employs powerful methods of machine learning for optimal nonlinear control laws. This machine learning control (MLC) is motivated and detailed in Chapters 1 and 2. In Chapter 3, methods of linear control theory are reviewed. In Chapter 4, MLC is shown to reproduce known optimal control laws for linear dynamics (LQR, LQG). In Chapter 5, MLC detects and exploits a strongly nonlinear actuation mechanism of a low-dimensional dynamical system when linear control methods are shown to fail. Experimental control demonstrations from a laminar shear-layer to turbulent boundary-layers are reviewed in Chapter 6, followed by general good practices for experiments in Chapter 7. The book concludes with an outlook on the vast future applications of MLC in Chapter 8. Matlab codes are provided for easy reproducibility of the presented results. The book includes interviews with leading r...
Nonlinear coupled dynamics analysis of a truss spar platform
Li, Cheng-xi; Zhang, Jun
2016-12-01
Accurate prediction of the offshore structure motion response and associate mooring line tension is important in both technical applications and scientific research. In our study, a truss spar platform, operated in Gulf of Mexico, is numerically simulated and analyzed by an in-house numerical code `COUPLE'. Both the platform motion responses and associated mooring line tension are calculated and investigated through a time domain nonlinear coupled dynamic analysis. Satisfactory agreement between the simulation and corresponding field measurements is in general reached, indicating that the numerical code can be used to conduct the time-domain analysis of a truss spar interacting with its mooring and riser system. Based on the comparison between linear and nonlinear results, the relative importance of nonlinearity in predicting the platform motion response and mooring line tensions is assessed and presented. Through the coupled and quasi-static analysis, the importance of the dynamic coupling effect between the platform hull and the mooring/riser system in predicting the mooring line tension and platform motions is quantified. These results may provide essential information pertaining to facilitate the numerical simulation and design of the large scale offshore structures.
Nonlinear Analysis and Intelligent Control of Integrated Vehicle Dynamics
Directory of Open Access Journals (Sweden)
C. Huang
2014-01-01
Full Text Available With increasing and more stringent requirements for advanced vehicle integration, including vehicle dynamics and control, traditional control and optimization strategies may not qualify for many applications. This is because, among other factors, they do not consider the nonlinear characteristics of practical systems. Moreover, the vehicle wheel model has some inadequacies regarding the sideslip angle, road adhesion coefficient, vertical load, and velocity. In this paper, an adaptive neural wheel network is introduced, and the interaction between the lateral and vertical dynamics of the vehicle is analyzed. By means of nonlinear analyses such as the use of a bifurcation diagram and the Lyapunov exponent, the vehicle is shown to exhibit complicated motions with increasing forward speed. Furthermore, electric power steering (EPS and active suspension system (ASS, which are based on intelligent control, are used to reduce the nonlinear effect, and a negotiation algorithm is designed to manage the interdependences and conflicts among handling stability, driving smoothness, and safety. Further, a rapid control prototype was built using the hardware-in-the-loop simulation platform dSPACE and used to conduct a real vehicle test. The results of the test were consistent with those of the simulation, thereby validating the proposed control.
Dupas, Julien; Verneuil, Emilie; Ramaioli, Marco; Forny, Laurent; Talini, Laurence; Lequeux, Francois
2013-10-08
The wetting dynamics of a solvent on a soluble substrate interestingly results from the rates of the solvent transfers into the substrate. When a supported film of a hydrosoluble polymer with thickness e is wet by a spreading droplet of water with instantaneous velocity U, the contact angle is measured to be inversely proportionate to the product of thickness and velocity, eU, over two decades. As for many hydrosoluble polymers, the polymer we used (a polysaccharide) has a strongly nonlinear sorption isotherm φ(a(w)), where φ is the volume fraction of water in the polymer and aw is the activity of water. For the first time, this nonlinearity is accounted for in the dynamics of water uptake by the substrate. Indeed, by measuring the water content in the polymer around the droplet φ at distances as small as 5 μm, we find that the hydration profile exhibits (i) a strongly distorted shape that results directly from the nonlinearities of the sorption isotherm and (ii) a cutoff length ξ below which the water content in the substrate varies very slowly. The nonlinearities in the sorption isotherm and the hydration at small distances from the line were not accounted for by Tay et al., Soft Matter 2011, 7, 6953. Here, we develop a comprehensive description of the hydration of the substrate ahead of the contact line that encompasses the two water transfers at stake: (i) the evaporation-condensation process by which water transfers into the substrate through the atmosphere by the condensation of the vapor phase, which is fed by the evaporation from the droplet itself, and (ii) the diffusion of liquid water along the polymer film. We find that the eU rescaling of the contact angle arises from the evaporation-condensation process at small distances. We demonstrate why it is not modified by the second process.
