Nonlinear regime-switching state-space (RSSS) models.
Chow, Sy-Miin; Zhang, Guangjian
2013-10-01
Nonlinear dynamic factor analysis models extend standard linear dynamic factor analysis models by allowing time series processes to be nonlinear at the latent level (e.g., involving interaction between two latent processes). In practice, it is often of interest to identify the phases--namely, latent "regimes" or classes--during which a system is characterized by distinctly different dynamics. We propose a new class of models, termed nonlinear regime-switching state-space (RSSS) models, which subsumes regime-switching nonlinear dynamic factor analysis models as a special case. In nonlinear RSSS models, the change processes within regimes, represented using a state-space model, are allowed to be nonlinear. An estimation procedure obtained by combining the extended Kalman filter and the Kim filter is proposed as a way to estimate nonlinear RSSS models. We illustrate the utility of nonlinear RSSS models by fitting a nonlinear dynamic factor analysis model with regime-specific cross-regression parameters to a set of experience sampling affect data. The parallels between nonlinear RSSS models and other well-known discrete change models in the literature are discussed briefly.
Discrete state space modeling and control of nonlinear unknown systems.
Savran, Aydogan
2013-11-01
A novel procedure for integrating neural networks (NNs) with conventional techniques is proposed to design industrial modeling and control systems for nonlinear unknown systems. In the proposed approach, a new recurrent NN with a special architecture is constructed to obtain discrete-time state-space representations of nonlinear dynamical systems. It is referred as the discrete state-space neural network (DSSNN). In the DSSNN, the outputs of the hidden layer neurons of the DSSNN represent the system's (pseudo) state. The inputs are fed to output neurons and the delayed outputs of the hidden layer neurons are fed to their inputs via adjustable weights. The discrete state space model of the actual system is directly obtained by training the DSSNN with the input-output data. A training procedure based on the back-propagation through time (BPTT) algorithm is developed. The Levenberg-Marquardt (LM) method with a trust region approach is used to update the DSSNN weights. Linear state space models enable to use well developed conventional analysis and design techniques. Thus, building a linear model of a system has primary importance in industrial applications. Thus, a suitable linearization procedure is proposed to derive the linear state space model from the nonlinear DSSNN representation. The controllability, observability and stability properties are examined. The state feedback controllers are designed with both the linear quadratic regulator (LQR) and the pole placement techniques. The regulator and servo control problems are both addressed. A full order observer is also designed to estimate the state variables. The performance of the proposed procedure is demonstrated by applying for both single-input single-output (SISO) and multiple-input multiple-output (MIMO) nonlinear control problems. © 2013 ISA. Published by Elsevier Ltd. All rights reserved.
Nonlinear State Space Modeling and System Identification for Electrohydraulic Control
Directory of Open Access Journals (Sweden)
Jun Yan
2013-01-01
Full Text Available The paper deals with nonlinear modeling and identification of an electrohydraulic control system for improving its tracking performance. We build the nonlinear state space model for analyzing the highly nonlinear system and then develop a Hammerstein-Wiener (H-W model which consists of a static input nonlinear block with two-segment polynomial nonlinearities, a linear time-invariant dynamic block, and a static output nonlinear block with single polynomial nonlinearity to describe it. We simplify the H-W model into a linear-in-parameters structure by using the key term separation principle and then use a modified recursive least square method with iterative estimation of internal variables to identify all the unknown parameters simultaneously. It is found that the proposed H-W model approximates the actual system better than the independent Hammerstein, Wiener, and ARX models. The prediction error of the H-W model is about 13%, 54%, and 58% less than the Hammerstein, Wiener, and ARX models, respectively.
A nonlinear state-space approach to hysteresis identification
Noël, J. P.; Esfahani, A. F.; Kerschen, G.; Schoukens, J.
2017-02-01
Most studies tackling hysteresis identification in the technical literature follow white-box approaches, i.e. they rely on the assumption that measured data obey a specific hysteretic model. Such an assumption may be a hard requirement to handle in real applications, since hysteresis is a highly individualistic nonlinear behaviour. The present paper adopts a black-box approach based on nonlinear state-space models to identify hysteresis dynamics. This approach is shown to provide a general framework to hysteresis identification, featuring flexibility and parsimony of representation. Nonlinear model terms are constructed as a multivariate polynomial in the state variables, and parameter estimation is performed by minimising weighted least-squares cost functions. Technical issues, including the selection of the model order and the polynomial degree, are discussed, and model validation is achieved in both broadband and sine conditions. The study is carried out numerically by exploiting synthetic data generated via the Bouc-Wen equations.
Estimation methods for nonlinear state-space models in ecology
DEFF Research Database (Denmark)
Pedersen, Martin Wæver; Berg, Casper Willestofte; Thygesen, Uffe Høgsbro
2011-01-01
The use of nonlinear state-space models for analyzing ecological systems is increasing. A wide range of estimation methods for such models are available to ecologists, however it is not always clear, which is the appropriate method to choose. To this end, three approaches to estimation in the theta...... logistic model for population dynamics were benchmarked by Wang (2007). Similarly, we examine and compare the estimation performance of three alternative methods using simulated data. The first approach is to partition the state-space into a finite number of states and formulate the problem as a hidden...... Markov model (HMM). The second method uses the mixed effects modeling and fast numerical integration framework of the AD Model Builder (ADMB) open-source software. The third alternative is to use the popular Bayesian framework of BUGS. The study showed that state and parameter estimation performance...
On a state space approach to nonlinear H∞ control
Schaft, van der A.J.
1991-01-01
We study the standard H∞ optimal control problem using state feedback for smooth nonlinear control systems. The main theorem obtained roughly states that the L2-induced norm (from disturbances to inputs and outputs) can be made smaller than a constant γ > 0 if the corresponding H∞ norm for the syste
Identification of a Class of Non-linear State Space Models using RPE Techniques
DEFF Research Database (Denmark)
Zhou, Wei-Wu; Blanke, Mogens
1989-01-01
The RPE (recursive prediction error) method in state-space form is developed in the nonlinear systems and extended to include the exact form of a nonlinearity, thus enabling structure preservation for certain classes of nonlinear systems. Both the discrete and the continuous-discrete versions...... of the algorithm in an innovations model are investigated, and a nonlinear simulation example shows a quite convincing performance of the filter as combined parameter and state estimator...
Identification of a class of nonlinear state-space models using RPE techniques
DEFF Research Database (Denmark)
Zhou, W. W.; Blanke, Mogens
1986-01-01
The recursive prediction error methods in state-space form have been efficiently used as parameter identifiers for linear systems, and especially Ljung's innovations filter using a Newton search direction has proved to be quite ideal. In this paper, the RPE method in state-space form is developed...... to the nonlinear case and extended to include the exact form of a nonlinearity, thus enabling structure preservation for certain classes of nonlinear systems. Both the discrete and the continuous-discrete versions of the algorithm in an innovations model are investigated, and a nonlinear simulation example shows...... a quite convincing performance of the filter as combined parameter and state estimator....
Identification of Nonlinear Nonautonomous State Space Systems from Input-Output Measurements
Verdult, Vincent; Verhaegen, Michel; Scherpen, Jacquelien
2000-01-01
This paper presents a method to determine a nonlinear state space model from a finite number of measurements of the inputs and outputs. The method is based on embedding theory for nonlinear systems, and can be viewed as an extension of the subspace identification method for linear systems. The paper
Nonlinear state space model identification of synchronous generators
Energy Technology Data Exchange (ETDEWEB)
Dehghani, M.; Nikravesh, S.K.Y. [Electrical Engineering Department, Amirkabir University of Technology, Tehran (Iran)
2008-05-15
A method for identification of a synchronous generator is suggested in this paper. The method uses the theoretical relations of machine parameters and the Prony method to find the state space model of the system. Such models are useful for controller design and stability tests. The proposed identification method is applied to a third order model of a synchronous generator. In this study, the field voltage is considered as the input and the active output power and the rotor angle are considered as the outputs of the synchronous generator. Simulation results show good accuracy of the identified model. (author)
MCMC for non-linear state space models using ensembles of latent sequences
2013-01-01
Non-linear state space models are a widely-used class of models for biological, economic, and physical processes. Fitting these models to observed data is a difficult inference problem that has no straightforward solution. We take a Bayesian approach to the inference of unknown parameters of a non-linear state model; this, in turn, requires the availability of efficient Markov Chain Monte Carlo (MCMC) sampling methods for the latent (hidden) variables and model parameters. Using the ensemble ...
Gain Scheduling Control of Nonlinear Systems Based on Neural State Space Models
DEFF Research Database (Denmark)
Bendtsen, Jan Dimon; Stoustrup, Jakob
2003-01-01
This paper presents a novel method for gain scheduling control of nonlinear systems based on extraction of local linear state space models from neural networks with direct application to robust control. A neural state space model of the system is first trained based on in- and output training...... samples from the system, after which linearized state space models are extracted from the neural network in a number of operating points according to a simple and computationally cheap scheme. Robust observer-based controllers can then be designed in each of these operating points,and gain scheduling...
Sun, Xiaodian; Jin, Li; Xiong, Momiao
2008-01-01
It is system dynamics that determines the function of cells, tissues and organisms. To develop mathematical models and estimate their parameters are an essential issue for studying dynamic behaviors of biological systems which include metabolic networks, genetic regulatory networks and signal transduction pathways, under perturbation of external stimuli. In general, biological dynamic systems are partially observed. Therefore, a natural way to model dynamic biological systems is to employ nonlinear state-space equations. Although statistical methods for parameter estimation of linear models in biological dynamic systems have been developed intensively in the recent years, the estimation of both states and parameters of nonlinear dynamic systems remains a challenging task. In this report, we apply extended Kalman Filter (EKF) to the estimation of both states and parameters of nonlinear state-space models. To evaluate the performance of the EKF for parameter estimation, we apply the EKF to a simulation dataset and two real datasets: JAK-STAT signal transduction pathway and Ras/Raf/MEK/ERK signaling transduction pathways datasets. The preliminary results show that EKF can accurately estimate the parameters and predict states in nonlinear state-space equations for modeling dynamic biochemical networks.
Recursive prediction error methods for online estimation in nonlinear state-space models
Directory of Open Access Journals (Sweden)
Dag Ljungquist
1994-04-01
Full Text Available Several recursive algorithms for online, combined state and parameter estimation in nonlinear state-space models are discussed in this paper. Well-known algorithms such as the extended Kalman filter and alternative formulations of the recursive prediction error method are included, as well as a new method based on a line-search strategy. A comparison of the algorithms illustrates that they are very similar although the differences can be important for the online tracking capabilities and robustness. Simulation experiments on a simple nonlinear process show that the performance under certain conditions can be improved by including a line-search strategy.
Liu, Peipei; Sohn, Hoon; Park, Byeongjin
2015-06-01
Damage often causes a structural system to exhibit severe nonlinear behaviors, and the resulting nonlinear features are often much more sensitive to the damage than their linear counterparts. This study develops a laser nonlinear wave modulation spectroscopy (LNWMS) so that certain types of damage can be detected without any sensor placement. The proposed LNWMS utilizes a pulse laser to generate ultrasonic waves and a laser vibrometer for ultrasonic measurement. Under the broadband excitation of the pulse laser, a nonlinear source generates modulations at various frequency values due to interactions among various input frequency components. State space attractors are reconstructed from the ultrasonic responses measured by LNWMS, and a damage feature called Bhattacharyya distance (BD) is computed from the state space attractors to quantify the degree of damage-induced nonlinearity. By computing the BD values over the entire target surface using laser scanning, damage can be localized and visualized without relying on the baseline data obtained from the pristine condition of a target structure. The proposed technique has been successfully used for visualizing fatigue crack in an aluminum plate and delamination and debonding in a glass fiber reinforced polymer wind turbine blade.
Directory of Open Access Journals (Sweden)
Esfandiar, H.
2013-05-01
Full Text Available In this paper, based on the VoigtKelvin constitutive model, nonlinear dynamic modelling and state space representation of a viscoelastic beam acting as a flexible robotic manipulator is investigated. Complete nonlinear dynamic modelling of a viscoelastic beam without premature linearisation of dynamic equations is developed. The adopted method is capable of reproducing nonlinear dynamic effects, such as beam stiffening due to centrifugal and Coriolis forces induced by rotation of the joints. Structural damping effects on the models dynamic behaviour are also shown. A reliable model for a viscoelastic beam is subsequently presented. The governing equations of motion are derived using Hamiltons principle, and using the finite difference method, nonlinear partial differential equations are reduced to ordinary differential equations. For the purpose of flexible manipulator control, the standard form of state space equations for the viscoelastic link and the actuator is obtained. Simulation results indicate substantial improvements in dynamic behaviour, and a parameter sensitivity study is carried out to investigate the effect of structural damping on the vibration amplitude.
Inferring gene regulatory networks via nonlinear state-space models and exploiting sparsity.
Noor, Amina; Serpedin, Erchin; Nounou, Mohamed; Nounou, Hazem N
2012-01-01
This paper considers the problem of learning the structure of gene regulatory networks from gene expression time series data. A more realistic scenario when the state space model representing a gene network evolves nonlinearly is considered while a linear model is assumed for the microarray data. To capture the nonlinearity, a particle filter-based state estimation algorithm is considered instead of the contemporary linear approximation-based approaches. The parameters characterizing the regulatory relations among various genes are estimated online using a Kalman filter. Since a particular gene interacts with a few other genes only, the parameter vector is expected to be sparse. The state estimates delivered by the particle filter and the observed microarray data are then subjected to a LASSO-based least squares regression operation which yields a parsimonious and efficient description of the regulatory network by setting the irrelevant coefficients to zero. The performance of the aforementioned algorithm is compared with the extended Kalman filter (EKF) and Unscented Kalman Filter (UKF) employing the Mean Square Error (MSE) as the fidelity criterion in recovering the parameters of gene regulatory networks from synthetic data and real biological data. Extensive computer simulations illustrate that the proposed particle filter-based network inference algorithm outperforms EKF and UKF, and therefore, it can serve as a natural framework for modeling gene regulatory networks with nonlinear and sparse structure.
Pan, Shuokai; Elliott, Stephen J; Teal, Paul D; Lineton, Ben
2015-06-01
Nonlinear models of the cochlea are best implemented in the time domain, but their computational demands usually limit the duration of the simulations that can reasonably be performed. This letter presents a modified state space method and its application to an example nonlinear one-dimensional transmission-line cochlear model. The sparsity pattern of the individual matrices for this alternative formulation allows the use of significantly faster numerical algorithms. Combined with a more efficient implementation of the saturating nonlinearity, the computational speed of this modified state space method is more than 40 times faster than that of the original formulation.
Scherpen, Jacquelien M.A.; Gray, W. Steven
2000-01-01
In this paper a set of sufficient conditions is developed in terms of controllability and observability functions under which a given state-space realization of a formal power series is minimal. Specifically, it is shown that positivity of these functions, in addition to a stability requirement and
Niemi, Jarad; West, Mike
2010-06-01
We describe a strategy for Markov chain Monte Carlo analysis of non-linear, non-Gaussian state-space models involving batch analysis for inference on dynamic, latent state variables and fixed model parameters. The key innovation is a Metropolis-Hastings method for the time series of state variables based on sequential approximation of filtering and smoothing densities using normal mixtures. These mixtures are propagated through the non-linearities using an accurate, local mixture approximation method, and we use a regenerating procedure to deal with potential degeneracy of mixture components. This provides accurate, direct approximations to sequential filtering and retrospective smoothing distributions, and hence a useful construction of global Metropolis proposal distributions for simulation of posteriors for the set of states. This analysis is embedded within a Gibbs sampler to include uncertain fixed parameters. We give an example motivated by an application in systems biology. Supplemental materials provide an example based on a stochastic volatility model as well as MATLAB code.
Nonlinear field space cosmology
Mielczarek, Jakub; Trześniewski, Tomasz
2017-08-01
We consider the FRW cosmological model in which the matter content of the Universe (playing the role of an inflaton or quintessence) is given by a novel generalization of the massive scalar field. The latter is a scalar version of the recently introduced nonlinear field space theory, where the physical phase space of a given field is assumed to be compactified at large energies. For our analysis, we choose the simple case of a field with the spherical phase space and endow it with the generalized Hamiltonian analogous to the XXZ Heisenberg model, normally describing a system of spins in condensed matter physics. Subsequently, we study both the homogenous cosmological sector and linear perturbations of such a test field. In the homogenous sector, we find that nonlinearity of the field phase space is becoming relevant for large volumes of the Universe and can lead to a recollapse, and possibly also at very high energies, leading to the phase of a bounce. Quantization of the field is performed in the limit where the nontrivial nature of its phase space can be neglected, while there is a nonvanishing contribution from the Lorentz symmetry breaking term of the Hamiltonian. As a result, in the leading order of the XXZ anisotropy parameter, we find that the inflationary spectral index remains unmodified with respect to the standard case but the total amplitude of perturbations is subject to a correction. The Bunch-Davies vacuum state also becomes appropriately corrected. The proposed new approach is bringing cosmology and condensed matter physics closer together, which may turn out to be beneficial for both disciplines.
Tao, Jili; Ma, Longhua; Zhu, Yong
2016-11-01
Inspired by the state space model based predictive control, this paper presents the combination design of extended non-minimal state space predictive control (ENMSSPC) and modified linear quadratic regulator (LQR) for a kind of nonlinear process with output feedback coupling, which shows improved control performance for both model/plant match and model/plant mismatch cases. In many previous control methods for this kind of nonlinear systems, the nonlinear part is treated in different ways such as ignored, represented as a rough linear one or assumed to be time-variant when corresponding predictive control methods are designed. However, the above methods will generally lead to information loss, resulting in the influenced control performance. This paper will show that the ENMSSPC-LQ control structure will further improve closed-loop control performance concerning tracking ability and disturbance rejection compared with previous predictive control methods.
Tkachova, P.; Krot, A.; Minervina, H.
It is well known that there is chaos in convective process in atmosphere and ocean. In particular,dynamic model of Lorenz [1] describes the Rayleigh-Benard convection phenomenon. Phase trajectories of Lorenz equation system are characterized by strange alternative properties: on the one hand, they diverge (because of positive Lyapunov exponents), on the second hand, they attract to the limited domain of phase space called an attractor [1]. The Lorenz attractor has specific geometrical structure and can be characterized by means of fractal dimension. In this connection the aim of this work is development of analysis of Lorenz attractor based on the proposed nonlinear decomposition into matrix series [2]. This analysis permits to estimate the values of characteristic parameters (including control one) of Lorenz attractors and predict their evolution in time. Using results of matrix decomposition [2], it is not difficult to see that the change of vector function (describing the Lorenz attractor) can be approximated by only linear and quadratic terms [3]. Because values of the first and second order derivatives can be calculated by means of numerical methods we can estimate the change of the vector function from computational experiment. In result, the values of parameters of the Lorenz's attractor can be estimated. This permits us to solve the identification task of the current dynamical state of a convective aerodynamic flows. Moreover, using the results of matrix decomposition we can estimate the minimal embedding dimension [4] for the Lorenz attractor based on experimental data. References: [1] P.Berge,Y.Pomeau and C.Vidal. L'ordre dans le chaos: Vers une approche deterministe de la turbulence. Hermann:Paris,1988. [2] A.M.Krot, "Matrix decompositions of vector functions and shift operators on the trajectories of a nonlinear dynamical system", Nonlinear Phenomena in Complex Systems,vol.4, N2, pp.106- 115, 2001. [3] A.M.Krot and P
Quach, Minh; Brunel, Nicolas; d'Alché-Buc, Florence
2007-12-01
Statistical inference of biological networks such as gene regulatory networks, signaling pathways and metabolic networks can contribute to build a picture of complex interactions that take place in the cell. However, biological systems considered as dynamical, non-linear and generally partially observed processes may be difficult to estimate even if the structure of interactions is given. Using the same approach as Sitz et al. proposed in another context, we derive non-linear state-space models from ODEs describing biological networks. In this framework, we apply Unscented Kalman Filtering (UKF) to the estimation of both parameters and hidden variables of non-linear state-space models. We instantiate the method on a transcriptional regulatory model based on Hill kinetics and a signaling pathway model based on mass action kinetics. We successfully use synthetic data and experimental data to test our approach. This approach covers a large set of biological networks models and gives rise to simple and fast estimation algorithms. Moreover, the Bayesian tool used here directly provides uncertainty estimates on parameters and hidden states. Let us also emphasize that it can be coupled with structure inference methods used in Graphical Probabilistic Models. Matlab code available on demand.
Zeng, Nianyin; Wang, Zidong; Li, Yurong; Du, Min; Liu, Xiaohui
2011-07-01
In this paper, a mathematical model for sandwich-type lateral flow immunoassay is developed via short available time series. A nonlinear dynamic stochastic model is considered that consists of the biochemical reaction system equations and the observation equation. After specifying the model structure, we apply the extended Kalman filter (EKF) algorithm for identifying both the states and parameters of the nonlinear state-space model. It is shown that the EKF algorithm can accurately identify the parameters and also predict the system states in the nonlinear dynamic stochastic model through an iterative procedure by using a small number of observations. The identified mathematical model provides a powerful tool for testing the system hypotheses and also for inspecting the effects from various design parameters in both rapid and inexpensive way. Furthermore, by means of the established model, the dynamic changes in the concentration of antigens and antibodies can be predicted, thereby making it possible for us to analyze, optimize, and design the properties of lateral flow immunoassay devices. © 2011 IEEE
The Pruned State-Space System for Non-Linear DSGE Models: Theory and Empirical Applications
Andreasen, Martin Møller; Fernández-Villaverde, Jesús; Juan F Rubio-Ramírez
2013-01-01
This paper studies the pruned state-space system for higher-order approximations to the solutions of DSGE models. For second- and third-order approximations, we derive the statistical properties of this system and provide closed-form expressions for first and second unconditional moments and impulse response functions. Thus, our analysis introduces GMM estimation for DSGE models approximated up to third-order and provides the foundation for indirect inference and SMM when simulation is requir...
Chu-Tong Wang; Tsai, Jason S. H.; Chia-Wei Chen; You Lin; Shu-Mei Guo; Leang-San Shieh
2010-01-01
An active fault-tolerant pulse-width-modulated tracker using the nonlinear autoregressive moving average with exogenous inputs model-based state-space self-tuning control is proposed for continuous-time multivariable nonlinear stochastic systems with unknown system parameters, plant noises, measurement noises, and inaccessible system states. Through observer/Kalman filter identification method, a good initial guess of the unknown parameters of the chosen model is obtained so as to reduce the ...
Stochastic State Space Modelling of Nonlinear systems - With application to Marine Ecosystems
DEFF Research Database (Denmark)
Møller, Jan Kloppenborg
to conflict with the concept of mass balances. One of the central conclusions of the thesis is that the stochastic formulations should be an integral part of the model formulation. As discrete-time stochastic processes are simpler to handle numerically than continuous-time stochastic processes, I start......This thesis deals with stochastic dynamical systems in discrete and continuous time. Traditionally dynamical systems in continuous time are modelled using Ordinary Differential Equations (ODEs). Even the most complex system of ODEs will not be able to capture every detail of a complex system like...... a natural ecosystem, and hence residual variation between the model and observations will always remain. In stochastic state-space models the residual variation is separated into observation and system noise and a main theme of the thesis is a proper description of the system noise. Additive Gaussian noise...
The Nonlinear Field Space Theory
Mielczarek, Jakub; Trześniewski, Tomasz
2016-08-01
In recent years the idea that not only the configuration space of particles, i.e. spacetime, but also the corresponding momentum space may have nontrivial geometry has attracted significant attention, especially in the context of quantum gravity. The aim of this letter is to extend this concept to the domain of field theories, by introducing field spaces (i.e. phase spaces of field values) that are not affine spaces. After discussing the motivation and general aspects of our approach we present a detailed analysis of the prototype (quantum) Nonlinear Field Space Theory of a scalar field on the Minkowski background. We show that the nonlinear structure of a field space leads to numerous interesting predictions, including: non-locality, generalization of the uncertainty relations, algebra deformations, constraining of the maximal occupation number, shifting of the vacuum energy and renormalization of the charge and speed of propagation of field excitations. Furthermore, a compact field space is a natural way to implement the "Principle of finiteness" of physical theories, which once motivated the Born-Infeld theory. Thus the presented framework has a variety of potential applications in the theories of fundamental interactions (e.g. quantum gravity), as well as in condensed matter physics (e.g. continuous spin chains), and can shed new light on the issue of divergences in quantum field theories.
The Nonlinear Field Space Theory
Energy Technology Data Exchange (ETDEWEB)
Mielczarek, Jakub, E-mail: jakub.mielczarek@uj.edu.pl [Institute of Physics, Jagiellonian University, ul. Łojasiewicza 11, 30-348 Kraków (Poland); Trześniewski, Tomasz, E-mail: tbwbt@ift.uni.wroc.pl [Institute of Physics, Jagiellonian University, ul. Łojasiewicza 11, 30-348 Kraków (Poland); Institute for Theoretical Physics, University of Wrocław, pl. Borna 9, 50-204 Wrocław (Poland)
2016-08-10
In recent years the idea that not only the configuration space of particles, i.e. spacetime, but also the corresponding momentum space may have nontrivial geometry has attracted significant attention, especially in the context of quantum gravity. The aim of this letter is to extend this concept to the domain of field theories, by introducing field spaces (i.e. phase spaces of field values) that are not affine spaces. After discussing the motivation and general aspects of our approach we present a detailed analysis of the prototype (quantum) Nonlinear Field Space Theory of a scalar field on the Minkowski background. We show that the nonlinear structure of a field space leads to numerous interesting predictions, including: non-locality, generalization of the uncertainty relations, algebra deformations, constraining of the maximal occupation number, shifting of the vacuum energy and renormalization of the charge and speed of propagation of field excitations. Furthermore, a compact field space is a natural way to implement the “Principle of finiteness” of physical theories, which once motivated the Born–Infeld theory. Thus the presented framework has a variety of potential applications in the theories of fundamental interactions (e.g. quantum gravity), as well as in condensed matter physics (e.g. continuous spin chains), and can shed new light on the issue of divergences in quantum field theories.
The Nonlinear Field Space Theory
Directory of Open Access Journals (Sweden)
Jakub Mielczarek
2016-08-01
Full Text Available In recent years the idea that not only the configuration space of particles, i.e. spacetime, but also the corresponding momentum space may have nontrivial geometry has attracted significant attention, especially in the context of quantum gravity. The aim of this letter is to extend this concept to the domain of field theories, by introducing field spaces (i.e. phase spaces of field values that are not affine spaces. After discussing the motivation and general aspects of our approach we present a detailed analysis of the prototype (quantum Nonlinear Field Space Theory of a scalar field on the Minkowski background. We show that the nonlinear structure of a field space leads to numerous interesting predictions, including: non-locality, generalization of the uncertainty relations, algebra deformations, constraining of the maximal occupation number, shifting of the vacuum energy and renormalization of the charge and speed of propagation of field excitations. Furthermore, a compact field space is a natural way to implement the “Principle of finiteness” of physical theories, which once motivated the Born–Infeld theory. Thus the presented framework has a variety of potential applications in the theories of fundamental interactions (e.g. quantum gravity, as well as in condensed matter physics (e.g. continuous spin chains, and can shed new light on the issue of divergences in quantum field theories.
Some nonlinear space decomposition algorithms
Energy Technology Data Exchange (ETDEWEB)
Tai, Xue-Cheng; Espedal, M. [Univ. of Bergen (Norway)
1996-12-31
Convergence of a space decomposition method is proved for a general convex programming problem. The space decomposition refers to methods that decompose a space into sums of subspaces, which could be a domain decomposition or a multigrid method for partial differential equations. Two algorithms are proposed. Both can be used for linear as well as nonlinear elliptic problems and they reduce to the standard additive and multiplicative Schwarz methods for linear elliptic problems. Two {open_quotes}hybrid{close_quotes} algorithms are also presented. They converge faster than the additive one and have better parallelism than the multiplicative method. Numerical tests with a two level domain decomposition for linear, nonlinear and interface elliptic problems are presented for the proposed algorithms.
Control of nonlinear flexible space structures
Shi, Jianjun
With the advances made in computer technology and efficiency of numerical algorithms over last decade, the MPC strategies have become quite popular among control community. However, application of MPC or GPC to flexible space structure control has not been explored adequately in the literature. The work presented in this thesis primarily focuses on application of GPC to control of nonlinear flexible space structures. This thesis is particularly devoted to the development of various approximate dynamic models, design and assessment of candidate controllers, and extensive numerical simulations for a realistic multibody flexible spacecraft, namely, Jupiter Icy Moons Orbiter (JIMO)---a Prometheus class of spacecraft proposed by NASA for deep space exploratory missions. A stable GPC algorithm is developed for Multi-Input-Multi-Output (MIMO) systems. An end-point weighting (penalty) is used in the GPC cost function to guarantee the nominal stability of the closed-loop system. A method is given to compute the desired end-point state from the desired output trajectory. The methodologies based on Fake Algebraic Riccati Equation (FARE) and constrained nonlinear optimization, are developed for synthesis of state weighting matrix. This makes this formulation more practical. A stable reconfigurable GPC architecture is presented and its effectiveness is demonstrated on both aircraft as well as spacecraft model. A representative in-orbit maneuver is used for assessing the performance of various control strategies using various design models. Different approximate dynamic models used for analysis include linear single body flexible structure, nonlinear single body flexible structure, and nonlinear multibody flexible structure. The control laws evaluated include traditional GPC, feedback linearization-based GPC (FLGPC), reconfigurable GPC, and nonlinear dissipative control. These various control schemes are evaluated for robust stability and robust performance in the presence of
Directory of Open Access Journals (Sweden)
Peter W. Tse
2017-02-01
Full Text Available Bearings are widely used in various industries to support rotating shafts. Their failures accelerate failures of other adjacent components and may cause unexpected machine breakdowns. In recent years, nonlinear vibration responses collected from a dynamic rotor-bearing system have been widely analyzed for bearing diagnostics. Numerous methods have been proposed to identify different bearing faults. However, these methods are unable to predict the future health conditions of bearings. To extend bearing diagnostics to bearing prognostics, this paper reports the design of a state space formulation of nonlinear vibration responses collected from a dynamic rotor-bearing system in order to intelligently predict bearing remaining useful life (RUL. Firstly, analyses of nonlinear vibration responses were conducted to construct a bearing health indicator (BHI so as to assess the current bearing health condition. Secondly, a state space model of the BHI was developed to mathematically track the health evolution of the BHI. Thirdly, unscented particle filtering was used to predict bearing RUL. Lastly, a new bearing acceleration life testing setup was designed to collect natural bearing degradation data, which were used to validate the effectiveness of the proposed bearing prognostic method. Results show that the prediction accuracy of the proposed bearing prognostic method is promising and the proposed bearing prognostic method is able to reflect future bearing health conditions.
Ławryńczuk, Maciej
2017-03-01
This paper details development of a Model Predictive Control (MPC) algorithm for a boiler-turbine unit, which is a nonlinear multiple-input multiple-output process. The control objective is to follow set-point changes imposed on two state (output) variables and to satisfy constraints imposed on three inputs and one output. In order to obtain a computationally efficient control scheme, the state-space model is successively linearised on-line for the current operating point and used for prediction. In consequence, the future control policy is easily calculated from a quadratic optimisation problem. For state estimation the extended Kalman filter is used. It is demonstrated that the MPC strategy based on constant linear models does not work satisfactorily for the boiler-turbine unit whereas the discussed algorithm with on-line successive model linearisation gives practically the same trajectories as the truly nonlinear MPC controller with nonlinear optimisation repeated at each sampling instant. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
Nonlinear approximation in alpha-modulation spaces
DEFF Research Database (Denmark)
Borup, Lasse; Nielsen, Morten
2006-01-01
The α-modulation spaces are a family of spaces that contain the Besov and modulation spaces as special cases. In this paper we prove that brushlet bases can be constructed to form unconditional and even greedy bases for the α-modulation spaces. We study m -term nonlinear approximation with brushlet...... bases, and give complete characterizations of the associated approximation spaces in terms of α-modulation spaces....
Space curves, anholonomy and nonlinearity
Indian Academy of Sciences (India)
Radha Balakrishnan
2005-04-01
Using classical differential geometry, we discuss the phenomenon of anholonomy that gets associated with a static and a moving curve. We obtain the expressions for the respective geometric phases in the two cases and interpret them. We show that there is a close connection between anholonomy and nonlinearity in a wide class of nonlinear systems.
Nonlinear Oscillators in Space Physics
Lester,Daniel; Thronson, Harley
2011-01-01
We discuss dynamical systems that produce an oscillation without an external time dependent source. Numerical results are presented for nonlinear oscillators in the Em1h's atmosphere, foremost the quasi-biennial oscillation (QBOl. These fluid dynamical oscillators, like the solar dynamo, have in common that one of the variables in a governing equation is strongly nonlinear and that the nonlinearity, to first order, has particular form. of 3rd or odd power. It is shown that this form of nonlinearity can produce the fundamental li'equency of the internal oscillation. which has a period that is favored by the dynamical condition of the fluid. The fundamental frequency maintains the oscillation, with no energy input to the system at that particular frequency. Nonlinearities of 2nd or even power could not maintain the oscillation.
Non-Linear Relativity in Position Space
Kimberly, D; Medeiros-Neto, J F; Kimberly, Dagny; Magueijo, João; Medeiros, João
2003-01-01
We propose two methods for obtaining the dual of non-linear relativity as previously formulated in momentum space. In the first we allow for the (dual) position space to acquire a non-linear representation of the Lorentz group independently of the chosen representation in momentum space. This requires a non-linear definition for the invariant contraction between momentum and position spaces. The second approach, instead, respects the linearity of the invariant contraction. This fully fixes the dual of momentum space and dictates a set of energy-dependent space-time Lorentz transformations. We discuss a variety of physical implications that would distinguish these two strategies. We also show how they point to two rather distinct formulations of theories of gravity with an invariant energy and/or length scale.
DEFF Research Database (Denmark)
Mailund, Thomas
The thesis describes the sweep-line method, a newly developed reduction method for alleviating the state explosion problem inherent in explicit-state state space exploration. The basic idea underlying the sweep-line method is, when calculating the state space, to recognise and delete states...... that are not reachable from the currently unprocessed states. Intuitively we drag a sweep-line through the state space with the invariant that all states behind the sweep-line have been processed and are unreachable from the states in front of the sweep-line. When calculating the state space of a system we iteratively...
DEFF Research Database (Denmark)
Mailund, Thomas
The thesis describes the sweep-line method, a newly developed reduction method for alleviating the state explosion problem inherent in explicit-state state space exploration. The basic idea underlying the sweep-line method is, when calculating the state space, to recognise and delete states...... that are not reachable from the currently unprocessed states. Intuitively we drag a sweep-line through the state space with the invariant that all states behind the sweep-line have been processed and are unreachable from the states in front of the sweep-line. When calculating the state space of a system we iteratively...
Directory of Open Access Journals (Sweden)
Chu-Tong Wang
2010-01-01
Full Text Available An active fault-tolerant pulse-width-modulated tracker using the nonlinear autoregressive moving average with exogenous inputs model-based state-space self-tuning control is proposed for continuous-time multivariable nonlinear stochastic systems with unknown system parameters, plant noises, measurement noises, and inaccessible system states. Through observer/Kalman filter identification method, a good initial guess of the unknown parameters of the chosen model is obtained so as to reduce the identification process time and enhance the system performances. Besides, by modifying the conventional self-tuning control, a fault-tolerant control scheme is also developed. For the detection of fault occurrence, a quantitative criterion is exploited by comparing the innovation process errors estimated by the Kalman filter estimation algorithm. In addition, the weighting matrix resetting technique is presented by adjusting and resetting the covariance matrix of parameter estimates to improve the parameter estimation for faulty system recovery. The technique can effectively cope with partially abrupt and/or gradual system faults and/or input failures with fault detection.
Lagrangian Space Nonlinear $E$-mode clustering
Yu, Hao-Ran; Zhu, Hong-Ming
2016-01-01
We study the nonlinear $E$-mode clustering in Lagrangian space by using large scale structure (LSS) $N$-body simulations and use the displacement field information in Lagrangian space to recover the primordial linear density field. We find that, compared to Eulerian nonlinear density fields, the $E$-mode displacement fields in Lagrangian space improves the cross-correlation scale $k$ with initial density field by factor of 6 $\\sim$ 7, containing 2 orders of magnitude more primordial information. This illustrates ability of potential density reconstruction algorithms, to improve the baryonic acoustic oscillation (BAO) measurements from current and future large scale structure surveys.
Spin squeezing in nonlinear spin coherent states
Wang, Xiaoguang
2001-01-01
We introduce the nonlinear spin coherent state via its ladder operator formalism and propose a type of nonlinear spin coherent state by the nonlinear time evolution of spin coherent states. By a new version of spectroscopic squeezing criteria we study the spin squeezing in both the spin coherent state and nonlinear spin coherent state. The results show that the spin coherent state is not squeezed in the x, y, and z directions, and the nonlinear spin coherent state may be squeezed in the x and...
Dreano, D.
2017-04-05
Specification and tuning of errors from dynamical models are important issues in data assimilation. In this work, we propose an iterative expectation-maximisation (EM) algorithm to estimate the model error covariances using classical extended and ensemble versions of the Kalman smoother. We show that, for additive model errors, the estimate of the error covariance converges. We also investigate other forms of model error, such as parametric or multiplicative errors. We show that additive Gaussian model error is able to compensate for non additive sources of error in the algorithms we propose. We also demonstrate the limitations of the extended version of the algorithm and recommend the use of the more robust and flexible ensemble version. This article is a proof of concept of the methodology with the Lorenz-63 attractor. We developed an open-source Python library to enable future users to apply the algorithm to their own nonlinear dynamical models.
New Tripartite Nonlinear Entangled State Representation in Quantum Mechanics
Institute of Scientific and Technical Information of China (English)
KUANG Mai-Hua; MA Shan-Jun; LIU Dong-Mei
2008-01-01
Based on the technique of integral within an ordered product of nonlinear bosonic operators, we construct a new kind of tripartite nonlinear entangled state |α,γ>λ in 3-mode Fock space, which can make up a complete set. We also simply discuss its properties and application.
Nonextensivity, Complexity and Nonlinearity in Space Plasmas
Pavlos, G. P.
2017-01-01
Experimental time series, extracted from many and different space plasma systems corresponding to, solar wind, magnetospheric and other space plasma systems reveal common dynamical, geometrical, or statistical characteristics. Such characteristics are the low dimensionality, the typical intermittent turbulence multifractality, the temporal or spatial multiscale correlations and power laws scale invariance, non Gaoussianity and others. This universal aspect of experimental time series profiles was understood in the past as the chaos or SOC universality. However, after two or three decades of theoretical development in understanding of the nonlinearity and complexity, we can give a more compact theoretical description of the underline universal physical processes that produce the experimental time series complexity. Finally, in this study, we present and explain the modern complex set of theoretical concepts from the point of view of physics as the unification theory of nonlinear theory of non-equilibrium plasma systems as well as the presupposed theoretical framework of time series analysis of space plasma charachteristics.
Approximate Methods for State-Space Models
Koyama, Shinsuke; Shalizi, Cosma Rohilla; Kass, Robert E; 10.1198/jasa.2009.tm08326
2010-01-01
State-space models provide an important body of techniques for analyzing time-series, but their use requires estimating unobserved states. The optimal estimate of the state is its conditional expectation given the observation histories, and computing this expectation is hard when there are nonlinearities. Existing filtering methods, including sequential Monte Carlo, tend to be either inaccurate or slow. In this paper, we study a nonlinear filter for nonlinear/non-Gaussian state-space models, which uses Laplace's method, an asymptotic series expansion, to approximate the state's conditional mean and variance, together with a Gaussian conditional distribution. This {\\em Laplace-Gaussian filter} (LGF) gives fast, recursive, deterministic state estimates, with an error which is set by the stochastic characteristics of the model and is, we show, stable over time. We illustrate the estimation ability of the LGF by applying it to the problem of neural decoding and compare it to sequential Monte Carlo both in simulat...
Processing Approach of Non-linear Adjustment Models in the Space of Non-linear Models
Institute of Scientific and Technical Information of China (English)
LI Chaokui; ZHU Qing; SONG Chengfang
2003-01-01
This paper investigates the mathematic features of non-linear models and discusses the processing way of non-linear factors which contributes to the non-linearity of a nonlinear model. On the basis of the error definition, this paper puts forward a new adjustment criterion, SGPE.Last, this paper investigates the solution of a non-linear regression model in the non-linear model space and makes the comparison between the estimated values in non-linear model space and those in linear model space.
Realization of non-linear coherent states by photonic lattices
Directory of Open Access Journals (Sweden)
Shahram Dehdashti
2015-06-01
Full Text Available In this paper, first, by introducing Holstein-Primakoff representation of α-deformed algebra, we achieve the associated non-linear coherent states, including su(2 and su(1, 1 coherent states. Second, by using waveguide lattices with specific coupling coefficients between neighbouring channels, we generate these non-linear coherent states. In the case of positive values of α, we indicate that the Hilbert size space is finite; therefore, we construct this coherent state with finite channels of waveguide lattices. Finally, we study the field distribution behaviours of these coherent states, by using Mandel Q parameter.
Realization of non-linear coherent states by photonic lattices
Energy Technology Data Exchange (ETDEWEB)
Dehdashti, Shahram, E-mail: shdehdashti@zju.edu.cn; Li, Rujiang; Chen, Hongsheng, E-mail: hansomchen@zju.edu.cn [State Key Laboratory of Modern Optical Instrumentations, Zhejiang University, Hangzhou 310027 (China); The Electromagnetics Academy at Zhejiang University, Zhejiang University, Hangzhou 310027 (China); Liu, Jiarui, E-mail: jrliu@zju.edu.cn; Yu, Faxin [School of Aeronautics and Astronautics, Zhejiang University, Hangzhou 310027 (China)
2015-06-15
In this paper, first, by introducing Holstein-Primakoff representation of α-deformed algebra, we achieve the associated non-linear coherent states, including su(2) and su(1, 1) coherent states. Second, by using waveguide lattices with specific coupling coefficients between neighbouring channels, we generate these non-linear coherent states. In the case of positive values of α, we indicate that the Hilbert size space is finite; therefore, we construct this coherent state with finite channels of waveguide lattices. Finally, we study the field distribution behaviours of these coherent states, by using Mandel Q parameter.
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.
Generalized non-linear strength theory and transformed stress space
Institute of Scientific and Technical Information of China (English)
YAO Yangping; LU Dechun; ZHOU Annan; ZOU Bo
2004-01-01
Based on the test data of frictional materials and previous research achievements in this field, a generalized non-linear strength theory (GNST) is proposed. It describes non-linear strength properties on the π-plane and the meridian plane using a unified formula, and it includes almost all the present non-linear strength theories, which can be used in just one material. The shape of failure function of the GNST is a smooth curve between the SMP criterion and the Mises criterion on the π-plane, and an exponential curve on the meridian plane. Through the transformed stress space based on the GNST, the combination of the GNST and various constitutive models using p and q as stress parameters can be realized simply and rationally in three-dimensional stress state.
Space vehicle pose estimation via optical correlation and nonlinear estimation
Rakoczy, John M.; Herren, Kenneth A.
2008-03-01
A technique for 6-degree-of-freedom (6DOF) pose estimation of space vehicles is being developed. This technique draws upon recent developments in implementing optical correlation measurements in a nonlinear estimator, which relates the optical correlation measurements to the pose states (orientation and position). For the optical correlator, the use of both conjugate filters and binary, phase-only filters in the design of synthetic discriminant function (SDF) filters is explored. A static neural network is trained a priori and used as the nonlinear estimator. New commercial animation and image rendering software is exploited to design the SDF filters and to generate a large filter set with which to train the neural network. The technique is applied to pose estimation for rendezvous and docking of free-flying spacecraft and to terrestrial surface mobility systems for NASA's Vision for Space Exploration. Quantitative pose estimation performance will be reported. Advantages and disadvantages of the implementation of this technique are discussed.