Classical and quantum dynamics in an inverse square potential
Energy Technology Data Exchange (ETDEWEB)
Guillaumín-España, Elisa, E-mail: ege@correo.azc.uam.mx [Laboratorio de Sistemas Dinámicos, Departamento de Ciencias Básicas, Universidad Autónoma Metropolitana, Unidad Azcapotzalco, Azcapotzalco CP 02200 D. F. (Mexico); Núñez-Yépez, H. N., E-mail: nyhn@xanum.uam.mx [Departamento de Física, Universidad Autónoma Metropolitana, Unidad Iztapalapa, Apartado Postal 55-534, Iztapalapa CP 09340 D. F. (Mexico); Salas-Brito, A. L., E-mail: asb@correo.azc.uam.mx [Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México (ICN-UNAM), Apartado Postal 70-543, 04510 México D F (Mexico)
2014-10-15
The classical motion of a particle in a 3D inverse square potential with negative energy, E, is shown to be geodesic, i.e., equivalent to the particle's free motion on a non-compact phase space manifold irrespective of the sign of the coupling constant. We thus establish that all its classical orbits with E < 0 are unbounded. To analyse the corresponding quantum problem, the Schrödinger equation is solved in momentum space. No discrete energy levels exist in the unrenormalized case and the system shows a complete “fall-to-the-center” with an energy spectrum unbounded by below. Such behavior corresponds to the non-existence of bound classical orbits. The symmetry of the problem is SO(3) × SO(2, 1) corroborating previously obtained results.
Nonlinear dynamics and chaos in an optomechanical beam
Navarro-Urrios, D; Colombano, M F; Garcia, P D; Sledzinska, M; Alzina, F; Griol, A; Martinez, A; Sotomayor-Torres, C M
2016-01-01
Optical non-linearities, such as thermo-optic effects and free-carrier-dispersion, are often considered as undesired effects in silicon-based resonators and, more specifically, optomechanical (OM) cavities, affecting the relative detuning between an optical resonance and the excitation laser. However, the interplay between such mechanisms could also enable unexpected physical phenomena to be used in new applications. In the present work, we exploit those non-linearities and their intercoupling with the mechanical degrees of freedom of a silicon OM nanobeam to unveil a rich set of fundamentally different complex dynamics. By smoothly changing the parameters of the excitation laser, namely its power and wavelength, we demonstrate accurate control for activating bi-dimensional and tetra-dimensional limit-cycles, a period doubling route and chaos. In addition, by scanning the laser parameters in opposite senses we demonstrate bistability and hysteresis between bi-dimensional and tetra-dimensional limit-cycles, be...
Exponential Stability of Stochastic Nonlinear Dynamical Price System with Delay
Directory of Open Access Journals (Sweden)
Wenli Zhu
2013-01-01
Full Text Available Based on Lyapunov stability theory, Itô formula, stochastic analysis, and matrix theory, we study the exponential stability of the stochastic nonlinear dynamical price system. Using Taylor's theorem, the stochastic nonlinear system with delay is reduced to an n-dimensional semilinear stochastic differential equation with delay. Some sufficient conditions of exponential stability and corollaries for such price system are established by virtue of Lyapunov function. The time delay upper limit is solved by using our theoretical results when the system is exponentially stable. Our theoretical results show that if the classical price Rayleigh equation is exponentially stable, so is its perturbed system with delay provided that both the time delay and the intensity of perturbations are small enough. Two examples are presented to illustrate our results.