NONLINEAR MULTIGRID SOLVER EXPLOITING AMGe COARSE SPACES WITH APPROXIMATION PROPERTIES
Energy Technology Data Exchange (ETDEWEB)
Christensen, Max La Cour [Technical Univ. of Denmark, Lyngby (Denmark); Villa, Umberto E. [Univ. of Texas, Austin, TX (United States); Engsig-Karup, Allan P. [Technical Univ. of Denmark, Lyngby (Denmark); Vassilevski, Panayot S. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2016-01-22
The paper introduces a nonlinear multigrid solver for mixed nite element discretizations based on the Full Approximation Scheme (FAS) and element-based Algebraic Multigrid (AMGe). The main motivation to use FAS for unstruc- tured problems is the guaranteed approximation property of the AMGe coarse spaces that were developed recently at Lawrence Livermore National Laboratory. These give the ability to derive stable and accurate coarse nonlinear discretization problems. The previous attempts (including ones with the original AMGe method, [5, 11]), were less successful due to lack of such good approximation properties of the coarse spaces. With coarse spaces with approximation properties, our FAS approach on un- structured meshes should be as powerful/successful as FAS on geometrically re ned meshes. For comparison, Newton's method and Picard iterations with an inner state-of-the-art linear solver is compared to FAS on a nonlinear saddle point problem with applications to porous media ow. It is demonstrated that FAS is faster than Newton's method and Picard iterations for the experiments considered here. Due to the guaranteed approximation properties of our AMGe, the coarse spaces are very accurate, providing a solver with the potential for mesh-independent convergence on general unstructured meshes.
Geometrically Nonlinear Finite Element Analysis of a Composite Space Reflector
Lee, Kee-Joo; Leet, Sung W.; Clark, Greg; Broduer, Steve (Technical Monitor)
2001-01-01
Lightweight aerospace structures, such as low areal density composite space reflectors, are highly flexible and may undergo large deflection under applied loading, especially during the launch phase. Accordingly, geometrically nonlinear analysis that takes into account the effect of finite rotation may be needed to determine the deformed shape for a clearance check and the stress and strain state to ensure structural integrity. In this study, deformation of the space reflector is determined under static conditions using a geometrically nonlinear solid shell finite element model. For the solid shell element formulation, the kinematics of deformation is described by six variables that are purely vector components. Because rotational angles are not used, this approach is free of the limitations of small angle increments. This also allows easy connections between substructures and large load increments with respect to the conventional shell formulation using rotational parameters. Geometrically nonlinear analyses were carried out for three cases of static point loads applied at selected points. A chart shows results for a case when the load is applied at the center point of the reflector dish. The computed results capture the nonlinear behavior of the composite reflector as the applied load increases. Also, they are in good agreement with the data obtained by experiments.
Miranowicz, A; Miranowicz, Adam; Leonski, Wieslaw
2006-01-01
Schemes for optical-state truncation of two cavity modes are analysed. The systems, referred to as the nonlinear quantum scissors devices, comprise two coupled nonlinear oscillators (Kerr nonlinear coupler) with one or two of them pumped by external classical fields. It is shown that the quantum evolution of the pumped couplers can be closed in a two-qubit Hilbert space spanned by vacuum and single-photon states only. Thus, the pumped couplers can behave as a two-qubit system. Analysis of time evolution of the quantum entanglement shows that Bell states can be generated. A possible implementation of the couplers is suggested in a pumped double-ring cavity with resonantly enhanced Kerr nonlinearities in an electromagnetically-induced transparency scheme. The fragility of the generated states and their entanglement due to the standard dissipation and phase damping are discussed by numerically solving two types of master equations.
Approximate Methods for State-Space Models.
Koyama, Shinsuke; Pérez-Bolde, Lucia Castellanos; Shalizi, Cosma Rohilla; Kass, Robert E
2010-03-01
State-space models provide an important body of techniques for analyzing time-series, but their use requires estimating unobserved states. The optimal estimate of the state is its conditional expectation given the observation histories, and computing this expectation is hard when there are nonlinearities. Existing filtering methods, including sequential Monte Carlo, tend to be either inaccurate or slow. In this paper, we study a nonlinear filter for nonlinear/non-Gaussian state-space models, which uses Laplace's method, an asymptotic series expansion, to approximate the state's conditional mean and variance, together with a Gaussian conditional distribution. This Laplace-Gaussian filter (LGF) gives fast, recursive, deterministic state estimates, with an error which is set by the stochastic characteristics of the model and is, we show, stable over time. We illustrate the estimation ability of the LGF by applying it to the problem of neural decoding and compare it to sequential Monte Carlo both in simulations and with real data. We find that the LGF can deliver superior results in a small fraction of the computing time.
A Null Space Approach for Solving Nonlinear Complementarity Problems
Institute of Scientific and Technical Information of China (English)
Pu-yan Nie
2006-01-01
In this work, null space techniques are employed to tackle nonlinear complementarity problems(NCPs). NCP conditions are transform into a nonlinear programming problem, which is handled by null space algorithms. The NCP conditions are divided into two groups. Some equalities and inequalities in an NCP are treated as constraints. While other equalities and inequalities in an NCP are to be regarded as objective function.Two groups are all updated in every step. Null space approaches are extended to nonlinear complementarity problems. Two different solvers are employed for an NCP in an algorithm.
Nonlinear damped Schrodinger equation in two space dimensions
Directory of Open Access Journals (Sweden)
Tarek Saanouni
2015-04-01
Full Text Available In this article, we study the initial value problem for a semi-linear damped Schrodinger equation with exponential growth nonlinearity in two space dimensions. We show global well-posedness and exponential decay.
Singularity-free Bianchi spaces with nonlinear electrodynamics
García-Salcedo, R; Garcia-Salcedo, Ricardo; Breton, Nora
2004-01-01
In this paper we present the analysis to determine the existence of singularities in spatially homogeneous anisotropic universes filled with nonlinear electromagnetic radiation. These spaces are conformal to Bianchi spaces admitting a three parameter group of motions G$_3$. We study analytical extensions as well as geodesic completeness. It is shown that with nonlinear electromagnetic field some of the Bianchi spaces are geodesically complete, like G$_3$II and G$_3$VIII; however Bianchi G$_3$IX presents the phenomenon of geodesics that are imprisoned. In contrast, diagonal Bianchi spaces like G$_3$I, G$_3$III and Kantowski-Sachs have a finite time existence ending in a scalar polynomial curvature singularity.
Nonlinear Parabolic Equations with Singularities in Colombeau Vector Spaces
Institute of Scientific and Technical Information of China (English)
Mirjana STOJANOVI(C)
2006-01-01
We consider nonlinear parabolic equations with nonlinear non-Lipschitz's term and singular initial data like Dirac measure, its derivatives and powers. We prove existence-uniqueness theorems in Colombeau vector space gC1,w2,2([O,T),Rn),n ≤ 3. Due to high singularity in a case of parabolic equation with nonlinear conservative term we employ the regularized derivative for the conservative term, in order to obtain the global existence-uniqueness result in Colombeau vector space gC1,L2([O,T),Rn),n ≤ 3.
Nonlinear differentiation equation and analytic function spaces
Li, Hao; Li, Songxiao
2015-01-01
In this paper we consider the nonlinear complex differential equation $$(f^{(k)})^{n_{k}}+A_{k-1}(z)(f^{(k-1)})^{n_{k-1}}+\\cdot\\cdot\\cdot+A_{1}(z)(f')^{n_{1}}+A_{0}(z)f^{n_{0}}=0, $$where $ A_{j}(z)$, $ j=0, \\cdots, k-1 $, are analytic in the unit disk $ \\mathbb{D} $, $ n_{j}\\in R^{+} $ for all $ j=0, \\cdots, k $. We investigate this nonlinear differential equation from two aspects. On one hand, we provide some sufficient conditions on coefficients such that all solutions of this equation bel...
A Right Coprime Factorization of Neural State Space Models
DEFF Research Database (Denmark)
Bendtsen, Jan Dimon
2007-01-01
In recent years, various methods for identification of nonlinear systems in closed loop using open-loop approaches have received considerable attention. However, these methods rely on differentially coprime factorizations of the nonlinear plants, which can be difficult to compute in practice....... To address this issue, this paper presents various technical results leading up to explicit formulae for right coprime factorizations of neural state space models, i.e., nonlinear system models represented in state space using neural networks, which satisfy a Bezout identity. ...
Directory of Open Access Journals (Sweden)
Thomas Doan
2011-05-01
Full Text Available This paper uses several examples to show how the econometrics program RATS can be used to analyze state space models. It demonstrates Kalman filtering and smoothing, estimation of hyperparameters, unconditional and conditional simulation. It also provides a more complicated example where a dynamic simultaneous equations model is transformed into a proper state space representation and its unknown parameters are estimated.
Nonlinear Interferometry via Fock State Projection
Khoury, G; Eisenberg, H S; Fonseca, E J S
2006-01-01
We use a photon-number resolving detector to monitor the photon number distribution of the output of an interferometer, as a function of phase delay. As inputs we use coherent states with mean photon number up to seven. The postselection of a specific Fock (photon-number) state effectively induces high-order optical non-linearities. Following a scheme by Bentley and Boyd [S.J. Bentley and R.W. Boyd, Optics Express 12, 5735 (2004)] we explore this effect to demonstrate interference patterns a factor of five smaller than the Rayleigh limit.
Nonlinear Interferometry via Fock-State Projection
Khoury, G.; Eisenberg, H. S.; Fonseca, E. J. S.; Bouwmeester, D.
2006-05-01
We use a photon-number-resolving detector to monitor the photon-number distribution of the output of an interferometer, as a function of phase delay. As inputs we use coherent states with mean photon number up to seven. The postselection of a specific Fock (photon-number) state effectively induces high-order optical nonlinearities. Following a scheme by Bentley and Boyd [Opt. Express 12, 5735 (2004).OPEXFF1094-408710.1364/OPEX.12.005735], we explore this effect to demonstrate interference patterns a factor of 5 smaller than the Rayleigh limit.
Geometric properties of Banach spaces and nonlinear iterations
Chidume, Charles
2009-01-01
Nonlinear functional analysis and applications is an area of study that has provided fascination for many mathematicians across the world. This monograph delves specifically into the topic of the geometric properties of Banach spaces and nonlinear iterations, a subject of extensive research over the past thirty years. Chapters 1 to 5 develop materials on convexity and smoothness of Banach spaces, associated moduli and connections with duality maps. Key results obtained are summarized at the end of each chapter for easy reference. Chapters 6 to 23 deal with an in-depth, comprehensive and up-to-date coverage of the main ideas, concepts and results on iterative algorithms for the approximation of fixed points of nonlinear nonexpansive and pseudo-contractive-type mappings. This includes detailed workings on solutions of variational inequality problems, solutions of Hammerstein integral equations, and common fixed points (and common zeros) of families of nonlinear mappings. Carefully referenced and full of recent,...
The nonlinear standing wave inside the space of liquid
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
Based on the basic equations of hydrodynamics, the nonlinear acoustic wave equation is obtained. By taking into account the boundary condition and properties of nonlinear standing wave, the equation is solved through perturbation method, and the stable expressions of fundamental wave and second harmonic are presented. The sound pressures in an ultrasonic cleaner are measured by hydrophones, and the relationship between the received voltages of hydrophones and the output voltages of the ultrasonic generator is researched. The study shows the existence of the nonlinear effect of liquid and analyzes the frequency spectrum of the received signals by hydrophones, by which the fundamental wave, second and high order harmonics are found coexisting in the bounded space filled with liquids. The theory and experimental results testify the existence of the nonlinear standing wave in liquid. Owing to the restricted applicability of perturbation method, the theoretical results of the fundamental wave and second harmonic are good only for the weak nonlinear phenomenon.
Coherent states in projected Hilbert spaces
Drummond, P. D.; Reid, M. D.
2016-12-01
Coherent states in a projected Hilbert space have many useful properties. When there are conserved quantities, a representation of the entire Hilbert space is not necessary. The same issue arises when conditional observations are made with postselected measurement results. In these cases, only a part of the Hilbert space needs to be represented, and one can define this restriction by way of a projection operator. Here coherent state bases and normally ordered phase-space representations are introduced for treating such projected Hilbert spaces, including existence theorems and dynamical equations. These techniques are very useful in studying novel optical or microwave integrated photonic quantum technologies, such as boson sampling or Josephson quantum computers. In these cases, states become strongly restricted due to inputs, nonlinearities, or conditional measurements. This paper focuses on coherent phase states, which have especially simple properties. Practical applications are reported on calculating recurrences in anharmonic oscillators, the effects of arbitrary phase noise on Schrödinger cat fringe visibility, and on boson sampling interferometry for large numbers of modes.
Optical nonlinearities of excitonic states in atomically thin 2D transition metal dichalcogenides.
Energy Technology Data Exchange (ETDEWEB)
Soh, Daniel Beom Soo
2017-09-01
We calculated the optical nonlinearities of the atomically thin monolayer transition metal dichalcogenide material (particularly MoS 2 ), particularly for those linear and nonlinear tran- sition processes that utilize the bound exciton states. We adopted the bound and the unbound exciton states as the basis for the Hilbert space, and derived all the dynamical density matri- ces that provides the induced current density, from which the nonlinear susceptibilities can be drawn order-by-order via perturbative calculations. We provide the nonlinear susceptibil- ities for the linear, the second-harmonic, the third-harmonic, and the kerr-type two-photon processes.
Nonlinear Mirror Modes in Space Plasmas
Sulem, P -L
2011-01-01
Since the first observations by Kaufmann et al.\\ (1970), special attention has been paid to static pressure-balanced structures in the form of magnetic holes or humps observed in regions of the solar wind and of planetary magnetosheaths where the $\\beta$ parameter is relatively large and the ion perpendicular temperature exceeds the parallel one. Although alternative interpretations have been proposed, these structures are usually viewed as associated with the mirror instability discovered in 1957 by Vedenov and Sagdeev. After reviewing observational results provided by satellite missions, high-resolution numerical simulations of the Vlasov--Maxwell equations together with asymptotic and phenomenological models of the nonlinear dynamics near the instability threshold are discussed. The constraining effect of the mirror instability on the temperature anisotropy associated with a dominant perpendicular ion heating observed in the solar wind is reported, and recent simulations of this phenomenon based on an elab...
Using Space as a Nonlinear Plasma Laboratory
Papadopoulos, Konstantinos
2008-11-01
Ionospheric heaters have been an important tool of plasma physics investigations. The extent that non-linear plasma phenomena can be triggered and observed depends critically on the heater power, its Effective Radiative Power (ERP) and its scanning capability. Increasing these parameters allows us to reach thresholds associated with effects that were not previously observed. The latest entry to ionospheric heating, the HF transmitter associated with the High Frequency Active Ionospheric Research Program (HAARP) was completed in June 2007. The transmitter consists of 180 antenna elements spanning 30.6 acres and can radiate 3.6 MW of HF power (a factor of almost 4 higher than any previous heater) in the 2.8-10.0 MHz range. With increasing frequency the beam-width varies from 15-5 degrees, corresponding to 20-30 dB gain and resulting in ERP between 1-5 GW. The antenna can point to any direction in a cone 30 degrees from the vertical, with reposition time of 15 microseconds resulting in superluminal scanning speeds. The transmitter can synthesize essentially any waveform and transmit any polarization. These capabilities far exceed those of any previous heater and allow for new frontier research in non-linear plasma physics. The presentation will focus first on the relationship of the new capabilities of the facility with thresholds of physical processes that had not been achieved previously. It will then present new spectacular results that have been achieved during the last year. They include whistler injection and amplification, injection of shear and magnetosonic waves in the magnetosphere, Langmuir turbulence, upper hybrid waves and thermal instabilities, electron acceleration, optical emissions and formation of artificial ducts for whistler propagation. The presentation will also discuss future experiments made possible for the first time by the new transmitter capabilities, large bandwidth and high ERP.
An analytic map for space charge in a nonlinear lattice
Energy Technology Data Exchange (ETDEWEB)
Benedetti, C. [Dipartimento di Fisica Universita di Bologna and INFN, Via Irnerio 46, 40126 Bologna (Italy)]. E-mail: benedetti@bo.infn.it; Turchetti, G. [Dipartimento di Fisica Universita di Bologna and INFN, Via Irnerio 46, 40126 Bologna (Italy)
2005-06-13
We propose a simple analytical model for an intense beam in a lattice with localized nonlinearities. In the thin lens limit a single nonlinearity leads to a Henon like map. When the space charge is present and the core radius is small with respect to the dynamic aperture, the use of a frozen core distribution like KV is justified. In this case we define an analytic map M by composing the phase advance due to space charge, computed at the first perturbation order, with the kick due to the nonlinear force. The corresponding dynamics is almost indistinguishable from the dynamics of the 'exact' map, which requires an accurate symplectic integration, if the tune depression is weak enough. The same accuracy is preserved for parametric modulations of the perveance or the beam core radius. The extension to any other distribution is straightforward.
Nonlinear Multigrid solver exploiting AMGe Coarse Spaces with Approximation Properties
DEFF Research Database (Denmark)
Christensen, Max la Cour; Villa, Umberto; Engsig-Karup, Allan Peter;
The paper introduces a nonlinear multigrid solver for mixed finite element discretizations based on the Full Approximation Scheme (FAS) and element-based Algebraic Multigrid (AMGe). The main motivation to use FAS for unstructured problems is the guaranteed approximation property of the AMGe coarse...... spaces that were developed recently at Lawrence Livermore National Laboratory. These give the ability to derive stable and accurate coarse nonlinear discretization problems. The previous attempts (including ones with the original AMGe method), were less successful due to lack of such good approximation...... are compared to FAS on a nonlinear saddle point problem with applications to porous media flow. It is demonstrated that FAS is faster than Newton’s method and Picard iterations for the experiments considered here. Due to the guaranteed approximation properties of our AMGe, the coarse spaces are very accurate...
State space modeling of Memristor-based Wien oscillator
Talukdar, Abdul Hafiz Ibne
2011-12-01
State space modeling of Memristor based Wien \\'A\\' oscillator has been demonstrated for the first time considering nonlinear ion drift in Memristor. Time dependant oscillating resistance of Memristor is reported in both state space solution and SPICE simulation which plausibly provide the basis of realizing parametric oscillation by Memristor based Wien oscillator. In addition to this part Memristor is shown to stabilize the final oscillation amplitude by means of its nonlinear dynamic resistance which hints for eliminating diode in the feedback network of conventional Wien oscillator. © 2011 IEEE.
On space enrichment estimator for nonlinear Poisson-Boltzmann
Randrianarivony, Maharavo
2013-10-01
We consider the mathematical aspect of the nonlinear Poisson-Boltzmann equation which physically governs the ionic interaction between solute and solvent media. The presented a-posteriori estimates can be computed locally in a very efficient manner. The a-posteriori error is based upon hierarchical space enrichment which ensures its efficiency and reliability. A brief survey of the solving of the nonlinear system resulting from the FEM discretization is reported. To corroborate the analysis, we report on a few numerical results for illustrations. We numerically examine some values of the constants encountered in the theoretical study.
Nonlinear Landau-Zener tunneling in quantum phase space
Energy Technology Data Exchange (ETDEWEB)
Trimborn, F [Institut fuer theoretische Physik, Leibniz Universitaet Hannover, D-30167 Hannover (Germany); Witthaut, D [QUANTOP, Niels Bohr Institute, University of Copenhagen, DK-2100 Copenhagen (Denmark); Kegel, V; Korsch, H J, E-mail: friederike.trimborn@itp.uni-hannover.d [Fachbereich Physik, TU Kaiserslautern, D-67663 Kaiserslautern (Germany)
2010-05-15
We present a detailed analysis of the Landau-Zener problem for an interacting Bose-Einstein condensate in a time-varying double-well trap, especially focusing on the relation between the full many-particle problem and the mean-field approximation. Due to the nonlinear self-interaction a dynamical instability occurs, which leads to a breakdown of adiabaticity and thus fundamentally alters the dynamics. It is shown that essentially all the features of the Landau-Zener problem including the depletion of the condensate mode can be already understood within a semiclassical phase-space picture. In particular, this treatment resolves the formerly imputed incommutability of the adiabatic and semiclassical limits. The possibility of exploiting Landau-Zener sweeps to generate squeezed states for spectroscopic tasks is analyzed in detail. Moreover, we study the influence of phase noise and propose a Landau-Zener sweep as a sensitive yet readily implementable probe for decoherence, since the noise has significant effect on the transition rate for slow parameter variations.
Nonlinear Landau-Zener tunneling in quantum phase space
Trimborn, F; Kegel, V; Korsch, H J; 10.1088/1367-2630/12/5/053010
2010-01-01
We present a detailed analysis of the Landau-Zener problem for an interacting Bose-Einstein condensate in a time-varying double-well trap, especially focussing on the relation between the full many-particle problem and the mean-field approximation. Due to the nonlinear self-interaction a dynamical instability occurs, which leads to a breakdown of adiabaticity condition and thus fundamentally alters the dynamics. It is shown that essentially all features of the Landau-Zener problem including the depletion of the condensate mode can be already understood within a semiclassical phase space picture. In particular, this treatment resolves the formerly imputed incommutability of the adiabatic and semiclassical limits. The possibility to exploit Landau-Zener sweeps to generate squeezed states for spectroscopic tasks is analysed in detail. Moreover, we study the influence of phase noise and propose a Landau-Zener sweep as a sensitive, yet readily implementable probe for decoherence, since this has a significant effec...
An extended nonlinear state predictor for a class of nonlinear time delay systems
Institute of Scientific and Technical Information of China (English)
WANG Dong; ZHOU Donghua; JIN Yihui
2004-01-01
An extended nonlinear state predictor (ENSP) for a class of nonlinear systems with input time delay is proposed. Based on the extended Kalman filter (EKF), the ENSP first estimates the current states according to the previous estimations and estimation errors, next calculates the future state values via the system model, and then adjusts the values based on the current errors. After a state predictive algorithm for a class of linear systems is presented, it is extended to a class of nonlinear time delay systems and the detailed ENSP algorithm is further proposed. Finally, computer simulations with the nonlinear example are presented, which demonstrates that the proposed ENSP can effectively and accurately predict the future states for a class of nonlinear time-delay systems no matter whether the state variables change quickly or slowly.
Galerkin approximations of nonlinear optimal control problems in Hilbert spaces
Directory of Open Access Journals (Sweden)
Mickael D. Chekroun
2017-07-01
Full Text Available Nonlinear optimal control problems in Hilbert spaces are considered for which we derive approximation theorems for Galerkin approximations. Approximation theorems are available in the literature. The originality of our approach relies on the identification of a set of natural assumptions that allows us to deal with a broad class of nonlinear evolution equations and cost functionals for which we derive convergence of the value functions associated with the optimal control problem of the Galerkin approximations. This convergence result holds for a broad class of nonlinear control strategies as well. In particular, we show that the framework applies to the optimal control of semilinear heat equations posed on a general compact manifold without boundary. The framework is then shown to apply to geoengineering and mitigation of greenhouse gas emissions formulated here in terms of optimal control of energy balance climate models posed on the sphere $\\mathbb{S}^2$.
Institute of Scientific and Technical Information of China (English)
卢道明
2008-01-01
Using the numerical method,the antibunching effects of a new kind of odd and even nonlinear CO- herent states in a finite-dimensional Hilbert space are studied.The results show that the new kind of odd non- 1inear coherent state exhibits antibunching effect and the new kind of even nonlinear coherent state does not exhibits antibunching effect in a finite-dimensional Hilbert space.%利用数值计算方法,研究了有限维Hilbert空间一种新的奇偶非线性相干态的反聚束效应.研究结果表明:各有限维Hilbert空间新的偶非线性相干态均不出现反聚束效应.但各有限维Hilbert空间新的奇非线性相干态均可出现反聚束效应.
State dependent matrices and balanced energy functions for nonlinear systems
Scherpen, Jacquelien M.A.; Gray, W. Steven
2000-01-01
The nonlinear extension of the balancing procedure requires the case of state dependent quadratic forms for the energy functions, i.e., the nonlinear extensions of the linear Gramians are state dependent matrices. These extensions have some interesting ambiguities that do not occur in the linear cas
New developments in state estimation for Nonlinear Systems
DEFF Research Database (Denmark)
Nørgård, Peter Magnus; Poulsen, Niels Kjølstad; Ravn, Ole
2000-01-01
Based on an interpolation formula, accurate state estimators for nonlinear systems can be derived. The estimators do not require derivative information which makes them simple to implement.; State estimators for nonlinear systems are derived based on polynomial approximations obtained with a multi...
Nonlinear Sigma Models with Compact Hyperbolic Target Spaces
Gubser, Steven; Schoenholz, Samuel S; Stoica, Bogdan; Stokes, James
2015-01-01
We explore the phase structure of nonlinear sigma models with target spaces corresponding to compact quotients of hyperbolic space, focusing on the case of a hyperbolic genus-2 Riemann surface. The continuum theory of these models can be approximated by a lattice spin system which we simulate using Monte Carlo methods. The target space possesses interesting geometric and topological properties which are reflected in novel features of the sigma model. In particular, we observe a topological phase transition at a critical temperature, above which vortices proliferate, reminiscent of the Kosterlitz-Thouless phase transition in the $O(2)$ model. Unlike in the $O(2)$ case, there are many different types of vortices, suggesting a possible analogy to the Hagedorn treatment of statistical mechanics of a proliferating number of hadron species. Below the critical temperature the spins cluster around six special points in the target space known as Weierstrass points. The diversity of compact hyperbolic manifolds suggest...
Principal Manifolds and Nonlinear Dimensionality Reduction via Tangent Space Alignment
Institute of Scientific and Technical Information of China (English)
张振跃; 查宏远
2004-01-01
We present a new algorithm for manifold learning and nonlinear dimensionality reduction. Based on a set of unorganized da-ta points sampled with noise from a parameterized manifold, the local geometry of the manifold is learned by constructing an approxi-mation for the tangent space at each point, and those tangent spaces are then aligned to give the global coordinates of the data pointswith respect to the underlying manifold. We also present an error analysis of our algorithm showing that reconstruction errors can bequite small in some cases. We illustrate our algorithm using curves and surfaces both in 2D/3D Euclidean spaces and higher dimension-al Euclidean spaces. We also address several theoretical and algorithmic issues for further research and improvements.
On nonlinear stability in various random normed spaces
Directory of Open Access Journals (Sweden)
Saadati Reza
2011-01-01
Full Text Available Abstract In this article, we prove the nonlinear stability of the quartic functional equation 1 6 f ( x + 4 y + f ( 4 x - y = 3 0 6 9 f x + y 3 + f ( x + 2 y (1 + 1 3 6 f ( x - y - 1 3 9 4 f ( x + y + 4 2 5 f ( y - 1 5 3 0 f ( x (2 (3 in the setting of random normed spaces Furthermore, the interdisciplinary relation among the theory of random spaces, the theory of non-Archimedean space, the theory of fixed point theory, the theory of intuitionistic spaces and the theory of functional equations are also presented in the article.
Uniqueness of ground states of some coupled nonlinear Schrodinger systems and their application
MA,LI; Lin ZHAO
2007-01-01
We establish the uniqueness of ground states of some coupled nonlinear Schrodinger systems in the whole space. We firstly use Schwartz symmetrization to obtain the existence of ground states for a more general case. To prove the uniqueness of ground states, we use the radial symmetry of the ground states to transform the systems into an ordinary differential system, and then we use the integral forms of the system. More interestingly, as an application of our uniqueness results, we derive a s...
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.
Superposition of nonlinear coherent states on a sphere
Directory of Open Access Journals (Sweden)
T Hosseinzadeh
2013-09-01
Full Text Available In this paper, by using the nonlinear coherent states on a sphere, we introduce superposition of the aforementioned coherent states. Then, we consider quantum optical properties of these new superposed states and compare these properties with the corresponding properties of the nonlinear coherent states on the sphere. Specifically, we investigate their characteristics function, photon-number distribution, Mandel parameter, quadrature squeezing, anti-bunching effect and Wigner function, and obtain the curvature effect on the properties of the superposed states. Finally, by using the trapped atom system, we introduce a theoretical scheme to generate superposition of the coherent states on the sphere.
Nonlinear rotordynamics analysis. [Space Shuttle Main Engine turbopumps
Noah, Sherif T.
1991-01-01
Effective analysis tools were developed for predicting the nonlinear rotordynamic behavior of the Space Shuttle Main Engine (SSME) turbopumps under steady and transient operating conditions. Using these methods, preliminary parametric studies were conducted on both generic and actual HPOTP (high pressure oxygen turbopump) models. In particular, a novel modified harmonic balance/alternating Fourier transform (HB/AFT) method was developed and used to conduct a preliminary study of the effects of fluid, bearing and seal forces on the unbalanced response of a multi-disk rotor in the presence of bearing clearances. The method makes it possible to determine periodic, sub-, super-synchronous and chaotic responses of a rotor system. The method also yields information about the stability of the obtained response, thus allowing bifurcation analyses. This provides a more effective capability for predicting the response under transient conditions by searching in proximity of resonance peaks. Preliminary results were also obtained for the nonlinear transient response of an actual HPOTP model using an efficient, newly developed numerical method based on convolution integration. Currently, the HB/AFT is being extended for determining the aperiodic response of nonlinear systems. Initial results show the method to be promising.
Advances in Derivative-Free State Estimation for Nonlinear Systems
DEFF Research Database (Denmark)
Nørgaard, Magnus; Poulsen, Niels Kjølstad; Ravn, Ole
In this paper we show that it involves considerable advantages to use polynomial approximations obtained with an interpolation formula for derivation of state estimators for nonlinear systems. The estimators become more accurate than estimators based on Taylor approximations, and yet...
My Life with State Space Models
DEFF Research Database (Denmark)
Lundbye-Christensen, Søren
2007-01-01
. The conceptual idea behind the state space model is that the evolution over time in the object we are observing and the measurement process itself are modelled separately. My very first serious analysis of a data set was done using a state space model, and since then I seem to have been "haunted" by state space...
Institute of Scientific and Technical Information of China (English)
Lu Jun
2004-01-01
The stationary-state nonlinear Schr(o)dinger equation, which models the dilute-gas Bose-Einstein condensate, is introduced within the framework of the quantum phase-space representation established by Torres-Vega and Frederick.The exact solutions of equation are obtained in the phase space, by means of the wave-mechanics method. The the phase space eigenfunctions. The eigenfunction with a hypersecant part is discussed as an example.
Optimal state discrimination and unstructured search in nonlinear quantum mechanics
Childs, Andrew M.; Young, Joshua
2016-02-01
Nonlinear variants of quantum mechanics can solve tasks that are impossible in standard quantum theory, such as perfectly distinguishing nonorthogonal states. Here we derive the optimal protocol for distinguishing two states of a qubit using the Gross-Pitaevskii equation, a model of nonlinear quantum mechanics that arises as an effective description of Bose-Einstein condensates. Using this protocol, we present an algorithm for unstructured search in the Gross-Pitaevskii model, obtaining an exponential improvement over a previous algorithm of Meyer and Wong. This result establishes a limitation on the effectiveness of the Gross-Pitaevskii approximation. More generally, we demonstrate similar behavior under a family of related nonlinearities, giving evidence that the ability to quickly discriminate nonorthogonal states and thereby solve unstructured search is a generic feature of nonlinear quantum mechanics.
Nonlinear sigma models with compact hyperbolic target spaces
Gubser, Steven; Saleem, Zain H.; Schoenholz, Samuel S.; Stoica, Bogdan; Stokes, James
2016-06-01
We explore the phase structure of nonlinear sigma models with target spaces corresponding to compact quotients of hyperbolic space, focusing on the case of a hyperbolic genus-2 Riemann surface. The continuum theory of these models can be approximated by a lattice spin system which we simulate using Monte Carlo methods. The target space possesses interesting geometric and topological properties which are reflected in novel features of the sigma model. In particular, we observe a topological phase transition at a critical temperature, above which vortices proliferate, reminiscent of the Kosterlitz-Thouless phase transition in the O(2) model [1, 2]. Unlike in the O(2) case, there are many different types of vortices, suggesting a possible analogy to the Hagedorn treatment of statistical mechanics of a proliferating number of hadron species. Below the critical temperature the spins cluster around six special points in the target space known as Weierstrass points. The diversity of compact hyperbolic manifolds suggests that our model is only the simplest example of a broad class of statistical mechanical models whose main features can be understood essentially in geometric terms.
Wang, Dong; Zhao, Yang; Yang, Fangfang; Tsui, Kwok-Leung
2017-09-01
Brownian motion with adaptive drift has attracted much attention in prognostics because its first hitting time is highly relevant to remaining useful life prediction and it follows the inverse Gaussian distribution. Besides linear degradation modeling, nonlinear-drifted Brownian motion has been developed to model nonlinear degradation. Moreover, the first hitting time distribution of the nonlinear-drifted Brownian motion has been approximated by time-space transformation. In the previous studies, the drift coefficient is the only hidden state used in state space modeling of the nonlinear-drifted Brownian motion. Besides the drift coefficient, parameters of a nonlinear function used in the nonlinear-drifted Brownian motion should be treated as additional hidden states of state space modeling to make the nonlinear-drifted Brownian motion more flexible. In this paper, a prognostic method based on nonlinear-drifted Brownian motion with multiple hidden states is proposed and then it is applied to predict remaining useful life of rechargeable batteries. 26 sets of rechargeable battery degradation samples are analyzed to validate the effectiveness of the proposed prognostic method. Moreover, some comparisons with a standard particle filter based prognostic method, a spherical cubature particle filter based prognostic method and two classic Bayesian prognostic methods are conducted to highlight the superiority of the proposed prognostic method. Results show that the proposed prognostic method has lower average prediction errors than the particle filter based prognostic methods and the classic Bayesian prognostic methods for battery remaining useful life prediction.
State-Space Modelling of Loudspeakers using Fractional Derivatives
DEFF Research Database (Denmark)
King, Alexander Weider; Agerkvist, Finn T.
2015-01-01
This work investigates the use of fractional order derivatives in modeling moving-coil loudspeakers. A fractional order state-space solution is developed, leading the way towards incorporating nonlinearities into a fractional order system. The method is used to calculate the response....... It is shown that the identified parameters can be used in a linear fractional order state-space model to simulate the loudspeakers’ time domain response...... of a fractional harmonic oscillator, representing the mechanical part of a loudspeaker, showing the effect of the fractional derivative and its relationship to viscoelasticity. Finally, a loudspeaker model with a fractional order viscoelastic suspension and fractional order voice coil is fit to measurement data...
Nonlinear self-flipping of polarization states in asymmetric waveguides
Zhang, Wen Qi; Monro, Tanya M; Afshar, V Shahraam
2012-01-01
Waveguides of subwavelength dimensions with asymmetric geometries, such as rib waveguides, can display nonlinear polarization effects in which the nonlinear phase difference dominates the linear contribution, provided the birefringence is sufficiently small. We demonstrate that self-flipping polarization states can appear in such rib waveguides at low (mW) power levels. We describe an optical power limiting device with optimized rib waveguide parameters that can operate at low powers with switching properties.
New developments in state estimation for Nonlinear Systems
DEFF Research Database (Denmark)
Nørgård, Peter Magnus; Poulsen, Niels Kjølstad; Ravn, Ole
2000-01-01
Based on an interpolation formula, accurate state estimators for nonlinear systems can be derived. The estimators do not require derivative information which makes them simple to implement.; State estimators for nonlinear systems are derived based on polynomial approximations obtained with a multi......-dimensional interpolation formula. It is shown that under certain assumptions the estimators perform better than estimators based on Taylor approximations. Nevertheless, the implementation is significantly simpler as no derivatives are required. Thus, it is believed that the new state estimators can replace well...
State-Space Methods for µ-Analysis
Helmersson, Anders
1994-01-01
This paper discusses state-space methods for analyzing stability of continuous time linear systems subject to structured uncertainties. Four types of uncertainties are discussed: linear parametric and dynamic uncertainties (real and complex µ) and nonlinear parametric and dynamic uncertainties. The method employs LMIs equipped with a scaling matrix adapted to the type of uncertainty. For parametric uncertainties conservativeness is reduced by branch and bound schemes. Different types of uncer...
Automatic Design of a Maglev Controller in State Space
1991-12-01
conventional trains with steel wheels on steel rails. Several experimen- tal maglev systems in Germany and Japan have demonstrated that this mode of...Design of a Maglev Controller in State Space Feng Zhao Richard Thornton Abstract We describe the automatic synthesis of a global nonlinear controller for...the global switching points of the controller is presented. The synthesized control system can stabilize the maglev vehicle with large initial displace
State-Space Methods for µ-Analysis
Helmersson, Anders
1994-01-01
This paper discusses state-space methods for analyzing stability of continuous time linear systems subject to structured uncertainties. Four types of uncertainties are discussed: linear parametric and dynamic uncertainties (real and complex µ) and nonlinear parametric and dynamic uncertainties. The method employs LMIs equipped with a scaling matrix adapted to the type of uncertainty. For parametric uncertainties conservativeness is reduced by branch and bound schemes. Different types of uncer...
State Space Methods for Timed Petri Nets
DEFF Research Database (Denmark)
Christensen, Søren; Jensen, Kurt; Mailund, Thomas
2001-01-01
We present two recently developed state space methods for timed Petri nets. The two methods reconciles state space methods and time concepts based on the introduction of a global clock and associating time stamps to tokens. The first method is based on an equivalence relation on states which makes...... it possible to condense the usually infinite state space of a timed Petri net into a finite condensed state space without loosing analysis power. The second method supports on-the-fly verification of certain safety properties of timed systems. We discuss the application of the two methods in a number...
Directory of Open Access Journals (Sweden)
W. Dzwinel
2005-01-01
Full Text Available We present a novel technique based on a multi-resolutional clustering and nonlinear multi-dimensional scaling of earthquake patterns to investigate observed and synthetic seismic catalogs. The observed data represent seismic activities around the Japanese islands during 1997-2003. The synthetic data were generated by numerical simulations for various cases of a heterogeneous fault governed by 3-D elastic dislocation and power-law creep. At the highest resolution, we analyze the local cluster structures in the data space of seismic events for the two types of catalogs by using an agglomerative clustering algorithm. We demonstrate that small magnitude events produce local spatio-temporal patches delineating neighboring large events. Seismic events, quantized in space and time, generate the multi-dimensional feature space characterized by the earthquake parameters. Using a non-hierarchical clustering algorithm and nonlinear multi-dimensional scaling, we explore the multitudinous earthquakes by real-time 3-D visualization and inspection of the multivariate clusters. At the spatial resolutions characteristic of the earthquake parameters, all of the ongoing seismicity both before and after the largest events accumulates to a global structure consisting of a few separate clusters in the feature space. We show that by combining the results of clustering in both low and high resolution spaces, we can recognize precursory events more precisely and unravel vital information that cannot be discerned at a single resolution.
Nonlinear sigma models with compact hyperbolic target spaces
Energy Technology Data Exchange (ETDEWEB)
Gubser, Steven [Joseph Henry Laboratories, Princeton University, Princeton, NJ 08544 (United States); Saleem, Zain H. [Department of Physics and Astronomy, University of Pennsylvania,Philadelphia, PA 19104 (United States); National Center for Physics, Quaid-e-Azam University Campus,Islamabad 4400 (Pakistan); Schoenholz, Samuel S. [Department of Physics and Astronomy, University of Pennsylvania,Philadelphia, PA 19104 (United States); Stoica, Bogdan [Walter Burke Institute for Theoretical Physics, California Institute of Technology,452-48, Pasadena, CA 91125 (United States); Stokes, James [Department of Physics and Astronomy, University of Pennsylvania,Philadelphia, PA 19104 (United States)
2016-06-23
We explore the phase structure of nonlinear sigma models with target spaces corresponding to compact quotients of hyperbolic space, focusing on the case of a hyperbolic genus-2 Riemann surface. The continuum theory of these models can be approximated by a lattice spin system which we simulate using Monte Carlo methods. The target space possesses interesting geometric and topological properties which are reflected in novel features of the sigma model. In particular, we observe a topological phase transition at a critical temperature, above which vortices proliferate, reminiscent of the Kosterlitz-Thouless phase transition in the O(2) model V.L. Berezinskii, Destruction of long-range order in one-dimensional and two-dimensional systems having a continuous symmetry group II. Quantum systems, Sov. Phys. JETP 34 (1972) 610. J.M. Kosterlitz and D.J. Thouless, Ordering, metastability and phase transitions in two-dimensional systems, J. Phys. C 6 (1973) 1181 [http://inspirehep.net/search?p=find+J+%22J.Phys.,C6,1181%22]. . Unlike in the O(2) case, there are many different types of vortices, suggesting a possible analogy to the Hagedorn treatment of statistical mechanics of a proliferating number of hadron species. Below the critical temperature the spins cluster around six special points in the target space known as Weierstrass points. The diversity of compact hyperbolic manifolds suggests that our model is only the simplest example of a broad class of statistical mechanical models whose main features can be understood essentially in geometric terms.
De Siena, S; Illuminati, F; Siena, Silvio De; Lisi, Antonio Di; Illuminati, Fabrizio
2002-01-01
We introduce nonlinear canonical transformations that yield effective Hamiltonians of multiphoton down conversion processes, and we define the associated non-Gaussian multiphoton squeezed states as the coherent states of the multiphoton Hamiltonians. We study in detail the four-photon processes and the associated non-Gaussian four-photon squeezed states. The realization of squeezing, the behavior of the field statistics, and the structure of the phase space distributions show that these states realize a natural four-photon generalization of the two-photon squeezed states.
Nonlinear H-ininity state feedback controllers:
DEFF Research Database (Denmark)
Cromme, Marc; Møller-Pedersen, Jens; Pagh Petersen, Martin
1997-01-01
From a general point of view the state feedback H∞ suboptimal control problem is reasonably well understood. Important problems remain with regard to a priori information of the size of the neighbourhood where the local state feedback H∞ problem is solvable. This problem is solved regionally (sem...
Mean Shift Detection for State Space Models
Kuhn, J.; Mandjes, M.; Taimre, T.; Weber, T.; McPhee, M.J.; Anderssen, R.S.
2015-01-01
In this paper we develop and validate a procedure for testing against a shift in mean in the observations and hidden state sequence of state space models with Gaussian noise. State space models are popular for modelling stochastic networks as they allow to take into account that observations of the
Stability properties of nonlinear dynamical systems and evolutionary stable states
Energy Technology Data Exchange (ETDEWEB)
Gleria, Iram, E-mail: iram@fis.ufal.br [Instituto de Física, Universidade Federal de Alagoas, 57072-970 Maceió-AL (Brazil); Brenig, Leon [Faculté des Sciences, Université Libre de Bruxelles, 1050 Brussels (Belgium); Rocha Filho, Tarcísio M.; Figueiredo, Annibal [Instituto de Física and International Center for Condensed Matter Physics, Universidade de Brasília, 70919-970 Brasília-DF (Brazil)
2017-03-18
Highlights: • We address the problem of equilibrium stability in a general class of non-linear systems. • We link Evolutionary Stable States (ESS) to stable fixed points of square quasi-polynomial (QP) systems. • We show that an interior ES point may be related to stable interior fixed points of QP systems. - Abstract: In this paper we address the problem of stability in a general class of non-linear systems. We establish a link between the concepts of asymptotic stable interior fixed points of square Quasi-Polynomial systems and evolutionary stable states, a property of some payoff matrices arising from evolutionary games.
Salient region detection Using Wasserstein distance measure based on nonlinear scale space
Zhu, Lei; Cao, Zhiguo
2013-10-01
Many existing bottom-up saliency detection methods measure the multi-scale local prominence by building the Gaussian scale space. As a kind of linear scale space, it is a natural representation of human perception. However the Gaussian filtering does not respect the boundaries of proto-objects and smooth both noises and details. In this paper, we compute the pixel level center-surround difference in a nonlinear scale space which makes blurring locally adaptive to the image regions. The nonlinear scale space is built by a efficient evolution techniques and extended to represent color images. In contrast to some widely used region-based measures, we represent feature statistics by multivariate normal distributions and compare them with the Wasserstein distance on l2 norm (W2 distance). From the perspective of visual organization in imaging, many priors are proved to be efficient in global consideration. In order to further precisely locate the proper salient object, we also use the background prior as a global cue to refine the obtained local saliency map. The experimental results show that our approach outperforms 5 recent state of the art saliency detection methods in terms of precision and recall on a newly published benchmark.
Robust Quasi-LPV Control Based on Neural State Space Models
DEFF Research Database (Denmark)
Bendtsen, Jan Dimon; Trangbæk, Klaus
2000-01-01
In this paper we derive a synthesis result for robust LPV output feedback controllers for nonlinear systems modelled by neural state space models. This result is achieved by writing the neural state space model on a linear fractional transformation form in a non-conservative way, separating...... the system description into a linear part and a nonlinear part. Linear parameter-varying control synthesis methods are then applied to design a nonlinear control law for this system. Since the model is assumed to have been identified from input-output measurement data only, it must be expected...
State space consistency and differentiability
Serakos, Demetrios
2014-01-01
By investigating the properties of the natural state, this book presents an analysis of input-output systems with regard to the mathematical concept of state. The state of a system condenses the effects of past inputs to the system in a useful manner. This monograph emphasizes two main properties of the natural state; the first has to do with the possibility of determining the input-output system from its natural state set and the second deals with differentiability properties involving the natural state inherited from the input-output system, including differentiability of the natural state and natural state trajectories. The results presented in this title aid in modeling physical systems since system identification from a state set holds in most models. Researchers and engineers working in electrical, aerospace, mechanical, and chemical fields along with applied mathematicians working in systems or differential equations will find this title useful due to its rigorous mathematics.
Coherent states in the fermionic Fock space
Oeckl, Robert
2015-01-01
We construct the coherent states in the sense of Gilmore and Perelomov for the fermionic Fock space. Our treatment is from the outset adapted to the infinite-dimensional case. The fermionic Fock space becomes in this way a reproducing kernel Hilbert space of continuous holomorphic functions.
State-Space Formulation for Circuit Analysis
Martinez-Marin, T.
2010-01-01
This paper presents a new state-space approach for temporal analysis of electrical circuits. The method systematically obtains the state-space formulation of nondegenerate linear networks without using concepts of topology. It employs nodal/mesh systematic analysis to reduce the number of undesired variables. This approach helps students to…
Continuous expected utility for arbitrary state spaces
Wakker, P.P.
1985-01-01
Subjective expected utility maximization with continuous utility is characterized, extending the result of Wakker (1984, Journal of Mathematical Psychology) to infinite state spaces. In Savage (1954, The Foundations of Statistics) the main restriction, P6, requires structure for the state space, e.g
Pruning state spaces with extended beam search
Dashti, M.T.; Wijs, A.J.
2007-01-01
This paper focuses on using beam search, a heuristic search algorithm, for pruning state spaces while generating. The original beam search is adapted to the state space generation setting and two new search variants are devised. The resulting framework encompasses some known algorithms, such as $A^*
A steady-state solver and stability calculator for nonlinear internal wave flows
Viner, Kevin C.; Epifanio, Craig C.; Doyle, James D.
2013-10-01
A steady solver and stability calculator is presented for the problem of nonlinear internal gravity waves forced by topography. Steady-state solutions are obtained using Newton's method, as applied to a finite-difference discretization in terrain-following coordinates. The iteration is initialized using a boundary-inflation scheme, in which the nonlinearity of the flow is gradually increased over the first few Newton steps. The resulting method is shown to be robust over the full range of nonhydrostatic and rotating parameter space. Examples are given for both nonhydrostatic and rotating flows, as well as flows with realistic upstream shear and static stability profiles. With a modest extension, the solver also allows for a linear stability analysis of the steady-state wave fields. Unstable modes are computed using a shifted-inverse method, combined with a parameter-space search over a set of realistic target values. An example is given showing resonant instability in a nonhydrostatic mountain wave.
Projective loop quantum gravity. I. State space
Lanéry, Suzanne; Thiemann, Thomas
2016-12-01
Instead of formulating the state space of a quantum field theory over one big Hilbert space, it has been proposed by Kijowski to describe quantum states as projective families of density matrices over a collection of smaller, simpler Hilbert spaces. Beside the physical motivations for this approach, it could help designing a quantum state space holding the states we need. In a latter work by Okolów, the description of a theory of Abelian connections within this framework was developed, an important insight being to use building blocks labeled by combinations of edges and surfaces. The present work generalizes this construction to an arbitrary gauge group G (in particular, G is neither assumed to be Abelian nor compact). This involves refining the definition of the label set, as well as deriving explicit formulas to relate the Hilbert spaces attached to different labels. If the gauge group happens to be compact, we also have at our disposal the well-established Ashtekar-Lewandowski Hilbert space, which is defined as an inductive limit using building blocks labeled by edges only. We then show that the quantum state space presented here can be thought as a natural extension of the space of density matrices over this Hilbert space. In addition, it is manifest from the classical counterparts of both formalisms that the projective approach allows for a more balanced treatment of the holonomy and flux variables, so it might pave the way for the development of more satisfactory coherent states.
Localized States in Discrete Nonlinear Schrödinger Equations
Cai, D; Grønbech-Jensen, N; Cai, David; Grønbech-Jensen, Niels
1993-01-01
A new 1-D discrete nonlinear Schrödinger (NLS) Hamiltonian is introduced which includes the integrable Ablowitz-Ladik system as a limit. The symmetry properties of the system are studied. The relationship between intrinsic localized states and the soliton of the Ablowitz-Ladik NLS is discussed. It is pointed out that a staggered localized state can be viewed as a particle of a {\\em negative} effective mass. It is shown that staggered localized states can exist in the discrete dark NLS. The motion of localized states and Peierls-Nabarro pinning are studied.
The light filament as a new nonlinear polarization state
Kovachev, Lubomir M
2015-01-01
We present an analytical approach to the theory of nonlinear propagation in gases of femtosecond optical pulses with broad-band spectrum . The vector character of the nonlinear third-order polarization of the electrical field in air is investigated in details. A new polarization state is presented by using left-hand and right-hand circular components of the electrical field . The corresponding system of vector amplitude equations is derived in the rotating basis. We found that this system of nonlinear equations has $3D+1$ vector soliton solutions with Lorentz shape. The solution presents a relatively stable propagation and rotation with GHz frequency of the vector of the electrical field in a plane orthogonal to the direction of propagation. The evolution of the intensity profile demonstrates a weak self-compression and a week spherical wave in the first milliseconds of propagation.
Advances in Derivative-Free State Estimation for Nonlinear Systems
DEFF Research Database (Denmark)
Nørgaard, Magnus; Poulsen, Niels Kjølstad; Ravn, Ole
In this paper we show that it involves considerable advantages to use polynomial approximations obtained with an interpolation formula for derivation of state estimators for nonlinear systems. The estimators become more accurate than estimators based on Taylor approximations, and yet the implemen......In this paper we show that it involves considerable advantages to use polynomial approximations obtained with an interpolation formula for derivation of state estimators for nonlinear systems. The estimators become more accurate than estimators based on Taylor approximations, and yet...... the implementation is significantly simpler as no derivatives are required. Thus, it is believed that estimators derived in this way can replace well-known filters, such as the extended Kalman filter (EKF) and its higher order relatives, in most practical applications. In addition to proposing a new set of state...
Directory of Open Access Journals (Sweden)
Houda Salhi
2016-01-01
Full Text Available This paper deals with the parameter estimation problem for multivariable nonlinear systems described by MIMO state-space Wiener models. Recursive parameters and state estimation algorithms are presented using the least squares technique, the adjustable model, and the Kalman filter theory. The basic idea is to estimate jointly the parameters, the state vector, and the internal variables of MIMO Wiener models based on a specific decomposition technique to extract the internal vector and avoid problems related to invertibility assumption. The effectiveness of the proposed algorithms is shown by an illustrative simulation example.
Graph Subsumption in Abstract State Space Exploration
Zambon, Eduardo; Rensink, Arend; Wijs, A.; Bosnacki, D.; Edelkamp, S.
In this paper we present the extension of an existing method for abstract graph-based state space exploration, called neighbourhood abstraction, with a reduction technique based on subsumption. Basically, one abstract state subsumes another when it covers more concrete states; in such a case, the
Analytical approximate solution for nonlinear space-time fractional Klein-Gordon equation
Institute of Scientific and Technical Information of China (English)
Khaled A.Gepreel; Mohamed S.Mohamed
2013-01-01
The fractional derivatives in the sense of Caputo and the homotopy analysis method are used to construct an approximate solution for the nonlinear space-time fractional derivatives Klein-Gordon equation.The numerical results show that the approaches are easy to implement and accurate when applied to the nonlinear space-time fractional derivatives KleinGordon equation.This method introduces a promising tool for solving many space-time fractional partial differential equations.This method is efficient and powerful in solving wide classes of nonlinear evolution fractional order equations.
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.
A dual approach in Orlicz spaces for the nonlinear Helmholtz equation
Evéquoz, Gilles
2015-12-01
In this paper, we present a variational framework in Orlicz spaces for the study of the nonlinear Helmholtz equation - Δ{u} - k2 u = f(x,u),quad {x} in {R}^N where N ≥ 3, k > 0 and f is a superlinear but subcritical nonlinearity, and we prove the existence of infinitely many real-valued solutions under additional decay assumptions on the nonlinear term. We also derive a far-field relation for these solutions.
New Space Weather and Nonlinear Waves and Processes Prize announced for 2013
Thompson, Victoria
2012-01-01
At the 2011 Fall Meeting in San Francisco, Calif., AGU announced the creation of a new award: the Space Weather and Nonlinear Waves and Processes Prize. The prize, which is being made possible by a generous contribution from longtime AGU members and NASA Jet Propulsion Laboratory (JPL), California Institute of Technology, scientists Bruce Tsurutani and Olga Verkhoglyadova, will recognize an AGU member scientist and will come with a $10,000 award. Tsurutani has served as a researcher with JPL since 1972 and is currently a senior research scientist. He was also the president of AGU's Space Physics and Aeronomy section from 1990 to 1992 and is a recipient of AGU's John Adam Fleming Medal, given “for original research and technical leadership in geomagnetism, atmospheric electricity, aeronomy, space physics, and related sciences.” Verkhoglyadova served as a professor of space physics in the Department of Astrophysics and Space Physics at Taras Shevchenko National University of Kyiv, in the Ukraine, prior to coming to the United States. Their leadership and dedication to AGU and to their field are apparent in their passion for this prize.
Energy Technology Data Exchange (ETDEWEB)
Belmonte-Beitia, Juan [Departamento de Matematicas, E.T.S. de Ingenieros Industriales and Instituto de Matematica Aplicada a la Ciencia y la Ingenieria (IMACI), Avda. Camilo Jose Cela 3, Universidad de Castilla-La Mancha, 13071 Ciudad Real (Spain)], E-mail: juan.belmonte@uclm.es; Calvo, Gabriel F. [Departamento de Matematicas, E.T.S. de Ingenieros Industriales and Instituto de Matematica Aplicada a la Ciencia y la Ingenieria (IMACI), Avda. Camilo Jose Cela 3, Universidad de Castilla-La Mancha, 13071 Ciudad Real (Spain)], E-mail: gabriel.fernandez@uclm.es
2009-01-19
In this Letter, by means of similarity transformations, we construct explicit solutions to the quintic nonlinear Schroedinger equation with potentials and nonlinearities depending both on time and on the spatial coordinates. We present the general approach and use it to study some examples and find nontrivial explicit solutions such as periodic (breathers), quasiperiodic and bright and dark soliton solutions.
Locally Bounded Function Spaces as the External Environment for Nonlinear Systems
Directory of Open Access Journals (Sweden)
Valery G. Fetisov
2013-01-01
Full Text Available . In this paper we consider locally bounded function spaces that act as the external environment for nonlinear dynamic systems. We give non-traditional examples of above spaces in which the basis of the selected function Orlicz space
On global attraction to stationary states for wave equations with concentrated nonlinearities
Kopylova, E.
2016-01-01
The global attraction to stationary states is established for solutions to 3D wave equations with concentrated nonlinearities: each finite energy solution converges as $t\\to\\pm\\infty$ to stationary states. The attraction is caused by nonlinear energy radiation.
Nonlinear Optical Spectroscopy of Excited States in Polyfluorene
Tong, M; Vardeny, Z V
2006-01-01
We used a variety of nonlinear optical (NLO) spectroscopies to study the singlet excited states order, and primary photoexcitations in polyfluorene; an important blue emitting p-conjugated polymer. The polarized NLO spectroscopies include ultrafast pump-probe photomodulation, two-photon absorption, and electroabsorption. For completeness we also measured the linear absorption and photoluminescence spectra. We found that the primary photoexcitations in polyfluorene are singlet excitons.
Institute of Scientific and Technical Information of China (English)
Wan-sheng WANG; Shou-fu LI; Run-sheng YANG
2012-01-01
A series of contractivity and exponential stability results for the solutions to nonlinear neutral functional differential equations (NFDEs) in Banach spaces are obtained,which provide unified theoretical foundation for the contractivity analysis of solutions to nonlinear problems in functional differential equations (FDEs),neutral delay differential equations (NDDEs) and NFDEs of other types which appear in practice.
NONLOCAL INITIAL PROBLEM FOR NONLINEAR NONAUTONOMOUS DIFFERENTIAL EQUATIONS IN A BANACH SPACE
Institute of Scientific and Technical Information of China (English)
M.I.Gil＇
2004-01-01
The nonlocal initial problem for nonlinear nonautonomous evolution equations in a Banach space is considered. It is assumed that the nonlinearities have the local Lipschitz properties. The existence and uniqueness of mild solutions are proved. Applications to integro-differential equations are discussed. The main tool in the paper is the normalizing mapping (the generalized norm).
Practical Application of Neural Networks in State Space Control
DEFF Research Database (Denmark)
Bendtsen, Jan Dimon
In the present thesis we address some problems in discrete-time state space control of nonlinear dynamical systems and attempt to solve them using generic nonlinear models based on artificial neural networks. The main aim of the work is to examine how well such control algorithms perform when...... applied to a realistic process. The thesis therefore strives to provide a thorough treatment of two classes of neural network-based controllers, and to make a rigorous comparison between them and a classical linear controller. Thus, the thesis starts out with a short review of some relevant system...... theoretic notions followed by a detailed description of the topology, neuron functions and learning rules of the two types of neural networks treated in the thesis, the multilayer perceptron and the neurofuzzy networks. In both cases, a Least Squares second-order gradient method is used to train...
Validation of ecological state space models using the Laplace approximation
DEFF Research Database (Denmark)
Thygesen, Uffe Høgsbro; Albertsen, Christoffer Moesgaard; Berg, Casper Willestofte
2017-01-01
Many statistical models in ecology follow the state space paradigm. For such models, the important step of model validation rarely receives as much attention as estimation or hypothesis testing, perhaps due to lack of available algorithms and software. Model validation is often based on a naive...... for estimation in general mixed effects models. Implementing one-step predictions in the R package Template Model Builder, we demonstrate that it is possible to perform model validation with little effort, even if the ecological model is multivariate, has non-linear dynamics, and whether observations...... are continuous or discrete. With both simulated data, and a real data set related to geolocation of seals, we demonstrate both the potential and the limitations of the techniques. Our results fill a need for convenient methods for validating a state space model, or alternatively, rejecting it while indicating...
Steady-state negative Wigner functions of nonlinear nanomechanical oscillators
Rips, Simon; Wilson-Rae, Ignacio; Hartmann, Michael J
2011-01-01
We propose a scheme to prepare nanomechanical oscillators in non-classical steady states, characterized by a pronounced negative Wigner function. In our optomechanical approach, the mechanical oscillator couples to multiple laser driven resonances of an optical cavity. By lowering the resonant frequency of the oscillator via an inhomogeneous electrostatic field, we significantly enhance its intrinsic geometric nonlinearity per phonon. This causes the motional sidebands to split into separate spectral lines for each phonon number and transitions between individual phonon Fock states can be selectively addressed. We show that this enables preparation of the nanomechanical oscillator in a single phonon Fock state. Our scheme can for example be implemented with a carbon nanotube dispersively coupled to the evanescent field of a state of the art whispering gallery mode microcavity.
Seljak, Uros
2012-01-01
On large scales a nonlinear transformation of matter density field can be viewed as a biased tracer of the density field itself. A nonlinear transformation also modifies the redshift space distortions in the same limit, giving rise to a velocity bias. In models with primordial nongaussianity a nonlinear transformation generates a scale dependent bias on large scales. We derive analytic expressions for these for a general nonlinear transformation. These biases can be expressed entirely in terms of the one point distribution function (PDF) of the final field and the parameters of the transformation. Our analysis allows one to devise nonlinear transformations with nearly arbitrary bias properties, which can be used to increase the signal in the large scale clustering limit. We apply the results to the ionizing equilibrium model of Lyman-alpha forest, in which Lyman-alpha flux F is related to the density perturbation delta via a nonlinear transformation. Velocity bias can be expressed as an average over the Lyman...
Projective Loop Quantum Gravity I. State Space
Lanéry, Suzanne
2014-01-01
Instead of formulating the state space of a quantum field theory over one big Hilbert space, it has been proposed by Kijowski to describe quantum states as projective families of density matrices over a collection of smaller, simpler Hilbert spaces. Beside the physical motivations for this approach, it could help designing a quantum state space holding the states we need. In [Oko{\\l}\\'ow 2013, arXiv:1304.6330] the description of a theory of Abelian connections within this framework was developed, an important insight being to use building blocks labeled by combinations of edges and surfaces. The present work generalizes this construction to an arbitrary gauge group G (in particular, G is neither assumed to be Abelian nor compact). This involves refining the definition of the label set, as well as deriving explicit formulas to relate the Hilbert spaces attached to different labels. If the gauge group happens to be compact, we also have at our disposal the well-established Ashtekar-Lewandowski Hilbert space, wh...
Exact solutions of SO(3) non-linear sigma model in a conic space background
Bezerra, V B; Romero, C
2005-01-01
We consider a nonlinear sigma model coupled to the metric of a conic space. We obtain restrictions for a nonlinear sigma model to be a source of the conic space. We then study nonlinear sigma model in the conic space background. We find coordinate transformations which reduce the chiral fields equations in the conic space background to field equations in Minkowski spacetime. This enables us to apply the same methods for obtaining exact solutions in Minkowski spacetime to the case of a conic spacetime. In the case the solutions depend on two spatial coordinates we employ Ivanov's geometrical ansatz. We give a general analysis and also present classes of solutions in which there is dependence on three and four coordinates. We discuss with special attention the intermediate instanton and meron solutions and their analogous in the conic space. We find differences in the total actions and topological charges of these solutions and discuss the role of the deficit angle.
Nonlinear system modeling with random matrices: echo state networks revisited.
Zhang, Bai; Miller, David J; Wang, Yue
2012-01-01
Echo state networks (ESNs) are a novel form of recurrent neural networks (RNNs) that provide an efficient and powerful computational model approximating nonlinear dynamical systems. A unique feature of an ESN is that a large number of neurons (the "reservoir") are used, whose synaptic connections are generated randomly, with only the connections from the reservoir to the output modified by learning. Why a large randomly generated fixed RNN gives such excellent performance in approximating nonlinear systems is still not well understood. In this brief, we apply random matrix theory to examine the properties of random reservoirs in ESNs under different topologies (sparse or fully connected) and connection weights (Bernoulli or Gaussian). We quantify the asymptotic gap between the scaling factor bounds for the necessary and sufficient conditions previously proposed for the echo state property. We then show that the state transition mapping is contractive with high probability when only the necessary condition is satisfied, which corroborates and thus analytically explains the observation that in practice one obtains echo states when the spectral radius of the reservoir weight matrix is smaller than 1.
Difference schemes for fully nonlinear pseudo-parabolic systems with two space dimensions
Institute of Scientific and Technical Information of China (English)
周毓麟; 袁光伟
1996-01-01
The first boundary value problem for the fully nonlinear pseudoparabolic systems of partial differential equations with two space dimensions by the finite difference method is studied. The existence and uniqueness of the discrete vector solutions for the difference systems are established by the fixed point technique. The stability and convergence of the discrete vector solutions of the difference schemes to the vector solutions of the original boundary problem of the fully nonlinear pseudo-parabolic system are obtained by way of a priori estimation. Here the unique smooth vector solution of the original problems for the fully nonlinear pseudo-parabolic system is assumed. Moreover, by the method used here, it can be proved that analogous results hold for fully nonlinear pseudo-parabolic system with three space dimensions, and improve the known results in the case of one space dimension.
Parameter and State Estimator for State Space Models
Directory of Open Access Journals (Sweden)
Ruifeng Ding
2014-01-01
Full Text Available This paper proposes a parameter and state estimator for canonical state space systems from measured input-output data. The key is to solve the system state from the state equation and to substitute it into the output equation, eliminating the state variables, and the resulting equation contains only the system inputs and outputs, and to derive a least squares parameter identification algorithm. Furthermore, the system states are computed from the estimated parameters and the input-output data. Convergence analysis using the martingale convergence theorem indicates that the parameter estimates converge to their true values. Finally, an illustrative example is provided to show that the proposed algorithm is effective.
Parameter and state estimator for state space models.
Ding, Ruifeng; Zhuang, Linfan
2014-01-01
This paper proposes a parameter and state estimator for canonical state space systems from measured input-output data. The key is to solve the system state from the state equation and to substitute it into the output equation, eliminating the state variables, and the resulting equation contains only the system inputs and outputs, and to derive a least squares parameter identification algorithm. Furthermore, the system states are computed from the estimated parameters and the input-output data. Convergence analysis using the martingale convergence theorem indicates that the parameter estimates converge to their true values. Finally, an illustrative example is provided to show that the proposed algorithm is effective.
Macro and micro view on steady states in state space
Sobota, Branislav
2010-01-01
This paper describes visualization of chaotic attractor and elements of the singularities in 3D space. 3D view of these effects enables to create a demonstrative projection about relations of chaos generated by physical circuit, the Chua's circuit. Via macro views on chaotic attractor is obtained not only visual space illustration of representative point motion in state space, but also its relation to planes of singularity elements. Our created program enables view on chaotic attractor both in 2D and 3D space together with plane objects visualization -- elements of singularities.
Li, Wan-Tong; Wang, Jia-Bing; Zhang, Li
2016-08-01
This paper is concerned with the new types of entire solutions other than traveling wave solutions of nonlocal dispersal equations with monostable nonlinearity in space periodic habitats. We first establish the existence and properties of spatially periodic solutions connecting two steady states. Then new types of entire solutions are constructed by combining the rightward and leftward pulsating traveling fronts with different speeds and a spatially periodic solution. Finally, for a class of special heterogeneous reaction, we further establish the uniqueness of entire solutions and the continuous dependence of such an entire solution on parameters, such as wave speeds and the shifted variables. In other words, we build a five-dimensional manifold of solutions and the traveling wave solutions are on the boundary of the manifold.
Robust Quasi-LPV Control Based on Neural State Space Models
DEFF Research Database (Denmark)
Bendtsen, Jan Dimon; Trangbæk, Klaus
2002-01-01
In this paper we derive a synthesis result for robust LPV output feedback controllers for nonlinear systems modelled by neural state space models. This result is achieved by writing the neural state space model on a linear fractional transformation form in a non-conservative way, separating...... that there is some uncertainty on the identified nonlinearities. The control law is therefore made robust to noise perturbations. After formulating the controller synthesis as a set of LMIs with added constraints, some implementation issues are addressed and a simulation example is presented....
The STAMP Software for State Space Models
Directory of Open Access Journals (Sweden)
Roy Mendelssohn
2011-05-01
Full Text Available This paper reviews the use of STAMP (Structural Time Series Analyser, Modeler and Predictor for modeling time series data using state-space methods with unobserved components. STAMP is a commercial, GUI-based program that runs on Windows, Linux and Macintosh computers as part of the larger OxMetrics System. STAMP can estimate a wide-variety of both univariate and multivariate state-space models, provides a wide array of diagnostics, and has a batch mode capability. The use of STAMP is illustrated for the Nile river data which is analyzed throughout this issue, as well as by modeling a variety of oceanographic and climate related data sets. The analyses of the oceanographic and climate data illustrate the breadth of models available in STAMP, and that state-space methods produce results that provide new insights into important scientific problems.
Institute of Scientific and Technical Information of China (English)
GAO Jie
2009-01-01
In this paper we treat first some nonlinear beam dynamics problems in storage rings, such as beam dynamic apertures due to magnetic multipoles, wiggles, beam-beam effects, nonlinear space charge effect, and then nonlinear electron cloud effect combined with beam-beam and space charge effects, analytically. This analytical treatment is applied to BEPC Ⅱ. The corresponding analytical expressions developed in this paper are useful both in understanding the physics behind these problems and also in making practical quick hand estimations.
Space groups for solid state scientists
Glazer, Michael; Glazer, Alexander N
2014-01-01
This Second Edition provides solid state scientists, who are not necessarily experts in crystallography, with an understandable and comprehensive guide to the new International Tables for Crystallography. The basic ideas of symmetry, lattices, point groups, and space groups are explained in a clear and detailed manner. Notation is introduced in a step-by-step way so that the reader is supplied with the tools necessary to derive and apply space group information. Of particular interest in this second edition are the discussions of space groups application to such timely topics as high-te
Fault Diagnosis of Nonlinear Systems Using Structured Augmented State Models
Institute of Scientific and Technical Information of China (English)
Jochen Aβfalg; Frank Allg(o)wer
2007-01-01
This paper presents an internal model approach for modeling and diagnostic functionality design for nonlinear systems operating subject to single- and multiple-faults. We therefore provide the framework of structured augmented state models. Fault characteristics are considered to be generated by dynamical exosystems that are switched via equality constraints to overcome the augmented state observability limiting the number of diagnosable faults. Based on the proposed model, the fault diagnosis problem is specified as an optimal hybrid augmented state estimation problem. Sub-optimal solutions are motivated and exemplified for the fault diagnosis of the well-known three-tank benchmark. As the considered class of fault diagnosis problems is large, the suggested approach is not only of theoretical interest but also of high practical relevance.
Nonlinear system identification and control using state transition algorithm
Yang, Chunhua; Gui, Weihua
2012-01-01
This paper presents a novel optimization method named state transition algorithm (STA) to solve the problem of identification and control for nonlinear system. In the proposed algorithm, a solution to optimization problem is considered as a state, and the updating of a solution equates to the process of state transition, which makes the STA easy to understand and convenient to be implemented. First, the STA is applied to identify the optimal parameters of the estimated system with previously known structure. With the accurate estimated model, an off-line PID controller is then designed optimally by using the STA as well. Experimental results demonstrate the validity of the methodology, and comparison to STA with other optimization algorithms confirms that STA is a promising alternative method for system identification and control due to its stronger search ability, faster convergence speed and more stable performance.
Progressive Bayes: a new framework for nonlinear state estimation
Hanebeck, Uwe D.; Briechle, Kai; Rauh, Andreas
2003-04-01
This paper is concerned with recursively estimating the internal state of a nonlinear dynamic system by processing noisy measurements and the known system input. In the case of continuous states, an exact analytic representation of the probability density characterizing the estimate is generally too complex for recursive estimation or even impossible to obtain. Hence, it is replaced by a convenient type of approximate density characterized by a finite set of parameters. Of course, parameters are desired that systematically minimize a given measure of deviation between the (often unknown) exact density and its approximation, which in general leads to a complicated optimization problem. Here, a new framework for state estimation based on progressive processing is proposed. Rather than trying to solve the original problem, it is exactly converted into a corresponding system of explicit ordinary first-order differential equations. Solving this system over a finite "time" interval yields the desired optimal density parameters.
On Volterra quadratic stochastic operators with continual state space
Energy Technology Data Exchange (ETDEWEB)
Ganikhodjaev, Nasir; Hamzah, Nur Zatul Akmar [Department of Computational and Theoretical Sciences, Faculty of Science, International Islamic University, Jalan Sultan Ahmad Shah, Bandar Indera Mahkota, 25200 Kuantan, Pahang (Malaysia)
2015-05-15
Let (X,F) be a measurable space, and S(X,F) be the set of all probability measures on (X,F) where X is a state space and F is σ - algebraon X. We consider a nonlinear transformation (quadratic stochastic operator) defined by (Vλ)(A) = ∫{sub X}∫{sub X}P(x,y,A)dλ(x)dλ(y), where P(x, y, A) is regarded as a function of two variables x and y with fixed A ∈ F . A quadratic stochastic operator V is called a regular, if for any initial measure the strong limit lim{sub n→∞} V{sup n }(λ) is exists. In this paper, we construct a family of quadratic stochastic operators defined on the segment X = [0,1] with Borel σ - algebra F on X , prove their regularity and show that the limit measure is a Dirac measure.
Design of nonlinear discrete-time controllers using a parameter space sampling procedure
Young, G. E.; Auslander, D. M.
1983-01-01
The design of nonlinear discrete-time controllers is investigated where the control algorithm assumes a special form. State-dependent control actions are obtained from tables whose values are the design parameters. A new design methodology capable of dealing with nonlinear systems containing parameter uncertainty is used to obtain the controller design. Various controller strategies are presented and illustrated through an example.
Directory of Open Access Journals (Sweden)
Banan Maayah
2014-01-01
Full Text Available A new algorithm called multistep reproducing kernel Hilbert space method is represented to solve nonlinear oscillator’s models. The proposed scheme is a modification of the reproducing kernel Hilbert space method, which will increase the intervals of convergence for the series solution. The numerical results demonstrate the validity and the applicability of the new technique. A very good agreement was found between the results obtained using the presented algorithm and the Runge-Kutta method, which shows that the multistep reproducing kernel Hilbert space method is very efficient and convenient for solving nonlinear oscillator’s models.
Leech Lattice Extension of the Non-linear Schrodinger Equation Theory of Einstein spaces
Chapline, George
2015-01-01
Although the nonlinear Schrodinger equation description of Einstein spaces has provided insights into how quantum mechanics might modify the classical general relativistic description of space-time, an exact quantum description of space-times with matter has remained elusive. In this note we outline how the nonlinear Schrodinger equation theory of Einstein spaces might be generalized to include matter by transplanting the theory to the 25+1 dimensional Lorentzian Leech lattice. Remarkably when a hexagonal section of the Leech lattice is set aside as the stage for the nonlinear Schrodinger equation, the discrete automorphism group of the complex Leech lattice with one complex direction fixed can be lifted to continuous Lie group symmetries. In this setting the wave function becomes an 11x11 complex matrix which represents matter degrees of freedom consisting of a 2-form abelian gauge field and vector nonabelian SU(3)xE6 gauge fields together with their supersymmetric partners. The lagrangian field equations fo...
Measurement-Induced Strong Kerr Nonlinearity for Weak Quantum States of Light
Costanzo, Luca S.; Coelho, Antonio S.; Biagi, Nicola; Fiurášek, Jaromír; Bellini, Marco; Zavatta, Alessandro
2017-07-01
Strong nonlinearity at the single photon level represents a crucial enabling tool for optical quantum technologies. Here we report on experimental implementation of a strong Kerr nonlinearity by measurement-induced quantum operations on weak quantum states of light. Our scheme coherently combines two sequences of single photon addition and subtraction to induce a nonlinear phase shift at the single photon level. We probe the induced nonlinearity with weak coherent states and characterize the output non-Gaussian states with quantum state tomography. The strong nonlinearity is clearly witnessed as a change of sign of specific off-diagonal density matrix elements in the Fock basis.
State-space Correlations and Stabilities
Bellucci, Stefano
2010-01-01
The state-space pair correlation functions and notion of stability of extremal and non-extremal black holes in string theory and M-theory are considered from the viewpoints of thermodynamic Ruppeiner geometry. From the perspective of intrinsic Riemannian geometry, the stability properties of these black branes are divulged from the positivity of principle minors of the space-state metric tensor. We have explicitly analyzed the state-space configurations for (i) the two and three charge extremal black holes, (ii) the four and six charge non-extremal black branes, which both arise from the string theory solutions. An extension is considered for the $D_6$-$D_4$-$D_2$-$D_0$ multi-centered black branes, fractional small black branes and two charge rotating fuzzy rings in the setup of Mathur's fuzzball configurations. The state-space pair correlations and nature of stabilities have been investigated for three charged bubbling black brane foams, and thereby the M-theory solutions are brought into the present conside...
State estimation of connected vehicles using a nonlinear ensemble filter
Institute of Scientific and Technical Information of China (English)
刘江; 陈华展; 蔡伯根; 王剑
2015-01-01
The concept of connected vehicles is with great potentials for enhancing the road transportation systems in the future. To support the functions and applications under the connected vehicles frame, the estimation of dynamic states of the vehicles under the cooperative environments is a fundamental issue. By integrating multiple sensors, localization modules in OBUs (on-board units) require effective estimation solutions to cope with various operation conditions. Based on the filtering estimation framework for sensor fusion, an ensemble Kalman filter (EnKF) is introduced to estimate the vehicle’s state with observations from navigation satellites and neighborhood vehicles, and the original EnKF solution is improved by using the cubature transformation to fulfill the requirements of the nonlinearity approximation capability, where the conventional ensemble analysis operation in EnKF is modified to enhance the estimation performance without increasing the computational burden significantly. Simulation results from a nonlinear case and the cooperative vehicle localization scenario illustrate the capability of the proposed filter, which is crucial to realize the active safety of connected vehicles in future intelligent transportation.
Extended phase space of Black Holes in Lovelock gravity with nonlinear electrodynamics
Hendi, S H; Panah, B Eslam
2015-01-01
In this paper, we consider Lovelock gravity in presence of two Born-Infeld types of nonlinear electrodynamics and study their thermodynamical behavior. We extend the phase space by considering cosmological constant as a thermodynamical pressure. We obtain critical values of pressure, volume and temperature and investigate the effects of both the Lovelock gravity and the nonlinear electrodynamics on these values. We plot $P-v$, $T-v$ and $G-T$ diagrams to study the phase transition of these thermodynamical systems. We show that power of the nonlinearity and gravity have opposite effects. We also show how considering cosmological constant, nonlinearity and Lovelock parameters as thermodynamical variables will modify Smarr formula and first law of thermodynamics. In addition, we study the behavior of universal ratio of $\\frac{P_{c}v_{c}}{T_{c}}$ for different values of nonlinearity power of electrodynamics as well as the Lovelock coefficients.
Rudra, Shubhobrata; Maitra, Madhubanti
2017-01-01
This book presents a novel, generalized approach to the design of nonlinear state feedback control laws for a large class of underactuated mechanical systems based on application of the block backstepping method. The control law proposed here is robust against the effects of model uncertainty in dynamic and steady-state performance and addresses the issue of asymptotic stabilization for the class of underactuated mechanical systems. An underactuated system is defined as one for which the dimension of space spanned by the configuration vector is greater than that of the space spanned by the control variables. Control problems concerning underactuated systems currently represent an active field of research due to their broad range of applications in robotics, aerospace, and marine contexts. The book derives a generalized theory of block backstepping control design for underactuated mechanical systems, and examines several case studies that cover interesting examples of underactuated mechanical systems. The math...
Variational space-time (dis)continuous Galerkin method for nonlinear free surface waves
Gagarina, E; Vegt, van der, N.F.A.; Ambati, V.R.; Bokhove, O.
2013-01-01
A new variational finite element method is developed for nonlinear free surface gravity water waves. This method also handles waves generated by a wave maker. Its formulation stems from Miles' variational principle for water waves together with a space-time finite element discretization that is continuous in space and discontinuous in time. The key features of this formulation are: (i) a discrete variational approach that gives rise to conservation of discrete energy and phase space and prese...
Nonlinear Filtering Techniques Comparison for Battery State Estimation
Directory of Open Access Journals (Sweden)
Aspasia Papazoglou
2014-09-01
Full Text Available The performance of estimation algorithms is vital for the correct functioning of batteries in electric vehicles, as poor estimates will inevitably jeopardize the operations that rely on un-measurable quantities, such as State of Charge and State of Health. This paper compares the performance of three nonlinear estimation algorithms: the Extended Kalman Filter, the Unscented Kalman Filter and the Particle Filter, where a lithium-ion cell model is considered. The effectiveness of these algorithms is measured by their ability to produce accurate estimates against their computational complexity in terms of number of operations and execution time required. The trade-offs between estimators' performance and their computational complexity are analyzed.
Institute of Scientific and Technical Information of China (English)
LI Shoufu
2005-01-01
A series of stability, contractivity and asymptotic stability results of the solutions to nonlinear stiff Volterra functional differential equations (VFDEs) in Banach spaces is obtained, which provides the unified theoretical foundation for the stability analysis of solutions to nonlinear stiff problems in ordinary differential equations(ODEs), delay differential equations(DDEs), integro-differential equations(IDEs) and VFDEs of other type which appear in practice.
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.
ANTI-PERIODIC SOLUTIONS FOR FIRST AND SECOND ORDER NONLINEAR EVOLUTION EQUATIONS IN BANACH SPACES
Institute of Scientific and Technical Information of China (English)
WEI Wei; XIANG Xiaoling
2004-01-01
In this paper, a new existence theorem of anti-periodic solutions for a class ofstrongly nonlinear evolution equations in Banach spaces is presentedThe equations con-tain nonlinear monotone operators and a nonmonotone perturbationMoreover, throughan appropriate transformation, the existence of anti-periodic solutions for a class of second-order nonlinear evolution equations is verifiedOur abstract results are illustrated by anexample from quasi-linear partial differential equations with time anti-periodic conditionsand an example from quasi-linear anti-periodic hyperbolic differential equations.
Simulating Nonlinear Dynamics of Deployable Space Structures Project
National Aeronautics and Space Administration — To support NASA's vital interest in developing much larger solar array structures over the next 20 years, MotionPort LLC's Phase I SBIR project will strengthen...
Gettman, Chang-Ching L.; Adams, Neil; Bedrossian, Nazareth; Valavani, Lena
1993-01-01
This paper demonstrates an approach to nonlinear control system design that uses linearization by state feedback to allow faster maneuvering of payloads by the Shuttle Remote Manipulator System (SRMS). A nonlinear feedback law is defined to cancel the nonlinear plant dynamics so that a linear controller can be designed for the SRMS. First a nonlinear design model was generated via SIMULINK. This design model included nonlinear arm dynamics derived from the Lagrangian approach, linearized servo model, and linearized gearbox model. The current SRMS position hold controller was implemented on this system. Next, a trajectory was defined using a rigid body kinematics SRMS tool, KRMS. The maneuver was simulated. Finally, higher bandwidth controllers were developed. Results of the new controllers were compared with the existing SRMS automatic control modes for the Space Station Freedom Mission Build 4 Payload extended on the SRMS.
Multimedia Mapping using Continuous State Space Models
DEFF Research Database (Denmark)
Lehn-Schiøler, Tue
2004-01-01
In this paper a system that transforms speech waveforms to animated faces are proposed. The system relies on continuous state space models to perform the mapping, this makes it possible to ensure video with no sudden jumps and allows continuous control of the parameters in 'face space'. Simulations...... are performed on recordings of 3-5 sec. video sequences with sentences from the Timit database. The model is able to construct an image sequence from an unknown noisy speech sequence fairly well even though the number of training examples are limited....
Explicit Integration of Friedmann's Equation with Nonlinear Equations of State
Chen, Shouxin; Yang, Yisong
2015-01-01
This paper is a continuation of our earlier study on the integrability of the Friedmann equations in the light of the Chebyshev theorem. Our main focus will be on a series of important, yet not previously touched, problems when the equation of state for the perfect-fluid universe is nonlinear. These include the generalized Chaplygin gas, two-term energy density, trinomial Friedmann, Born--Infeld, and two-fluid models. We show that some of these may be integrated using Chebyshev's result while other are out of reach by the theorem but may be integrated explicitly by other methods. With the explicit integration, we are able to understand exactly the roles of the physical parameters in various models play in the cosmological evolution. For example, in the Chaplygin gas universe, it is seen that, as far as there is a tiny presence of nonlinear matter, linear matter makes contribution to the dark matter, which becomes significant near the phantom divide line. The Friedmann equations also arise in areas of physics ...
Nonlinear Approximation and the Space BV(R2)
1997-01-01
number t let Uf t infgBVQ kf gk LI tVQg where the inmum is taken over all functions g BV of bounded variation on I This and related...all functions g BV of bounded variation on I This and related extremal problems arise in several areas of mathematics such as interpolation of...Q tVQg Here BVQ is the space of functions of bounded variation on Q see x for the de nition of this space and VQf jf jBV is the
Energy Technology Data Exchange (ETDEWEB)
Subalakshmi, R. [Department of Mathematics, Bharathiar University, Coimbatore 641 046 (India)], E-mail: suba.ab.bu@gmail.com; Balachandran, K. [Department of Mathematics, Bharathiar University, Coimbatore 641 046 (India)], E-mail: balachandran_k@lycos.com
2009-11-30
Many practical systems in physical and biological sciences have impulsive dynamical behaviours during the evolution process which can be modeled by impulsive differential equations. This paper studies the approximate controllability properties of nonlinear stochastic impulsive integrodifferential and neutral functional stochastic impulsive integrodifferential equations in Hilbert spaces. Assuming the conditions for the approximate controllability of these linear systems we obtain the sufficient conditions for the approximate controllability of these associated nonlinear stochastic impulsive integrodifferential systems in Hilbert spaces. The results are obtained by using the Nussbaum fixed-point theorem. Finally, two examples are presented to illustrate the utility of the proposed result.
Linear and Nonlinear Time-Frequency Analysis for Parameter Estimation of Resident Space Objects
2017-02-22
AFRL-AFOSR-UK-TR-2017-0023 Linear and Nonlinear Time-Frequency Analysis for Parameter Estimation of Resident Space Objects Marco Martorella... UNIVERSITY DI PISA, DEPARTMENT DI INGEGNERIA Final Report 02/22/2017 DISTRIBUTION A: Distribution approved for public release. AF Office Of Scientific Research...Nonlinear Time-Frequency Analysis for Parameter Estimation of Resident Space Objects 5a. CONTRACT NUMBER 5b. GRANT NUMBER FA9550-14-1-0183 5c. PROGRAM
Tensorial dynamics on the space of quantum states
Cariñena, J. F.; Clemente-Gallardo, J.; Jover-Galtier, J. A.; Marmo, G.
2017-09-01
A geometric description of the space of states of a finite-dimensional quantum system and of the Markovian evolution associated with the Kossakowski-Lindblad operator is presented. This geometric setting is based on two composition laws on the space of observables defined by a pair of contravariant tensor fields. The first one is a Poisson tensor field that encodes the commutator product and allows us to develop a Hamiltonian mechanics. The other tensor field is symmetric, encodes the Jordan product and provides the variances and covariances of measures associated with the observables. This tensorial formulation of quantum systems is able to describe, in a natural way, the Markovian dynamical evolution as a vector field on the space of states. Therefore, it is possible to consider dynamical effects on non-linear physical quantities, such as entropies, purity and concurrence. In particular, in this work the tensorial formulation is used to consider the dynamical evolution of the symmetric and skew-symmetric tensors and to read off the corresponding limits as giving rise to a contraction of the initial Jordan and Lie products.
Jeribi, Aref
2015-01-01
Uncover the Useful Interactions of Fixed Point Theory with Topological StructuresNonlinear Functional Analysis in Banach Spaces and Banach Algebras: Fixed Point Theory under Weak Topology for Nonlinear Operators and Block Operator Matrices with Applications is the first book to tackle the topological fixed point theory for block operator matrices with nonlinear entries in Banach spaces and Banach algebras. The book provides researchers and graduate students with a unified survey of the fundamental principles of fixed point theory in Banach spaces and algebras. The authors present several exten
State-variable analysis of non-linear circuits with a desk computer
Cohen, E.
1981-01-01
State variable analysis was used to analyze the transient performance of non-linear circuits on a desk top computer. The non-linearities considered were not restricted to any circuit element. All that is required for analysis is the relationship defining each non-linearity be known in terms of points on a curve.
Effect of dielectric medium on the nonclassical properties of nonlinear sphere coherent states
Directory of Open Access Journals (Sweden)
E Amooghorban
2014-04-01
Full Text Available In order to investigate the effect of a medium with dissipation and dispersion and also the curvature of the physical space on the properties of the incident quantum states, we use the quantization of electromagnetic field based on phenomenological approach to obtain input-output relations between radiations on both sides of dielectric slab. By using these relations the fidelity, the Wigner function, and also the quantum correlation of the outgoing state through dielectric slab are obtained for a situation in which the rightward incident state is a nonlinear coherent state on a sphere and the leftward incident state is a vacuum state. Here, the incident states are considered monochromatic and the modeling of the medium is given by the Lorentz' model. Accordingly, we study nonclassical properties of the output states such as the quantum entanglement. It will be observed that the nonclassical properties of the outgoing states depend strongly on the optical property of the medium and also on the curvature of the physical state.
The State Space Models Toolbox for MATLAB
Directory of Open Access Journals (Sweden)
Jyh-Ying Peng
2011-05-01
Full Text Available State Space Models (SSM is a MATLAB toolbox for time series analysis by state space methods. The software features fully interactive construction and combination of models, with support for univariate and multivariate models, complex time-varying (dy- namic models, non-Gaussian models, and various standard models such as ARIMA and structural time-series models. The software includes standard functions for Kalman fil- tering and smoothing, simulation smoothing, likelihood evaluation, parameter estimation, signal extraction and forecasting, with incorporation of exact initialization for filters and smoothers, and support for missing observations and multiple time series input with com- mon analysis structure. The software also includes implementations of TRAMO model selection and Hillmer-Tiao decomposition for ARIMA models. The software will provide a general toolbox for time series analysis on the MATLAB platform, allowing users to take advantage of its readily available graph plotting and general matrix computation capabilities.