An introduction to complex systems society, ecology, and nonlinear dynamics
Fieguth, Paul
2017-01-01
This undergraduate text explores a variety of large-scale phenomena - global warming, ice ages, water, poverty - and uses these case studies as a motivation to explore nonlinear dynamics, power-law statistics, and complex systems. Although the detailed mathematical descriptions of these topics can be challenging, the consequences of a system being nonlinear, power-law, or complex are in fact quite accessible. This book blends a tutorial approach to the mathematical aspects of complex systems together with a complementary narrative on the global/ecological/societal implications of such systems. Nearly all engineering undergraduate courses focus on mathematics and systems which are small scale, linear, and Gaussian. Unfortunately there is not a single large-scale ecological or social phenomenon that is scalar, linear, and Gaussian. This book offers students insights to better understand the large-scale problems facing the world and to realize that these cannot be solved by a single, narrow academic field or per...
Swarming behaviors in multi-agent systems with nonlinear dynamics
Energy Technology Data Exchange (ETDEWEB)
Yu, Wenwu, E-mail: wenwuyu@gmail.com [Department of Mathematics, Southeast University, Nanjing 210096 (China); School of Electrical and Computer Engineering, RMIT University, Melbourne VIC 3001 (Australia); Chen, Guanrong [Department of Electronic Engineering, City University of Hong Kong, Hong Kong (China); Cao, Ming [Faculty of Mathematics and Natural Sciences, ITM, University of Groningen (Netherlands); Lü, Jinhu [Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190 (China); Zhang, Hai-Tao [Department of Control Science and Engineering, State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074 (China)
2013-12-15
The dynamic analysis of a continuous-time multi-agent swarm model with nonlinear profiles is investigated in this paper. It is shown that, under mild conditions, all agents in a swarm can reach cohesion within a finite time, where the upper bounds of the cohesion are derived in terms of the parameters of the swarm model. The results are then generalized by considering stochastic noise and switching between nonlinear profiles. Furthermore, swarm models with limited sensing range inducing changing communication topologies and unbounded repulsive interactions between agents are studied by switching system and nonsmooth analysis. Here, the sensing range of each agent is limited and the possibility of collision among nearby agents is high. Finally, simulation results are presented to demonstrate the validity of the theoretical analysis.
Emergent geometries and nonlinear-wave dynamics in photon fluids.
Marino, F; Maitland, C; Vocke, D; Ortolan, A; Faccio, D
2016-03-22
Nonlinear waves in defocusing media are investigated in the framework of the hydrodynamic description of light as a photon fluid. The observations are interpreted in terms of an emergent curved spacetime generated by the waves themselves, which fully determines their dynamics. The spacetime geometry emerges naturally as a result of the nonlinear interaction between the waves and the self-induced background flow. In particular, as observed in real fluids, different points of the wave profile propagate at different velocities leading to the self-steepening of the wave front and to the formation of a shock. This phenomenon can be associated to a curvature singularity of the emergent metric. Our analysis offers an alternative insight into the problem of shock formation and provides a demonstration of an analogue gravity model that goes beyond the kinematic level.
Investigation of the nonlinear dynamics of a partially cracked plate
Energy Technology Data Exchange (ETDEWEB)
Israr, A [School of Engineering and Physical Sciences, Heriot Watt University - Dubai Campus, Block 2, Dubai International Academic City, P O Box 294345, Dubai (United Arab Emirates); Atepor, L, E-mail: a.israr@hw.ac.u, E-mail: katepor@yahoo.co [Department of Mechanical Engineering, James Watt South Building, University of Glasgow, Glasgow, G12 8QQ Scotland (United Kingdom)
2009-08-01
In this paper the nonlinear vibration of an aircraft panel structure modelled as an isotropic cracked plate and subjected to transverse harmonic excitation is considered for studying the dynamic response, both analytically and experimentally. A crack is arbitrarily located at the centre of the plate, consisting of a continuous line. This mathematical model is in the form of Duffing equation with a cubic nonlinear term. The perturbation method of multiple scales is used to solve the algebraic equation, and then investigated with the results of the direct integration within Mathematica{sup TM} and finite element analysis in ABAQUS for the first mode only. In addition, experimental measurements are also carried out to verify the dependence of the cracked plate's fundamental mode shape and resonance frequency on the vibration displacement amplitude. An extermely close agreement between these results is observed.