Charged anisotropic matter with linear or nonlinear equation of state
Varela, Victor; Ray, Saibal; Chakraborty, Kaushik; Kalam, Mehedi
2010-01-01
Ivanov pointed out substantial analytical difficulties associated with self-gravitating, static, isotropic fluid spheres when pressure explicitly depends on matter density. Simplification achieved with the introduction of electric charge were noticed as well. We deal with self-gravitating, charged, anisotropic fluids and get even more flexibility in solving the Einstein-Maxwell equations. In order to discuss analytical solutions we extend Krori and Barua's method to include pressure anisotropy and linear or non-linear equations of state. The field equations are reduced to a system of three algebraic equations for the anisotropic pressures as well as matter and electrostatic energy densities. Attention is paid to compact sources characterized by positive matter density and positive radial pressure. Arising solutions satisfy the energy conditions of general relativity. Spheres with vanishing net charge contain fluid elements with unbounded proper charge density located at the fluid-vacuum interface. Notably the...
Condensed State Spaces for Symmetrical Coloured Petri Nets
DEFF Research Database (Denmark)
Jensen, Kurt
1996-01-01
This paper deals with state spaces. A state space is a directed graph with a node for each reachable state and an arc for each possible state change. We describe how symmetries of the modelled system can be exploited to obtain much more succinct state space analysis. The symmetries induce equival...
Liquid-state acoustically-nonlinear nanoplasmonic source of optical frequency combs
Maksymov, Ivan S
2016-01-01
Nonlinear acoustic interactions in liquids are effectively stronger than nonlinear optical interactions in solids. Thus, harnessing these interactions will offer new possibilities in the design of ultra-compact nonlinear photonic devices. We theoretically demonstrate a hybrid, liquid-state and nanoplasmonic, source of optical frequency combs compatible with fibre-optic technology. This source relies on a nanoantenna to harness the strength of nonlinear acoustic effects and synthesise optical spectra from ultrasound.
Directory of Open Access Journals (Sweden)
Xia Liu
2017-02-01
Full Text Available The discrete nonlinear Schrodinger equation is a nonlinear lattice system that appears in many areas of physics such as nonlinear optics, biomolecular chains and Bose-Einstein condensates. In this article, we consider a class of discrete nonlinear Schrodinger equations with unbounded potentials. We obtain some new sufficient conditions on the multiplicity results of ground state solutions for the equations by using the symmetric mountain pass lemma. Recent results in the literature are greatly improved.
The nonlinear evolution of de Sitter space instabilities
Niemeyer, J C; Niemeyer, Jens C.; Bousso, Raphael
2000-01-01
We investigate the quantum evolution of large black holes that nucleate spontaneously in de Sitter space. By numerical computation in the s-wave and one-loop approximations, we verify claims that such black holes can initially "anti-evaporate" instead of shrink. We show, however, that this is a transitory effect. It is followed by an evaporating phase, which we are able to trace until the black holes are small enough to be treated as Schwarzschild. Under generic perturbations, the nucleated geometry is shown to decay into a ring of de Sitter regions connected by evaporating black holes. This confirms that de Sitter space is globally unstable and fragments into disconnected daughter universes.
Finite element method for nonlinear Riesz space fractional diffusion equations on irregular domains
Yang, Z.; Yuan, Z.; Nie, Y.; Wang, J.; Zhu, X.; Liu, F.
2017-02-01
In this paper, we consider two-dimensional Riesz space fractional diffusion equations with nonlinear source term on convex domains. Applying Galerkin finite element method in space and backward difference method in time, we present a fully discrete scheme to solve Riesz space fractional diffusion equations. Our breakthrough is developing an algorithm to form stiffness matrix on unstructured triangular meshes, which can help us to deal with space fractional terms on any convex domain. The stability and convergence of the scheme are also discussed. Numerical examples are given to verify accuracy and stability of our scheme.
Nonlinear dynamics of phase space zonal structures and energetic particle physics in fusion plasmas
Zonca, Fulvio; Briguglio, Sergio; Fogaccia, Giuliana; Vlad, Gregorio; Wang, Xin
2014-01-01
A general theoretical framework for investigating nonlinear dynamics of phase space zonal structures is presented in this work. It is then, more specifically, applied to the limit where the nonlinear evolution time scale is smaller or comparable to the wave-particle trapping period. In this limit, both theoretical and numerical simulation studies show that non-adiabatic frequency chirping and phase locking could lead to secular resonant particle transport on meso- or macro-scales. The interplay between mode structures and resonant particles then provides the crucial ingredient to properly understand and analyze the nonlinear dynamics of Alfv\\'en wave instabilities excited by non-perturbative energetic particles in burning fusion plasmas. Analogies with autoresonance in nonlinear dynamics and with superradiance in free electron lasers are also briefly discussed.
Suppression of space charge induced beam halo in nonlinear focusing channel
Batygin, Yuri K.; Scheinker, Alexander; Kurennoy, Sergey; Li, Chao
2016-04-01
An intense non-uniform particle beam exhibits strong emittance growth and halo formation in focusing channels due to nonlinear space charge forces of the beam. This phenomenon limits beam brightness and results in particle losses. The problem is connected with irreversible distortion of phase space volume of the beam in conventional focusing structures due to filamentation in phase space. Emittance growth is accompanied by halo formation in real space, which results in inevitable particle losses. A new approach for solving a self-consistent problem for a matched non-uniform beam in two-dimensional geometry is discussed. The resulting solution is applied to the problem of beam transport, while avoiding emittance growth and halo formation by the use of nonlinear focusing field. Conservation of a beam distribution function is demonstrated analytically and by particle-in-cell simulation for a beam with a realistic beam distribution.
Suppression of Space Charge Induced Beam Halo in Nonlinear Focusing Channel
Batygin, Yuri K; Kurennoy, Sergey; Li, Chao
2016-01-01
An intense non-uniform particle beam exhibits strong emittance growth and halo formation in focusing channels due to nonlinear space charge forces of the beam. This phenomenon limits beam brightness and results in particle losses. The problem is connected with irreversible distortion of phase space volume of the beam in conventional focusing structures due to filamentation in phase space. Emittance growth is accompanied by halo formation in real space, which results in inevitable particle losses. A new approach for solving a self-consistent problem for a matched non-uniform beam in two-dimensional geometry is discussed. The resulting solution is applied to the problem of beam transport, while avoiding emittance growth and halo formation by the use of nonlinear focusing field. Conservation of a beam distribution function is demonstrated analytically and by particle-in-cell simulation for a beam with a realistic beam distribution.
Existence and Boundedness of Solutions for Nonlinear Volterra Difference Equations in Banach Spaces
Directory of Open Access Journals (Sweden)
Rigoberto Medina
2016-01-01
Full Text Available We consider a class of nonlinear discrete-time Volterra equations in Banach spaces. Estimates for the norm of operator-valued functions and the resolvents of quasi-nilpotent operators are used to find sufficient conditions that all solutions of such equations are elements of an appropriate Banach space. These estimates give us explicit boundedness conditions. The boundedness of solutions to Volterra equations with infinite delay is also investigated.
Energy Technology Data Exchange (ETDEWEB)
Belmonte-Beitia, Juan [Departamento de Matematicas, E. T. S. de Ingenieros Industriales and Instituto de Matematica Aplicada a la Ciencia y la IngenierIa (IMACI), E. T. S. I. Industriales, Avda. Camilo Jose Cela, s/n Universidad de Castilla-La Mancha 13071 Ciudad Real (Spain)
2009-01-23
We introduce a model of a Bose-Einstein condensate based on the one-dimensional nonlinear Schroedinger equation, in which the nonlinear term depends on the domain. The nonlinear term changes a cubic term into a quintic term, according to the domain considered. We study the existence, stability and bifurcation of solutions, and use the qualitative theory of dynamical systems to study certain properties of such solutions.
On the correct formulation of a nonlinear differential equations in Banach space
Directory of Open Access Journals (Sweden)
Mahmoud M. El-Borai
2001-01-01
Full Text Available We study, the existence and uniqueness of the initial value problems in a Banach space E for the abstract nonlinear differential equation (dn−1/dtn−1(du/dt+Au=B(tu+f(t,W(t, and consider the correct solution of this problem. We also give an application of the theory of partial differential equations.
On Landau damping of dipole modes by non-linear space charge and octupoles
Möhl, D
1995-01-01
The joint effect of space-charge non-linearities and octupole lenses is important for Landau damping of coherent instabilities. The octupole strength required for stabilisation can depend strongly on the sign of the excitation current of the lenses. This note tries to extend results, previously obtained for coasting beams and rigid bunches, to more general head--tail modes.
Institute of Scientific and Technical Information of China (English)
Tetsuya Ishiwata; Masayoshi Tsutsumi
2000-01-01
Semidiscretization in space of nonlinear degenerate parabolic equations of nondivergent form is presented, under zero Dirichlet boundary condition. It is shown that semidiscrete solutions blow up in finite time. In particular, the asymptotic behavior of blowing-up solutions, is discussed precisely.
Variational space-time (dis)continuous Galerkin method for nonlinear free surface waves
Gagarina, E.; Vegt, van der J.J.W.; Ambati, V.R.; Bokhove, O.
2013-01-01
A new variational finite element method is developed for nonlinear free surface gravity water waves. This method also handles waves generated by a wave maker. Its formulation stems from Miles' variational principle for water waves together with a space-time finite element discretization that is cont
Integrability of Nonlinear Equations of Motion on Two-Dimensional World Sheet Space-Time
Institute of Scientific and Technical Information of China (English)
YAN Jun
2005-01-01
The integrability character of nonlinear equations of motion of two-dimensional gravity with dynamical torsion and bosonic string coupling is studied in this paper. The space-like and time-like first integrals of equations of motion are also found.
Energy Technology Data Exchange (ETDEWEB)
Cloutier, J.R.; D`Souza, C.N.; Mracek, C.P. [Air Force Armament Directorate, Eglin, FL (United States)
1994-12-31
A little known technique for systematically designing nonlinear regulators is analyzed. The technique consists of first using direct parameterization to bring the nonlinear system to a linear structure having state-dependent coefficients (SDC). A state-dependent Riccati equation (SDRE) is then solved at each point x along the trajectory to obtain a nonlinear feedback controller of the form u = -R{sup -1}(x)B{sup T}(x)P(x)x, where P(x) is the solution of the SDRE. In the case of scalar x, it is shown that the SDRE approach yields a control solution which satisfies all of the necessary conditions for optimality even when the state and control weightings are functions of the state. It is also shown that the solution is globally asymptotically stable. In the multivariable case, the optimality, suboptimality and stability properties of the SDRE method are investigated. Under various mild assumptions of controllability and observability, the following is shown: (a) concerning the necessary conditions for optimality, where H is the Hamiltonian of the system, H{sub u} = 0 is always satisfied and, under stability, {lambda} = -H{sub x} is asymptotically satisfied at a quadratic rate as the states are driven toward the origin, (b) if it exists, a parameter-dependent SDC parameterization can be computed such that the multivariable SDRE closed loop solution satisfies all of the necessary conditions for optimality for a given initial condition, and (c) the method is locally asymptotically stable. A general nonlinear minimum-energy (nonlinear H{sub {infinity}}) problem is then posed. For this problem, the SDRF, method involves the solution of two coupled state-dependent Riccati equations at each point x along the trajectory. In the case of full state information, again under mild assumptions of controllability and observability, it is shown that the SDRE non-linear H{sub {infinity}} controller is internally locally asymptotically stable.
Metastability of the Nonlinear Wave Equation: Insights from Transition State Theory
Newhall, Katherine A.; Vanden-Eijnden, Eric
2017-06-01
This paper is concerned with the longtime dynamics of the nonlinear wave equation in one-space dimension, u_{tt} - κ ^2 u_{xx} +V'(u) =0 \\quad x\\in [0,1] where κ >0 is a parameter and V( u) is a potential bounded from below and growing at least like u^2 as |u|→ ∞. Infinite energy solutions of this equation preserve a natural Gibbsian invariant measure, and when the potential is double-welled, for example when V(u) = 1/4 (1-u^2)^2, there is a regime such that two small disjoint sets in the system's phase-space concentrate most of the mass of this measure. This suggests that the solutions to the nonlinear wave equation can be metastable over these sets, in the sense that they spend long periods of time in these sets and only rarely transition between them. Here, we quantify this phenomenon by calculating exactly via transition state theory (TST) the mean frequency at which the solutions of the nonlinear wave equation with initial conditions drawn from its invariant measure cross a dividing surface lying in between the metastable sets. We also investigate numerically how the mean TST frequency compares to the rate at which a typical solution crosses this dividing surface. These numerical results suggest that the dynamics of the nonlinear wave equation is ergodic and rapidly mixing with respect to the Gibbs invariant measure when the parameter κ in small enough. In this case, successive transitions between the two regions are roughly uncorrelated and their dynamics can be coarse-grained to jumps in a two-state Markov chain whose rate can be deduced from the mean TST frequency. This is a regime in which the dynamics of the nonlinear wave equation displays a metastable behavior that is not fundamentally different from that observed in its stochastic counterpart in which random noise and damping terms are added to the equation. For larger κ , however, the dynamics either stops being ergodic, or its mixing time becomes larger than the inverse of the TST frequency
Metastability of the Nonlinear Wave Equation: Insights from Transition State Theory
Newhall, Katherine A.; Vanden-Eijnden, Eric
2017-01-01
This paper is concerned with the longtime dynamics of the nonlinear wave equation in one-space dimension, u_{tt} - κ^2 u_{xx} +V'(u) =0 quad xin [0,1] where κ >0 is a parameter and V(u) is a potential bounded from below and growing at least like u^2 as |u|→ ∞. Infinite energy solutions of this equation preserve a natural Gibbsian invariant measure, and when the potential is double-welled, for example when V(u) = 1/4 (1-u^2)^2 , there is a regime such that two small disjoint sets in the system's phase-space concentrate most of the mass of this measure. This suggests that the solutions to the nonlinear wave equation can be metastable over these sets, in the sense that they spend long periods of time in these sets and only rarely transition between them. Here, we quantify this phenomenon by calculating exactly via transition state theory (TST) the mean frequency at which the solutions of the nonlinear wave equation with initial conditions drawn from its invariant measure cross a dividing surface lying in between the metastable sets. We also investigate numerically how the mean TST frequency compares to the rate at which a typical solution crosses this dividing surface. These numerical results suggest that the dynamics of the nonlinear wave equation is ergodic and rapidly mixing with respect to the Gibbs invariant measure when the parameter κ in small enough. In this case, successive transitions between the two regions are roughly uncorrelated and their dynamics can be coarse-grained to jumps in a two-state Markov chain whose rate can be deduced from the mean TST frequency. This is a regime in which the dynamics of the nonlinear wave equation displays a metastable behavior that is not fundamentally different from that observed in its stochastic counterpart in which random noise and damping terms are added to the equation. For larger κ, however, the dynamics either stops being ergodic, or its mixing time becomes larger than the inverse of the TST frequency
Luo, Xiaodong
2014-10-01
The ensemble Kalman filter (EnKF) is an efficient algorithm for many data assimilation problems. In certain circumstances, however, divergence of the EnKF might be spotted. In previous studies, the authors proposed an observation-space-based strategy, called residual nudging, to improve the stability of the EnKF when dealing with linear observation operators. The main idea behind residual nudging is to monitor and, if necessary, adjust the distances (misfits) between the real observations and the simulated ones of the state estimates, in the hope that by doing so one may be able to obtain better estimation accuracy. In the present study, residual nudging is extended and modified in order to handle nonlinear observation operators. Such extension and modification result in an iterative filtering framework that, under suitable conditions, is able to achieve the objective of residual nudging for data assimilation problems with nonlinear observation operators. The 40-dimensional Lorenz-96 model is used to illustrate the performance of the iterative filter. Numerical results show that, while a normal EnKF may diverge with nonlinear observation operators, the proposed iterative filter remains stable and leads to reasonable estimation accuracy under various experimental settings.
Nonlinear scale space with spatially varying stopping time.
Gilboa, Guy
2008-12-01
A general scale space algorithm is presented for denoising signals and images with spatially varying dominant scales. The process is formulated as a partial differential equation with spatially varying time. The proposed adaptivity is semi-local and is in conjunction with the classical gradient-based diffusion coefficient, designed to preserve edges. The new algorithm aims at maximizing a local SNR measure of the denoised image. It is based on a generalization of a global stopping time criterion presented recently by the author and colleagues. Most notably, the method works well also for partially textured images and outperforms any selection of a global stopping time. Given an estimate of the noise variance, the procedure is automatic and can be applied well to most natural images.
Free-Space Nonlinear Beam Combining Towards Filamentation
Rostami, Shermineh; Kepler, Daniel; Baudelet, Matthieu; Litchinitser, Natalia M; Richardson, Martin
2016-01-01
Multi-filamentation opens new degrees of freedom for manipulating electromagnetic waves in air. However, without control, multiple filament interactions, including attraction, repulsion or fusion often result in formation of complex disordered filament distributions. Moreover, high power beams conventionally used in multi-filament formation experiments often cause significant surface damage. The growing number of applications for laser filaments requires fine control of their formation and propagation. We demonstrate, experimentally and theoretically, that the attraction and fusion of ultrashort beams with initial powers below the critical value enable the eventual formation of a filament downstream. Filament formation is delayed to a predetermined distance in space, avoiding optical damage to external beam optics while still enabling robust filaments with controllable properties as if formed from a single high power beam. This paradigm introduces new opportunities for filament engineering eliminating the nee...
Geometry of state space in plane Couette flow
Cvitanović, P.; Gibson, J. F.
A large conceptual gap separates the theory of low-dimensional chaotic dynamics from the infinite-dimensional nonlinear dynamics of turbulence. Recent advances in experimental imaging, computational methods, and dynamical systems theory suggest a way to bridge this gap in our understanding of turbulence. Recent discoveries show that recurrent coherent structures observed in wall-bounded shear flows (such as pipes and plane Couette flow) result from close passes to weakly unstable invariant solutions of the Navier-Stokes equations. These 3D, fully nonlinear solutions (equilibria, traveling waves, and periodic orbits) structure the state space of turbulent flows and provide a skeleton for analyzing their dynamics. We calculate a hierarchy of invariant solutions for plane Couette, a canonical wall-bounded shear flow. These solutions reveal organization in the flow's turbulent dynamics and can be used to predict directly from the fundamental equations physical quantities such as bulk flow rate and mean wall drag. All results and the code that generates them are disseminated through through our group's open-source CFD software and solution database Channelflow.org and the collaborative e-book ChaosBook.org.
Computation of Value Functions in Nonlinear Differential Games with State Constraints
Botkin, Nikolai
2013-01-01
Finite-difference schemes for the computation of value functions of nonlinear differential games with non-terminal payoff functional and state constraints are proposed. The solution method is based on the fact that the value function is a generalized viscosity solution of the corresponding Hamilton-Jacobi-Bellman-Isaacs equation. Such a viscosity solution is defined as a function satisfying differential inequalities introduced by M. G. Crandall and P. L. Lions. The difference with the classical case is that these inequalities hold on an unknown in advance subset of the state space. The convergence rate of the numerical schemes is given. Numerical solution to a non-trivial three-dimensional example is presented. © 2013 IFIP International Federation for Information Processing.
Lin, Tai-Chia; Petrovic, Milan S; Hajaiej, Hichem; Chen, Goong
2016-01-01
The virial theorem is a nice property for the linear Schrodinger equation in atomic and molecular physics as it gives an elegant ratio between the kinetic and potential energies and is useful in assessing the quality of numerically computed eigenvalues. If the governing equation is a nonlinear Schrodinger equation with power-law nonlinearity, then a similar ratio can be obtained but there seems no way of getting any eigenvalue estimate. It is surprising as far as we are concerned that when the nonlinearity is either square-root or saturable nonlinearity (not a power-law), one can develop a virial theorem and eigenvalue estimate of nonlinear Schrodinger (NLS) equations in R2 with square-root and saturable nonlinearity, respectively. Furthermore, we show here that the eigenvalue estimate can be used to obtain the 2nd order term (which is of order $ln\\Gamma$) of the lower bound of the ground state energy as the coefficient $\\Gamma$ of the nonlinear term tends to infinity.
Fractional State Space Analysis of Economic Systems
Directory of Open Access Journals (Sweden)
J. A. Tenreiro Machado
2015-07-01
Full Text Available This paper examines modern economic growth according to the multidimensional scaling (MDS method and state space portrait (SSP analysis. Electing GDP per capita as the main indicator for economic growth and prosperity, the long-run perspective from 1870 to 2010 identifies the main similarities among 34 world partners’ modern economic growth and exemplifies the historical waving mechanics of the largest world economy, the USA. MDS reveals two main clusters among the European countries and their old offshore territories, and SSP identifies the Great Depression as a mild challenge to the American global performance, when compared to the Second World War and the 2008 crisis.
Chaotic behaviour of nonlinear coupled reaction–diffusion system in four-dimensional space
Indian Academy of Sciences (India)
Li Zhang; Shutang Liu; Chenglong Yu
2014-06-01
In recent years, nonlinear coupled reaction–diffusion (CRD) system has been widely investigated by coupled map lattice method. Previously, nonlinear behaviour was observed dynamically when one or two of the three variables in the discrete system change. In this paper, we consider the chaotic behaviour when three variables change, which is called as four-dimensional chaos. When two parameters in the discrete system are unknown, we first give the existing condition of the chaos in four-dimensional space by the generalized definitions of spatial periodic orbits and spatial chaos. In addition, the chaotic behaviour will vary with the parameters. Then we propose a generalized Lyapunov exponent in four-dimensional space to characterize the different effects of parameters on the chaotic behaviour, which has not been studied in detail. In order to verify the chaotic behaviour of the system and the different effects clearly, we simulate the dynamical behaviour in two- and three-dimensional spaces.
Existence Results for Differential Inclusions with Nonlinear Growth Conditions in Banach Spaces
Directory of Open Access Journals (Sweden)
Messaoud Bounkhel
2013-01-01
Full Text Available In the Banach space setting, the existence of viable solutions for differential inclusions with nonlinear growth; that is, ẋ(t∈F(t,x(t a.e. on I, x(t∈S, ∀t∈I, x(0=x0∈S, (*, where S is a closed subset in a Banach space , I=[0,T], (T>0, F:I×S→, is an upper semicontinuous set-valued mapping with convex values satisfying F(t,x⊂c(tx+xp, ∀(t,x∈I×S, where p∈ℝ, with p≠1, and c∈C([0,T],ℝ+. The existence of solutions for nonconvex sweeping processes with perturbations with nonlinear growth is also proved in separable Hilbert spaces.
Ground state solutions for nonlinear fractional Schrodinger equations involving critical growth
Directory of Open Access Journals (Sweden)
Hua Jin
2017-03-01
Full Text Available This article concerns the ground state solutions of nonlinear fractional Schrodinger equations involving critical growth. We obtain the existence of ground state solutions when the potential is not a constant and not radial. We do not use the Ambrosetti-Rabinowitz condition, or the monotonicity condition on the nonlinearity.
Integral input-to-state stability of nonlinear control systems with delays
Energy Technology Data Exchange (ETDEWEB)
Zhu Wenli [Department of Economics Mathematics, South Western University of Finance and Economics, Chengdu 610074 (China)]. E-mail: zhuwl@swufe.edu.cn; Yi Zhang [Computational Intelligence Laboratory, School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 610054 (China)]. E-mail: zhangyi@uestc.edu.cn
2007-10-15
Integral input-to-state stability is an interesting concept that has been recently introduced to nonlinear control systems. This paper generalizes this concept to nonlinear control systems with delays. These delays can be bounded, unbounded, and even infinite. Theorems for integral input-to-state stability are derived by developing the method of Razumikhin technique in the theory of functional differential equations.
Multivariable Wind Modeling in State Space
DEFF Research Database (Denmark)
Sichani, Mahdi Teimouri; Pedersen, B. J.
2011-01-01
Turbulence of the incoming wind field is of paramount importance to the dynamic response of wind turbines. Hence reliable stochastic models of the turbulence should be available from which time series can be generated for dynamic response and structural safety analysis. In the paper an empirical...... cross-spectral density function for the along-wind turbulence component over the rotor plane is taken as the starting point. The spectrum is spatially discretized in terms of a Hermitian cross-spectral density matrix for the turbulence state vector which turns out not to be positive definite. Since...... the succeeding state space and ARMA modeling of the turbulence rely on the positive definiteness of the cross-spectral density matrix, the problem with the non-positive definiteness of such matrices is at first addressed and suitable treatments regarding it are proposed. From the adjusted positive definite cross...
Characterizaticr of Solid State Laser and Nonlinear Optical Materials.
1995-02-02
materials useful in the different methods for obtaining frequency agility: narrow line emitters with multiple lasing channels and nonlinear optical materials . In...codoped with two or more rare earth ions were studied and computers models developed to explain their spectral dynamics. The nonlinear optical materials investigated
A Sweep-Line Method for State Space Exploration
DEFF Research Database (Denmark)
Christensen, Søren; Kristensen, Lars Michael; Mailund, Thomas
2001-01-01
We present a state space exploration method for on-the-fly verification. The method is aimed at systems for which it is possible to define a measure of progress based on the states of the system. The measure of progress makes it possible to delete certain states on-the-fly during state space...... of the method on a number of Coloured Petri Net models, and give a first evaluation of its practicality by means of an implementation based on the Design/CPN state space tool. Our experiments show significant reductions in both space and time used during state space exploration. The method is not specific...
Dyja, Robert; van der Zee, Kristoffer G
2016-01-01
We present an adaptive methodology for the solution of (linear and) non-linear time dependent problems that is especially tailored for massively parallel computations. The basic concept is to solve for large blocks of space-time unknowns instead of marching sequentially in time. The methodology is a combination of a computationally efficient implementation of a parallel-in-space-time finite element solver coupled with a posteriori space-time error estimates and a parallel mesh generator. This methodology enables, in principle, simultaneous adaptivity in both space and time (within the block) domains. We explore this basic concept in the context of a variety of time-steppers including $\\Theta$-schemes and Backward Differentiate Formulas. We specifically illustrate this framework with applications involving time dependent linear, quasi-linear and semi-linear diffusion equations. We focus on investigating how the coupled space-time refinement indicators for this class of problems affect spatial adaptivity. Final...
Deliktaş, Ekin; Teymür, Mevlüt
2017-07-01
In this study, the propagation of shear horizontal (SH) waves in a nonlinear elastic half space covered by a nonlinear elastic layer with a slowly varying interface is examined. The constituent materials are assumed to be homogenous, isotropic, elastic and having different mechanical properties. By employing the method of multiple scales, a nonlinear Schrödinger equation (NLS) with variable coefficients is derived for the nonlinear self-modulation of SH waves. We examine the effects of dispersion, irregularity of the interface and nonlinearity on the propagation characteristics of SH waves.
Nonlinear free vibrations of beams in space due to internal resonance
Stoykov, S.; Ribeiro, P.
2011-08-01
The geometrically nonlinear free vibrations of beams with rectangular cross section are investigated using a p-version finite element method. The beams may vibrate in space, hence they may experience longitudinal, torsional and non-planar bending deformations. The model is based on Timoshenko's theory for bending and assumes that, under torsion, the cross section rotates as a rigid body and is free to warp in the longitudinal direction, as in Saint-Venant's theory. The geometrical nonlinearity is taken into account by considering Green's nonlinear strain tensor. Isotropic and elastic beams are investigated and generalised Hooke's law is used. The equation of motion is derived by the principle of virtual work. Mostly clamped-clamped beams are investigated, although other boundary conditions are considered for validation purposes. Employing the harmonic balance method, the differential equations of motion are converted into a nonlinear algebraic form and then solved by a continuation method. One constant term, odd and even harmonics are assumed in the Fourier series and convergence with the number of harmonics is analysed. The variation of the amplitude of vibration with the frequency of vibration is determined and presented in the form of backbone curves. Coupling between modes is investigated, internal resonances are found and the ensuing multimodal oscillations are described. Some of the couplings discovered lead from planar oscillations to oscillations in the three dimensional space.
Center for Space Telemetering and Telecommunications Systems, New Mexico State University
Horan, Stephen; DeLeon, Phillip; Borah, Deva; Lyman, Ray
2002-01-01
This viewgraph presentation gives an overview of the Center for Space Telemetering and Telecommunications Systems activities at New Mexico State University. Presentations cover the following topics: (1) small satellite communications, including nanosatellite radio and virtual satellite development; (2) modulation and detection studies, including details on smooth phase interpolated keying (SPIK) spectra and highlights of an adaptive turbo multiuser detector; (3) decoupled approaches to nonlinear ISI compensation; (4) space internet testing; (4) optical communication; (5) Linux-based receiver for lightweight optical communications without a laser in space, including software design, performance analysis, and the receiver algorithm; (6) carrier tracking hardware; and (7) subband transforms for adaptive direct sequence spread spectrum receivers.
An Inhomogeneous Space-Time Patching Model Based on a Nonlocal and Nonlinear Schrodinger Equation
Dantas, Christine C
2016-01-01
We consider an integrable, nonlocal and nonlinear, Schr\\"odinger equation (NNSE) as a model for building space-time patchings in inhomogeneous loop quantum cosmology (LQC). We briefly review exact solutions of the NNSE, specially those obtained through "geometric equivalence" methods. Furthemore, we argue that the integrability of the NNSE could be linked to consistency conditions derived from LQC, under the assumption that the patchwork dynamics behaves as an integrable many-body system.
Non-linear shape functions over time in the space-time finite element method
Directory of Open Access Journals (Sweden)
Kacprzyk Zbigniew
2017-01-01
Full Text Available This work presents a generalisation of the space-time finite element method proposed by Kączkowski in his seminal of 1970’s and early 1980’s works. Kączkowski used linear shape functions in time. The recurrence formula obtained by Kączkowski was conditionally stable. In this paper, non-linear shape functions in time are proposed.
Numerical Simulations for the Space-Time Variable Order Nonlinear Fractional Wave Equation
Directory of Open Access Journals (Sweden)
Nasser Hassan Sweilam
2013-01-01
Full Text Available The explicit finite-difference method for solving variable order fractional space-time wave equation with a nonlinear source term is considered. The concept of variable order fractional derivative is considered in the sense of Caputo. The stability analysis and the truncation error of the method are discussed. To demonstrate the effectiveness of the method, some numerical test examples are presented.
On the System of Nonlinear Mixed Implicit Equilibrium Problems in Hilbert Spaces
Directory of Open Access Journals (Sweden)
Yeol Je Cho
2010-01-01
Full Text Available We use the Wiener-Hopf equations and the Yosida approximation notions to prove the existence theorem of a system of nonlinear mixed implicit equilibrium problems (SMIE in Hilbert spaces. The algorithm for finding a solution of the problem (SMIE is suggested; the convergence criteria and stability of the iterative algorithm are discussed. The results presented in this paper are more general and are viewed as an extension, refinement, and improvement of the previously known results in the literature.
Frequency map analysis of resonances in a nonlinear lattice with space charge
Energy Technology Data Exchange (ETDEWEB)
Turchetti, G. E-mail: turchetti@bo.infn.it; Bazzani, A.; Bergamini, F.; Rambaldi, S.; Hofmann, I.; Bongini, L.; Franchetti, G
2001-05-21
In storage rings for heavy ion fusion beam losses must be minimized. During bunch compression high space charge is reached and the reciprocal effects between the collective modes of the beam and the single particle lattice nonlinearities must be considered to understand the problem of resonance crossing and halo formation. We show that the frequency map analysis of particle in core models gives an adequate description of the resonance network and of the chaotic regions where the halo particles can diffuse.
GLOBAL SOLUTIONS OF SYSTEMS OF NONLINEAR IMPULSIVE VOLTERRA INTEGRAL EQUATIONS IN BANACH SPACES
Institute of Scientific and Technical Information of China (English)
陈芳启; 陈予恕
2001-01-01
The existence of solutions for systems of nonlinear impulsive Volterra integral equations on the infinite interval R+ with an infinite number of moments of impulse effect in Banach spaces is studied. Some existence theorems of extremal solutions are obtained,which extend the related results for this class of equations on a finite interval with a finite number of moments of impulse effect. The results are demonstrated by means of an example of an infinite systems for impulsive integral equations.
Hamiltonian realizations of nonlinear adjoint operators
Fujimoto, Kenji; Scherpen, Jacquelien M.A.; Gray, W. Steven
2002-01-01
This paper addresses the issue of state-space realizations for nonlinear adjoint operators. In particular, the relationships between nonlinear Hilbert adjoint operators, Hamiltonian extensions and port-controlled Hamiltonian systems are established. Then, characterizations of the adjoints of control
Hamiltonian Realizations of Nonlinear Adjoint Operators
Fujimoto, Kenji; Scherpen, Jacquelien M.A.; Gray, W. Steven
2000-01-01
This paper addresses state-space realizations for nonlinear adjoint operators. In particular the relationship among nonlinear Hilbert adjoint operators, Hamiltonian extensions and port-controlled Hamiltonian systems are clarified. The characterization of controllability, observability and Hankel ope
Directory of Open Access Journals (Sweden)
M. Boudjema
2003-01-01
Full Text Available The elastic response of many rocks to quasistatic stress changes is highly nonlinear and hysteretic, displaying discrete memory. Rocks also display unusual nonlinear response to dynamic stress changes. A model to describe the elastic behavior of rocks and other consolidated materials is called the Preisach-Mayergoyz (PM space model. In contrast to the traditional analytic approach to stress-strain, the PM space picture establishes a relationship between the quasistatic data and a number density of hysteretic mesoscopic elastic elements in the rock. The number density allows us to make quantitative predictions of dynamic elastic properties. Using the PM space model, we analyze a complex suite of quasistatic stress-strain data taken on Berea sandstone. We predict a dynamic bulk modulus and a dynamic shear modulus surface as a function of mean stress and shear stress. Our predictions for the dynamic moduli compare favorably to moduli derived from time of flight measurements. We derive a set of nonlinear elastic constants and a set of constants that describe the hysteretic behavior of the sandstone.
Persistence of solutions to nonlinear evolution equations in weighted Sobolev spaces
Directory of Open Access Journals (Sweden)
Xavier Carvajal Paredes
2010-11-01
Full Text Available In this article, we prove that the initial value problem associated with the Korteweg-de Vries equation is well-posed in weighted Sobolev spaces $mathcal{X}^{s,heta}$, for $s geq 2heta ge 2$ and the initial value problem associated with the nonlinear Schrodinger equation is well-posed in weighted Sobolev spaces $mathcal{X}^{s,heta}$, for $s geq heta geq 1$. Persistence property has been proved by approximation of the solutions and using a priori estimates.
A Fully Discrete Galerkin Method for a Nonlinear Space-Fractional Diffusion Equation
Directory of Open Access Journals (Sweden)
Yunying Zheng
2011-01-01
Full Text Available The spatial transport process in fractal media is generally anomalous. The space-fractional advection-diffusion equation can be used to characterize such a process. In this paper, a fully discrete scheme is given for a type of nonlinear space-fractional anomalous advection-diffusion equation. In the spatial direction, we use the finite element method, and in the temporal direction, we use the modified Crank-Nicolson approximation. Here the fractional derivative indicates the Caputo derivative. The error estimate for the fully discrete scheme is derived. And the numerical examples are also included which are in line with the theoretical analysis.
Abdel-Salam, Emad A-B; Hassan, Gmal F
2015-01-01
In this paper, the fractional projective Riccati expansion method is proposed to solve fractional differential equations. To illustrate the effectiveness of the method, we discuss the space-time fractional Burgers equation, the space-time fractional mKdV equation and time fractional biological population model. The solutions are expressed in terms of fractional hyperbolic functions. These solutions are useful to understand the mechanisms of the complicated nonlinear physical phenomena and fractional differential equations. Among these solutions, some are found for the first time. The fractal index for the obtained results is equal to one. Counter examples to compute the fractal index are introduced in appendix.
Maj, Omar
2008-01-01
This is the second part of a work aimed to study complex-phase oscillatory solutions of nonlinear symmetric hyperbolic systems. We consider, in particular, the case of one space dimension. That is a remarkable case, since one can always satisfy the \\emph{naive} coherence condition on the complex phases, which is required in the construction of the approximate solution. Formally the theory applies also in several space dimensions, but the \\emph{naive} coherence condition appears to be too restrictive; the identification of the optimal coherence condition is still an open problem.
Küchler, Sebastian; Meurer, Thomas; Jacobs, Laurence J; Qu, Jianmin
2009-03-01
This study investigates two-dimensional wave propagation in an elastic half-space with quadratic nonlinearity. The problem is formulated as a hyperbolic system of conservation laws, which is solved numerically using a semi-discrete central scheme. These numerical results are then analyzed in the frequency domain to interpret the nonlinear effects, specifically the excitation of higher-order harmonics. To quantify and compare the nonlinearity of different materials, a new parameter is introduced, which is similar to the acoustic nonlinearity parameter beta for one-dimensional longitudinal waves. By using this new parameter, it is found that the nonlinear effects of a material depend on the point of observation in the half-space, both the angle and the distance to the excitation source. Furthermore it is illustrated that the third-order elastic constants have a linear effect on the acoustic nonlinearity of a material.
Institute of Scientific and Technical Information of China (English)
文双春; 范滇元
2002-01-01
Spatiotemporal instability in nonlinear dispersive media is investigated on the basis of the nonlinear envelope equation. A general expression for instability gain which includes the effects of space-time focusing, arbitrarily higher-order dispersions and self-steepening is obtained. It is found that, for both normal and anomalous group-velocity dispersions, space-time focusing may lead to the appearance of new instability regions and influence the original instability gain spectra mainly by shrinking their regions. The region of the original instability gain spectrum shrinks much more in normal dispersion case than in anomalous one. In the former case, space-time focusing completely suppresses the growing of higher frequency components. In addition, we find that all the oddth-order dispersions contribute none to instability, while all the eventh-order dispersions influence instability region and do not influence the maximum instability gain, therein the fourth-order dispersion plays the same role as space-time focusing in spatiotemporal instability. The main role played by self-steepening in spatiotemporal instability is that it reduces the instability gain and exerts much more significant influence on the new instability regions resulting from space-time focusing.
Non-linear diffusion in RD and in Hilbert Spaces, a Cylindrical/Functional Integral Study
Botelho, Luiz Carlos Lobato
2010-01-01
We present a proof for the existence and uniqueness of weak solutions for a cut-off and non cut-off model of non-linear diffusion equation in finite-dimensional space RD useful for modelling flows on porous medium with saturation, turbulent advection, etc. - and subject to deterministic or stochastic (white noise) stirrings. In order to achieve such goal, we use the powerful results of compacity on functional Lp spaces (the Aubin-Lion Theorem). We use such results to write a path-integral solution for this problem. Additionally, we present the rigourous functional integral solutions for the Linear Diffussion equation defined in Infinite-Dimensional Spaces (Separable Hilbert Spaces). These further results are presented in order to be useful to understand Polymer cylindrical surfaces probability distributions and functionals on String theory.
Contamination and Radiation Effects on Nonlinear Crystals for Space Laser Systems
Abdeldayem, Hossain A.; Dowdye, Edward; Jamison, Tracee; Canham, John; Jaeger, Todd
2005-01-01
Space Lasers are vital tools for NASA s space missions and military applications. Although, lasers are highly reliable on the ground, several past space laser missions proved to be short-lived and unreliable. In this communication, we are shedding more light on the contamination and radiation issues, which are the most common causes for optical damages and laser failures in space. At first, we will present results based on the study of liquids and subsequently correlate these results to the particulates of the laser system environment. We present a model explaining how the laser beam traps contaminants against the optical surfaces and cause optical damages and the role of gravity in the process. We also report the results of the second harmonic generation efficiency for nonlinear optical crystals irradiated with high-energy beams of protons. In addition, we are proposing to employ the technique of adsorption to minimize the presence of adsorbing molecules present in the laser compartment.
Stabilization of nonlinear sandwich systems via state feedback-Discrete-time systems
Wang, Xu; Stoorvogel, Anton A.; Saberi, Ali; Grip, H°avard Fjær; Sannuti, Peddapullaiah
2011-01-01
A recent paper (IEEE Trans. Aut. Contr. 2010; 55(9):2156–2160) considered stabilization of a class of continuous-time nonlinear sandwich systems via state feedback. This paper is a discrete-time counterpart of it. The class of nonlinear sandwich systems consists of saturation elements sandwiched bet
A Sweep-Line Method for State Space Exploration
DEFF Research Database (Denmark)
Christensen, Søren; Kristensen, Lars Michael; Mailund, Thomas
2001-01-01
We present a state space exploration method for on-the-fly verification. The method is aimed at systems for which it is possible to define a measure of progress based on the states of the system. The measure of progress makes it possible to delete certain states on-the-fly during state space...... of the method on a number of Coloured Petri Net models, and give a first evaluation of its practicality by means of an implementation based on the Design/CPN state space tool. Our experiments show significant reductions in both space and time used during state space exploration. The method is not specific...... generation, since these states can never be reached again. This in turn reduces the memory used for state space storage during the task of verification. Examples of progress measures are sequence numbers in communication protocols and time in certain models with time. We illustrate the application...
Nonlinear Dependence of Global Warming Prediction on Ocean State
Liang, M.; Lin, L.; Tung, K. K.; Yung, Y. L.; Sun, S.
2010-12-01
Global temperature has increased by 0.8 C since the pre-industrial era, and is likely to increase further if greenhouse gas emission continues unchecked. Various mitigation efforts are being negotiated among nations to keep the increase under 2 C, beyond which the outcome is believed to be catastrophic. Such policy efforts are currently based on predictions by the state-of-the-art coupled atmosphere ocean models (AOGCM). Caution is advised for their use for the purpose of short-term (less than a century) climate prediction as the predicted warming and spatial patterns vary depending on the initial state of the ocean, even in an ensemble mean. The range of uncertainty in such predictions by Intergovernmental Panel on Climate Change (IPCC) models may be underreported when models were run with their oceans at various stages of adjustment with their atmospheres. By comparing a very long run (> 1000 years) of the coupled Goddard Institute for Space Studies (GISS) model with what was reported to IPCC Fourth Assessment Report (AR4), we show that the fully adjusted model transient climate sensitivity should be 30% higher for the same model, and the 2 C warming should occur sooner than previously predicted. Using model archives we further argue that this may be a common problem for the IPCC AR4 models, since few, if any, of the models has a fully adjusted ocean. For all models, multi-decadal climate predictions to 2050 are highly dependent on the initial ocean state (and so are unreliable). Such dependence cannot be removed simply by subtracting the climate drift from control runs.
Indian Academy of Sciences (India)
Hari Prakash; Devendra K Singh
2010-03-01
It is shown that all optical polarization states of light except plane and circular polarization states undergo an intensity-dependent change in normal incidence of light in an isotropic nonlinear Kerr medium. This effect should be detectable and we propose an experiment for detecting nonlinear susceptibility involved in that part of nonlinear polarization, which depends on the polarization state of light also.
A simplified state-space model of biventricular assist device-cardiovascular system interaction.
Koh, Vivian C A; Einly Lim; Boon Chiang Ng; Yong Kuen Ho; Lovell, Nigel H
2016-08-01
A simplified state-space model of biventricular assist device (BiVAD)-cardiovascular system (CVS) interaction is presented. The state-space equations includes a six-compartments CVS model incorporating the ventricles, the pulmonary and systemic circulations as well as the non-linear behavior of the valve flow, together with a left ventricular assist device (LVAD) and a right ventricular assist device (RVAD) component. The left and right pump speeds serve as the input variables for the state-space model. The model is simulated with three operational modes, i.e. (i) RVAD speed state hemodynamics is also studied with and without an outflow banding restriction. Our simulated results are validated with experimental data obtained from clinical, in vivo and in vitro studies provided in the literatures. We observed that despite its simplicity, the model is able to reproduce the observed trends in the reported studies, thus making it feasible for the development of robust yet practical control algorithms.
Modeling and Simulation of DC Power Electronics Systems Using Harmonic State Space (HSS) Method
DEFF Research Database (Denmark)
Kwon, Jun Bum; Wang, Xiongfei; Bak, Claus Leth
2015-01-01
For the efficiency and simplicity of electric systems, the dc based power electronics systems are widely used in variety applications such as electric vehicles, ships, aircrafts and also in homes. In these systems, there could be a number of dynamic interactions between loads and other dc...... based on the state-space averaging and generalized averaging, these also have limitations to show the same results as with the non-linear time domain simulations. This paper presents a modeling and simulation method for a large dc power electronic system by using Harmonic State Space (HSS) modeling....... Through this method, the required computation time and CPU memory for large dc power electronics systems can be reduced. Besides, the achieved results show the same results as with the non-linear time domain simulation, but with the faster simulation time which is beneficial in a large network....
State-space-split method for some generalized Fokker-Planck-Kolmogorov equations in high dimensions.