On-line control of the nonlinear dynamics for synchrotrons
Bengtsson, J.; Martin, I. P. S.; Rowland, J. H.; Bartolini, R.
2015-07-01
We propose a simple approach to the on-line control of the nonlinear dynamics in storage rings, based on compensation of the nonlinear resonance driving terms using beam losses as the main indicator of the strength of a resonance. The correction scheme is built on the analysis of the resonance driving terms in first perturbative order and on the possibility of using independent power supplies in the sextupole magnets, which is nowadays present in many synchrotron light sources. Such freedom allows the definition of "smart sextupole knobs" attacking each resonance separately. The compensation scheme has been tested at the Diamond light source and proved to be effective in opening up the betatron tune space, resonance free, available to the electron beam and to improve the beam lifetime.
Nonlinear dynamic response of stay cables under axial harmonic excitation
Institute of Scientific and Technical Information of China (English)
Xu XIE; He ZHAN; Zhi-cheng ZHANG
2008-01-01
This paper proposes a new numerical simulation method for analyzing the parametric vibration of stay cables based on the theory of nonlinear dynamic response of structures under the asynchronous support excitation.The effects of important parameters related to parametric vibration of cables,I.e., characteristics of structure,excitation frequency,excitation amplitude,damping effect of the air and the viscous damping coefficient of the cables,were investigated by using the proposed method for the cables with significant length difference as examples.The analysis results show that nonlinear finite element method is a powerful technique in analyzing the parametric vibration of cables,the behavior of parametric vibration of the two cables with different Irvine parameters has similar properties,the amplitudes of parametric vibration of cables are related to the frequency and amplitude of harmonic support excitations and the effect of distributed viscous damping on parametric vibration of the cables is very small.
Nonlinear problems of complex natural systems: Sun and climate dynamics.
Bershadskii, A
2013-01-13
The universal role of the nonlinear one-third subharmonic resonance mechanism in generation of strong fluctuations in complex natural dynamical systems related to global climate is discussed using wavelet regression detrended data. The role of the oceanic Rossby waves in the year-scale global temperature fluctuations and the nonlinear resonance contribution to the El Niño phenomenon have been discussed in detail. The large fluctuations in the reconstructed temperature on millennial time scales (Antarctic ice core data for the past 400,000 years) are also shown to be dominated by the one-third subharmonic resonance, presumably related to the Earth's precession effect on the energy that the intertropical regions receive from the Sun. The effects of galactic turbulence on the temperature fluctuations are also discussed.
Swarming behaviors in multi-agent systems with nonlinear dynamics.
Yu, Wenwu; Chen, Guanrong; Cao, Ming; Lü, Jinhu; Zhang, Hai-Tao
2013-12-01
The dynamic analysis of a continuous-time multi-agent swarm model with nonlinear profiles is investigated in this paper. It is shown that, under mild conditions, all agents in a swarm can reach cohesion within a finite time, where the upper bounds of the cohesion are derived in terms of the parameters of the swarm model. The results are then generalized by considering stochastic noise and switching between nonlinear profiles. Furthermore, swarm models with limited sensing range inducing changing communication topologies and unbounded repulsive interactions between agents are studied by switching system and nonsmooth analysis. Here, the sensing range of each agent is limited and the possibility of collision among nearby agents is high. Finally, simulation results are presented to demonstrate the validity of the theoretical analysis.
Study of the nonlinear longitudinal dynamics of a stochastic system
Directory of Open Access Journals (Sweden)
Cunha Americo
2014-01-01
Full Text Available This paper deals with the theoretical study of how discrete elements attached to a continuous stochastic systems can affect their dynamical behavior. For this, it is studied the nonlinear longitudinal dynamics of an elastic bar, attached to springs and a lumped mass, with a random elastic modulus and subjected to a Gaussian white-noise distributed external force. Numerical simulations are conducted and their results are analyzed in function of the ratio between the masses of the discrete and the continuous parts of the system. This analysis reveals that the dynamic behavior of the bar is significantly altered when the lumped mass is varied, being more inﬂuenced by the randomness for small values of the lumped mass.
Romano, F.; Piatanesi, A.; Lorito, S.; Tolomei, C.; Atzori, S.; Murphy, S.
2016-11-01
Tsunami waveform inversion is often used to retrieve information about the causative seismic tsunami source. Tide gauges record tsunamis routinely; however, compared to deep-ocean sensor data, tide-gauge waveform modeling is more difficult due to coarse/inaccurate local bathymetric models resulting in a time mismatch between observed and predicted waveforms. This can affect the retrieved tsunami source model, thus limiting the use of tide-gauge data. A method for nonlinear inversion with an automatic optimal time alignment (OTA), calculated by including a time shift parameter in the cost function, is presented. The effectiveness of the method is demonstrated through a series of synthetic tests and is applied as part of a joint inversion with interferometric synthetic aperture radar data for the slip distribution of the 2015 Mw 8.3 Illapel earthquake. The results show that without OTA, the resolution on the slip model degrades significantly and that using this method for a real case strongly affects the retrieved slip pattern.
Liu, Pengcheng; Archuleta, Ralph J.
2004-02-01
We present a new procedure to invert for kinematic source parameters on a finite fault. On the basis of the reciprocity relation of the Green's functions, we use a newly developed fourth-order viscoelastic finite-difference algorithm to calculate three-dimensional (3-D) Green's functions (actually the tractions) on the fault. We invert the data for the unknown source parameters at the nodes (or corners) of the subfaults. The source parameters within a subfault area are allowed to vary; this variation is calculated through bilinear interpolation of the four nodal quantities. We have developed a global nonlinear inversion algorithm that is based on simulated annealing methods to solve efficiently for the nodal parameters. We apply this method to the 1989 Loma Prieta, California, M 6.9 earthquake for both a 1-D and 3-D velocity structure. We show (1) the bilinear interpolation technique reduces the dependence of inversion results on the subfault size by naturally including the effects of nearby subfaults. (2) While the number of synthetic seismograms that must be computed is greatly increased by the bilinear interpolation, the structure of the inversion method minimizes the actual numbers of computations. (3) As expected, complexity in the velocity structure is mapped into the source parameters that describe the rupture process; there are significant differences between faulting models derived from 1-D and 3-D structural models.
Hybrid simulation theory for a classical nonlinear dynamical system
Drazin, Paul L.; Govindjee, Sanjay
2017-03-01
Hybrid simulation is an experimental and computational technique which allows one to study the time evolution of a system by physically testing a subset of it while the remainder is represented by a numerical model that is attached to the physical portion via sensors and actuators. The technique allows one to study large or complicated mechanical systems while only requiring a subset of the complete system to be present in the laboratory. This results in vast cost savings as well as the ability to study systems that simply can not be tested due to scale. However, the errors that arise from splitting the system in two requires careful attention, if a valid simulation is to be guaranteed. To date, efforts to understand the theoretical limitations of hybrid simulation have been restricted to linear dynamical systems. In this work we consider the behavior of hybrid simulation when applied to nonlinear dynamical systems. As a model problem, we focus on the damped, harmonically-driven nonlinear pendulum. This system offers complex nonlinear characteristics, in particular periodic and chaotic motions. We are able to show that the application of hybrid simulation to nonlinear systems requires a careful understanding of what one expects from such an experiment. In particular, when system response is chaotic we advocate the need for the use of multiple metrics to characterize the difference between two chaotic systems via Lyapunov exponents and Lyapunov dimensions, as well as correlation exponents. When system response is periodic we advocate the use of L2 norms. Further, we are able to show that hybrid simulation can falsely predict chaotic or periodic response when the true system has the opposite characteristic. In certain cases, we are able to show that control system parameters can mitigate this issue.