Er, Guo-Kang; Iu, Vai Pan
2012-06-01
The state-space-split method for solving the Fokker-Planck-Kolmogorov equations in high dimensions is extended to solving the generalized Fokker-Planck-Kolmogorov equations in high dimensions for stochastic dynamical systems with a polynomial type of nonlinearity and excited by Poissonian white noise. The probabilistic solution of the motion of the stretched Euler-Bernoulli beam with cubic nonlinearity and excited by uniformly distributed Poissonian white noise is analyzed with the presented solution procedure. The numerical analysis shows that the results obtained with the state-space-split method together with the exponential polynomial closure method are close to those obtained with the Monte Carlo simulation when the relative value of the basic system relaxation time and the mean arrival time of the Poissonian impulse is in some limited range.
Energy Technology Data Exchange (ETDEWEB)
Chekhov, L.O.
1985-12-01
Matrix nonlinear sigma models are discussed and the matrix nonlinear sigma model in the case of N x ..cap alpha..N rectangular matrices is considered. The authors show that in two-dimensional Euclidean space, the model is renormalizable with respect to ..cap alpha.. and 1/N. The fulfillment of the chirality identity is demonstrated in the operator expansion for the renormalized theory.
Rosenblatt, Marcus; Timmer, Jens; Kaschek, Daniel
2016-01-01
Ordinary differential equation models have become a wide-spread approach to analyze dynamical systems and understand underlying mechanisms. Model parameters are often unknown and have to be estimated from experimental data, e.g., by maximum-likelihood estimation. In particular, models of biological systems contain a large number of parameters. To reduce the dimensionality of the parameter space, steady-state information is incorporated in the parameter estimation process. For non-linear models, analytical steady-state calculation typically leads to higher-order polynomial equations for which no closed-form solutions can be obtained. This can be circumvented by solving the steady-state equations for kinetic parameters, which results in a linear equation system with comparatively simple solutions. At the same time multiplicity of steady-state solutions is avoided, which otherwise is problematic for optimization. When solved for kinetic parameters, however, steady-state constraints tend to become negative for particular model specifications, thus, generating new types of optimization problems. Here, we present an algorithm based on graph theory that derives non-negative, analytical steady-state expressions by stepwise removal of cyclic dependencies between dynamical variables. The algorithm avoids multiple steady-state solutions by construction. We show that our method is applicable to most common classes of biochemical reaction networks containing inhibition terms, mass-action and Hill-type kinetic equations. Comparing the performance of parameter estimation for different analytical and numerical methods of incorporating steady-state information, we show that our approach is especially well-tailored to guarantee a high success rate of optimization.
A Space-Time Finite Element Model for Design and Control Optimization of Nonlinear Dynamic Response
Directory of Open Access Journals (Sweden)
P.P. Moita
2008-01-01
Full Text Available A design and control sensitivity analysis and multicriteria optimization formulation is derived for flexible mechanical systems. This formulation is implemented in an optimum design code and it is applied to the nonlinear dynamic response. By extending the spatial domain to the space-time domain and treating the design variables as control variables that do not change with time, the design space is included in the control space. Thus, one can unify in one single formulation the problems of optimum design and optimal control. Structural dimensions as well as lumped damping and stiffness parameters plus control driven forces, are considered as decision variables. The dynamic response and its sensitivity with respect to the design and control variables are discretized via space-time finite elements, and are integrated at-once, as it is traditionally used for static response. The adjoint system approach is used to determine the design sensitivities. Design optimization numerical examples are performed. Nonlinear programming and optimality criteria may be used for the optimization process. A normalized weighted bound formulation is used to handle multicriteria problems.
Enhancement of Kerr nonlinearity and its application to entangled state discrimination
Institute of Scientific and Technical Information of China (English)
NIU Yue-ping; QIAN Jun; FENG Xun-li; GONG Shang-qing
2007-01-01
In this paper, the recent research on the enhan-ced Kerr nonlinearity and its application in entangled state discrimination is reported. Two kinds of dynamics, including interacting double dark resonances and spontaneously gen-erated coherence, are presented to enhance the Kerr nonlin-earity. The application of Kerr nonlinearity in quantum state discrimination is also discussed. An arbitrary Greenberger-Horne-Zeilinger state can be discriminated using two-photon polarization parity detection which resorts to cross-Kerr no-nlinearity between a single-photon qubit and probe field. In addition, a scheme for Greenberger-Home-Zeilinger state discrimination of matter qubits is also proposed using the dipole induced transparency in a cavity-dipole system.
Nonlinear supercoherent states and geometric phases for the supersymmetric harmonic oscillator
Díaz-Bautista, Erik
2016-01-01
Nonlinear supercoherent states, which are eigenstates of nonlinear deformations of the Kornbluth-Zypman annihilation operator for the supersymmetric harmonic oscillator, will be studied. They turn out to be expressed in terms of nonlinear coherent states, associated to the corresponding deformations of the standard annihilation operator. We will discuss as well the Heisenberg uncertainty relation for a special particular case, in order to compare our results with those obtained for the Kornbluth-Zypman linear supercoherent states. As the supersymmetric harmonic oscillator executes an evolution loop, such that the evolution operator becomes the identity at a certain time, thus the linear and nonlinear supercoherent states turn out to be cyclic and the corresponding geometric phases will be evaluated.
Granger causality for state-space models.
Barnett, Lionel; Seth, Anil K
2015-04-01
Granger causality has long been a prominent method for inferring causal interactions between stochastic variables for a broad range of complex physical systems. However, it has been recognized that a moving average (MA) component in the data presents a serious confound to Granger causal analysis, as routinely performed via autoregressive (AR) modeling. We solve this problem by demonstrating that Granger causality may be calculated simply and efficiently from the parameters of a state-space (SS) model. Since SS models are equivalent to autoregressive moving average models, Granger causality estimated in this fashion is not degraded by the presence of a MA component. This is of particular significance when the data has been filtered, downsampled, observed with noise, or is a subprocess of a higher dimensional process, since all of these operations-commonplace in application domains as diverse as climate science, econometrics, and the neurosciences-induce a MA component. We show how Granger causality, conditional and unconditional, in both time and frequency domains, may be calculated directly from SS model parameters via solution of a discrete algebraic Riccati equation. Numerical simulations demonstrate that Granger causality estimators thus derived have greater statistical power and smaller bias than AR estimators. We also discuss how the SS approach facilitates relaxation of the assumptions of linearity, stationarity, and homoscedasticity underlying current AR methods, thus opening up potentially significant new areas of research in Granger causal analysis.
Topological properties of flat electroencephalography's state space
Ken, Tan Lit; Ahmad, Tahir bin; Mohd, Mohd Sham bin; Ngien, Su Kong; Suwa, Tohru; Meng, Ong Sie
2016-02-01
Neuroinverse problem are often associated with complex neuronal activity. It involves locating problematic cell which is highly challenging. While epileptic foci localization is possible with the aid of EEG signals, it relies greatly on the ability to extract hidden information or pattern within EEG signals. Flat EEG being an enhancement of EEG is a way of viewing electroencephalograph on the real plane. In the perspective of dynamical systems, Flat EEG is equivalent to epileptic seizure hence, making it a great platform to study epileptic seizure. Throughout the years, various mathematical tools have been applied on Flat EEG to extract hidden information that is hardly noticeable by traditional visual inspection. While these tools have given worthy results, the journey towards understanding seizure process completely is yet to be succeeded. Since the underlying structure of Flat EEG is dynamic and is deemed to contain wealthy information regarding brainstorm, it would certainly be appealing to explore in depth its structures. To better understand the complex seizure process, this paper studies the event of epileptic seizure via Flat EEG in a more general framework by means of topology, particularly, on the state space where the event of Flat EEG lies.
An analysis of a new nonlinear estimation technique: The state-dependent Ricatti equation method
Ewing, Craig Michael
1999-10-01
Research into nonlinear estimation techniques for terminal homing missiles has been conducted for many decades. The terminal state estimator, also called the guidance filter, is responsible for providing accurate estimates of target motion for use in guiding the missile to a collision course with the target. Some form of the extended-Kalman filter (EKF) has become the standard estimation technique employed in most modern weapon guidance systems. EKF linearization of nonlinear dynamics and/or measurements can cause problems of divergence when confronted by highly nonlinear conditions. The objective of this dissertation is to analyze a new nonlinear estimation technique that is based on the parameterization of the nonlinearities. This parameterization converts the nonlinear estimation problem into the form of a steady-state continuous Kalman filtering problem with state-dependent coefficients. This new technique, called the state-dependent Ricatti equation filter (SDREF), allows the nonlinearities of the system to be fully incorporated into the filter design, before stochastic uncertainties are imposed, without the need for linearization. The SDREF was investigated in three problems: an exoatmospheric, terminal homing, ballistic-missile intercept problem; a highly nonlinear pendulum example; and an algorithmic loss of observability problem. The exoatmospheric guidance problem examined nonlinear measurements with linear dynamics. To investigate the SDREF when used with a combination of nonlinear dynamics and nonlinear measurements, a highly nonlinear, two-state pendulum problem was also examined. While these problems were useful in gaining insight into the performance characteristics of the SDREF, no formal proof of stability could be determined for the original formulation of the estimator. The original SDREF solved an algebraic SDRE that arose from an infinite-time horizon formulation of the nonlinear filtering problem. A modification to the SDREF formulation was
A bias identification and state estimation methodology for nonlinear systems
Caglayan, A. K.; Lancraft, R. E.
1983-01-01
A computational algorithm for the identification of input and output biases in discrete-time nonlinear stochastic systems is derived by extending the separate bias estimation results for linear systems to the extended Kalman filter formulation. The merits of the approach are illustrated by identifying instrument biases using a terminal configured vehicle simulation.
State-Feedback Control for Fractional-Order Nonlinear Systems Subject to Input Saturation
Directory of Open Access Journals (Sweden)
Junhai Luo
2014-01-01
Full Text Available We give a state-feedback control method for fractional-order nonlinear systems subject to input saturation. First, a sufficient condition is derived for the asymptotical stability of a class of fractional-order nonlinear systems. Then based on Gronwall-Bellman lemma and a sector bounded condition of the saturation function, a linear state-feed back controller is designed. Finally, two simulation examples are presented to show the validity of the proposed method.
Xu, Zhi-Jie
2015-01-01
We first propose fundamental solutions of wave propagation in dispersive chain subject to a localized initial perturbation in the displacement. Analytical solutions are obtained for both second order nonlinear dispersive chain and homogenous harmonic chain using stationary phase approximation. Solution is also compared with numerical results from molecular dynamics (MD) simulations. Locally dominant phonon modes (k-space) are introduced based on these solutions. These locally defined spatially and temporally varying phonon modes k(x, t) are critical to the concept of the local thermodynamic equilibrium (LTE). Wave propagation accompanying with the nonequilibrium dynamics leads to the excitation of these locally defined phonon modes. It is found that the system energy is gradually redistributed among these excited phonons modes (k-space). This redistribution process is only possible with nonlinear dispersion and requires a finite amount of time to achieve a steady state distribution. This time scale is dependent on the spatial distribution (or frequency content) of the initial perturbation and the dispersion relation. Sharper and more concentrated perturbation leads to a faster energy redistribution and dissipation. This energy redistribution generates localized phonons with various frequencies that can be important for phonon-phonon interaction and energy dissipation in nonlinear systems. Depending on the initial perturbation and temperature, the time scale associated with this energy distribution can be critical for energy dissipation compared to the Umklapp scattering process. Ballistic type of heat transport along the harmonic chain reveals that at any given position, the lowest mode (k = 0) is excited first and gradually expanding to the highest mode (kmax(x,t)), where kmax(x,t) can only asymptotically approach the maximum mode kB of the first Brillouin zone (kmax(x,t) → kB). No energy distributed into modes with kmax(x,t) proportional to the sound speed
A Compositional Sweep-Line State Space Exploration Method
DEFF Research Database (Denmark)
Kristensen, Lars Michael; Mailund, Thomas
2002-01-01
State space exploration is a main approach to verification of finite-state systems. The sweep-line method exploits a certain kind of progress present in many systems to reduce peak memory usage during state space exploration. We present a new sweep-line algorithm for a compositional setting where...
On Path Dependent State Space for the Proca Field
Gaitan, R
1999-01-01
A gauge formulation for the Proca model quantum theory in an open path functional space representation is revisited. The path dependent vacuum state is obtained. Starting from this one, other excited states can be obtained too. Additionally, the functional integration measure needed to define an internal product in the state space is constructed.
Variational principle and a perturbative solution of non-linear string equations in curved space
Roshchupkin, S N
1999-01-01
String dynamics in a curved space-time is studied on the basis of an action functional including a small parameter of rescaled tension constant. A rescaled slow worldsheet time $T=\\epsilon\\tau$ is introduced, and general covariant non-linear string equation are derived. It is shown that in the first order of an $\\epsilon $-expansion these equations are reduced to the known equation for geodesic derivation but complemented by a string oscillatory term. These equations are solved for the de Sitter and Friedmann -Robertson-Walker spaces. The primary string constraints are found to be split into a chain of perturbative constraints and their conservation and consistency are proved. It is established that in the proposed realization of the perturbative approach the string dynamics in the de Sitter space is stable for a large Hubble constant $H
Miksovsky, J.; Raidl, A.
Time delays phase space reconstruction represents one of useful tools of nonlinear time series analysis, enabling number of applications. Its utilization requires the value of time delay to be known, as well as the value of embedding dimension. There are sev- eral methods how to estimate both these parameters. Typically, time delay is computed first, followed by embedding dimension. Our presented approach is slightly different - we reconstructed phase space for various combinations of mentioned parameters and used it for prediction by means of the nearest neighbours in the phase space. Then some measure of prediction's success was computed (correlation or RMSE, e.g.). The position of its global maximum (minimum) should indicate the suitable combination of time delay and embedding dimension. Several meteorological (particularly clima- tological) time series were used for the computations. We have also created a MS- Windows based program in order to implement this approach - its basic features will be presented as well.
Barut—Girardello Coherent States for Nonlinear Oscillator with Position-Dependent Mass
Amir, Naila; Iqbal, Shahid
2016-07-01
Using ladder operators for the non-linear oscillator with position-dependent effective mass, realization of the dynamic group SU(1,1) is presented. Keeping in view the algebraic structure of the non-linear oscillator, coherent states are constructed using Barut—Girardello formalism and their basic properties are discussed. Furthermore, the statistical properties of these states are investigated by means of Mandel parameter and second order correlation function. Moreover, it is shown that in the harmonic limit, all the results obtained for the non-linear oscillator with spatially varying mass reduce to corresponding results of the linear oscillator with constant mass.
Systems of general nonlinear set-valued mixed variational inequalities problems in Hilbert spaces
Directory of Open Access Journals (Sweden)
Cho Yeol
2011-01-01
Full Text Available Abstract In this paper, the existing theorems and methods for finding solutions of systems of general nonlinear set-valued mixed variational inequalities problems in Hilbert spaces are studied. To overcome the difficulties, due to the presence of a proper convex lower semi-continuous function, φ and a mapping g, which appeared in the considered problem, we have used some applications of the resolvent operator technique. We would like to point out that although many authors have proved results for finding solutions of the systems of nonlinear set-valued (mixed variational inequalities problems, it is clear that it cannot be directly applied to the problems that we have considered in this paper because of φ and g. 2000 AMS Subject Classification: 47H05; 47H09; 47J25; 65J15.
Finite Element Solutions for the Space Fractional Diffusion Equation with a Nonlinear Source Term
Directory of Open Access Journals (Sweden)
Y. J. Choi
2012-01-01
Full Text Available We consider finite element Galerkin solutions for the space fractional diffusion equation with a nonlinear source term. Existence, stability, and order of convergence of approximate solutions for the backward Euler fully discrete scheme have been discussed as well as for the semidiscrete scheme. The analytical convergent orders are obtained as O(k+hγ˜, where γ˜ is a constant depending on the order of fractional derivative. Numerical computations are presented, which confirm the theoretical results when the equation has a linear source term. When the equation has a nonlinear source term, numerical results show that the diffusivity depends on the order of fractional derivative as we expect.
Nonlinear Superconducting Metamaterials in Free-Space at mm-wave Frequencies
Anlage, Steven; Zhang, Daimeng; Trepanier, Melissa; Mukhanov, Oleg; Delfanazari, K.; Savinov, V.; Zheludev, N.
2014-03-01
Superconducting metamaterials show the promise of low loss, compact size and extreme tunability and nonlinearity, allowing for new applications. Most demonstrations of these metamaterials have been conducted in waveguide geometries, either in co-planar form or three-dimensional single-conductor structures. Here we demonstrate for the first time a widely tunable superconducting metamaterial operating under the free-space illumination of a quasi-optical beam in the 100 GHz regime. The meta-atoms are Radio Frequency Superconducting QUantum Interference Devices (RF SQUIDs) that form compact self-resonant objects endowed with the nonlinearity of the Josephson effect. The metamaterial is tuned with dc magnetic flux, temperature and mm-wave power, and holds promise for a new generation of mm-wave agile devices. This work is supported by the NSF-GOALI and OISE programs through grant # ECCS-1158644, and CNAM.
An introduction to state space time series analysis.
Commandeur, J.J.F. & Koopman, S.J.
2007-01-01
Providing a practical introduction to state space methods as applied to unobserved components time series models, also known as structural time series models, this book introduces time series analysis using state space methodology to readers who are neither familiar with time series analysis, nor with state space methods. The only background required in order to understand the material presented in the book is a basic knowledge of classical linear regression models, of which a brief review is...
ASAP: An Extensible Platform for State Space Analysis
DEFF Research Database (Denmark)
Westergaard, Michael; Evangelista, Sami; Kristensen, Lars Michael
2009-01-01
The ASCoVeCo State space Analysis Platform (ASAP) is a tool for performing explicit state space analysis of coloured Petri nets (CPNs) and other formalisms. ASAP supports a wide range of state space reduction techniques and is intended to be easy to extend and to use, making it a suitable tool...... for students, researchers, and industrial users that would like to analyze protocols and/or experiment with different algorithms. This paper presents ASAP from these two perspectives....
State space Newton's method for topology optimization
DEFF Research Database (Denmark)
Evgrafov, Anton
2014-01-01
We introduce a new algorithm for solving certain classes of topology optimization problems, which enjoys fast local convergence normally achieved by the full space methods while working in a smaller reduced space. The computational complexity of Newton’s direction finding subproblem in the algori......We introduce a new algorithm for solving certain classes of topology optimization problems, which enjoys fast local convergence normally achieved by the full space methods while working in a smaller reduced space. The computational complexity of Newton’s direction finding subproblem...
Nonlinear morphoelastic plates II: Exodus to buckled states
McMahon, J.
2011-05-11
Morphoelasticity is the theory of growing elastic materials. The theory is based on the multiplicative decomposition of the deformation gradient and provides a formulation of the deformation and stresses induced by growth. Following a companion paper, a general theory of growing non-linear elastic Kirchhoff plate is described. First, a complete geometric description of incompatibility with simple examples is given. Second, the stability of growing Kirchhoff plates is analyzed. © SAGE Publications 2011.
The State-of-the-art in Space Robotics
da Fonseca, Ijar M.; Pontuschka, Maurício N.
2015-10-01
This paper deals with the space robotics and associate space applications. An overview of the space era and the robotic space probes is presented to contextualize the space robotics in the space exploration scenario. Concepts, classification and key-questions associated with robotics for space applications are presented and discussed. Safety-critical aspects of the space robotics are discussed as well the human limitation to operate in the hostile space environment and long time duration missions. The paper also focuses on the state-of-the- art of robotics for the International Space Station EVA operations, for the planetary exploration such as the ongoing Mars exploration, Hayabusa rendezvous and landing in asteroids and the robotic probe Rosetta landed in a comet recently. The paper also includes a discussion of the applications of new concepts like the robonauts, the space tugs applications and robots for future planetary exploration.
Coherent states for nonlinear harmonic oscillator and some of its properties
Energy Technology Data Exchange (ETDEWEB)
Amir, Naila, E-mail: naila.amir@live.com, E-mail: naila.amir@sns.nust.edu.pk; Iqbal, Shahid, E-mail: sic80@hotmail.com, E-mail: siqbal@sns.nust.edu.pk [School of Natural Sciences, National University of Sciences and Technology, Islamabad (Pakistan)
2015-06-15
A one-dimensional nonlinear harmonic oscillator is studied in the context of generalized coherent states. We develop a perturbative framework to compute the eigenvalues and eigenstates for the quantum nonlinear oscillator and construct the generalized coherent states based on Gazeau-Klauder formalism. We analyze their statistical properties by means of Mandel parameter and second order correlation function. Our analysis reveals that the constructed coherent states exhibit super-Poissonian statistics. Moreover, it is shown that the coherent states mimic the phenomena of quantum revivals and fractional revivals during their time evolution. The validity of our results has been discussed in terms of various parametric bounds imposed by our computational scheme.
Directory of Open Access Journals (Sweden)
Mourad Kerboua
2014-12-01
Full Text Available We introduce a new notion called fractional stochastic nonlocal condition, and then we study approximate controllability of class of fractional stochastic nonlinear differential equations of Sobolev type in Hilbert spaces. We use Hölder's inequality, fixed point technique, fractional calculus, stochastic analysis and methods adopted directly from deterministic control problems for the main results. A new set of sufficient conditions is formulated and proved for the fractional stochastic control system to be approximately controllable. An example is given to illustrate the abstract results.
Directory of Open Access Journals (Sweden)
Emad A.-B. Abdel-Salam
2013-01-01
Full Text Available The fractional Riccati expansion method is proposed to solve fractional differential equations. To illustrate the effectiveness of the method, space-time fractional Korteweg-de Vries equation, regularized long-wave equation, Boussinesq equation, and Klein-Gordon equation are considered. As a result, abundant types of exact analytical solutions are obtained. These solutions include generalized trigonometric and hyperbolic functions solutions which may be useful for further understanding of the mechanisms of the complicated nonlinear physical phenomena and fractional differential equations. Among these solutions, some are found for the first time. The periodic and kink solutions are founded as special case.
Existence of Solutions to Nonlinear Impulsive Volterra Integral Equations in Banach Spaces
Institute of Scientific and Technical Information of China (English)
CHEN Fangqi; TIAN Ruilan
2005-01-01
In this paper, the existence of solutions is studied for nonlinear impulsive Volterra integral equations with infinite moments of impulse effect on the half line R+ in Banach spaces.By the use of a new comparison result and recurrence method, the new existence theorems are achieved under a weaker compactness-type condition, which generalize and improve the related results for this class of equations with finite moments of impulse effect on finite interval and infinite moments of impulse effect on infinite interval.
Active Affordance Learning in Continuous State and Action Spaces
Wang, C.; Hindriks, K.V.; Babuska, R.
2014-01-01
Learning object affordances and manipulation skills is essential for developing cognitive service robots. We propose an active affordance learning approach in continuous state and action spaces without manual discretization of states or exploratory motor primitives. During exploration in the action
A General Theory of Additive State Space Abstractions
Yang, Fan; Holte, Robert; Zahavi, Uzi; Felner, Ariel; 10.1613/jair.2486
2011-01-01
Informally, a set of abstractions of a state space S is additive if the distance between any two states in S is always greater than or equal to the sum of the corresponding distances in the abstract spaces. The first known additive abstractions, called disjoint pattern databases, were experimentally demonstrated to produce state of the art performance on certain state spaces. However, previous applications were restricted to state spaces with special properties, which precludes disjoint pattern databases from being defined for several commonly used testbeds, such as Rubiks Cube, TopSpin and the Pancake puzzle. In this paper we give a general definition of additive abstractions that can be applied to any state space and prove that heuristics based on additive abstractions are consistent as well as admissible. We use this new definition to create additive abstractions for these testbeds and show experimentally that well chosen additive abstractions can reduce search time substantially for the (18,4)-TopSpin puz...
Interferometric and nonlinear-optical spectral-imaging techniques for outer space and live cells
Itoh, Kazuyoshi
2015-12-01
Multidimensional signals such as the spectral images allow us to have deeper insights into the natures of objects. In this paper the spectral imaging techniques that are based on optical interferometry and nonlinear optics are presented. The interferometric imaging technique is based on the unified theory of Van Cittert-Zernike and Wiener-Khintchine theorems and allows us to retrieve a spectral image of an object in the far zone from the 3D spatial coherence function. The retrieval principle is explained using a very simple object. The promising applications to space interferometers for astronomy that are currently in progress will also be briefly touched on. An interesting extension of interferometric spectral imaging is a 3D and spectral imaging technique that records 4D information of objects where the 3D and spectral information is retrieved from the cross-spectral density function of optical field. The 3D imaging is realized via the numerical inverse propagation of the cross-spectral density. A few techniques suggested recently are introduced. The nonlinear optical technique that utilizes stimulated Raman scattering (SRS) for spectral imaging of biomedical targets is presented lastly. The strong signals of SRS permit us to get vibrational information of molecules in the live cell or tissue in real time. The vibrational information of unstained or unlabeled molecules is crucial especially for medical applications. The 3D information due to the optical nonlinearity is also the attractive feature of SRS spectral microscopy.
Some results of a nodal method for nonlinear space-time reactor dynamics
Energy Technology Data Exchange (ETDEWEB)
Le, T.T. (Westinghouse Savannah River Co., Aiken, SC (United States)); Grossman, L.M. (California Univ., Berkeley, CA (United States). Dept. of Nuclear Engineering)
1991-01-01
There are many reports about nodal methods for static and dynamic problems, but not many for the nonlinear feedback cases. In this paper, a class of nodal methods called mathematical nodal method'' (MNM) is studied with the temperature feedback problems. The spatially complex domain of the problem is represented as a collection of geometrically simple subdomains of the size of fuel assemblies called nodes. Over each node, the time dependent coefficients of the neutron flux, precursor concentrations, fuel and coolant temperatures are the surface and volume weighted average (moment) values of the unknown solutions; the space dependent basis functions are a combination of Legendre polynomials. If the material parameters are a linear function of fuel and coolant temperatures, the coupled equations can be put in a dimensionless form and a system of time dependent ordinary differential equations containing nonlinear feedback terms is obtained. These nonlinear feedback terms are updated at each time step during the time iteration process. Results of some benchmark problems are included in this report.
Some results of a nodal method for nonlinear space-time reactor dynamics
Energy Technology Data Exchange (ETDEWEB)
Le, T.T. [Westinghouse Savannah River Co., Aiken, SC (United States); Grossman, L.M. [California Univ., Berkeley, CA (United States). Dept. of Nuclear Engineering
1991-12-31
There are many reports about nodal methods for static and dynamic problems, but not many for the nonlinear feedback cases. In this paper, a class of nodal methods called ``mathematical nodal method`` (MNM) is studied with the temperature feedback problems. The spatially complex domain of the problem is represented as a collection of geometrically simple subdomains of the size of fuel assemblies called nodes. Over each node, the time dependent coefficients of the neutron flux, precursor concentrations, fuel and coolant temperatures are the surface and volume weighted average (moment) values of the unknown solutions; the space dependent basis functions are a combination of Legendre polynomials. If the material parameters are a linear function of fuel and coolant temperatures, the coupled equations can be put in a dimensionless form and a system of time dependent ordinary differential equations containing nonlinear feedback terms is obtained. These nonlinear feedback terms are updated at each time step during the time iteration process. Results of some benchmark problems are included in this report.
Bergboer, N.H; Verdult, V.; Verhaegen, M.H.G.
2002-01-01
We present a numerically efficient implementation of the nonlinear least squares and maximum likelihood identification of multivariable linear time-invariant (LTI) state-space models. This implementation is based on a local parameterization of the system and a gradient search in the resulting parame
Determining state-space models from sequential output data
Lin, Jiguan Gene
1988-01-01
This talk focuses on the determination of state-space models for large space systems using only the output data. The output data could be generated by the unknown or deliberate initial conditions of the space structure in question. We shall review some relevant fundamental work on the state-space modeling of sequential output data that is potentially applicable to large space structures. If formulated in terms of some generalized Markov parameters, this approach is in some sense similar to, but much simpler than, the Juang-Pappa Eigensystem Realization Algorithm (ERA) and the Ho-Kalman construction procedure.
Nonlinear robust control of proton exchange membrane fuel cell by state feedback exact linearization
Energy Technology Data Exchange (ETDEWEB)
Li, Q.; Chen, W. [School of Electrical Engineering, Southwest Jiaotong University, Chengdu 610031, Sichuan Province (China); Wang, Y.; Jia, J. [School of Electrical and Electronic Engineering, Nanyang Technological University, Nanyang Avenue 639798, Singapore (Singapore); Han, M. [School of Engineering, Temasek Polytechnic, Tampines 529757, Singapore (Singapore)
2009-10-20
By utilizing the state feedback exact linearization approach, a nonlinear robust control strategy is designed based on a multiple-input multiple-output (MIMO) dynamic nonlinear model of proton exchange membrane fuel cell (PEMFC). The state feedback exact linearization approach can achieve the global exact linearization via the nonlinear coordinate transformation and the dynamic extension algorithm such that H{sub {infinity}} robust control strategy can be directly utilized to guarantee the robustness of the system. The proposed dynamic nonlinear model is tested by comparing the simulation results with the experimental data in Fuel Cell Application Centre in Temasek Polytechnic. The comprehensive results of simulation manifest that the dynamic nonlinear model with nonlinear robust control law has better transient and robust stability when the vehicle running process is simulated. The proposed nonlinear robust controller will be very useful to protect the membrane damage by keeping the pressure deviations as small as possible during large disturbances and prolong the stack life of PEMFC. (author)
Peng, Haijun; Wang, Xinwei; Zhang, Sheng; Chen, Biaosong
2017-07-01
Nonlinear state-delayed optimal control problems have complex nonlinear characters. To solve this complex nonlinear problem, an iterative symplectic pseudospectral method based on quasilinearization techniques, the dual variational principle and pseudospectral methods is proposed in this paper. First, the proposed method transforms the original nonlinear optimal control problem into a series of linear quadratic optimal control problems. Then, a symplectic pseudospectral method is developed to solve these converted linear quadratic state-delayed optimal control problems. Coefficient matrices in the proposed method are sparse and symmetric since the dual variational principle is used, which makes the proposed method highly efficient. Converged numerical solutions with high precision can be obtained after a few iterations due to the benefit of the local pseudospectral method and quasilinearization techniques. In the numerical simulations, other numerical methods were used for comparisons. The numerical simulation results show that the proposed method is highly accurate, efficient and robust.
Adriaensen, Maarten; Giannopapa, Christina; Sagath, Daniel; Papastefanou, Anastasia
2015-12-01
The European Space Agency (ESA) has twenty Member States with a variety of strategic priorities and governance structures regarding their space activities. A number of countries engage in space activities exclusively though ESA, while others have also their own national space programme. Some consider ESA as their prime space agency and others have additionally their own national agency with respective programmes. The main objective of this paper is to provide an up-to date overview and a holistic assessment of strategic priorities and the national space governance structures in 20 ESA Member States. This analysis and assessment has been conducted by analysing the Member States public documents, information provided at ESA workshop on this topic and though unstructured interviews. The paper is structured to include two main elements: priorities and trends in national space strategies and space governance in ESA Member States. The first part of this paper focuses on the content and analysis of the national space strategies and indicates the main priorities and trends in Member States. The priorities are categorised with regards to technology domains, the role of space in the areas of sustainability and the motivators that boost engagement in space. These vary from one Member State to another and include with different levels of engagement in technology domains amongst others: science and exploration, navigation, Earth observation, human space flight, launchers, telecommunications, and integrated applications. Member States allocate a different role of space as enabling tool adding to the advancement of sustainability areas including: security, resources, environment and climate change, transport and communication, energy, and knowledge and education. The motivators motivating reasoning which enhances or hinders space engagement also differs. The motivators identified are industrial competitiveness, job creation, technology development and transfer, social benefits
Non-Linear Trans-Planckian Corrections of Spectra due to the Non-trivial Initial States
Yusofi, E
2014-01-01
Recent Planck results motivated us to use non-Bunch-Davies vacuum. In this paper, we use the excited-de Sitter mode as non-linear initial states during inflation to calculate the corrected spectra of the initial fluctuations of the scalar field. First, we consider the field in de Sitter space-time as background field and for the non-Bunch-Davies mode, we use the perturbation theory to the second order approximation. Also, unlike conventional renormalization method, we offer de Sitter space-time as the background instead Minkowski space-time. This approach preserve the symmetry of curved space-time and stimulate us to use excited mode. By taking into account this alternative mode and the effects of trans-Planckian physics, we calculate the power spectrum in standard approach and Danielsson argument. The calculated power spectrum with this method is finite, corrections of it is non-linear, and in de Sitter limit corrections reduce to linear form that obtained from several previous conventional methods.
Embedding a State Space Model Into a Markov Decision Process
DEFF Research Database (Denmark)
Nielsen, Lars Relund; Jørgensen, Erik; Højsgaard, Søren
2011-01-01
estimated from data collected from the animal or herd. State space models (SSMs) are a general tool for modeling repeated measurements over time where the model parameters can evolve dynamically. In this paper we consider methods for embedding an SSM into an MDP with finite state and action space. Different...
Complexity in Simplicity: Flexible Agent-based State Space Exploration
DEFF Research Database (Denmark)
Rasmussen, Jacob Illum; Larsen, Kim Guldstrand
2007-01-01
In this paper, we describe a new flexible framework for state space exploration based on cooperating agents. The idea is to let various agents with different search patterns explore the state space individually and communicate information about fruitful subpaths of the search tree to each other...
An introduction to state space modeling (in Russian)
Alexander Tsyplakov
2011-01-01
Many time series models, primarily various models with unobservable components, can be represented in a so called state space form. A state space model is a powerful tool that allows one to apply to the original model a wide range of standard procedures including estimation and forecasting. This essay provides a survey of this universal class of models and related procedures.
Adaptive importance sampling of random walks on continuous state spaces
Energy Technology Data Exchange (ETDEWEB)
Baggerly, K.; Cox, D.; Picard, R.
1998-11-01
The authors consider adaptive importance sampling for a random walk with scoring in a general state space. Conditions under which exponential convergence occurs to the zero-variance solution are reviewed. These results generalize previous work for finite, discrete state spaces in Kollman (1993) and in Kollman, Baggerly, Cox, and Picard (1996). This paper is intended for nonstatisticians and includes considerable explanatory material.
An introduction to state space time series analysis.
Commandeur, J.J.F. & Koopman, S.J.
2007-01-01
Providing a practical introduction to state space methods as applied to unobserved components time series models, also known as structural time series models, this book introduces time series analysis using state space methodology to readers who are neither familiar with time series analysis, nor wi
Complexity in Simplicity: Flexible Agent-based State Space Exploration
DEFF Research Database (Denmark)
Rasmussen, Jacob Illum; Larsen, Kim Guldstrand
2007-01-01
In this paper, we describe a new flexible framework for state space exploration based on cooperating agents. The idea is to let various agents with different search patterns explore the state space individually and communicate information about fruitful subpaths of the search tree to each other...
Discrete Localized States and Localization Dynamics in Discrete Nonlinear Schrödinger Equations
DEFF Research Database (Denmark)
Christiansen, Peter Leth; Gaididei, Yu.B.; Mezentsev, V.K.
1996-01-01
Dynamics of two-dimensional discrete structures is studied in the framework of the generalized two-dimensional discrete nonlinear Schrodinger equation. The nonlinear coupling in the form of the Ablowitz-Ladik nonlinearity is taken into account. Stability properties of the stationary solutions...... are examined. The importance of the existence of stable immobile solitons in the two-dimensional dynamics of the travelling pulses is demonstrated. The process of forming narrow states from initially broad standing or moving excitations through the quasi-collapse mechanism is analyzed. The typical scenario...
The sweep-line state space exploration method
DEFF Research Database (Denmark)
Jensen, Kurt; Kristensen, Lars M.; Mailund, Thomas
2012-01-01
The sweep-line method exploits intrinsic progress in concurrent systems to alleviate the state explosion problem in explicit state model checking. The concept of progress makes it possible to delete states from the memory during state space exploration and thereby reduce peak memory usage...
Nonlinear model of space manipulator joint considering time-variant stiffness and backlash
Yang, Tianfu; Yan, Shaoze; Han, Zengyao
2015-04-01
Modeling of space manipulator joints has been studied for years but accurate positioning control is still unsatisfactory. One of the primary reasons is that, in the past researches, effects of the high-ratio reducers in the joints have usually been neglected. In this paper, a nonlinear dynamic model of the manipulator joint with planetary gear train transmission is developed by considering time-variant joint stiffness, backlash and reduction ratio. Based on the gear parameters and meshing phase relationship, the stiffness of the joint model is presented, in which the time-variant stiffness of 2K-H planetary gear train and the backlash are taken into consideration. The backlash effect is modeled as an alternate engagement mechanism, and the transmitted torque is defined as a dead zone function. This model is simulated on a two-link space manipulator system. The results show that the time-variant stiffness effect can be simplified as a constant value in most cases when other shafting parts are flexible, while if the total stiffness is approximate to the nonlinear stiffness, the positioning accuracy is reduced if neglecting the time-variant part. On the other hand, the backlash is the main source of positioning error and impact. Minimizing backlash is the most effective way to improve positioning accuracy and avoid the impact in the gearing system.
Nonlinear Markov Control Processes and Games
2012-11-15
further research we indicated possible extensions to state spaces with nontrivial geometry, to the controlled nonlinear quantum dynamic semigroups and...space nonlinear Markov semigroup is a one-parameter semigroup of (possibly nonlinear) transformations of the unit simplex in n-dimensional Euclidean...certain mixing property of nonlinear transition probabilities. In case of the semigroup parametrized by continuous time one defines its generator as the
Localized excitations in nonlinear complex systems current state of the art and future perspectives
Cuevas-Maraver, Jesús; Frantzeskakis, Dimitri; Karachalios, Nikos; Kevrekidis, Panayotis; Palmero-Acebedo, Faustino
2014-01-01
The study of nonlinear localized excitations is a long-standing challenge for research in basic and applied science, as well as engineering, due to their importance in understanding and predicting phenomena arising in nonlinear and complex systems, but also due to their potential for the development and design of novel applications. This volume is a compilation of chapters representing the current state-of-the-art on the field of localized excitations and their role in the dynamics of complex physical systems.
Using State Space Methods to Reveal Dynamical Associations Between Cortisol and Depression.
Toonen, Roelof B; Wardenaar, Klaas J; van Ockenburg, Sonja L; Bos, Elisabeth H; de Jonge, Peter
2016-01-01
Despite extensive research, the link between etiological factors and depression remains poorly understood. This may in part be due to a focus on strictly linear definitions of causality, derived at the group level. However, etiological relations in depression are likely to be dynamical, nonlinear and potentially unquantifiable with traditional statistics. Therefore the aim of this study was to evaluate the use of the convergent cross-mapping (CCM) method in investigating possible nonlinear relationships between supposed etiological factors and depressive symptomatology. Time series data from six healthy individuals were used to model the relationship between 24-h urinary free cortisol and negative affect using CCM and dewdrop embeddings. CCM is a nonlinear measure of causality, based on state space reconstruction with lagged coordinate embeddings. The results showed that nonlinear dynamical relationships between cortisol and negative affect may be present within participants, as demonstrated by a positive cross-map convergence from negative affect to cortisol. However, analyses also showed that noise and influential points had considerable impact on the results. Convergent crossmapping can be used to reveal possible nonlinear dynamical relationships between etiological factors and psychopathology that may remain undetected with traditional linear causality measures.
A new method for observing the running states of a single-variable nonlinear system.
Meng, Yu; Chen, Hong; Chen, Cheng
2015-03-01
In order to timely grasp a single variable nonlinear system running states, a new method called Scatter Point method is put forward in this paper. It can be used to observe or monitor the running states of a single variable nonlinear system in real-time. In this paper, the definition of the method is given at first, and then its working principle is expounded theoretically, after this, some physical experiments based on Chua's nonlinear system are conducted. At the same time, many scatter point graphs are measured by a general analog oscilloscope. The motion, number, and distribution of these scatter points shown on the oscilloscope screen can directly reflect the current states of the tested system. The experimental results further confirm that the method is effective and practical, in which the system running states are not easily lost. In addition, this method is not only suitable for single variable systems but also for multivariable systems.
Linear and nonlinear photonic Jackiw-Rebbi states in interfaced binary waveguide arrays
Tran, Truong X.; Biancalana, Fabio
2017-07-01
We study analytically and numerically the optical analog of the Jackiw-Rebbi states in quantum-field theory. These solutions exist at the interface of two binary waveguide arrays, which are described by two Dirac equations with masses of opposite sign. We show that these special states are topologically robust not only in the linear regime, but also in the nonlinear one (with both focusing and defocusing nonlinearities). We also reveal that one can effectively generate Jackiw-Rebbi states starting from Dirac solitons.
Predictive Control Based upon State Space Models
Directory of Open Access Journals (Sweden)
Jens G. Balchen
1989-04-01
Full Text Available Repetitive online computation of the control vector by solving the optimal control problem of a non-linear multivariable process with arbitrary performance indices is investigated. Two different methods are considered in the search for an optimal, parameterized control vector: Pontryagin's Maximum Principle and optimization by using the performance index and its gradient directly. Unfortunately, solving this optimization problem has turned out to be a rather time-consuming task which has resulted in a time delay that cannot be accepted when the actual process is exposed to rapidly-varying disturbances. However, an instantaneous feedback strategy operating in parallel with the original control aogorithm was found to be able to cope with this problem.
Chaotic and steady state behaviour of a nonlinear controlled gyro subjected to harmonic disturbances
Energy Technology Data Exchange (ETDEWEB)
Perez Polo, Manuel F. [Department of Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Escuela Politecnica Superior, Campus de San Vicente, 03071 Alicante (Spain)]. E-mail: manolo@dfists.ua.es; Perez Molina, Manuel [Facultad de Ciencias Matematicas, Universidad Nacional de Educacion a Distancia, UNED, C/Boyero 12-1A, Alicante 03007 (Spain)]. E-mail: ma_perez_m@hotmail.com
2007-07-15
Chaotic and steady state motions of a nonlinear controlled gimbals suspension gyro used to stabilize an external body are studied in this paper. The equations of the gyro without nonlinear control are deduced from the Euler-Lagrange equations by using the nutation theory. The equations of the system show that a cyclic variable appears. Its elimination allows us to find an auxiliary nonlinear system from which it is possible to deduce a nonlinear control law in order to obtain a desired equilibrium point. From the analysis of the nonlinear control law it is possible to show that due to both harmonic disturbances in the platform of the gyro and in the body to stabilize, regular and chaotic motions can appear. The chaotic motion is researched by means of chaos maps, bifurcation diagrams, sensitivity to initial conditions, Lyapunov exponents and Fourier spectrum density. The transition from chaotic to steady state motion by eliminating the harmonic disturbances from the modification of the initial nonlinear control law is also researched. Next, the paper shows how to use the chaotic motion in order to obtain small input signals so that the desired equilibrium state of the gyro can be reached. The developed methodology and its compared performance are evaluated through analytical methods and numerical simulations.
TBA equations for excited states in the O(3) and O(4) nonlinear $\\sigma$-model
Balog, J.; Hegedus, A
2003-01-01
TBA integral equations are proposed for 1-particle states in the sausage- and SS-models and their $\\sigma$-model limits. Combined with the ground state TBA equations the exact mass gap is computed in the O(3) and O(4) nonlinear $\\sigma$-model and the results are compared to 3-loop perturbation theory and Monte Carlo data.
Unification and extension of monolithic state space and iterative cochlear models.
Rapson, Michael J; Tapson, Jonathan C; Karpul, David
2012-05-01
Time domain cochlear models have primarily followed a method introduced by Allen and Sondhi [J. Acoust. Soc. Am. 66, 123-132 (1979)]. Recently the "state space formalism" proposed by Elliott et al. [J. Acoust. Soc. Am. 122, 2759-2771 (2007)] has been used to simulate a wide range of nonlinear cochlear models. It used a one-dimensional approach that is extended to two dimensions in this paper, using the finite element method. The recently developed "state space formalism" in fact shares a close relationship to the earlier approach. Working from Diependaal et al. [J. Acoust. Soc. Am. 82, 1655-1666 (1987)] the two approaches are compared and the relationship formalized. Understanding this relationship allows models to be converted from one to the other in order to utilize each of their strengths. A second method to derive the state space matrices required for the "state space formalism" is also presented. This method offers improved numerical properties because it uses the information available about the model more effectively. Numerical results support the claims regarding fluid dimension and the underlying similarity of the two approaches. Finally, the recent advances in the state space formalism [Bertaccini and Sisto, J. Comp. Phys. 230, 2575-2587 (2011)] are discussed in terms of this relationship.
A non-linear model predictive controller with obstacle avoidance for a space robot
Wang, Mingming; Luo, Jianjun; Walter, Ulrich
2016-04-01
This study investigates the use of the non-linear model predictive control (NMPC) strategy for a kinematically redundant space robot to approach an un-cooperative target in complex space environment. Collision avoidance, traditionally treated as a high level planning problem, can be effectively translated into control constraints as part of the NMPC. The objective of this paper is to evaluate the performance of the predictive controller in a constrained workspace and to investigate the feasibility of imposing additional constraints into the NMPC. In this paper, we reformulated the issue of the space robot motion control by using NMPC with predefined objectives under input, output and obstacle constraints over a receding horizon. An on-line quadratic programming (QP) procedure is employed to obtain the constrained optimal control decisions in real-time. This study has been implemented for a 7 degree-of-freedom (DOF) kinematically redundant manipulator mounted on a 6 DOF free-floating spacecraft via simulation studies. Real-time trajectory tracking and collision avoidance particularly demonstrate the effectiveness and potential of the proposed NMPC strategy for the space robot.
On Exact Controllability of Networks of Nonlinear Elastic Strings in 3-Dimensional Space
Institute of Scientific and Technical Information of China (English)
Günter R. LEUGERING; E. J. P. Georg SCHMIDT
2012-01-01
This paper concerns a system of nonlinear wave equations describing the vibrations of a 3-dimensional network of elastic strings.The authors derive the equations and appropriate nodal conditions,determine equilibrium solutions,and,by using the methods of quasilinear hyperbolic systems,prove that for tree networks the natural initial,bound-ary value problem has classical solutions existing in neighborhoods of the "stretched" equilibrium solutions.Then the local controllability of such networks near such equilibrium configurations in a certain specified time interval is proved.Finally,it is proved that,given two different equilibrium states satisfying certain conditions,it is possible to control the network from states in a small enough neighborhood of one equilibrium to any state in a suitable neighborhood of the second equilibrium over a sufficiently large time interval.
Hypersonic entry vehicle state estimation using nonlinearity-based adaptive cubature Kalman filters
Sun, Tao; Xin, Ming
2017-05-01
Guidance, navigation, and control of a hypersonic vehicle landing on the Mars rely on precise state feedback information, which is obtained from state estimation. The high uncertainty and nonlinearity of the entry dynamics make the estimation a very challenging problem. In this paper, a new adaptive cubature Kalman filter is proposed for state trajectory estimation of a hypersonic entry vehicle. This new adaptive estimation strategy is based on the measure of nonlinearity of the stochastic system. According to the severity of nonlinearity along the trajectory, the high degree cubature rule or the conventional third degree cubature rule is adaptively used in the cubature Kalman filter. This strategy has the benefit of attaining higher estimation accuracy only when necessary without causing excessive computation load. The simulation results demonstrate that the proposed adaptive filter exhibits better performance than the conventional third-degree cubature Kalman filter while maintaining the same performance as the uniform high degree cubature Kalman filter but with lower computation complexity.
Direct measurement of non-linear properties of bipartite quantum states
Bovino, F A; Castagnoli, G C; Ekert, A; Horodecki, P; Sergienko, A V; Alves, Carolina Moura; Bovino, Fabio Antonio; Castagnoli, Giuseppe; Ekert, Artur; Horodecki, Pawel; Sergienko, Alexander Vladimir
2005-01-01
Non-linear properties of quantum states, such as entropy or entanglement, quantify important physical resources and are frequently used in quantum information science. They are usually calculated from a full description of a quantum state, even though they depend only on a small number parameters that specify the state. Here we extract a non-local and a non-linear quantity, namely the Renyi entropy, from local measurements on two pairs of polarization entangled photons. We also introduce a "phase marking" technique which allows to select uncorrupted outcomes even with non-deterministic sources of entangled photons. We use our experimental data to demonstrate the violation of entropic inequalities. They are examples of a non-linear entanglement witnesses and their power exceeds all linear tests for quantum entanglement based on all possible Bell-CHSH inequalities.
A nonlinear plasmonic resonator for three-state all-optical switching
Amin, Muhammad
2014-01-01
A nonlinear plasmonic resonator design is proposed for three-state all-optical switching at frequencies including near infrared and lower red parts of the spectrum. The tri-stable response required for three-state operation is obtained by enhancing nonlinearities of a Kerr medium through multiple (higher order) plasmons excited on resonator\\'s metallic surfaces. Indeed, simulations demonstrate that exploitation of multiple plasmons equips the proposed resonator with a multi-band tri-stable response, which cannot be obtained using existing nonlinear plasmonic devices that make use of single mode Lorentzian resonances. Multi-band three-state optical switching that can be realized using the proposed resonator has potential applications in optical communications and computing. © 2014 Optical Society of America.
Tsurutani, Bruce T.
1995-01-01
As the lead-off presentation for the topic of nonlinear waves and their evolution, we will illustrate some prominent examples of waves in space plasmas. We will describe recent observations detected within planetary foreshocks, near comets and in interplanetary space. It is believed that the nonlinear LF plasma wave features discussed here are part of and may be basic to the development of plasma turbulence. In this sense, this is one area of space plasma physics that is fundamental, with applications to fusion physics and astrophysics as well. It is hoped that the reader(s) will be stimulated to study nonlinear wave development themselves, if he/she is not already involved.
Non-linear ultimate strength and stability limit state analysis of a wind turbine blade
DEFF Research Database (Denmark)
Rosemeier, Malo; Berring, Peter; Branner, Kim
2016-01-01
flap-wise loading has been compared with a linear response to determine the blade's resistance in the ultimate strength and stability limit states. The linear analysis revealed an unrealistic failure mechanism and failure mode. Further, it did not capture the highly non-linear response of the blade...... of an imperfection. The more realistic non-linear approaches yielded more optimistic results than the mandatory linear bifurcation analysis. Consequently, the investigated blade designed after the lesser requirements was sufficient. Using the non-linear approaches, considering inter-fibre failure as the critical...... failure mode, yielded still a significant safety margin for the designer (7–28%). The non-linear response was significantly dependent on the scaling of the imperfection. Eurocode's method of applying an imperfection appeared more realistic than the GL method. Since the considered blade withstood 135...
Duan, Zhaoxia; Xiang, Zhengrong; Karimi, Hamid Reza
2014-07-01
This paper is concerned with the state feedback control problem for a class of two-dimensional (2D) discrete-time stochastic systems with time-delays, randomly occurring uncertainties and nonlinearities. Both the sector-like nonlinearities and the norm-bounded uncertainties enter into the system in random ways, and such randomly occurring uncertainties and nonlinearities obey certain mutually uncorrelated Bernoulli random binary distribution laws. Sufficient computationally tractable linear matrix inequality-based conditions are established for the 2D nonlinear stochastic time-delay systems to be asymptotically stable in the mean-square sense, and then the explicit expression of the desired controller gains is derived. An illustrative example is provided to show the usefulness and effectiveness of the proposed method.
Inexact Picard iterative scheme for steady-state nonlinear diffusion in random heterogeneous media.
Mohan, P Surya; Nair, Prasanth B; Keane, Andy J
2009-04-01
In this paper, we present a numerical scheme for the analysis of steady-state nonlinear diffusion in random heterogeneous media. The key idea is to iteratively solve the nonlinear stochastic governing equations via an inexact Picard iteration scheme, wherein the nonlinear constitutive law is linearized using the current guess of the solution. The linearized stochastic governing equations are then spatially discretized and approximately solved using stochastic reduced basis projection schemes. The approximation to the solution process thus obtained is used as the guess for the next iteration. This iterative procedure is repeated until an appropriate convergence criterion is met. Detailed numerical studies are presented for diffusion in a square domain for varying degrees of nonlinearity. The numerical results are compared against benchmark Monte Carlo simulations, and it is shown that the proposed approach provides good approximations for the response statistics at modest computational effort.
Yang, Haijian
2016-07-26
Fully implicit methods are drawing more attention in scientific and engineering applications due to the allowance of large time steps in extreme-scale simulations. When using a fully implicit method to solve two-phase flow problems in porous media, one major challenge is the solution of the resultant nonlinear system at each time step. To solve such nonlinear systems, traditional nonlinear iterative methods, such as the class of the Newton methods, often fail to achieve the desired convergent rate due to the high nonlinearity of the system and/or the violation of the boundedness requirement of the saturation. In the paper, we reformulate the two-phase model as a variational inequality that naturally ensures the physical feasibility of the saturation variable. The variational inequality is then solved by an active-set reduced-space method with a nonlinear elimination preconditioner to remove the high nonlinear components that often causes the failure of the nonlinear iteration for convergence. To validate the effectiveness of the proposed method, we compare it with the classical implicit pressure-explicit saturation method for two-phase flow problems with strong heterogeneity. The numerical results show that our nonlinear solver overcomes the often severe limits on the time step associated with existing methods, results in superior convergence performance, and achieves reduction in the total computing time by more than one order of magnitude.
Experiments in Nonlinear Adaptive Control of Multi-Manipulator, Free-Flying Space Robots
Chen, Vincent Wei-Kang
1992-01-01
Sophisticated robots can greatly enhance the role of humans in space by relieving astronauts of low level, tedious assembly and maintenance chores and allowing them to concentrate on higher level tasks. Robots and astronauts can work together efficiently, as a team; but the robot must be capable of accomplishing complex operations and yet be easy to use. Multiple cooperating manipulators are essential to dexterity and can broaden greatly the types of activities the robot can achieve; adding adaptive control can ease greatly robot usage by allowing the robot to change its own controller actions, without human intervention, in response to changes in its environment. Previous work in the Aerospace Robotics Laboratory (ARL) have shown the usefulness of a space robot with cooperating manipulators. The research presented in this dissertation extends that work by adding adaptive control. To help achieve this high level of robot sophistication, this research made several advances to the field of nonlinear adaptive control of robotic systems. A nonlinear adaptive control algorithm developed originally for control of robots, but requiring joint positions as inputs, was extended here to handle the much more general case of manipulator endpoint-position commands. A new system modelling technique, called system concatenation was developed to simplify the generation of a system model for complicated systems, such as a free-flying multiple-manipulator robot system. Finally, the task-space concept was introduced wherein the operator's inputs specify only the robot's task. The robot's subsequent autonomous performance of each task still involves, of course, endpoint positions and joint configurations as subsets. The combination of these developments resulted in a new adaptive control framework that is capable of continuously providing full adaptation capability to the complex space-robot system in all modes of operation. The new adaptive control algorithm easily handles free
Solid-State Thermionic Power Generators: An Analytical Analysis in the Nonlinear Regime
Zebarjadi, M.
2017-07-01
Solid-state thermionic power generators are an alternative to thermoelectric modules. In this paper, we develop an analytical model to investigate the performance of these generators in the nonlinear regime. We identify dimensionless parameters determining their performance and provide measures to estimate an acceptable range of thermal and electrical resistances of thermionic generators. We find the relation between the optimum load resistance and the internal resistance and suggest guidelines for the design of thermionic power generators. Finally, we show that in the nonlinear regime, thermionic power generators can have efficiency values higher than the state-of-the-art thermoelectric modules.
Becis-Aubry, Yasmina; Boutayeb, Mohamed; Darouach, Mohamed
2006-01-01
International audience; This contribution proposes a recursive and easily implementable online algorithm for state estimation of multi-output discrete-time systems with nonlinear dynamics and linear measurements in presence of unknown but bounded disturbances corrupting both the state and measurement equations. The proposed algorithm is based on state bounding techniques and is decomposed into two steps : time update and observation update that uses a switching estimation Kalman-like gain mat...
Energy Technology Data Exchange (ETDEWEB)
Belmonte-Beitia, J [Departamento de Matematicas, E T S de Ingenieros Industriales and Instituto de Matematica Aplicada a la Ciencia y la IngenierIa (IMACI), Avda Camilo Jose Cela, 3 Universidad de Castilla-La Mancha 13071 Ciudad Real (Spain); Cuevas, J [Grupo de Fisica No Lineal, Departamento de Fisica Aplicada I, Escuela Universitaria Politecnica, C/Virgen de Africa, 7, 41011 Sevilla (Spain)], E-mail: juan.belmonte@uclm.es, E-mail: jcuevas@us.es
2009-04-24
In this paper, we construct, by means of similarity transformations, explicit solutions to the cubic-quintic nonlinear Schroedinger equation with potentials and nonlinearities depending on both time and spatial coordinates. We present the general approach and use it to calculate bright and dark soliton solutions for nonlinearities and potentials of physical interest in applications to Bose-Einstein condensates and nonlinear optics.
A Space-time Smooth Artificial Viscosity Method For Nonlinear Conservation Laws
Reisner, Jon; Shkoller, Steve
2012-01-01
We introduce the $C$-method, a simple scheme for adding localized, space-time smooth, artificial viscosity to nonlinear systems of conservation laws which propagate shock waves, rarefactions, and contact discontinuities. In particular, we focus our attention on the compressible Euler equations which form a 3x3 system in one space dimension. The novel feature of our approach involves the coupling of a linear scalar reaction diffusion equation to our system of conservation laws, whose solution $C(x,t)$ is the coefficient to an additional (and artificial) term added to the flux, which determines both the location and strength of the added viscosity. Near shock discontinuities, $C(x,t)$ is large and localized, and transitions smoothly in space-time to zero away from the shock. This simple approach has two fundamental features: (1) our regularization is at the continuum level--i.e., the level of he partial differential equations (PDE)-- so that any higher-order numerical discretization scheme can be employed, and ...
Variational space-time (dis)continuous Galerkin method for nonlinear free surface water waves
Gagarina, E.; Ambati, V. R.; van der Vegt, J. J. W.; Bokhove, O.
2014-10-01
A new variational finite element method is developed for nonlinear free surface gravity water waves using the potential flow approximation. This method also handles waves generated by a wave maker. Its formulation stems from Miles' variational principle for water waves together with a finite element discretization that is continuous in space and discontinuous in time. One novel feature of this variational finite element approach is that the free surface evolution is variationally dependent on the mesh deformation vis-à-vis the mesh deformation being geometrically dependent on free surface evolution. Another key feature is the use of a variational (dis)continuous Galerkin finite element discretization in time. Moreover, in the absence of a wave maker, it is shown to be equivalent to the second order symplectic Störmer-Verlet time stepping scheme for the free-surface degrees of freedom. These key features add to the stability of the numerical method. Finally, the resulting numerical scheme is verified against nonlinear analytical solutions with long time simulations and validated against experimental measurements of driven wave solutions in a wave basin of the Maritime Research Institute Netherlands.
Asymptotic behaviour for Schrodinger equations with a quadratic nonlinearity in one-space dimension
Directory of Open Access Journals (Sweden)
Nakao Hayashi
2001-07-01
Full Text Available We consider the Cauchy problem for the Schr"{o}dinger equation with a quadratic nonlinearity in one space dimension $$ iu_{t}+frac{1}{2}u_{xx}=t^{-alpha}| u_x| ^2,quad u(0,x = u_0(x, $$ where $alpha in (0,1$. From the heuristic point of view, solutions to this problem should have a quasilinear character when $alpha in (1/2,1$. We show in this paper that the solutions do not have a quasilinear character for all $alpha in (0,1$ due to the special structure of the nonlinear term. We also prove that for $alpha in [1/2,1$ if the initial data $u_0in H^{3,0}cap H^{2,2}$ are small, then the solution has a slow time decay such as $t^{-alpha /2}$. For $alpha in (0,1/2$, if we assume that the initial data $u_0$ are analytic and small, then the same time decay occurs.
Red'kov, V
2011-01-01
Non-linear electrodynamics arising in the frames of field theories in non-commutative space-time is examined on the base of the Riemann-Silberstein-Majorana-Oppenheimer formalism. The problem of form-invariance of the non-linear constitutive relations governed by six non-commutative parameters \\theta_{kl} \\sim {\\bf K} = {\\bf n} + i {\\bf m} is explored in detail on the base of the complex orthogonal group theory SO(3.C). Two Abelian 2-parametric small groups, isomorphic to each other in abstract sense, and leaving unchangeable the extended constitutive relations at arbitrary six parameters \\theta_{kl} of effective media have been found, their realization depends explicitly on invariant length {\\bf K}^{2}. In the case of non-vanishing length a special reference frame in which the small group has the structure SO(2) \\otimes SO(1,1) has been found. In isotropic case no such reference frame exists. The way to interpret both Abelian small groups in physical terms consists in factorizing corresponding Lorentz transf...
Ground-state energies of the nonlinear sigma model and the Heisenberg spin chains
Zhang, Shoucheng; Schulz, H. J.; Ziman, Timothy
1989-01-01
A theorem on the O(3) nonlinear sigma model with the topological theta term is proved, which states that the ground-state energy at theta = pi is always higher than the ground-state energy at theta = 0, for the same value of the coupling constant g. Provided that the nonlinear sigma model gives the correct description for the Heisenberg spin chains in the large-s limit, this theorem makes a definite prediction relating the ground-state energies of the half-integer and the integer spin chains. The ground-state energies obtained from the exact Bethe ansatz solution for the spin-1/2 chain and the numerical diagonalization on the spin-1, spin-3/2, and spin-2 chains support this prediction.
Nonlinear Time Series Analysis Since 1990:Some Personal Reflections
Institute of Scientific and Technical Information of China (English)
Howel Tong
2002-01-01
I reflect upon the development of nonlinear time series analysis since 1990 by focusing on five major areas of development. These areas include the interface between nonlinear time series analysis and chaos, the nonparametric/semiparametric approach, nonlinear state space modelling, financial time series and nonlinear modelling of panels of time series.
The HIVE Tool for Informed Swarm State Space Exploration
Wijs, Anton
2011-01-01
Swarm verification and parallel randomised depth-first search are very effective parallel techniques to hunt bugs in large state spaces. In case bugs are absent, however, scalability of the parallelisation is completely lost. In recent work, we proposed a mechanism to inform the workers which parts of the state space to explore. This mechanism is compatible with any action-based formalism, where a state space can be represented by a labelled transition system. With this extension, each worker can be strictly bounded to explore only a small fraction of the state space at a time. In this paper, we present the HIVE tool together with two search algorithms which were added to the LTSmin tool suite to both perform a preprocessing step, and execute a bounded worker search. The new tool is used to coordinate informed swarm explorations, and the two new LTSmin algorithms are employed for preprocessing a model and performing the individual searches.
Black Strings, Black Rings and State-space Manifold
Bellucci, Stefano
2011-01-01
State-space geometry is considered, for diverse three and four parameter non-spherical horizon rotating black brane configurations, in string theory and $M$-theory. We have explicitly examined the case of unit Kaluza-Klein momentum $D_1D_5P$ black strings, circular strings, small black rings and black supertubes. An investigation of the state-space pair correlation functions shows that there exist two classes of brane statistical configurations, {\\it viz.}, the first category divulges a degenerate intrinsic equilibrium basis, while the second yields a non-degenerate, curved, intrinsic Riemannian geometry. Specifically, the solutions with finitely many branes expose that the two charged rotating $D_1D_5$ black strings and three charged rotating small black rings consort real degenerate state-space manifolds. Interestingly, arbitrary valued $M_5$-dipole charged rotating circular strings and Maldacena Strominger Witten black rings exhibit non-degenerate, positively curved, comprehensively regular state-space con...
Nonlinear closed loop optimal control: a modified state-dependent Riccati equation.
Rafee Nekoo, S
2013-03-01
The state-dependent Riccati equation (SDRE), as a controller, has been introduced and implemented since the 90s. In this article, the other aspects of this controller are declared which shows the capability of this technique. First, a general case which has control nonlinearities and time varying weighting matrix Q is solved with three approaches: exact solution (ES), online control update (OCU) and power series approximation (PSA). The proposed PSA in this paper is able to deal with time varying or state-dependent Q in nonlinear systems. As a result of having the solution of nonlinear systems with complex Q containing constraints, using OCU and proposed PSA, a method is introduced to prevent the collision of an end-effector of a robot and an obstacle which shows the adaptability of the SDRE controller. Two examples to support the idea are presented and conferred. Supplementing constraints to the SDRE via matrix Q, this approach is named a modified SDRE.
RESULTS OF INTERBANK EXCHANGE RATES FORECASTING USING STATE SPACE MODEL
Directory of Open Access Journals (Sweden)
Muhammad Kashif
2008-07-01
Full Text Available This study evaluates the performance of three alternative models for forecasting daily interbank exchange rate of U.S. dollar measured in Pak rupees. The simple ARIMA models and complex models such as GARCH-type models and a state space model are discussed and compared. Four different measures are used to evaluate the forecasting accuracy. The main result is the state space model provides the best performance among all the models.
Generalized exponential input-to-state stability of nonlinear systems with time delay
Sun, Fenglan; Gao, Lingxia; Zhu, Wei; Liu, Feng
2017-03-01
This paper studies the general input-to-state stability problem of the nonlinear delay systems. By employing Lypaunov-Razumikhin technique, several general input-to-state stability concepts, that is generalized globally exponential integral input-to-state stability (GGE-iISS), generalized globally integral exponential integral input-to-state stability (GGIE-iISS), and eλt-weighted generalized globally integral exponential integral input-to-state stability (eλt-weighted GGIE-iISS) are studied. An example is given to illustrate the correctness of the obtained theoretical results.
Directory of Open Access Journals (Sweden)
Emran Tohidi
2013-01-01
Full Text Available The idea of approximation by monomials together with the collocation technique over a uniform mesh for solving state-space analysis and optimal control problems (OCPs has been proposed in this paper. After imposing the Pontryagins maximum principle to the main OCPs, the problems reduce to a linear or nonlinear boundary value problem. In the linear case we propose a monomial collocation matrix approach, while in the nonlinear case, the general collocation method has been applied. We also show the efficiency of the operational matrices of differentiation with respect to the operational matrices of integration in our numerical examples. These matrices of integration are related to the Bessel, Walsh, Triangular, Laguerre, and Hermite functions.
Induced measures in the space of mixed quantum states
Energy Technology Data Exchange (ETDEWEB)
Zyczkowski, Karol [Centrum Fizyki Teoretycznej, Polska Akademia Nauk, Warsaw, Poland and Instytut Fizyki, Uniwersytet Jagiellonski, Crakow (Poland)). E-mail: karol@cft.edu.pl; Sommers, Hans-Juergen [Fachbereich Physik, Universitaet-Gesamthochschule Essen, Essen (Germany)). E-mail: sommers@next30.theo-phys.uni-essen.de
2001-09-07
We analyse several product measures in the space of mixed quantum states. In particular, we study measures induced by the operation of partial tracing. The natural, rotationally invariant measure on the set of all pure states of a NxK composite system, induces a unique measure in the space of NxN mixed states (or in the space of KxK mixed states, if the reduction takes place with respect to the first subsystem). For K=N the induced measure is equal to the Hilbert-Schmidt measure, which is shown to coincide with the measure induced by singular values of non-Hermitian random Gaussian matrices pertaining to the Ginibre ensemble. We compute several averages with respect to this measure and show that the mean entanglement of NxN pure states behaves as lnN-1/2. (author)
Induced measures in the space of mixed quantum states
Zyczkowski, K; Zyczkowski, Karol; Sommers, Hans-Juergen
2001-01-01
We analyze several product measures in the space of mixed quantum states. In particular we study measures induced by the operation of partial tracing. The natural, rotationally invariant measure on the set of all pure states of a N x K composite system, induces a unique measure in the space of N x N mixed states (or in the space of K x K mixed states, if the reduction takes place with respect to the first subsystem). For K=N the induced measure is equal to the Hilbert-Schmidt measure, which is shown to coincide with the measure induced by singular values of non-Hermitian random Gaussian matrices pertaining to the Ginibre ensemble. We compute several averages with respect to this measure and show that the mean entanglement of $N \\times N$ pure states behaves as lnN-1/2.
Application of nonlinear ultrasonic method for monitoring of stress state in concrete
Energy Technology Data Exchange (ETDEWEB)
Kim, Gyu Jin; Kwak, Hyo Gyoung [Dept. of Civil and Environmental Engineering, Korea Advanced Institute of Science and Technology, Daejeon (Korea, Republic of); Park, Sun Jong [Dept. of Structural System and Site Safety Evaluation, Korea Institute of Nuclear Safety, Daejeon (Korea, Republic of)
2016-04-15
As the lifespan of concrete structures increases, their load carrying capacity decreases owing to cyclic loads and long-term effects such as creep and shrinkage. For these reasons, there is a necessity for stress state monitoring of concrete members. Particularly, it is necessary to evaluate the concrete structures for behavioral changes by using a technique that can overcome the measuring limitations of usual ultrasonic nondestructive evaluation methods. This paper proposes the use of a nonlinear ultrasonic method, namely, nonlinear resonant ultrasonic spectroscopy (NRUS) for the measurement of nonlinearity parameters for stress monitoring. An experiment compared the use of NRUS method and a linear ultrasonic method, namely, ultrasonic pulse velocity (UPV) to study the effects of continuously increasing loads and cyclic loads on the nonlinearity parameter. Both NRUS and UPV methods found a similar direct relationship between load level and that parameter. The NRUS method showed a higher sensitivity to micro-structural changes of concrete than UPV method. Thus, the experiment confirms the possibility of using the nonlinear ultrasonic method for stress state monitoring of concrete members.
Directory of Open Access Journals (Sweden)
Mohammad Shahzad
2016-05-01
Full Text Available This study deals with the control of chaotic dynamics of tumor cells, healthy host cells, and effector immune cells in a chaotic Three Dimensional Cancer Model (TDCM by State Space Exact Linearization (SSEL technique based on Lie algebra. A non-linear feedback control law is designed which induces a coordinate transformation thereby changing the original chaotic TDCM system into a controlled one linear system. Numerical simulation has been carried using Mathematica that witness the robustness of the technique implemented on the chosen chaotic system.
White noise theory of robust nonlinear filtering with correlated state and observation noises
Bagchi, Arunabha; Karandikar, Rajeeva
1994-01-01
In the existing `direct¿ white noise theory of nonlinear filtering, the state process is still modelled as a Markov process satisfying an Itô stochastic differential equation, while a `finitely additive¿ white noise is used to model the observation noise. We remove this asymmetry by modelling the st
White noise theory of robust nonlinear filtering with correlated state and observation noises
Bagchi, Arunabha; Karandikar, Rajeeva
1992-01-01
In the direct white noise theory of nonlinear filtering, the state process is still modeled as a Markov process satisfying an Ito stochastic differential equation, while a finitely additive white noise is used to model the observation noise. In the present work, this asymmetry is removed by modeling
Transient and Steady-State Responses of an Asymmetric Nonlinear Oscillator
Directory of Open Access Journals (Sweden)
Alex Elías-Zúñiga
2013-01-01
oscillator that describes the motion of a damped, forced system supported symmetrically by simple shear springs on a smooth inclined bearing surface. We also use the percentage overshoot value to study the influence of damping and nonlinearity on the transient and steady-state oscillatory amplitudes.
Directory of Open Access Journals (Sweden)
Pabitra Pal Choudhury
2011-01-01
Full Text Available Dynamics of a nonlinear cellular automaton (CA is, in general asymmetric, irregular, and unpredictable as opposed to that of a linear CA, which is highly systematic and tractable, primarily due to the presence of a matrix handle. In this paper, we present a novel technique of studying the properties of the State Transition Diagram of a nonlinear uniform one-dimensional cellular automaton in terms of its deviation from a suggested linear model. We have considered mainly elementary cellular automata with neighborhood of size three, and, in order to facilitate our analysis, we have classified the Boolean functions of three variables on the basis of number and position(s of bit mismatch with linear rules. The concept of deviant and nondeviant states is introduced, and hence an algorithm is proposed for deducing the State Transition Diagram of a nonlinear CA rule from that of its nearest linear rule. A parameter called the proportion of deviant states is introduced, and its dependence on the length of the CA is studied for a particular class of nonlinear rules.
Excited state nonlinear integral equations for an integrable anisotropic spin-1 chain
Energy Technology Data Exchange (ETDEWEB)
Suzuki, J [Department of Physics, Faculty of Science, Shizuoka University, Ohya 836, Shizuoka (Japan)
2004-12-17
We propose a set of nonlinear integral equations to describe the excited states of an integrable the spin-1 chain with anisotropy. The scaling dimensions, evaluated numerically in previous studies, are recovered analytically by using the equations. This result may be relevant to the study of the supersymmetric sine-Gordon model.
Knaus, H.; Blab, G.; Agronskaia, A.V.; van den Heuvel, D.J.; Gerritsen, H.C.; Wösten, H.A.B.
2013-01-01
Label-free nonlinear spectral imaging microscopy (NLSM) records two-photon-excited fluorescence emission spectra of endogenous fluorophores within the specimen. Here, NLSM is introduced as a novel, minimally invasive method to analyze the metabolic state of fungal hyphae by monitoring the autofluore
ESTIMATE ACCURACY OF NONLINEAR COEFFICIENTS OF SQUEEZEFILM DAMPER USING STATE VARIABLE FILTER METHOD
Institute of Scientific and Technical Information of China (English)
1998-01-01
The estimate model for a nonlinear system of squeeze-film damper (SFD) is described.The method of state variable filter (SVF) is used to estimate the coefficients of SFD.The factors which are critical to the estimate accuracy are discussed.
Wu, Huilan; Yao, Yuqin
2017-01-01
The time- and space-modulated nonlinearity is the important character of the Bose-Einstein condensates (BECs). Many works have been done on atomic BECs with spatially modulated nonlinearity, but there is little work on atomic-molecular BECs. In this paper, we construct one family of explicitly exact solutions of the atomic-molecular BECs with time- and space-modulated nonlinearities and trapping potential by similarity transformations. We discuss the dynamics of matter waves including breathing solitons, quasi-breathing solitons, resonant solitons and moving solitons. We analyze the linear stability of the solutions by adding various initial stochastic noise. We also provide the experimental parameters to produce these phenomena in future experiments.
Experimental nonlinear beam dynamics studies with turn- by-turn phase space monitors
Terebilo, Andrei Gennadyevich
1999-10-01
This thesis presents an experimental study of single particle and collective beam dynamics undertaken by the author in SPEAR electron storage ring. The technique used for measurement consists of exciting transverse oscillations of a bunch circulating in the ring with a fast kicker and observing the center of mass oscillations every turn for several thousand turns. The goal of this study was to develop new applications of the turn-by-turn technique to accelerator diagnostics. One innovation introduced is the use of a collective mode of the beam motion as a phase space probe. When in this mode the bunch behaves similar to a macroparticle and oscillates coherently. It is possible to control the growth/damping rate of this oscillation by adjusting the accelerator parameters. Another new tool proposed is the analysis of phase space trajectories in the time-frequency domain. This technique makes it possible to conduct nonlinear dynamics experiments such as observation of high order resonances in the frequency map and single-kick measurement of the tune dependence on the amplitude of oscillations.
Space research scientific and educational project of Moscow State University
Krasotkin, S. A.; Mjagkova, I. N.; Panasyuk, M. I.; Radchenko, V. V.; Ryazantseva, M. O.
The scientific and educational project of space research was initiated in Lomonosov Moscow State University in order to incorporate modern space research in the university and high education, to popularize basics of space physics, and to enhance public interest in space exploration. On 20 January, 2005 the First Russian University Satellite UNIVERSITETSKIY was launched into circular polar orbit (inclination 83 deg., altitude 940-980 km). The onboard scientific complex TATYANA as well as the mission control and information receiving center, was designed and developed in Moscow State University. The scientific program of the mission include measurements of space radiation in different energy channels, and Earth UV luminosity and lightening. A multimedia lectures "Life of the Earth in the Solar Atmosphere" containing the basic information and demonstrations of the heliophysics (including Sun structure and solar activity, heliosphere and geophysics, solar-terrestrial connections and solar influence on the Earth's life) was created for upper high-school and junior university students. For the upper-university students there was created a dozen of special computerized lab exercises based on the experimental quasi-realtime data obtained from our satellites. Students specialized in space physics from a few Russian universities are involved in scientific work based. Educational program of the project (both the multimedia lectures and lab exercises) is concentrated to upper high school, middle university and special level for space physics students. The space research scientific and educational activity of Moscow State University is a non-profit project and is open for all interested parties.
A Learning State-Space Model for Image Retrieval
Directory of Open Access Journals (Sweden)
Lee Greg C
2007-01-01
Full Text Available This paper proposes an approach based on a state-space model for learning the user concepts in image retrieval. We first design a scheme of region-based image representation based on concept units, which are integrated with different types of feature spaces and with different region scales of image segmentation. The design of the concept units aims at describing similar characteristics at a certain perspective among relevant images. We present the details of our proposed approach based on a state-space model for interactive image retrieval, including likelihood and transition models, and we also describe some experiments that show the efficacy of our proposed model. This work demonstrates the feasibility of using a state-space model to estimate the user intuition in image retrieval.
Non-linear supersymmetric {sigma}-models and their gauging in the Atiyah-Ward space-time
Energy Technology Data Exchange (ETDEWEB)
Carvalho, M.; Vilar, L.C.Q.; Helayel-Neto, J.A.
1995-10-01
We present a supersymmetric non-linear {sigma}-model built up in the N 1 superspace of Atiyah-ward space-time. A manifold of the Kaehler type comes out that is restricted by a a particular decomposition of the Kaehler potential. The gauging of the {sigma}-model isometries is also accomplished in superspace. (author). 20 refs.
Institute of Scientific and Technical Information of China (English)
WU YUE-XIANG; HUO YAN-MEI; WU YA-KUN
2012-01-01
The main purpose of this paper is to examine the existence of coupled solutions and coupled minimal-maximal solutions for a kind of nonlinear operator equations in partial ordered linear topology spaces by employing the semi-order method.Some new existence results are obtained.
Energy Technology Data Exchange (ETDEWEB)
Chekhov, L.O.
1985-06-01
Matrix nonlinear sigma-model is considered in the case of rectangular matrices of the dimension Nx..alpha..N. Renormalizability of the model with respect to ..alpha.. and 1/N is demonstrated for the case of two-dimensional Euclidean space. Validity of the chiral identity is proved in the operator expansion for the renormalized theory.
The emergence of a coherent structure for coherent structures: localized states in nonlinear systems
Dawes, Jonathan
2010-01-01
Coherent structures emerge from the dynamics of many kinds of dissipative, externally driven, nonlinear systems, and continue to provoke new questions that challenge our physical and mathematical understanding. In one specific sub-class of such problems, where a pattern-forming, or `Turing', instability occurs, rapid progress has been made recently in our understanding of the formation of localized states: patches of regular pattern surrounded by the unpatterned homogeneous background state. ...
On the Squeezed Number States and their Phase Space Representations
Albano, L; Stephany, J
2002-01-01
We compute the photon number distribution, the Q distribution function and the wave functions in the momentum and position representation for a single mode squeezed number state. We discuss the oscillations which appear in the photon number distribution of squeezed number states for high values of the squeezing parameter. We compare our results with the formalism based on the interference in phase space.
Dynamic State Space Partitioning for External Memory Model Checking
DEFF Research Database (Denmark)
Evangelista, Sami; Kristensen, Lars Michael
2009-01-01
We describe a dynamic partitioning scheme usable by model checking techniques that divide the state space into partitions, such as most external memory and distributed model checking algorithms. The goal of the scheme is to reduce the number of transitions that link states belonging to different...
Balanced state-space representations : a polynomial algebraic approach
Rapisarda, P.; Trentelman, H.L.
2009-01-01
We show how to compute a minimal Riccati-balanced state map and a minimal Riccati-balanced state space representation starting from an image representation of a strictly dissipative system. The result is based on an iterative procedure to solve a generalization of the Nevanlinna interpolation proble
Analysis and design for the second order nonlinear continuous extended states observer
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
The extended state observer (ESO) is a novel observer for a class of uncertain systems. Since ESO adopts the continuous non-smooth structure, the classical observer design theory is hard to use for ESO analysis. In this note, the self-stable region (SSR) approach, which is a nonlinear synthesis method for nonlinear uncertain systems, will be used for ESO design and its stability analysis. The advantages of the non-smooth structure in ESO for improving the convergence properties and the estimation precision will be shown.
Nonlinear optics and solid-state lasers advanced concepts, tuning-fundamentals and applications
Yao, Jianquan
2012-01-01
This book covers the complete spectrum of nonlinear optics and all solid state lasers.The book integrates theory, calculations and practical design, technology, experimental schemes and applications. With the expansion and further development of Laser technology, the wavelength spectrum of Lasers had to be enlarged, even to be tunable which requires the use of nonlinear optical and Laser tunable technology. It systematically summarizes and integrates the analysis of international achievements within the last 20 years in this field. It will be helpful for university teachers, graduate students as well as engineers.
Full-State Linearization and Stabilization of SISO Markovian Jump Nonlinear Systems
Directory of Open Access Journals (Sweden)
Zhongwei Lin
2013-01-01
Full Text Available This paper investigates the linearization and stabilizing control design problems for a class of SISO Markovian jump nonlinear systems. According to the proposed relative degree set definition, the system can be transformed into the canonical form through the appropriate coordinate changes followed with the Markovian switchings; that is, the system can be full-state linearized in every jump mode with respect to the relative degree set n,…,n. Then, a stabilizing control is designed through applying the backstepping technique, which guarantees the asymptotic stability of Markovian jump nonlinear systems. A numerical example is presented to illustrate the effectiveness of our results.
Distributed Consensus of Nonlinear Multi-Agent Systems on State-Controlled Switching Topologies
Directory of Open Access Journals (Sweden)
Kairui Chen
2016-01-01
Full Text Available This paper considers the consensus problem of nonlinear multi-agent systems under switching directed topologies. Specifically, the dynamics of each agent incorporates an intrinsic nonlinear term and the interaction topology may not contain a spanning tree at any time. By designing a state-controlled switching law, we show that the multi-agent system with the neighbor-based protocol can achieve consensus if the switching topologies jointly contain a spanning tree. Moreover, an easily manageable algebraic criterion is deduced to unravel the underlying mechanisms in reaching consensus. Finally, a numerical example is exploited to illustrate the effectiveness of the developed theoretical results.
Directory of Open Access Journals (Sweden)
Baiyu Liu
2014-01-01
Full Text Available We consider a class of coupled nonlinear Schrödinger systems with potential terms and combined power-type nonlinearities. We establish the existence of ground states, by using a variational method. As an application, some symmetry results for ground states of Schrödinger systems with harmonic potential terms are obtained.
A Compositional Sweep-Line State Space Exploration Method
DEFF Research Database (Denmark)
Kristensen, Lars Michael; Mailund, Thomas
2002-01-01
State space exploration is a main approach to verification of finite-state systems. The sweep-line method exploits a certain kind of progress present in many systems to reduce peak memory usage during state space exploration. We present a new sweep-line algorithm for a compositional setting where...... systems are composed of subsystems. The compositional setting makes it possible to divide subsystem progress measures into monotone and non-monotone progress measures to further reduce peak memory usage. We show that in a compositional setting, it is possible to automatically obtain a progress measure...
A one-step-ahead pseudo-DIC for comparison of Bayesian state-space models.
Millar, R B; McKechnie, S
2014-12-01
In the context of state-space modeling, conventional usage of the deviance information criterion (DIC) evaluates the ability of the model to predict an observation at time t given the underlying state at time t. Motivated by the failure of conventional DIC to clearly choose between competing multivariate nonlinear Bayesian state-space models for coho salmon population dynamics, and the computational challenge of alternatives, this work proposes a one-step-ahead DIC, DICp, where prediction is conditional on the state at the previous time point. Simulations revealed that DICp worked well for choosing between state-space models with different process or observation equations. In contrast, conventional DIC could be grossly misleading, with a strong preference for the wrong model. This can be explained by its failure to account for inflated estimates of process error arising from the model mis-specification. DICp is not based on a true conditional likelihood, but is shown to have interpretation as a pseudo-DIC in which the compensatory behavior of the inflated process errors is eliminated. It can be easily calculated using the DIC monitors within popular BUGS software when the process and observation equations are conjugate. The improved performance of DICp is demonstrated by application to the multi-stage modeling of coho salmon abundance in Lobster Creek, Oregon. © 2014, The International Biometric Society.
Excited-state dynamics and nonlinear optical response of Ge nanocrystals embedded in silica matrix
Razzari, Luca; Gnoli, Andrea; Righini, Marcofabio; Dâna, Aykutlu; Aydinli, Atilla
2006-05-01
We use a dedicated Z-scan setup, arranged to account for cumulative effects, to study the nonlinear optical response of Ge nanocrystals embedded in silica matrix. Samples are prepared with plasma-enchanced chemical-vapor deposition and post-thermal annealing. We measure a third-order nonlinear refraction coefficient of γ =1×10-16m2/W. The nonlinear absorption shows an intensity-independent coefficient of β =4×10-10m/W related to fast processes. In addition, we measure a second β component around 10-9m /W with a relaxation time of 300μs that rises linearly with the laser intensity. We associate its origin to the absorption of excited carriers from a surface-defect state with a long depopulation time.
On the existence of two-dimensional nonlinear steady states in plane Couette flow
Rincon, Francois
2007-01-01
The problem of two-dimensional steady nonlinear dynamics in plane Couette flow is revisited using homotopy from either plane Poiseuille flow or from plane Couette flow perturbed by a small symmetry-preserving identity operator. Our results show that it is not possible to obtain the nonlinear plane Couette flow solutions reported by Cherhabili and Ehrenstein [Eur. J. Mech. B/Fluids, 14, 667 (1995)] using their Poiseuille-Couette homotopy. We also demonstrate that the steady solutions obtained by Mehta and Healey [Phys. Fluids, 17, 4108 (2005)] for small symmetry-preserving perturbations are influenced by an artefact of the modified system of equations used in their paper. However, using a modified version of their model does not help to find plane Couette flow solution in the limit of vanishing symmetry-preserving perturbations either. The issue of the existence of two-dimensional nonlinear steady states in plane Couette flow remains unsettled.
Directory of Open Access Journals (Sweden)
Wen-Jer Chang
2014-01-01
Full Text Available For nonlinear discrete-time stochastic systems, a fuzzy controller design methodology is developed in this paper subject to state variance constraint and passivity constraint. According to fuzzy model based control technique, the nonlinear discrete-time stochastic systems considered in this paper are represented by the discrete-time Takagi-Sugeno fuzzy models with multiplicative noise. Employing Lyapunov stability theory, upper bound covariance control theory, and passivity theory, some sufficient conditions are derived to find parallel distributed compensation based fuzzy controllers. In order to solve these sufficient conditions, an iterative linear matrix inequality algorithm is applied based on the linear matrix inequality technique. Finally, the fuzzy stabilization problem for nonlinear discrete ship steering stochastic systems is investigated in the numerical example to illustrate the feasibility and validity of proposed fuzzy controller design method.
Non-linear conductivity of NbS{sub 3} in pressure induced metal state
Energy Technology Data Exchange (ETDEWEB)
Dizhur, Eugene; Kostyleva, Irina; Voronovskii, Anatoly [Institute for High Pressure Physics of RAS, Kaluzhskoe sh. 14, 142190 Troitsk (Russian Federation); Zaitzev-Zotov, Sergey [Institute of Radioengineering and Electronics of the RAS, Mokhovaya ul. 11, 125009 Moscow (Russian Federation)
2011-05-15
Temperature and voltage dependencies of conduction of a quasi-one-dimensional conductor NbS{sub 3} after its transition into a metallic state has been studied at pressures higher than 6 GPa. The differential resistance R = dV /dI measured at small biases (the electric field E below 2 V/cm) demonstrate a considerable growth upon cooling below 20 K accompanied by appearance of the non-linear conduction. Both the growth and nonlinear conduction disappear at E > 3 V/cm or when the temperature exceeds 40 K. A narrow dip visible only at much smaller fields E < 20 mV/cm is superimposed over that nonlinear background when cooling below 3.7 K. (copyright 2011 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)
Generalized Two-State Theory for an Atom Laser with Nonlinear Couplings
Institute of Scientific and Technical Information of China (English)
JING Hui; TIAN Li-Jun
2002-01-01
We present a generalized two-state theory to investigate the quantum dynamics and statistics of an atom laser with nonlinear couplings. The rotating wave approximate Hamiltonian of the system is proved to be analytically solvable. The fraction of output atoms is then showed to exhibit an interesting collapse and revival phenomenon with respect to the evolution time, a sign of nonlinear couplings. Several nonclassical effects, such as sub-Poissonian distribution, quadrature squeezing effects, second-order cross-correlation and accompanied violation of Cauchy-Schwartz inequality are also revealed for the output matter wave. The initial global phase of the trapped condensate, in weak nonlinear coupling limits, is found to exert an interesting impact on the quantum statistical properties of the propagating atom laser beam.
Energy Technology Data Exchange (ETDEWEB)
Russell, Steven J. [Los Alamos National Laboratory; Carlsten, Bruce E. [Los Alamos National Laboratory
2012-06-26
We will quickly go through the history of the non-linear transmission lines (NLTLs). We will describe how they work, how they are modeled and how they are designed. Note that the field of high power, NLTL microwave sources is still under development, so this is just a snap shot of their current state. Topics discussed are: (1) Introduction to solitons and the KdV equation; (2) The lumped element non-linear transmission line; (3) Solution of the KdV equation; (4) Non-linear transmission lines at microwave frequencies; (5) Numerical methods for NLTL analysis; (6) Unipolar versus bipolar input; (7) High power NLTL pioneers; (8) Resistive versus reactive load; (9) Non-lineaer dielectrics; and (10) Effect of losses.