Towards adjoint-based inversion of time-dependent mantle convection with non-linear viscosity
Li, Dunzhu; Gurnis, Michael; Stadler, Georg
2017-01-01
We develop and study an adjoint-based inversion method for the simultaneous recovery of initial temperature conditions and viscosity parameters in time-dependent mantle convection from the current mantle temperature and historic plate motion. Based on a realistic rheological model with temperature- and strain rate-dependent viscosity, we formulate the inversion as a PDE-constrained optimization problem. The objective functional includes the misfit of surface velocity (plate motion) history, the misfit of the current mantle temperature, and a regularization for the uncertain initial condition. The gradient of this functional with respect to the initial temperature and the uncertain viscosity parameters is computed by solving the adjoint of the mantle convection equations. This gradient is used in a preconditioned quasi-Newton minimization algorithm. We study the prospects and limitations of the inversion, as well as the computational performance of the method using two synthetic problems, a sinking cylinder and a realistic subduction model. The subduction model is characterized by the migration of a ridge toward a trench whereby both plate motions and subduction evolve. The results demonstrate: (1) for known viscosity parameters, the initial temperature can be well recovered, as in previous initial condition-only inversions where the effective viscosity was given; (2) for known initial temperature, viscosity parameters can be recovered accurately, despite the existence of trade-offs due to ill-conditioning; (3) for the joint inversion of initial condition and viscosity parameters, initial condition and effective viscosity can be reasonably recovered, but the high dimension of the parameter space and the resulting ill-posedness may limit recovery of viscosity parameters.
Nonlinear dynamic response of beam and its application in nanomechanical resonator
Institute of Scientific and Technical Information of China (English)
Yin Zhang; Yun Liu; Kevin D. Murphy
2012-01-01
Nonlinear dynamic response of nanomechanical resonator is of very important characteristics in its application.Two categories of the tension-dominant and curvaturedominant nonlinearities are analyzed.The dynamic nonlinearity of four beam structures of nanomechanical resonator is quantitatively studied via a dimensional analysis approach.The dimensional analysis shows that for the nanomechanical resonator of tension-dominant nonlinearity,its dynamic nonlinearity decreases monotonically with increasing axial loading and increases monotonically with the increasing aspect ratio of length to thickness; the dynamic nonlinearity can only result in the hardening effects.However,for the nanomechanical resonator of the curvature-dominant nonlinearity,its dynamic nonlinearity is only dependent on axial loading.Compared with the tension-dominant nonlinearity,the curvature-dominant nonlinearity increases monotonically with increasing axial loading; its dynamic nonlinearity can result in both hardening and softening effects.The analysis on the dynamic nonlinearity can be very helpful to the tuning application of the nanomechanical resonator.
Kalman filtering, smoothing and recursive robot arm forward and inverse dynamics
Rodriguez, G.
1986-01-01
The inverse and forward dynamics problems for multi-link serial manipulators are solved by using recursive techniques from linear filtering and smoothing theory. The pivotal step is to cast the system dynamics and kinematics as a two-point boundary-value problem. Solution of this problem leads to filtering and smoothing techniques identical to the equations of Kalman filtering and Bryson-Frazier fixed time-interval smoothing. The solutions prescribe an inward filtering recursion to compute a sequence of constraint moments and forces followed by an outward recursion to determine a corresponding sequence of angular and linear accelerations. In addition to providing techniques to compute joint accelerations from applied joint moments (and vice versa), the report provides an approach to evaluate recursively the composite multi-link system inertia matrix and its inverse. The report lays the foundation for the potential use of filtering and smoothing techniques in robot inverse and forward dynamics and in robot control design.