Quantum-dot Semiconductor Optical Amplifiers in State Space Model
Institute of Scientific and Technical Information of China (English)
Hussein Taleb; Kambiz Abedi; Saeed Golmohammadi
2013-01-01
A state space model (SSM) is derived for quantum-dot semiconductor optical amplifiers (QD-SOAs).Rate equations of QD-SOA are formulated in the form of state update equations,where average occupation probabilities along QD-SOA cavity are considered as state variables of the system.Simulations show that SSM calculates QD-SOA's static and dynamic characteristics with high accuracy.
Real-space renormalization yields finitely correlated states
Barthel, Thomas; Eisert, Jens
2010-01-01
Real-space renormalization approaches for quantum lattice systems generate certain hierarchical classes of states that are subsumed by the multi-scale entanglement renormalization ansatz (MERA). It is shown that, with the exception of one dimension, MERA states can be efficiently mapped to finitely-correlated states, also known as projected entangled pair states (PEPS), with a bond dimension independent of the system size. Hence, MERA states form an efficiently contractible class of PEPS and obey an area law for the entanglement entropy. It is shown further that there exist other efficiently contractible schemes violating the area law.
Directory of Open Access Journals (Sweden)
Gao Dexin
2012-10-01
Full Text Available This paper concentrates on the solution of state feedback exact linearization zero steady-state error optimal control problem for nonlinear systems affected by external disturbances. Firstly, the nonlinear system model with external disturbances is converted to quasi-linear system model by differential homeomorphism. Using Internal Model Optional Control (IMOC, the disturbances compensator is designed, which exactly offset the impact of external disturbances on the system. Taking the system and the disturbances compensator in series, a new augmented system is obtained. Then the zero steady-state error optimal control problem is transformed into the optimal regulator design problem of an augmented system, and the optimal static error feedback control law is designed according to the different quadratic performance index. At last, the simulation results show the effectiveness of the method.
Short-lived two-soliton bound states in weakly perturbed nonlinear Schrodinger equation.
Dmitriev, Sergey V.; Shigenari, Takeshi
2002-06-01
Resonant soliton collisions in the weakly discrete nonlinear Schrodinger equation are studied numerically. The fractal nature of the soliton scattering, described in our previous works, is investigated in detail. We demonstrate that the fractal scattering pattern is related to the existence of the short-lived two-soliton bound states. The bound state can be regarded as a two-soliton quasiparticle of a new type, different from the breather. We establish that the probability P of a bound state with the lifetime L follows the law P approximately L(-3). In the frame of a simple two-particle model, we derive the nonlinear map, which generates the fractal pattern similar to that observed in the numerical study of soliton collisions. (c) 2002 American Institute of Physics.
State-Vector Space and Canonical Coherent States in Noncommutative Plane
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
The structure of the state-vector space of identical bosons in noncommutative spaces is investigated. To maintain Bose-Einstein statistics the commutation relations of phase space variables should simultaneously include coordinate-coordinate non-commutativity and momentum-momentum non-commutativity, which leads to a kind of de-formed Heisenberg-Weyl algebra. Although there is no ordinary number representation in this state-vector space, several set of orthogonal and complete state-vectors can be derived which are common eigenvectors of corresponding pairs of commuting Hermitian operators. As a simple application of this state-vector space, an explicit form of two-dimensional canonical coherent state is constructed and its properties are discussed.
Prakash, J; Srinivasan, K
2009-07-01
In this paper, the authors have represented the nonlinear system as a family of local linear state space models, local PID controllers have been designed on the basis of linear models, and the weighted sum of the output from the local PID controllers (Nonlinear PID controller) has been used to control the nonlinear process. Further, Nonlinear Model Predictive Controller using the family of local linear state space models (F-NMPC) has been developed. The effectiveness of the proposed control schemes has been demonstrated on a CSTR process, which exhibits dynamic nonlinearity.
Bethe-Salpeter bound-state structure in Minkowski space
Gutierrez, C; Frederico, T; Salmè, G; Viviani, M; Tomio, Lauro
2016-01-01
The quantitative investigation of the scalar Bethe-Salpeter equation in Minkowski space, within the ladder-approximation framework, is extended to include the excited states. This study has been carried out for an interacting system composed by two massive bosons exchanging a massive scalar, by adopting (i) the Nakanishi integral representation of the Bethe-Salpeter amplitude, and (ii) the formally exact projection onto the null plane. Our analysis, on one hand, confirms the reliability of the method already applied to the ground state and, on the other one, extends the investigation from the valence distribution in momentum space to the corresponding quantity in the impact-parameter space, pointing out some relevant features, like (i) the equivalence between Minkowski and Euclidean transverse-momentum amplitudes, and (ii) the leading exponential fall-off of the valence wave function in the impact-parameter space.
Ongoing Space Nuclear Systems Development in the United States
Energy Technology Data Exchange (ETDEWEB)
S. Bragg-Sitton; J. Werner; S. Johnson; Michael G. Houts; Donald T. Palac; Lee S. Mason; David I. Poston; A. Lou Qualls
2011-10-01
Reliable, long-life power systems are required for ambitious space exploration missions. Nuclear power and propulsion options can enable a bold, new set of missions and introduce propulsion capabilities to achieve access to science destinations that are not possible with more conventional systems. Space nuclear power options can be divided into three main categories: radioisotope power for heating or low power applications; fission power systems for non-terrestrial surface application or for spacecraft power; and fission power systems for electric propulsion or direct thermal propulsion. Each of these areas has been investigated in the United States since the 1950s, achieving various stages of development. While some nuclear systems have achieved flight deployment, others continue to be researched today. This paper will provide a brief overview of historical space nuclear programs in the U.S. and will provide a summary of the ongoing space nuclear systems research, development, and deployment in the United States.
Bethe–Salpeter bound-state structure in Minkowski space
Energy Technology Data Exchange (ETDEWEB)
Gutierrez, C. [Instituto de Física Teórica, Universidade Estadual Paulista, 01156-970 São Paulo, SP (Brazil); Gigante, V.; Frederico, T. [Instituto Tecnológico de Aeronáutica, DCTA, 12.228-900 São José dos Campos, SP (Brazil); Salmè, G. [Istituto Nazionale di Fisica Nucleare, Sezione di Roma, P.le A. Moro 2, 00185 Roma (Italy); Viviani, M. [Istituto Nazionale di Fisica Nucleare, Sezione di Pisa, Largo Pontecorvo 3, 56100 Pisa (Italy); Tomio, Lauro, E-mail: tomio@ift.unesp.br [Instituto de Física Teórica, Universidade Estadual Paulista, 01156-970 São Paulo, SP (Brazil); Instituto Tecnológico de Aeronáutica, DCTA, 12.228-900 São José dos Campos, SP (Brazil)
2016-08-10
The quantitative investigation of the scalar Bethe–Salpeter equation in Minkowski space, within the ladder-approximation framework, is extended to include the excited states. This study has been carried out for an interacting system composed by two massive bosons exchanging a massive scalar, by adopting (i) the Nakanishi integral representation of the Bethe–Salpeter amplitude, and (ii) the formally exact projection onto the null plane. Our analysis, on one hand, confirms the reliability of the method already applied to the ground state and, on the other one, extends the investigation from the valence distribution in momentum space to the corresponding quantity in the impact-parameter space, pointing out some relevant features, like (i) the equivalence between Minkowski and Euclidean transverse-momentum amplitudes, and (ii) the leading exponential fall-off of the valence wave function in the impact-parameter space.
The structures of state space concerning Quantum Dynamical Semigroups
Baumgartner, Bernhard
2011-01-01
Each semigroup describing the time evolution of an open quantum system on a finite dimensional Hilbert space is related to a special structure of this space. It is shown how the space can be decomposed into subspaces: One is related to decay, orthogonal subspaces support the stationary states. Specialities where the complete positivity of evolutions is actually needed for analysis, mainly for evolution of coherence, are highlighted. Decompositions are done the same way for evolutions in discrete as in continuous time, but evolutions may show differences, only for discrete semigroups there may appear cases of sudden decay and of perpetual oscillation. Concluding the analysis we identify the relation of the state space structure to the processes of Decay, Decoherence, Dissipation and Dephasing.
Hendi, S H; Panah, B Eslam
2016-01-01
In this paper, we take into account the black hole solutions of Einstein gravity in the presence of logarithmic and exponential forms of nonlinear electrodynamics. At first, we consider the cosmological constant as a dynamic pressure to study the analogy of the black hole solutions with the Van der Waals liquid--gas system in the extended phase space. We plot $P-V$, $T-V$ and $G-T$ diagrams and investigate the phase transition of adS black holes in the canonical ensemble. Moreover, we discuss about the effect of nonlinear electrodynamics on the the critical values and the universal ratio $P_{c}v_{c}/T_{c}$.
Space Sciences Education and Outreach Project of Moscow State University
Krasotkin, S.
2006-11-01
sergekras@mail.ru The space sciences education and outreach project was initiated at Moscow State University in order to incorporate modern space research into the curriculum popularize the basics of space physics, and enhance public interest in space exploration. On 20 January 2005 the first Russian University Satellite “Universitetskiy-Tatyana” was launched into circular polar orbit (inclination 83 deg., altitude 940-980 km). The onboard scientific complex “Tatyana“, as well as the mission control and information receiving centre, was designed and developed at Moscow State University. The scientific programme of the mission includes measurements of space radiation in different energy channels and Earth UV luminosity and lightning. The current education programme consists of basic multimedia lectures “Life of the Earth in the Solar Atmosphere” and computerized practice exercises “Space Practice” (based on the quasi-real-time data obtained from “Universitetskiy-Tatyana” satellite and other Internet resources). A multimedia lectures LIFE OF EARTH IN THE SOLAR ATMOSPHERE containing the basic information and demonstrations of heliophysics (including Sun structure and solar activity, heliosphere and geophysics, solar-terrestrial connections and solar influence on the Earth’s life) was created for upper high-school and junior university students. For the upper-university students there a dozen special computerized hands-on exercises were created based on the experimental quasi-real-time data obtained from our satellites. Students specializing in space physics from a few Russian universities are involved in scientific work. Educational materials focus on upper high school, middle university and special level for space physics students. Moscow State University is now extending its space science education programme by creating multimedia lectures on remote sensing, space factors and materials study, satellite design and development, etc. The space
Directory of Open Access Journals (Sweden)
Il Young Song
2015-01-01
Full Text Available This paper focuses on estimation of a nonlinear function of state vector (NFS in discrete-time linear systems with time-delays and model uncertainties. The NFS represents a multivariate nonlinear function of state variables, which can indicate useful information of a target system for control. The optimal nonlinear estimator of an NFS (in mean square sense represents a function of the receding horizon estimate and its error covariance. The proposed receding horizon filter represents the standard Kalman filter with time-delays and special initial horizon conditions described by the Lyapunov-like equations. In general case to calculate an optimal estimator of an NFS we propose using the unscented transformation. Important class of polynomial NFS is considered in detail. In the case of polynomial NFS an optimal estimator has a closed-form computational procedure. The subsequent application of the proposed receding horizon filter and nonlinear estimator to a linear stochastic system with time-delays and uncertainties demonstrates their effectiveness.
Optical Characterization of Deep-Space Object Rotation States
2014-09-01
Optical Characterization of Deep-Space Object Rotation States Doyle Hall 1 and Paul Kervin 2 1 Boeing LTS, Kihei, Maui, HI and Colorado Springs, CO...0646, OPS-14-6494) Cleared for Public Release (Release # 377ABW-2014-0646, OPS-14-6494) 3. Wallach, B., Somers, P. and Scott , R., “Determination of...Wallace, B., Somers, P., and Scott , R. L., “Determination of Spin Axis Orientation of Geosynchronous Objects Using Space-Based Sensors: An Initial
Iwai, Akinori; Nakamura, Yoshihiro; Sakai, Osamu
2016-09-01
We clarify the relation between second harmonic wave (SH wave) and plasma generation in various experimental conditions by detecting properties of propagating electromagnetic waves (EM waves). Plasma has a nonlinear reaction against EM wave, generating harmonic waves which depends on electron density ne. In the case with increased ne, EM wave comes to be prevented from going into plasma with negative permittivity ɛp. Double-split-ring resonators (DSRRs), one of metamaterials, make permeability μD negative. We have shown that EM wave being volume wave can propagate into the combination of overdense plasma and DSRRs because of real negative value refractive index N. In our previous paper, we have confirmed enhanced SH wave (4.9 GHz) generation in the composite with 2.45-GHz input. In this report, we show the dependence of the SH wave emission with plasma generation on plasma parameters and gas conditions of plasma. Furthermore, we show the phase change with N variation of the composite space in the case with various input power as the proof of the negative index state.
State Space Exploration of RT Systems in the Cloud
Bellettini, Carlo; Capra, Lorenzo; Monga, Mattia
2012-01-01
The growing availability of distributed and cloud computing frameworks make it possible to face complex computational problems in a more effective and convenient way. A notable example is state-space exploration of discrete-event systems specified in a formal way. The exponential complexity of this task is a major limitation to the usage of consolidated analysis techniques and tools. We present and compare two different approaches to state-space explosion, relying on distributed and cloud frameworks, respectively. These approaches were designed and implemented following the same computational schema, a sort of map & fold. They are applied on symbolic state-space exploration of real-time systems specified by (a timed extension of) Petri Nets, by readapting a sequential algorithm implemented as a command-line Java tool. The outcome of several tests performed on a benchmarking specification are presented, thus showing the convenience of cloud approaches.
Neuromorphic Continuous-Time State Space Pole Placement Adaptive Control
Institute of Scientific and Technical Information of China (English)
卢钊; 孙明伟
2003-01-01
A neuromorphic continuous-time state space pole assignment adaptive controller is proposed, which is particularly appropriate for controlling a large-scale time-variant state-space model due to the parallely distributed nature of neurocomputing. In our approach, Hopfield neural network is exploited to identify the parameters of a continuous-time state-space model, and a dedicated recurrent neural network is designed to compute pole placement feedback control law in real time. Thus the identification and the control computation are incorporated in the closed-loop, adaptive, real-time control system. The merit of this approach is that the neural networks converge to their solutions very quickly and simultaneously.
Multivariate time series with linear state space structure
Gómez, Víctor
2016-01-01
This book presents a comprehensive study of multivariate time series with linear state space structure. The emphasis is put on both the clarity of the theoretical concepts and on efficient algorithms for implementing the theory. In particular, it investigates the relationship between VARMA and state space models, including canonical forms. It also highlights the relationship between Wiener-Kolmogorov and Kalman filtering both with an infinite and a finite sample. The strength of the book also lies in the numerous algorithms included for state space models that take advantage of the recursive nature of the models. Many of these algorithms can be made robust, fast, reliable and efficient. The book is accompanied by a MATLAB package called SSMMATLAB and a webpage presenting implemented algorithms with many examples and case studies. Though it lays a solid theoretical foundation, the book also focuses on practical application, and includes exercises in each chapter. It is intended for researchers and students wor...
Energy Technology Data Exchange (ETDEWEB)
Kobayashi, Yasuaki [Meme Media Laboratory, Hokkaido University, Sapporo 060-0813 (Japan); Kori, Hiroshi [Division of Advanced Sciences, Ochadai Academic Production, Ochanomizu University, Tokyo 112-8610 (Japan)], E-mail: kobayashi@nsc.es.hokudai.ac.jp, E-mail: kori.hiroshi@ocha.ac.jp
2009-03-15
A theoretical framework is developed for the precise control of spatial patterns in oscillatory media using nonlinear global feedback, where a proper form of the feedback function corresponding to a specific pattern is predicted through the analysis of a phase diffusion equation with global coupling. In particular, feedback functions that generate the following spatial patterns are analytically given: (i) 2-cluster states with an arbitrary population ratio, (ii) equally populated multi-cluster states and (iii) a desynchronized state. Our method is demonstrated numerically by using the Brusselator model in the oscillatory regime. Experimental realization is also discussed.
Investigating Mesoscopic Non-linear Series Circuit with the Coherent Thermo State Representation
Wang, Xiu-Xia
2017-03-01
For the first time we considered the quantum effects of mesoscopic non-linear series circuit with the coherent thermo state representation | τ rangle . After introducing the representation |τ rangle , we derived the expression of the density matrix ρ and find that | ρ rangle T presents Gauss type with the representation | τ rangle . In addition, we derived the Wigner function and calculated the quantum fluctuation in the thermo vacuum state |0( β)>. It is shown that the circuit has the zero current fluctuation because the diode has the reverse saturation current, and the temperature affects the Wigner function of the circuit in thermo vacuum state deeply.
Static black holes in equilibrium with matter: nonlinear equation of state
Zaslavskii, Oleg B
2010-01-01
We consider a spherically symmetric black hole in equilibrium with surrounding classical matter that is characterized by a nonlinear dependence of the radial pressure p_{r} on the density {\\rho}. We examine under which requirements such an equilibrium is possible. It is shown that if the radial and transverse pressures are equal (Pascal perfect fluid), equation of state should be approximately linear near the horizon. The corresponding restriction on ((dp_{r})/(d{\\rho})) is a direct generalization of the result, previously found for an exactly linear equation of state. In the anisotropic case there is no restriction on equation of state but the horizon should be simple (nondegenerate).
Pre-Trained Neural Networks used for Non-Linear State Estimation
DEFF Research Database (Denmark)
Bayramoglu, Enis; Andersen, Nils Axel; Ravn, Ole
2011-01-01
The paper focuses on nonlinear state estimation assuming non-Gaussian distributions of the states and the disturbances. The posterior distribution and the aposteriori distribution is described by a chosen family of paramtric distributions. The state transformation then results in a transformation...... of the paramters in the distribution. This transformation is approximated by a neural network using offline training, which is based on monte carlo sampling. In the paper, there will also be presented a method to construct a flexible distributions well suited for covering the effect of the non...
Generation of squeezed-state superpositions via time-dependent Kerr nonlinearities
León-Montiel, R de J
2015-01-01
We put forward an experimental scheme for direct generation of optical squeezed coherent-state superpositions. The proposed setup makes use of an optical cavity, filled with a nonlinear Kerr medium, whose frequency is allowed to change during time evolution. By exactly solving the corresponding time-dependent anharmonic-oscillator Hamiltonian, we demonstrate that squeezed-state superpositions can be generated in an optical cavity. Furthermore, we show that the squeezing degree of the produced states can be tuned by properly controlling the frequency shift of the cavity, a feature that could be useful in many quantum information protocols, such as quantum teleportation and quantum computing.
Cosmic flows and the expansion of the Local Universe from nonlinear phase-space reconstructions
Hess, Steffen
2014-01-01
We investigate the impact of cosmic flows and density perturbations on Hubble constant $H_0$ measurements using nonlinear phase-space reconstructions of the Local Universe (LU). We rely on a set of 25 N-body simulations which are constrained to resemble the LU within distances of about 90 Mpc/h. These have been randomly extended up to volumes enclosing distances of 360 Mpc/h with augmented Lagrangian perturbation theory (=750 simulations), accounting in this way for effects from from larger scales ($\\sigma_{\\rm large}=134$ km/s). We report on Local Group (LG) speed reconstructions, which are compatible with those derived from the CMB-dipole: $|v_{\\rm LG}|=685\\pm137$ km/s. The direction $(l,b)=(260.5\\pm 13.3,39.1\\pm 10.4)^\\circ$ is found to be compatible with observations. We use the CMB-dipole information to estimate the missing large scale bulk flow component, indicating that we miss a closely perpendicular flow with a magnitude corresponding to $1.4 \\sigma_{\\rm large}$. Considering this, our bulk flow estim...
Set point control in the state space setting
DEFF Research Database (Denmark)
Poulsen, Niels Kjølstad
. The focus is in this report related to the problem of handling a set point or a constant reference in a state space setting. In principle just about any (state space control) design methodology may be applied. Here the presentation is based on LQ design, but other types such as poleplacement can be applied......This report is intented as a supplement or an extension to the material used in connection to or after the courses Stochastic Adaptive Control (02421) and Static and Dynamic Optimization (02711) given at the Department of Informatics and Mathematical Modelling, The Technical University of Denmark...
Transformation of state space for two-parameter Markov processes
Institute of Scientific and Technical Information of China (English)
周健伟
1996-01-01
Let X=(X) be a two-parameter *-Markov process with a transition function (p1, p2, p), where X, takes values in the state space (Er,), T=[0,)2. For each r T, let f, be a measurable transformation of (E,) into the state space (E’r, ). Set Y,=f,(X,), r T. A sufficient condition is given for the process Y=(Yr) still to be a two-parameter *-Markov process with a transition function in terms of transition function (p1, p2, p) and fr. For *-Markov families of two-parameter processes with a transition function, a similar problem is also discussed.
Interaction Network, State Space and Control in Social Dynamics
Aydogdu, Aylin; McQuade, Sean; Piccoli, Benedetto; Duteil, Nastassia Pouradier; Rossi, Francesco; Trélat, Emmanuel
2016-01-01
In the present chapter we study the emergence of global patterns in large groups in first and second-order multi-agent systems, focusing on two ingredients that influence the dynamics: the interaction network and the state space. The state space determines the types of equilibrium that can be reached by the system. Meanwhile, convergence to specific equilibria depends on the connectivity of the interaction network and on the interaction potential. When the system does not satisfy the necessary conditions for convergence to the desired equilibrium, control can be exerted, both on finite-dimensional systems and on their mean-field limit.
Optimal State-Space Reduction for Pedigree Hidden Markov Models
Kirkpatrick, Bonnie
2012-01-01
To analyze whole-genome genetic data inherited in families, the likelihood is typically obtained from a Hidden Markov Model (HMM) having a state space of 2^n hidden states where n is the number of meioses or edges in the pedigree. There have been several attempts to speed up this calculation by reducing the state-space of the HMM. One of these methods has been automated in a calculation that is more efficient than the naive HMM calculation; however, that method treats a special case and the efficiency gain is available for only those rare pedigrees containing long chains of single-child lineages. The other existing state-space reduction method treats the general case, but the existing algorithm has super-exponential running time. We present three formulations of the state-space reduction problem, two dealing with groups and one with partitions. One of these problems, the maximum isometry group problem was discussed in detail by Browning and Browning. We show that for pedigrees, all three of these problems hav...
Liu, Qian; OuYang, Liangfei; Liang, Heng; Li, Nan; Geng, Xindu
2012-06-01
A novel thermodynamic state recursion (TSR) method, which is based on nonequilibrium thermodynamic path described by the Lagrangian-Eulerian representation, is presented to simulate the whole chromatographic process of frontal analysis using the spatial distribution of solute bands in time series like as a series of images. TSR differs from the current numerical methods using the partial differential equations in Eulerian representation. The novel method is used to simulate the nonideal, nonlinear hydrophobic interaction chromatography (HIC) processes of lysozyme and myoglobin under the discrete complex boundary conditions. The results show that the simulated breakthrough curves agree well with the experimental ones. The apparent diffusion coefficient and the Langmuir isotherm parameters of the two proteins in HIC are obtained by the state recursion inverse method. Due to its the time domain and Markov characteristics, TSR is applicable to the design and online control of the nonlinear multicolumn chromatographic systems.
Adaptive Neural Control of Uncertain MIMO Nonlinear Systems With State and Input Constraints.
Chen, Ziting; Li, Zhijun; Chen, C L Philip
2016-03-17
An adaptive neural control strategy for multiple input multiple output nonlinear systems with various constraints is presented in this paper. To deal with the nonsymmetric input nonlinearity and the constrained states, the proposed adaptive neural control is combined with the backstepping method, radial basis function neural network, barrier Lyapunov function (BLF), and disturbance observer. By ensuring the boundedness of the BLF of the closed-loop system, it is demonstrated that the output tracking is achieved with all states remaining in the constraint sets and the general assumption on nonsingularity of unknown control coefficient matrices has been eliminated. The constructed adaptive neural control has been rigorously proved that it can guarantee the semiglobally uniformly ultimate boundedness of all signals in the closed-loop system. Finally, the simulation studies on a 2-DOF robotic manipulator system indicate that the designed adaptive control is effective.
STEADY-STATE RESPONSES AND THEIR STABILITY OF NONLINEAR VIBRATION OF AN AXIALLY ACCELERATING STRING
Institute of Scientific and Technical Information of China (English)
吴俊; 陈立群
2004-01-01
The steady-state transverse vibration of an axially moving string with geometric nonlinearity was investigated. The transport speed was assumed to be a constant mean speed with small harmonic variations. The nonlinear partial-differential equation that governs the transverse vibration of the string was derived by use of the Hamilton principle. The method of multiple scales was applied directly to the equation. The solvability condition of eliminating the secular terms was established. Closed form solutions for the amplitude and the existence conditions of nontrivial steady-state response of the two-to-one parametric resonance were obtained. Some numerical examples showing effects of the mean transport speed, the amplitude and the frequency of speed variation were presented. The Liapunov linearized stability theory was employed to derive the instability conditions of the trivial solution and the nontrivial solutions for the two-to-one parametric resonance. Some numerical examples highlighting influences of the related parameters on the instability conditions were presented.
Robust control of a class of non-affine nonlinear systems by state and output feedback
Institute of Scientific and Technical Information of China (English)
陈贞丰; 章云
2014-01-01
Robust control design is presented for a general class of uncertain non-affine nonlinear systems. The design employs feedback linearization, coupled with two high-gain observers:the first to estimate the feedback linearization error based on the full state information and the second to estimate the unmeasured states of the system when only the system output is available for feedback. All the signals in the closed loop are guaranteed to be uniformly ultimately bounded (UUB) and the output of the system is proven to converge to a small neighborhood of the origin. The proposed approach not only handles the difficulty in controlling non-affine nonlinear systems but also simplifies the stability analysis of the closed loop due to its linear control structure. Simulation results show the effectiveness of the approach.
Nonlinear Sensing With Collective States of Ultracold Atoms in Optical Lattices
2015-04-02
decimation algorithm , a method that takes into account quantum correlations. B.1. In collaboration with D. Blume and X.Y. Yin at Washington State...Office P.O. Box 12211 Research Triangle Park, NC 27709-2211 Nonlinear quantum sensing, quantum metrology, ultracold atoms, optical lattices REPORT...with applications to interaction-based quantum metrology, Physical Review A, (10 2014): 0. doi: 10.1103/PhysRevA.90.041602 Khan W Mahmud, Lei Jiang
Interconnected delay and state observer for nonlinear systems with time-varying input delay
Léchappé, V; Moulay, Emmanuel; Plestan, F; Glumineau, A.
2016-01-01
International audience; This work presents a general framework to estimate both state and delay thanks to two interconnected observers. This scheme can be applied to a large class of nonlinear systems with time-varying input delay. In order to illustrate this approach, a new delay observer based on an optimization technique is proposed. Theoretical results are illustrated and compared with existing works in simulation.
Rabi oscillations of two-photon states in nonlinear optical resonators
Sherkunov, Y.; Whittaker, David M.; Fal'ko, Vladimir
2016-02-01
We demonstrate that four-wave mixing processes in high-quality nonlinear resonators can lead to Rabi-like oscillations in photon occupation numbers and second-order correlation functions, being a characteristic feature of the presence of entangled photon pairs in the optical signal. In the case of a system driven by a continuous coherent pump, the oscillations occur in the transient regime. We show that driving the system with pulsed coherent pumping would generate strongly antibunched photon states.
Adaptive Stabilization for a Class of Dynamical Systems with Nonlinear Delayed State Perturbations
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
The problem of adaptive stabilization for a class of systems with nonlinear delayed state perturbations is considered. The bound of the perturbations is assumed to be unknown, by using the adaptive control method, an adaptive controller is designed. Based on the Lyapunov- Karasovskii functional, it is shown that the dynamical system can be stabilized by the adaptive controller. The effectiveness of the proposed controller is demonstrated by some simulations.
Solution of Macroscopic State Equations of Blume-Capel Model Using Nonlinear Dynamics Concepts
Directory of Open Access Journals (Sweden)
Asaf Tolga Ülgen
2013-01-01
Full Text Available The macroscopic state equations of Blume-Capel Model were solved by using the concepts of nonlinear dynamics. Negative and positive exchange constant values yield bifurcations of pitchfork and subcritical flip types, respectively. Hence, we obtained bifurcations corresponding to second order phase transitions. The critical values of parameters were calculated from the neutral stability condition and the 3-dimensional phase diagram was plotted.
Semiclassical Approximations in Phase Space with Coherent States
Baranger, Michel; de Aguiar, Marcus A. M.; Keck, Frank; Korsch, Hans-Jürgen; Schellhaaß, Bernd
2001-01-01
We present a complete derivation of the semiclassical limit of the coherent state propagator in one dimension, starting from path integrals in phase space. We show that the arbitrariness in the path integral representation, which follows from the overcompleteness of the coherent states, results in many different semiclassical limits. We explicitly derive two possible semiclassical formulae for the propagator, we suggest a third one, and we discuss their relationships. We also derive an initia...
Soft Sensor for Inputs and Parameters Using Nonlinear Singular State Observer in Chemical Processes
Institute of Scientific and Technical Information of China (English)
许锋; 汪晔晔; 罗雄麟
2013-01-01
Chemical processes are usually nonlinear singular systems. In this study, a soft sensor using nonlinear singular state observer is established for unknown inputs and uncertain model parameters in chemical processes, which are augmented as state variables. Based on the observability of the singular system, this paper presents a simplified observability criterion under certain conditions for unknown inputs and uncertain model parameters. When the observability is satisfied, the unknown inputs and the uncertain model parameters are estimated online by the soft sensor using augmented nonlinear singular state observer. The riser reactor of fluid catalytic cracking unit is used as an example for analysis and simulation. With the catalyst circulation rate as the only unknown input without model error, one temperature sensor at the riser reactor outlet will ensure the correct estimation for the catalyst cir-culation rate. However, when uncertain model parameters also exist, additional temperature sensors must be used to ensure correct estimation for unknown inputs and uncertain model parameters of chemical processes.
Bayesian state space models for inferring and predicting temporal gene expression profiles.
Liang, Yulan; Kelemen, Arpad
2007-12-01
Prediction of gene dynamic behavior is a challenging and important problem in genomic research while estimating the temporal correlations and non-stationarity are the keys in this process. Unfortunately, most existing techniques used for the inclusion of the temporal correlations treat the time course as evenly distributed time intervals and use stationary models with time-invariant settings. This is an assumption that is often violated in microarray time course data since the time course expression data are at unequal time points, where the difference in sampling times varies from minutes to days. Furthermore, the unevenly spaced short time courses with sudden changes make the prediction of genetic dynamics difficult. In this paper, we develop two types of Bayesian state space models to tackle this challenge for inferring and predicting the gene expression profiles associated with diseases. In the univariate time-varying Bayesian state space models we treat both the stochastic transition matrix and the observation matrix time-variant with linear setting and point out that this can easily be extended to nonlinear setting. In the multivariate Bayesian state space model we include temporal correlation structures in the covariance matrix estimations. In both models, the unevenly spaced short time courses with unseen time points are treated as hidden state variables. Bayesian approaches with various prior and hyper-prior models with MCMC algorithms are used to estimate the model parameters and hidden variables. We apply our models to multiple tissue polygenetic affymetrix data sets. Results show that the predictions of the genomic dynamic behavior can be well captured by the proposed models. (c) 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Noor, A. K.
1983-01-01
Advances in continuum modeling, progress in reduction methods, and analysis and modeling needs for large space structures are covered with specific attention given to repetitive lattice trusses. As far as continuum modeling is concerned, an effective and verified analysis capability exists for linear thermoelastic stress, birfurcation buckling, and free vibration problems of repetitive lattices. However, application of continuum modeling to nonlinear analysis needs more development. Reduction methods are very effective for bifurcation buckling and static (steady-state) nonlinear analysis. However, more work is needed to realize their full potential for nonlinear dynamic and time-dependent problems. As far as analysis and modeling needs are concerned, three areas are identified: loads determination, modeling and nonclassical behavior characteristics, and computational algorithms. The impact of new advances in computer hardware, software, integrated analysis, CAD/CAM stems, and materials technology is also discussed.
A state-space algorithm for the spectral factorization
Kraffer, F.; Kwakernaak, H.
1997-01-01
This paper presents an algorithm for the spectral factorization of a para-Hermitian polynomial matrix. The algorithm is based on polynomial matrix to state space and vice versa conversions, and avoids elementary polynomial operations in computations; It relies on well-proven methods of numerical lin
Hybrid state-space time integration of rotating beams
DEFF Research Database (Denmark)
Krenk, Steen; Nielsen, Martin Bjerre
2012-01-01
An efficient time integration algorithm for the dynamic equations of flexible beams in a rotating frame of reference is presented. The equations of motion are formulated in a hybrid state-space format in terms of local displacements and local components of the absolute velocity. With inspiration ...
Fast Filtering and Smoothing for Multivariate State Space Models
Koopman, S.J.M.; Durbin, J.
1998-01-01
This paper gives a new approach to diffuse filtering and smoothing for multivariate state space models. The standard approach treats the observations as vectors while our approach treats each element of the observational vector individually. This strategy leads to computationally efficient methods f
Parameter redundancy in discrete state-space and integrated models.
Cole, Diana J; McCrea, Rachel S
2016-09-01
Discrete state-space models are used in ecology to describe the dynamics of wild animal populations, with parameters, such as the probability of survival, being of ecological interest. For a particular parametrization of a model it is not always clear which parameters can be estimated. This inability to estimate all parameters is known as parameter redundancy or a model is described as nonidentifiable. In this paper we develop methods that can be used to detect parameter redundancy in discrete state-space models. An exhaustive summary is a combination of parameters that fully specify a model. To use general methods for detecting parameter redundancy a suitable exhaustive summary is required. This paper proposes two methods for the derivation of an exhaustive summary for discrete state-space models using discrete analogues of methods for continuous state-space models. We also demonstrate that combining multiple data sets, through the use of an integrated population model, may result in a model in which all parameters are estimable, even though models fitted to the separate data sets may be parameter redundant. © 2016 The Author. Biometrical Journal published by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Projective Limits of State Spaces IV. Fractal Label Sets
Lanéry, Suzanne
2015-01-01
Instead of formulating the state space of a quantum field theory over one big Hilbert space, it has been proposed by Kijowski [Kijowski 1977] to represent quantum states as projective families of density matrices over a collection of smaller, simpler Hilbert spaces. One can thus bypass the need to select a vacuum state for the theory, and still be provided with an explicit and constructive description of the quantum state space, at least as long as the label set indexing the projective structure is countable. Because uncountable label sets are much less practical in this context, we develop in the present article a general procedure to trim an originally uncountable label set down to countable cardinality. In particular, we investigate how to perform this tightening of the label set in a way that preserves both the physical content of the algebra of observables and its symmetries. This work is notably motivated by applications to the holonomy-flux algebra underlying Loop Quantum Gravity. Building on earlier w...
State Space Reduction of Linear Processes Using Control Flow Reconstruction
Pol, van de Jaco; Timmer, Mark; Liu, Z.; Ravn, A.P.
2009-01-01
We present a new method for fighting the state space explosion of process algebraic specifications, by performing static analysis on an intermediate format: linear process equations (LPEs). Our method consists of two steps: (1) we reconstruct the LPE's control flow, detecting control flow parameters
State Space Reduction of Linear Processes using Control Flow Reconstruction
Pol, van de Jaco; Timmer, Mark
2009-01-01
We present a new method for fighting the state space explosion of process algebraic specifications, by performing static analysis on an intermediate format: linear process equations (LPEs). Our method consists of two steps: (1) we reconstruct the LPE's control flow, detecting control flow parameters
An Embeddable Virtual Machine for State Space Generation
Weber, M.; Bosnacki, D.; Edelkamp, S.
2007-01-01
The semantics of modelling languages are not always specified in a precise and formal way, and their rather complex underlying models make it a non-trivial exercise to reuse them in newly developed tools. We report on experiments with a virtual machine-based approach for state space generation. The
Nonlinear ion-acoustic solitary waves with warm ions and non-Maxwellian electrons in space plasmas
Hussain Shah, Khalid; Qureshi, Nouman
2017-04-01
Electrons velocity distributions are often observed with non-Maxwellian features such flat tops at low energies and/or superthermal tails at high energies from different regions of near Earth plasmas such as Earth's bow shock, auroral zone and magnetosphere by numerous satellites. Such non-Maxwellian distributions are well modelled by generalized (r,q) distribution or Cairns distribution. Solitons are nonlinear solitary structures and are integral part of space plasmas. In this paper, we present a fluid model containing Cairns (r,q) distributed non-Maxwellian electrons and derive the Sagdeev potential for fully nonlinear fluid equations. We found that compressive solitons can be developed in such a plasma. The results from our model can be used to interpret solitary structures in space plasmas when electrons are obeying the non-Maxwellian flat tops along with the high energy tails.
A Neural-Network-Based Nonlinear Adaptive State-Observer for Pressurized Water Reactors
Directory of Open Access Journals (Sweden)
Zhe Dong
2013-10-01
Full Text Available Although there have been some severe nuclear accidents such as Three Mile Island (USA, Chernobyl (Ukraine and Fukushima (Japan, nuclear fission energy is still a source of clean energy that can substitute for fossil fuels in a centralized way and in a great amount with commercial availability and economic competitiveness. Since the pressurized water reactor (PWR is the most widely used nuclear fission reactor, its safe, stable and efficient operation is meaningful to the current rebirth of the nuclear fission energy industry. Power-level regulation is an important technique which can deeply affect the operation stability and efficiency of PWRs. Compared with the classical power-level controllers, the advanced power-level regulators could strengthen both the closed-loop stability and control performance by feeding back the internal state-variables. However, not all of the internal state variables of a PWR can be obtained directly by measurements. To implement advanced PWR power-level control law, it is necessary to develop a state-observer to reconstruct the unmeasurable state-variables. Since a PWR is naturally a complex nonlinear system with parameters varying with power-level, fuel burnup, xenon isotope production, control rod worth and etc., it is meaningful to design a nonlinear observer for the PWR with adaptability to system uncertainties. Due to this and the strong learning capability of the multi-layer perceptron (MLP neural network, an MLP-based nonlinear adaptive observer is given for PWRs. Based upon Lyapunov stability theory, it is proved theoretically that this newly-built observer can provide bounded and convergent state-observation. This observer is then applied to the state-observation of a special PWR, i.e., the nuclear heating reactor (NHR, and numerical simulation results not only verify its feasibility but also give the relationship between the observation performance and observer parameters.
Entangler and analyzer for multiphotonGreenberger-Horne-Zeilinger states using weak nonlinearities
Institute of Scientific and Technical Information of China (English)
DING Dong; YAN FengLi; GAO Ting
2014-01-01
In the regime of weak nonlinearity we present two general,feasible schemes for manipulating photon states.One is an entangler for generating any one of the n-photon Greenberger-Home-Zeilinger (GHZ) states.Interactions of the incoming photons with crossKerr media followed by a phase shift gate and a measurement on a probe beam plus appropriate local operations using classical feed-forward of the measurement results allow one to obtain the desired states in a nearly deterministic manner.The second scheme discussed is an analyzer for multiphoton maximally entangled states,which is derived from the above entangler.In this scheme,all of the 2n n-photon GHZ states can,nearly deterministically,be discriminated.
Selective measurement of quantronium qubit states by using of mesoscopic non-linear oscillator
Denisenko, M. V.; Satanin, A. M.
2016-12-01
We study the process of selective measurements of states of individual quantum systems - Josephson qubit - using nonlinear oscillator, working in the mesoscopic regime, when the number of quanta in the measuring process varies from a few dozen to a few hundred. Quantum Monte-Carlo method simulated dissipative dynamics of the system "qubit - oscillator" and the measurement process of a qubit state to modify the number of quanta of the oscillator. It is shown that for different Rabi-pulses of the recording state of a qubit the discrimination of states is possible, as well as the measurement of the effect of back-action of the measuring device, including separation of the prepared superposition state - carrying out statistical projective measurements.
Nonlinear Adaptive Descriptor Observer for the Joint States and Parameters Estimation
2016-08-29
In this note, the joint state and parameters estimation problem for nonlinear multi-input multi-output descriptor systems is considered. Asymptotic convergence of the adaptive descriptor observer is established by a sufficient set of linear matrix inequalities for the noise-free systems. The noise corrupted systems are also considered and it is shown that the state and parameters estimation errors are bounded for bounded noises. In addition, if the noises are bounded and have zero mean, then the estimation errors asymptotically converge to zero in the mean. The performance of the proposed adaptive observer is illustrated by a numerical example.
Amir, Naila; Iqbal, Shahid
2017-08-01
We develop generalized coherent states for a class of nonlinear oscillators with position-dependent effective mass in the context of the Gazeau-Klauder formalism and discuss some of their properties. In order to investigate the temporal evolution we first explore the statistical properties by means of weighting distribution and the Mandel parameter. It is found that the temporal evolution of the coherent states may exhibit the phenomena of quantum revivals and fractional revivals for a particular choice of position-dependent mass oscillator.
Institute of Scientific and Technical Information of China (English)
Meng Xiang-Guo; Wang Ji-Suo; Liu Tang-Kun
2008-01-01
In this paper a new class of finite-dimensional even and odd nonlinear pair coherent states(EONLPCSs),which can be realized via operating the superposed evolution operators D±(τ)on the state |q,0),is constructed,then their orthonormalized property,completeness relations and some nonclassical properties are discussed.It is shown that the finite-dimensional EONLPCSs possess normalization and completeness relations.Moreover,the finite-dimensional EONLPCSs exhibit remarkably different sub-Poissonian distributions and phase probability distributions for different values of parameters q,η and ξ.
Hendi, S H; Momennia, M
2015-01-01
In this paper, we consider quadratic Maxwell invariant as a correction to the Maxwell theory and study thermodynamic behavior of the black holes in Einstein (EN) and Gauss-Bonnet (GB) gravities. We consider cosmological constant as a thermodynamic pressure to extend phase space. Next, we obtain critical values in case of variation of nonlinearity and GB parameters. We generalized the study by considering the effects of dimensionality on critical values and make comparisons between our models with their special sub classes.
Rudra, Shubhobrata; Barai, Ranjit Kumar; Maitra, Madhubanti
2014-03-01
This paper presents the formulation of a novel block-backstepping based control algorithm to address the stabilization problem for a generalized nonlinear underactuated mechanical system. For the convenience of compact design, first, the state model of the underactuated system has been converted into the block-strict feedback form. Next, we have incorporated backstepping control action to derive the expression of the control input for the generic nonlinear underactuated system. The proposed block backstepping technique has further been enriched by incorporating an integral action additionally for enhancing the steady state performance of the overall system. Asymptotic stability of the overall system has been analyzed using Lyapunov stability criteria. Subsequently, the stability of the zero dynamics has also been analyzed to ensure the global asymptotic stability of the entire nonlinear system at its desired equilibrium point. The proposed control algorithm has been applied for the stabilization of a benchmarked underactuated mechanical system to verify the effectiveness of the proposed control law in real-time environment.
Mircea, Dragos I.; Anlage, Steven M.
2004-03-01
Traditionally, the Andreev Bound States (ABS) have been studied by means of tunneling experiments and global electromagnetic resonant techniques. The zero bias conductance peak and the strong upturn in the penetration depth at low temperature are considered strong evidence for the existence of ABS. The nonlinear inductance arising from the current-dependent penetration depth leads to a nonlinear electrodynamic response that can be probed with our non-resonant near-field microwave microscope [S. C. Lee and S. M. Anlage, Appl. Phys. Lett. 82, 1893 (2003)]. In the experiment, microwave currents have been applied locally along different directions on the surface of YBCO films exposing the (110) surface in order to investigate the angular dependence of the second and third order harmonics generated by the sample. The temperature and the angular dependence measured for different levels of the applied microwave power, will be presented and compared with the theoretical predictions. This low-temperature anisotropic nonlinear behavior is relevant for the study of ABS as well as for identifying the existence of local pairing states with symmetry different from that of the bulk order parameter.
Projective limits of state spaces II. Quantum formalism
Lanéry, Suzanne; Thiemann, Thomas
2017-06-01
In this series of papers, we investigate the projective framework initiated by Kijowski (1977) and Okołów (2009, 2014, 2013), which describes the states of a quantum theory as projective families of density matrices. A short reading guide to the series can be found in Lanéry (2016). After discussing the formalism at the classical level in a first paper (Lanéry, 2017), the present second paper is devoted to the quantum theory. In particular, we inspect in detail how such quantum projective state spaces relate to inductive limit Hilbert spaces and to infinite tensor product constructions (Lanéry, 2016, subsection 3.1) [1]. Regarding the quantization of classical projective structures into quantum ones, we extend the results by Okołów (2013), that were set up in the context of linear configuration spaces, to configuration spaces given by simply-connected Lie groups, and to holomorphic quantization of complex phase spaces (Lanéry, 2016, subsection 2.2) [1].