Relation between observability and differential embeddings for nonlinear dynamics
Letellier, Christophe; Aguirre, Luis A.; Maquet, Jean
2005-06-01
In the analysis of a scalar time series, which lies on an m -dimensional object, a great number of techniques will start by embedding such a time series in a d -dimensional space, with d>m . Therefore there is a coordinate transformation Φs from the original phase space to the embedded one. The embedding space depends on the observable s(t) . In theory, the main results reached are valid regardless of s(t) . In a number of practical situations, however, the choice of the observable does influence our ability to extract dynamical information from the embedded attractor. This may arise in problems in nonlinear dynamics such as model building, control and synchronization. To some degree, ease of success will depend on the choice of the observable simply because it is related to the observability of the dynamics. In this paper the observability matrix for nonlinear systems, which uses Lie derivatives, is revisited. It is shown that such a matrix can be interpreted as the Jacobian matrix of Φs —the map between the original phase space and the differential embedding induced by the observable—thus establishing a link between observability and embedding theory.
Nonlinear dynamical systems for theory and research in ergonomics.
Guastello, Stephen J
2017-02-01
Nonlinear dynamical systems (NDS) theory offers new constructs, methods and explanations for phenomena that have in turn produced new paradigms of thinking within several disciplines of the behavioural sciences. This article explores the recent developments of NDS as a paradigm in ergonomics. The exposition includes its basic axioms, the primary constructs from elementary dynamics and so-called complexity theory, an overview of its methods, and growing areas of application within ergonomics. The applications considered here include: psychophysics, iconic displays, control theory, cognitive workload and fatigue, occupational accidents, resilience of systems, team coordination and synchronisation in systems. Although these applications make use of different subsets of NDS constructs, several of them share the general principles of the complex adaptive system. Practitioner Summary: Nonlinear dynamical systems theory reframes problems in ergonomics that involve complex systems as they change over time. The leading applications to date include psychophysics, control theory, cognitive workload and fatigue, biomechanics, occupational accidents, resilience of systems, team coordination and synchronisation of system components.
Nonlinear dynamics of direction-selective recurrent neural media.
Xie, Xiaohui; Giese, Martin A
2002-05-01
The direction selectivity of cortical neurons can be accounted for by asymmetric lateral connections. Such lateral connectivity leads to a network dynamics with characteristic properties that can be exploited for distinguishing in neurophysiological experiments this mechanism for direction selectivity from other possible mechanisms. We present a mathematical analysis for a class of direction-selective neural models with asymmetric lateral connections. Contrasting with earlier theoretical studies that have analyzed approximations of the network dynamics by neglecting nonlinearities using methods from linear systems theory, we study the network dynamics with nonlinearity taken into consideration. We show that asymmetrically coupled networks can stabilize stimulus-locked traveling pulse solutions that are appropriate for the modeling of the responses of direction-selective neurons. In addition, our analysis shows that outside a certain regime of stimulus speeds the stability of these solutions breaks down, giving rise to lurching activity waves with specific spatiotemporal periodicity. These solutions, and the bifurcation by which they arise, cannot be easily accounted for by classical models for direction selectivity.
Nonlinear Dynamic Buckling of Damaged Composite Cylindrical Shells
Institute of Scientific and Technical Information of China (English)
WANG Tian-lin; TANG Wen-yong; ZHANG Sheng-kun
2007-01-01
Based on the first order shear deformation theory(FSDT), the nonlinear dynamic equations involving transverse shear deformation and initial geometric imperfections were obtained by Hamilton's philosophy. Geometric deformation of the composite cylindrical shell was treated as the initial geometric imperfection in the dynamic equations, which were solved by the semi-analytical method in this paper. Stiffness reduction was employed for the damaged sub-layer, and the equivalent stiffness matrix was obtained for the delaminated area. By circumferential Fourier series expansions for shell displacements and loads and by using Galerkin technique, the nonlinear partial differential equations were transformed to ordinary differential equations which were finally solved by the finite difference method. The buckling was judged from shell responses by B-R criteria, and critical loads were then determined. The effect of the initial geometric deformation on the dynamic response and buckling of composite cylindrical shell was also discussed, as well as the effects of concomitant delamination and sub-layer matrix damages.