Tam, Leo K; Stockmann, Jason P; Galiana, Gigi; Constable, R Todd
2012-10-01
To increase image acquisition efficiency, we develop alternative gradient encoding strategies designed to provide spatial encoding complementary to the spatial encoding provided by the multiple receiver coil elements in parallel image acquisitions. Intuitively, complementary encoding is achieved when the magnetic field encoding gradients are designed to encode spatial information where receiver spatial encoding is ambiguous, for example, along sensitivity isocontours. Specifically, the method generates a basis set for the null space of the coil sensitivities with the singular value decomposition and calculates encoding fields from the null space vectors. A set of nonlinear gradients is used as projection imaging readout magnetic fields, replacing the conventional linear readout field and phase encoding. Multiple encoding fields are used as projections to capture the null space information, hence the term null space imaging. The method is compared to conventional Cartesian SENSitivity Encoding as evaluated by mean squared error and robustness to noise. Strategies for developments in the area of nonlinear encoding schemes are discussed. The null space imaging approach yields a parallel imaging method that provides high acceleration factors with a limited number of receiver coil array elements through increased time efficiency in spatial encoding.
State Space Path Integrals for Electronically Nonadiabatic Reaction Rates
Duke, Jessica Ryan
2016-01-01
We present a state-space-based path integral method to calculate the rate of electron transfer (ET) in multi-state, multi-electron condensed-phase processes. We employ an exact path integral in discrete electronic states and continuous Cartesian nuclear variables to obtain a transition state theory (TST) estimate to the rate. A dynamic recrossing correction to the TST rate is then obtained from real-time dynamics simulations using mean field ring polymer molecular dynamics. We employ two different reaction coordinates in our simulations and show that, despite the use of mean field dynamics, the use of an accurate dividing surface to compute TST rates allows us to achieve remarkable agreement with Fermi's golden rule rates for nonadiabatic ET in the normal regime of Marcus theory. Further, we show that using a reaction coordinate based on electronic state populations allows us to capture the turnover in rates for ET in the Marcus inverted regime.
Nonlinear neural network for hemodynamic model state and input estimation using fMRI data
Karam, Ayman M.
2014-11-01
Originally inspired by biological neural networks, artificial neural networks (ANNs) are powerful mathematical tools that can solve complex nonlinear problems such as filtering, classification, prediction and more. This paper demonstrates the first successful implementation of ANN, specifically nonlinear autoregressive with exogenous input (NARX) networks, to estimate the hemodynamic states and neural activity from simulated and measured real blood oxygenation level dependent (BOLD) signals. Blocked and event-related BOLD data are used to test the algorithm on real experiments. The proposed method is accurate and robust even in the presence of signal noise and it does not depend on sampling interval. Moreover, the structure of the NARX networks is optimized to yield the best estimate with minimal network architecture. The results of the estimated neural activity are also discussed in terms of their potential use.
Replacement Capability Options for the United States Space Shuttle
2013-09-01
first designed for reuse ” (NASA, 2000). 1. United States Space Shuttle Program (1981–2011) The first operational Space Shuttle was Columbia (OV-102...Week article on China’s future plans for their Long March Launch vehicles, “China is developing three basic rocket modules, with diameters of 2.25... wastewater , which will burn up with the spacecraft when it re-enters the Earth’s atmosphere. The Cargo Module can hold 1,000 to 1,700 kilograms (2,205
Tomsk State University: Space-planning development concept
Directory of Open Access Journals (Sweden)
Elena Grigoryeva
2015-05-01
Full Text Available The article features the space-planning development concept for National Research Tomsk State University and the subsequent sketch design. Together with extension of educational and laboratory area, the system of open exterior and interior public spaces is created for interpersonal communication, independent work, leisure, self-presentations, team building events, etc. One of the leading principles is preservation of the University historical heritage together with appliance of advanced architectural and spatial methods and integration of facilities built at different times into one complex.
Arefi, Mohammad Mehdi; Jahed-Motlagh, Mohammad Reza; Karimi, Hamid Reza
2015-08-01
In this paper, first, an adaptive neural network (NN) state-feedback controller for a class of nonlinear systems with mismatched uncertainties is proposed. By using a radial basis function NN (RBFNN), a bound of unknown nonlinear functions is approximated so that no information about the upper bound of mismatched uncertainties is required. Then, an observer-based adaptive controller based on RBFNN is designed to stabilize uncertain nonlinear systems with immeasurable states. The state-feedback and observer-based controllers are based on Lyapunov and strictly positive real-Lyapunov stability theory, respectively, and it is shown that the asymptotic convergence of the closed-loop system to zero is achieved while maintaining bounded states at the same time. The presented methods are more general than the previous approaches, handling systems with no restriction on the dimension of the system and the number of inputs. Simulation results confirm the effectiveness of the proposed methods in the stabilization of mismatched nonlinear systems.
Bauman Moscow State Technical University Youth Space Centre: Student's Way in Space Technologies
Mayorova, Victoria; Zelentsov, Victor
2002-01-01
The Youth Space Center (YSC) was established in Bauman Moscow State Technical University (BMSTU) in 1989 to provide primary aerospace education for young people, stimulate youth creative research thinking, promote space science and technology achievements and develop cooperation with other youth organizations in the international aerospace community. The center is staffed by the Dr. Victoria Mayorova, BMSTU Associate Professor, the YSC director, Dr. Boris Kovalev, BMSTU Associate Professor, the YSC scientific director, 5 student consultants and many volunteers. Informally YSC is a community of space enthusiasts, an open club for BMSTU students interested in space science and technology and faculty teaching in this field. YSC educational activities are based on the concept of uninterrupted aerospace education, developed and implemented by the center. The concept includes working with young space interested people both in school and university and then assisting them in getting interesting job in Russian Space Industry. The school level educational activities of the center has got different forms, such as lecturing, summer scientific camps and even Classes from Space given by Mir space station flight crew in Mission Control Center - Moscow and done in cooperation with All- Russian Aerospace Society Soyuz (VAKO Soyuz). This helps to stimulate the young people interest to the fundamental sciences ( physics, mathematics, computer science, etc.) exploiting and developing their interest to space and thus increase the overall educational level in the country. YSC hosts annual Cosmonautics conference for high school students that provides the University with capability to select well-prepared and motivated students for its' rocket and space related departments. For the conference participants it's a good opportunity to be enrolled to the University without entrance examinations. BMSTU students can participate in such YSC activities as annual international workshop for space
Liu, Yan-Jun; Li, Jing; Tong, Shaocheng; Chen, C L Philip
2016-07-01
In order to stabilize a class of uncertain nonlinear strict-feedback systems with full-state constraints, an adaptive neural network control method is investigated in this paper. The state constraints are frequently emerged in the real-life plants and how to avoid the violation of state constraints is an important task. By introducing a barrier Lyapunov function (BLF) to every step in a backstepping procedure, a novel adaptive backstepping design is well developed to ensure that the full-state constraints are not violated. At the same time, one remarkable feature is that the minimal learning parameters are employed in BLF backstepping design. By making use of Lyapunov analysis, we can prove that all the signals in the closed-loop system are semiglobal uniformly ultimately bounded and the output is well driven to follow the desired output. Finally, a simulation is given to verify the effectiveness of the method.
Three-state interactions determine the second-order nonlinear optical response
Perez-Moreno, Javier
2016-01-01
Using the sum-rules, the sum-over-states expression for the diagonal term of first hyperpolarizability can be expressed as the sum of three-state interaction terms. We study the behavior of a generic three-state term to show that is possible to tune the contribution of resonant terms by tuning the spectrum of the molecule. When extrapolated to the off-resonance regime, the three-state interaction terms are shown to behave in a similar manner as the three-level model used to derive the fundamental limits. We finally show that most results derived using the three-level ansatz are general, and apply to molecules where more than three levels contribute to the second-order nonlinear response or/and far from optimization.
Pure state consciousness and its local reduction to neuronal space
Duggins, A. J.
2013-01-01
The single neuronal state can be represented as a vector in a complex space, spanned by an orthonormal basis of integer spike counts. In this model a scalar element of experience is associated with the instantaneous firing rate of a single sensory neuron over repeated stimulus presentations. Here the model is extended to composite neural systems that are tensor products of single neuronal vector spaces. Depiction of the mental state as a vector on this tensor product space is intended to capture the unity of consciousness. The density operator is introduced as its local reduction to the single neuron level, from which the firing rate can again be derived as the objective correlate of a subjective element. However, the relational structure of perceptual experience only emerges when the non-local mental state is considered. A metric of phenomenal proximity between neuronal elements of experience is proposed, based on the cross-correlation function of neurophysiology, but constrained by the association of theoretical extremes of correlation/anticorrelation in inseparable 2-neuron states with identical and opponent elements respectively.
Consensus Control of Nonlinear Multiagent Systems With Time-Varying State Constraints.
Meng, Wenchao; Yang, Qinmin; Si, Jennie; Sun, Youxian
2016-12-01
In this paper, we present a novel adaptive consensus algorithm for a class of nonlinear multiagent systems with time-varying asymmetric state constraints. As such, our contribution is a step forward beyond the usual consensus stabilization result to show that the states of the agents remain within a user defined, time-varying bound. To prove our new results, the original multiagent system is transformed into a new one. Stabilization and consensus of transformed states are sufficient to ensure the consensus of the original networked agents without violating of the predefined asymmetric time-varying state constraints. A single neural network (NN), whose weights are tuned online, is used in our design to approximate the unknown functions in the agent's dynamics. To account for the NN approximation residual, reconstruction error, and external disturbances, a robust term is introduced into the approximating system equation. Additionally in our design, each agent only exchanges the information with its neighbor agents, and thus the proposed consensus algorithm is decentralized. The theoretical results are proved via Lyapunov synthesis. Finally, simulations are performed on a nonlinear multiagent system to illustrate the performance of our consensus design scheme.
Institute of Scientific and Technical Information of China (English)
陈化; 罗壮初
2002-01-01
In this paper the authors study a class of non-linear singular partial differential equation in complex domain Ct × Cnx. Under certain assumptions, they prove the existence and uniqueness of holomorphic solution near origin of Ct × Cnx.
ITERATIVE SOLUTIONS FOR SYSTEMS OF NONLINEAR OPERATOR EQUATIONS IN BANACH SPACE
Institute of Scientific and Technical Information of China (English)
宋光兴
2003-01-01
By using partial order method, the existence, uniqueness and iterative ap-proximation of solutions for a class of systems of nonlinear operator equations in Banachspace are discussed. The results obtained in this paper extend and improve recent results.
Indian Academy of Sciences (India)
K Balachandran; K Uchiyama
2000-05-01
In this paper we prove the existence of mild and strong solutions of a nonlinear integrodifferential equation of Sobolev type with nonlocal condition. The results are obtained by using semigroup theory and the Schauder fixed point theorem.
State-space model with deep learning for functional dynamics estimation in resting-state fMRI.
Suk, Heung-Il; Wee, Chong-Yaw; Lee, Seong-Whan; Shen, Dinggang
2016-04-01
Studies on resting-state functional Magnetic Resonance Imaging (rs-fMRI) have shown that different brain regions still actively interact with each other while a subject is at rest, and such functional interaction is not stationary but changes over time. In terms of a large-scale brain network, in this paper, we focus on time-varying patterns of functional networks, i.e., functional dynamics, inherent in rs-fMRI, which is one of the emerging issues along with the network modelling. Specifically, we propose a novel methodological architecture that combines deep learning and state-space modelling, and apply it to rs-fMRI based Mild Cognitive Impairment (MCI) diagnosis. We first devise a Deep Auto-Encoder (DAE) to discover hierarchical non-linear functional relations among regions, by which we transform the regional features into an embedding space, whose bases are complex functional networks. Given the embedded functional features, we then use a Hidden Markov Model (HMM) to estimate dynamic characteristics of functional networks inherent in rs-fMRI via internal states, which are unobservable but can be inferred from observations statistically. By building a generative model with an HMM, we estimate the likelihood of the input features of rs-fMRI as belonging to the corresponding status, i.e., MCI or normal healthy control, based on which we identify the clinical label of a testing subject. In order to validate the effectiveness of the proposed method, we performed experiments on two different datasets and compared with state-of-the-art methods in the literature. We also analyzed the functional networks learned by DAE, estimated the functional connectivities by decoding hidden states in HMM, and investigated the estimated functional connectivities by means of a graph-theoretic approach. Copyright © 2016 Elsevier Inc. All rights reserved.
Korayem, M H; Nekoo, S R
2015-07-01
This work studies an optimal control problem using the state-dependent Riccati equation (SDRE) in differential form to track for time-varying systems with state and control nonlinearities. The trajectory tracking structure provides two nonlinear differential equations: the state-dependent differential Riccati equation (SDDRE) and the feed-forward differential equation. The independence of the governing equations and stability of the controller are proven along the trajectory using the Lyapunov approach. Backward integration (BI) is capable of solving the equations as a numerical solution; however, the forward solution methods require the closed-form solution to fulfill the task. A closed-form solution is introduced for SDDRE, but the feed-forward differential equation has not yet been obtained. Different ways of solving the problem are expressed and analyzed. These include BI, closed-form solution with corrective assumption, approximate solution, and forward integration. Application of the tracking problem is investigated to control robotic manipulators possessing rigid or flexible joints. The intention is to release a general program for automatic implementation of an SDDRE controller for any manipulator that obeys the Denavit-Hartenberg (D-H) principle when only D-H parameters are received as input data.
Some Modal Relations and Generalized Velocity Method in State Space
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
Real mode theory in configuration space has shown that the mode acceleration method converges faster than the mode displacement method. This paper demonstrates a similar conclusion in the state space. Some new expressions on modal parameter matrices were set up first. A generalized velocity method (GVM) is then demonstrated in a systematic way. This method is the so-called complex mode velocity method, but the expressions and schemes are given in terms of parametric matrices in configuration space. Theoretical comparison of this GVM with the traditional complex mode method shows some interesting conclusions. The latter approach is actually a generalized displacement method (GDM). Without mode reduction, the displacement responses of the concerned system resulting from both approaches are identical. On the other hand, both approaches have to adopt mode reduction to become practical. Under this situation, GVM has advantages because it compensates for the contribution of the omitted high-order modes to the displacement responses.
Latent state-space models for neural decoding.
Aghagolzadeh, Mehdi; Truccolo, Wilson
2014-01-01
Ensembles of single-neurons in motor cortex can show strong low-dimensional collective dynamics. In this study, we explore an approach where neural decoding is applied to estimated low-dimensional dynamics instead of to the full recorded neuronal population. A latent state-space model (SSM) approach is used to estimate the low-dimensional neural dynamics from the measured spiking activity in population of neurons. A second state-space model representation is then used to decode kinematics, via a Kalman filter, from the estimated low-dimensional dynamics. The latent SSM-based decoding approach is illustrated on neuronal activity recorded from primary motor cortex in a monkey performing naturalistic 3-D reach and grasp movements. Our analysis show that 3-D reach decoding performance based on estimated low-dimensional dynamics is comparable to the decoding performance based on the full recorded neuronal population.
State-space Manifold and Rotating Black Holes
Bellucci, Stefano
2010-01-01
We study a class of fluctuating higher dimensional black hole configurations obtained in string theory/ $M$-theory compactifications. We explore the intrinsic Riemannian geometric nature of Gaussian fluctuations arising from the Hessian of the coarse graining entropy, defined over an ensemble of brane microstates. It has been shown that the state-space geometry spanned by the set of invariant parameters is non-degenerate, regular and has a negative scalar curvature for the rotating Myers-Perry black holes, Kaluza-Klein black holes, supersymmetric $AdS_5$ black holes, $D_1$-$D_5$ configurations and the associated BMPV black holes. Interestingly, these solutions demonstrate that the principal components of the state-space metric tensor admit a positive definite form, while the off diagonal components do not. Furthermore, the ratio of diagonal components weakens relatively faster than the off diagonal components, and thus they swiftly come into an equilibrium statistical configuration. Novel aspects of the scali...
Semiclassical approximations in phase space with coherent states
Energy Technology Data Exchange (ETDEWEB)
Baranger, M. [Center for Theoretical Physics, Laboratory for Nuclear Science and Department of Physics, Massachusetts Institute of Technology, Cambridge, MA (United States); De Aguiar, M.A.M. [Center for Theoretical Physics, Laboratory for Nuclear Science and Department of Physics, Massachusetts Institute of Technology, Cambridge, MA (United States); Instituto de Fisica ' Gleb Wataghin' , Universidade Estadual de Campinas, Campinas (Brazil); Keck, F.; Korsch, H.J.; Schellhaass, B. [FB Physik, Universitaet Kaiserslautern, Kaiserslautern (Germany)
2001-09-14
We present a complete derivation of the semiclassical limit of the coherent-state propagator in one dimension, starting from path integrals in phase space. We show that the arbitrariness in the path integral representation, which follows from the overcompleteness of the coherent states, results in many different semiclassical limits. We explicitly derive two possible semiclassical formulae for the propagator, we suggest a third one, and we discuss their relationships. We also derive an initial-value representation for the semiclassical propagator, based on an initial Gaussian wavepacket. It turns out to be related to, but different from, Heller's thawed Gaussian approximation. It is very different from the Herman-Kluk formula, which is not a correct semiclassical limit. We point out errors in two derivations of the latter. Finally we show how the semiclassical coherent-state propagators lead to WKB-type quantization rules and to approximations for the Husimi distributions of stationary states. (author)
Semiclassical approximations in phase space with coherent states
Baranger, M.; de Aguiar, M. A. M.; Keck, F.; Korsch, H. J.; Schellhaaß, B.
2001-09-01
We present a complete derivation of the semiclassical limit of the coherent-state propagator in one dimension, starting from path integrals in phase space. We show that the arbitrariness in the path integral representation, which follows from the overcompleteness of the coherent states, results in many different semiclassical limits. We explicitly derive two possible semiclassical formulae for the propagator, we suggest a third one, and we discuss their relationships. We also derive an initial-value representation for the semiclassical propagator, based on an initial Gaussian wavepacket. It turns out to be related to, but different from, Heller's thawed Gaussian approximation. It is very different from the Herman-Kluk formula, which is not a correct semiclassical limit. We point out errors in two derivations of the latter. Finally we show how the semiclassical coherent-state propagators lead to WKB-type quantization rules and to approximations for the Husimi distributions of stationary states.
Entangled Bloch Spheres: Bloch Matrix And Two Qubit State Space
Gamel, Omar
2016-01-01
We represent a two qubit density matrix in the basis of Pauli matrix tensor products, with the coefficients constituting a Bloch matrix, analogous to the single qubit Bloch vector. We find the quantum state positivity requirements on the Bloch matrix components, leading to three important inequalities, allowing us to parameterize and visualize the two qubit state space. Applying the singular value decomposition naturally separates the degrees of freedom to local and nonlocal, and simplifies the positivity inequalities. It also allows us to geometrically represent a state as two entangled Bloch spheres with superimposed correlation axes. It is shown that unitary transformations, local or nonlocal, have simple interpretations as axis rotations or mixing of certain degrees of freedom. The nonlocal unitary invariants of the state are then derived in terms of local unitary invariants. The positive partial transpose criterion for entanglement is generalized, and interpreted as a reflection, or a change of a single ...
Attention control learning in the decision space using state estimation
Gharaee, Zahra; Fatehi, Alireza; Mirian, Maryam S.; Nili Ahmadabadi, Majid
2016-05-01
The main goal of this paper is modelling attention while using it in efficient path planning of mobile robots. The key challenge in concurrently aiming these two goals is how to make an optimal, or near-optimal, decision in spite of time and processing power limitations, which inherently exist in a typical multi-sensor real-world robotic application. To efficiently recognise the environment under these two limitations, attention of an intelligent agent is controlled by employing the reinforcement learning framework. We propose an estimation method using estimated mixture-of-experts task and attention learning in perceptual space. An agent learns how to employ its sensory resources, and when to stop observing, by estimating its perceptual space. In this paper, static estimation of the state space in a learning task problem, which is examined in the WebotsTM simulator, is performed. Simulation results show that a robot learns how to achieve an optimal policy with a controlled cost by estimating the state space instead of continually updating sensory information.
Model Updating Nonlinear System Identification Toolbox Project
National Aeronautics and Space Administration — ZONA Technology proposes to develop an enhanced model updating nonlinear system identification (MUNSID) methodology by adopting the flight data with state-of-the-art...
Prediction and interpolation of time series by state space models
Helske, Jouni
2015-01-01
A large amount of data collected today is in the form of a time series. In order to make realistic inferences based on time series forecasts, in addition to point predictions, prediction intervals or other measures of uncertainty should be presented. Multiple sources of uncertainty are often ignored due to the complexities involved in accounting them correctly. In this dissertation, some of these problems are reviewed and some new solutions are presented. A state space approach...
State Space identification of Civil Engineering Structures from Output Measurements
1996-01-01
This paper presents the results from a state space system identification simulation study of a 5-degrees-of freedom system driven by white noise. The aim of the study is to compare the durability of the fairly new Stochastic Subspace Technique (SST) with more well-known techniques for identification of civil engineering structures. The SST is compared with the stochastic realization estimator Matrix Block Hankel (MBH) and a prediction error method (PEM). The results show that the investigated...
Solving Bethe-Salpeter scattering state equation in Minkowski space
Carbonell, J
2014-01-01
We present a method to directly solving the Bethe-Salpeter equation in Minkowski space, both for bound and scattering states. It is based on a proper treatment of the singularities which appear in the kernel, propagators and Bethe-Salpeter amplitude itself. The off-mass shell scattering amplitude for spinless particles interacting by a one boson exchange is computed for the first time.
State Space identification of Civil Engineering Structures from Output Measurements
DEFF Research Database (Denmark)
Kirkegaard, Poul Henning; Andersen, P.
1997-01-01
This paper presents the results from a state space system identification simulation study of a 5-degrees-of freedom system driven by white noise. The aim of the study is to compare the durability of the fairly new Stochastic Subspace Technique (SST) with more well-known techniques......, it is found that the new SST technique gives quickly good results compared with the PEM which takes more time with only a limited improvement of the fit on data....
Advanced Solid State Lighting for AES Deep Space Hab Project
Holbert, Eirik
2015-01-01
The advanced Solid State Lighting (SSL) assemblies augmented 2nd generation modules under development for the Advanced Exploration Systems Deep Space Habitat in using color therapy to synchronize crew circadian rhythms. Current RGB LED technology does not produce sufficient brightness to adequately address general lighting in addition to color therapy. The intent is to address both through a mix of white and RGB LEDs designing for fully addressable alertness/relaxation levels as well as more dramatic circadian shifts.
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.
Elenchezhiyan, M; Prakash, J
2015-09-01
In this work, state estimation schemes for non-linear hybrid dynamic systems subjected to stochastic state disturbances and random errors in measurements using interacting multiple-model (IMM) algorithms are formulated. In order to compute both discrete modes and continuous state estimates of a hybrid dynamic system either an IMM extended Kalman filter (IMM-EKF) or an IMM based derivative-free Kalman filters is proposed in this study. The efficacy of the proposed IMM based state estimation schemes is demonstrated by conducting Monte-Carlo simulation studies on the two-tank hybrid system and switched non-isothermal continuous stirred tank reactor system. Extensive simulation studies reveal that the proposed IMM based state estimation schemes are able to generate fairly accurate continuous state estimates and discrete modes. In the presence and absence of sensor bias, the simulation studies reveal that the proposed IMM unscented Kalman filter (IMM-UKF) based simultaneous state and parameter estimation scheme outperforms multiple-model UKF (MM-UKF) based simultaneous state and parameter estimation scheme.
Modeling Bivariate Longitudinal Hormone Profiles by Hierarchical State Space Models.
Liu, Ziyue; Cappola, Anne R; Crofford, Leslie J; Guo, Wensheng
2014-01-01
The hypothalamic-pituitary-adrenal (HPA) axis is crucial in coping with stress and maintaining homeostasis. Hormones produced by the HPA axis exhibit both complex univariate longitudinal profiles and complex relationships among different hormones. Consequently, modeling these multivariate longitudinal hormone profiles is a challenging task. In this paper, we propose a bivariate hierarchical state space model, in which each hormone profile is modeled by a hierarchical state space model, with both population-average and subject-specific components. The bivariate model is constructed by concatenating the univariate models based on the hypothesized relationship. Because of the flexible framework of state space form, the resultant models not only can handle complex individual profiles, but also can incorporate complex relationships between two hormones, including both concurrent and feedback relationship. Estimation and inference are based on marginal likelihood and posterior means and variances. Computationally efficient Kalman filtering and smoothing algorithms are used for implementation. Application of the proposed method to a study of chronic fatigue syndrome and fibromyalgia reveals that the relationships between adrenocorticotropic hormone and cortisol in the patient group are weaker than in healthy controls.
Bayesian State-Space Modelling on High-Performance Hardware Using LibBi
Directory of Open Access Journals (Sweden)
Lawrence M. Murray
2015-10-01
Full Text Available LibBi is a software package for state space modelling and Bayesian inference on modern computer hardware, including multi-core central processing units, many-core graphics processing units, and distributed-memory clusters of such devices. The software parses a domain-specific language for model specification, then optimizes, generates, compiles and runs code for the given model, inference method and hardware platform. In presenting the software, this work serves as an introduction to state space models and the specialized methods developed for Bayesian inference with them. The focus is on sequential Monte Carlo (SMC methods such as the particle filter for state estimation, and the particle Markov chain Monte Carlo and SMC2 methods for parameter estimation. All are well-suited to current computer hardware. Two examples are given and developed throughout, one a linear three-element windkessel model of the human arterial system, the other a nonlinear Lorenz '96 model. These are specified in the prescribed modelling language, and LibBi demonstrated by performing inference with them. Empirical results are presented, including a performance comparison of the software with different hardware configurations.
Bayesian State-Space Modelling on High-Performance Hardware Using LibBi
Directory of Open Access Journals (Sweden)
Lawrence M. Murray
2015-10-01
Full Text Available LibBi is a software package for state space modelling and Bayesian inference on modern computer hardware, including multi-core central processing units, many-core graphics processing units, and distributed-memory clusters of such devices. The software parses a domain-specific language for model specification, then optimizes, generates, compiles and runs code for the given model, inference method and hardware platform. In presenting the software, this work serves as an introduction to state space models and the specialized methods developed for Bayesian inference with them. The focus is on sequential Monte Carlo (SMC methods such as the particle filter for state estimation, and the particle Markov chain Monte Carlo and SMC2 methods for parameter estimation. All are well-suited to current computer hardware. Two examples are given and developed throughout, one a linear three-element windkessel model of the human arterial system, the other a nonlinear Lorenz '96 model. These are specified in the prescribed modelling language, and LibBi demonstrated by performing inference with them. Empirical results are presented, including a performance comparison of the software with different hardware configurations.
Institute of Scientific and Technical Information of China (English)
王自东; 胡汉起
1997-01-01
The nonlinear dynamics equations of the time dependence of the perturbation amplitude of the solid/ liquid interface during unidirectional solidification of a dilute binary alloy are established. The solutions to these equations are obtained, and the condition of the initial steady state growth of the cellular and dendritic structure after the planar solid/liquid interface bifurcates (mGc> G) with the increase of the growth rate is given. The condition of the steady state growth of fine cellular and dendritic structure in the beginning after the coarse dendrites bifurcate ( mGc<Γw2 + G) under the rapid solidification is obtained. The relationship of the steady state cell and dendrite tip radius, the perturbation amplitude and wavelength at the solid/liquid interface is presented.
Phase sensitivity in deformed-state superposition considering nonlinear phase shifts
Berrada, K.
2016-07-01
We study the problem of the phase estimation for the deformation-state superposition (DSS) under perfect and lossy (due to a dissipative interaction of DSS with their environment) regimes. The study is also devoted to the phase enhancement of the quantum states resulting from a generalized non-linearity of the phase shifts, both without and with losses. We find that such a kind of superposition can give the smallest variance in the phase parameter in comparison with usual Schrödinger cat states in different order of non-linearity even if for a larger average number of photons. Due to the significance of how a system is quantum correlated with its environment in the construction of a scalable quantum computer, the entanglement between the DSS and its environment is investigated during the dissipation. We show that partial entanglement trapping occurs during the dynamics depending on the kind of deformation and mean photon number. These features make the DSS with a larger average number of photons a good candidate for implementation of schemes of quantum optics and information with high precision.
Miao, Zhiyong; Shi, Hongyang; Zhang, Yi; Xu, Fan
2017-10-01
In this paper, a new variational Bayesian adaptive cubature Kalman filter (VBACKF) is proposed for nonlinear state estimation. Although the conventional VBACKF performs better than cubature Kalman filtering (CKF) in solving nonlinear systems with time-varying measurement noise, its performance may degrade due to the uncertainty of the system model. To overcome this drawback, a multilayer feed-forward neural network (MFNN) is used to aid the conventional VBACKF, generalizing it to attain higher estimation accuracy and robustness. In the proposed neural-network-aided variational Bayesian adaptive cubature Kalman filter (NN-VBACKF), the MFNN is used to turn the state estimation of the VBACKF adaptively, and it is used for both state estimation and in the online training paradigm simultaneously. To evaluate the performance of the proposed method, it is compared with CKF and VBACKF via target tracking problems. The simulation results demonstrate that the estimation accuracy and robustness of the proposed method are better than those of the CKF and VBACKF.
Nanda, Sudarsan
2013-01-01
"Nonlinear analysis" presents recent developments in calculus in Banach space, convex sets, convex functions, best approximation, fixed point theorems, nonlinear operators, variational inequality, complementary problem and semi-inner-product spaces. Nonlinear Analysis has become important and useful in the present days because many real world problems are nonlinear, nonconvex and nonsmooth in nature. Although basic concepts have been presented here but many results presented have not appeared in any book till now. The book could be used as a text for graduate students and also it will be useful for researchers working in this field.
Institute of Scientific and Technical Information of China (English)
CHEN Ming-jie; LI Dian-pu; ZHANG Ai-jun
2004-01-01
Chaotic synchronization is a branch of chaotic control. Nowadays, the research and application of chaotic synchronization have become a hot topic and one of the development directions is for the research on chaos. In this paper, a universal nonlinear stateobserver is presented for a class of universal chaotic systems to realize the chaotic synchronization, according to the theory of state-observer in the modern control theory. And theoretic analysis and simulation results have illustrated the validity of the approach. Moreover, the approach of synchronization proposed in this paper is very easy, flexible and universal with high synchronization precision.When the approach is applied to secure communication, the results are satisfying.
DEFF Research Database (Denmark)
Petersen, Lars Norbert; Jørgensen, John Bagterp; Rawlings, James B.
2015-01-01
In this paper, we develop an economically optimizing Nonlinear Model Predictive Controller (E-NMPC) for a complete spray drying plant with multiple stages. In the E-NMPC the initial state is estimated by an extended Kalman Filter (EKF) with noise covariances estimated by an autocovariance least...... squares method (ALS). We present a model for the spray drying plant and use this model for simulation as well as for prediction in the E-NMPC. The open-loop optimal control problem in the E-NMPC is solved using the single-shooting method combined with a quasi-Newton Sequential Quadratic programming (SQP...
Uniqueness of non-linear ground states for fractional Laplacians in R
DEFF Research Database (Denmark)
Frank, Rupert L.; Lenzmann, Enno
2013-01-01
We prove uniqueness of ground state solutions Q = Q(|x|) ≥ 0 of the non-linear equation (−Δ)sQ+Q−Qα+1=0inR,where 0 ... recently raised by Kenig–Martel–Robbiano and we generalize (by completely different techniques) the specific uniqueness result obtained by Amick and Toland for s=12 and α = 1 in [5] for the Benjamin–Ono equation. As a technical key result in this paper, we show that the associated linearized operator L...... Benjamin–Ono (BO) and Benjamin–Bona–Mahony (BBM) water wave equations....
DEFF Research Database (Denmark)
Rahman, Imadur Mohamed; Marchetti, Nicola; Fitzek, Frank;
2005-01-01
In this work, we have analyzed a joint spatial diversity and multiplexing transmission structure for MIMO-OFDM system, where Orthogonal Space-Frequency Block Coding (OSFBC) is used across all spatial multiplexing branches. We have derived a BLAST-like non-linear Successive Interference Cancellation...... in this paper. We have found that a linear two-stage receiver for the proposed system [1] performs very close to the non-linear receiver studied in this work. Finally, we compared the system performance in spatially correlated scenario. It is found that higher amount of spatial correlation at the transmitter...... (SIC) receiver where the detection is done on subcarrier by sub-carrier basis based on both Zero Forcing (ZF) and Minimum Mean Square Error (MMSE) nulling criterion for the system. In terms of Frame Error Rate (FER), MMSE based SIC receiver performs better than all other receivers compared...
14 CFR 1217.106 - Articles brought into the United States by NASA from space.
2010-01-01
... NASA from space. 1217.106 Section 1217.106 Aeronautics and Space NATIONAL AERONAUTICS AND SPACE ADMINISTRATION DUTY-FREE ENTRY OF SPACE ARTICLES § 1217.106 Articles brought into the United States by NASA from... territory of the United States by NASA from space shall not be considered an importation, and...
State space modeling of reactor core in a pressurized water reactor
Ashaari, A.; Ahmad, T.; Shamsuddin, Mustaffa; M, Wan Munirah W.; Abdullah, M. Adib
2014-07-01
The power control system of a nuclear reactor is the key system that ensures a safe operation for a nuclear power plant. However, a mathematical model of a nuclear power plant is in the form of nonlinear process and time dependent that give very hard to be described. One of the important components of a Pressurized Water Reactor is the Reactor core. The aim of this study is to analyze the performance of power produced from a reactor core using temperature of the moderator as an input. Mathematical representation of the state space model of the reactor core control system is presented and analyzed in this paper. The data and parameters are taken from a real time VVER-type Pressurized Water Reactor and will be verified using Matlab and Simulink. Based on the simulation conducted, the results show that the temperature of the moderator plays an important role in determining the power of reactor core.
State space modeling of reactor core in a pressurized water reactor
Energy Technology Data Exchange (ETDEWEB)
Ashaari, A.; Ahmad, T.; M, Wan Munirah W. [Department of Mathematical Science, Faculty of Science, Universiti Teknologi Malaysia, 81310 Skudai, Johor (Malaysia); Shamsuddin, Mustaffa [Institute of Ibnu Sina, Universiti Teknologi Malaysia, 81310 Skudai, Johor (Malaysia); Abdullah, M. Adib [Swinburne University of Technology, Faculty of Engineering, Computing and Science, Jalan Simpang Tiga, 93350 Kuching, Sarawak (Malaysia)
2014-07-10
The power control system of a nuclear reactor is the key system that ensures a safe operation for a nuclear power plant. However, a mathematical model of a nuclear power plant is in the form of nonlinear process and time dependent that give very hard to be described. One of the important components of a Pressurized Water Reactor is the Reactor core. The aim of this study is to analyze the performance of power produced from a reactor core using temperature of the moderator as an input. Mathematical representation of the state space model of the reactor core control system is presented and analyzed in this paper. The data and parameters are taken from a real time VVER-type Pressurized Water Reactor and will be verified using Matlab and Simulink. Based on the simulation conducted, the results show that the temperature of the moderator plays an important role in determining the power of reactor core.
Complex network analysis of state spaces for random Boolean networks
Energy Technology Data Exchange (ETDEWEB)
Shreim, Amer [Complexity Science Group, Department of Physics and Astronomy, University of Calgary, Calgary, AB, T2N 1N4 (Canada); Berdahl, Andrew [Complexity Science Group, Department of Physics and Astronomy, University of Calgary, Calgary, AB, T2N 1N4 (Canada); Sood, Vishal [Complexity Science Group, Department of Physics and Astronomy, University of Calgary, Calgary, AB, T2N 1N4 (Canada); Grassberger, Peter [Complexity Science Group, Department of Physics and Astronomy, University of Calgary, Calgary, AB, T2N 1N4 (Canada); Paczuski, Maya [Complexity Science Group, Department of Physics and Astronomy, University of Calgary, Calgary, AB, T2N 1N4 (Canada)
2008-01-15
We apply complex network analysis to the state spaces of random Boolean networks (RBNs). An RBN contains N Boolean elements each with K inputs. A directed state space network (SSN) is constructed by linking each dynamical state, represented as a node, to its temporal successor. We study the heterogeneity of these SSNs at both local and global scales, as well as sample to-sample fluctuations within an ensemble of SSNs. We use in-degrees of nodes as a local topological measure, and the path diversity (Shreim A et al 2007 Phys. Rev. Lett. 98 198701) of an SSN as a global topological measure. RBNs with 2 {<=} K {<=} 5 exhibit non-trivial fluctuations at both local and global scales, while K = 2 exhibits the largest sample-to-sample (possibly non-self-averaging) fluctuations. We interpret the observed 'multi scale' fluctuations in the SSNs as indicative of the criticality and complexity of K = 2 RBNs. 'Garden of Eden' (GoE) states are nodes on an SSN that have in-degree zero. While in-degrees of non-GoE nodes for K > 1 SSNs can assume any integer value between 0 and 2{sup N}, for K = 1 all the non-GoE nodes in a given SSN have the same in-degree which is always a power of two.
Space Monitoring Data Center at Moscow State University
Kalegaev, Vladimir; Bobrovnikov, Sergey; Barinova, Vera; Myagkova, Irina; Shugay, Yulia; Barinov, Oleg; Dolenko, Sergey; Mukhametdinova, Ludmila; Shiroky, Vladimir
Space monitoring data center of Moscow State University provides operational information on radiation state of the near-Earth space. Internet portal http://swx.sinp.msu.ru/ gives access to the actual data characterizing the level of solar activity, geomagnetic and radiation conditions in the magnetosphere and heliosphere in the real time mode. Operational data coming from space missions (ACE, GOES, ELECTRO-L1, Meteor-M1) at L1, LEO and GEO and from the Earth’s surface are used to represent geomagnetic and radiation state of near-Earth environment. On-line database of measurements is also maintained to allow quick comparison between current conditions and conditions experienced in the past. The models of space environment working in autonomous mode are used to generalize the information obtained from observations on the whole magnetosphere. Interactive applications and operational forecasting services are created on the base of these models. They automatically generate alerts on particle fluxes enhancements above the threshold values, both for SEP and relativistic electrons using data from LEO orbits. Special forecasting services give short-term forecast of SEP penetration to the Earth magnetosphere at low altitudes, as well as relativistic electron fluxes at GEO. Velocities of recurrent high speed solar wind streams on the Earth orbit are predicted with advance time of 3-4 days on the basis of automatic estimation of the coronal hole areas detected on the images of the Sun received from the SDO satellite. By means of neural network approach, Dst and Kp indices online forecasting 0.5-1.5 hours ahead, depending on solar wind and the interplanetary magnetic field, measured by ACE satellite, is carried out. Visualization system allows representing experimental and modeling data in 2D and 3D.
Image quality assessment method based on nonlinear feature extraction in kernel space
Institute of Scientific and Technical Information of China (English)
Yong DING‡; Nan LI; Yang ZHAO; Kai HUANG
2016-01-01
To match human perception, extracting perceptual features effectively plays an important role in image quality assessment. In contrast to most existing methods that use linear transformations or models to represent images, we employ a complex mathematical expression of high dimensionality to reveal the statistical characteristics of the images. Furthermore, by introducing kernel methods to transform the linear problem into a nonlinear one, a full-reference image quality assessment method is proposed based on high-dimensional nonlinear feature extraction. Experiments on the LIVE, TID2008, and CSIQ databases demonstrate that nonlinear features offer competitive performance for image inherent quality representation and the proposed method achieves a promising performance that is consistent with human subjective evaluation.
Energy Technology Data Exchange (ETDEWEB)
Kharkovskiy, A. I., E-mail: akharkovskiy@inbox.ru [International Laboratory of High Magnetic Fields and Low Temperatures, Gajowicka 95, 53-421 Wrocław (Poland); L.F. Vereshchagin Institute for High Pressure Physics RAS, 142190 Troitsk, Moscow (Russian Federation); Shaldin, Yu. V. [International Laboratory of High Magnetic Fields and Low Temperatures, Gajowicka 95, 53-421 Wrocław (Poland); Institute for Crystallography RAS, Lenin' s Avenue 59, 119333 Moscow (Russian Federation); Nizhankovskii, V. I. [International Laboratory of High Magnetic Fields and Low Temperatures, Gajowicka 95, 53-421 Wrocław (Poland)
2016-01-07
The direct nonlinear magnetoelectric (ME) effect and the magnetostriction of piezoelectric CsCuCl{sub 3} single crystals were comprehensively studied over a wide temperature range in stationary magnetic fields of up to 14 T. The direct nonlinear ME effect measurements were also performed in pulsed magnetic fields up to 31 T, at liquid helium temperature in the antiferromagnetic (AF) state for the crystallographic direction in which effect has the maximum value. The nonlinear ME effect was quadratic in the paramagnetic state for the whole range of magnetic fields. In the AF state the phase transition between different configurations of spins manifested itself as plateau-like peculiarity on the nonlinear ME effect. The nonlinear ME effect was saturated by the phase transition to the spin-saturated paramagnetic state. Two contributions to the nonlinear ME effects in CsCuCl{sub 3} were extracted from the experimental data: the intrinsic ME effect originated from the magnetoelectric interactions, and the extrinsic one, which resulted from a magnetostriction-induced piezoelectric effect.
Interfaces Supporting Surface Gap Soliton Ground States in the 1D Nonlinear Schroedinger Equation
Dohnal, Tomas; Plum, Michael; Reichel, Wolfgang
2012-01-01
We consider the problem of verifying the existence of $H^1$ ground states of the 1D nonlinear Schr\\"odinger equation for an interface of two periodic structures: $$-u" +V(x)u -\\lambda u = \\Gamma(x) |u|^{p-1}u \\ {on} \\R$$ with $V(x) = V_1(x), \\Gamma(x)=\\Gamma_1(x)$ for $x\\geq 0$ and $V(x) = V_2(x), \\Gamma(x)=\\Gamma_2(x)$ for $x1$. The article [T. Dohnal, M. Plum and W. Reichel, "Surface Gap Soliton Ground States for the Nonlinear Schr\\"odinger Equation," \\textit{Comm. Math. Phys.} \\textbf{308}, 511-542 (2011)] provides in the 1D case an existence criterion in the form of an integral inequality involving the linear potentials $V_{1},V_2$ and the Bloch waves of the operators $-\\tfrac{d^2}{dx^2}+V_{1,2}-\\lambda$. We choose here the classes of piecewise constant and piecewise linear potentials $V_{1,2}$ and check this criterion for a set of parameter values. In the piecewise constant case the Bloch waves are calculated explicitly and in the piecewise linear case verified enclosures of the Bloch waves are computed ...
Nonlinear response and two stable electroconducting states in transparent plasticized PVC films
Vlasov, D. V.; Apresyan, L. A.; Vlasova, T. V.; Kryshtob, V. I.
2010-10-01
The electric conductivity of transparent plasticized poly(vinyl chloride) (PVC) films with thicknesses about 30-50 μm has been studied in electric fields with strengths significantly below the breakdown level. It is established that the PVC films exhibit spontaneous reversible transitions between two stable states—with high and relatively low conductivities, in which the bulk resistivity amounts to ˜103 and 106 Ω m, respectively. Relaxation current-voltage characteristics have been measured in a continuous regime, which allowed the Debye relaxation processes to be taken into consideration and effects related to the nonlinearity and transitions between indicated states to be separated. A regime with deterministic switching between the two conducting states has been observed. A simple qualitative model that describes the anomalous character of conductivity in polymer films is proposed.
Mapping from Speech to Images Using Continuous State Space Models
DEFF Research Database (Denmark)
Lehn-Schiøler, Tue; Hansen, Lars Kai; Larsen, Jan
2005-01-01
In this paper a system that transforms speech waveforms to animated faces are proposed. The system relies on continuous state space models to perform the mapping, this makes it possible to ensure video with no sudden jumps and allows continuous control of the parameters in 'face space......'. The performance of the system is critically dependent on the number of hidden variables, with too few variables the model cannot represent data, and with too many overfitting is noticed. Simulations are performed on recordings of 3-5 sec.\\$\\backslash\\$ video sequences with sentences from the Timit database. From...... a subjective point of view the model is able to construct an image sequence from an unknown noisy speech sequence even though the number of training examples are limited....
Nonlinear Electromagnetic Waves and Spherical Arc-Polarized Waves in Space Plasmas
Tsurutani, B.; Ho, Christian M.; Arballo, John K.; Lakhina, Gurbax S.; Glassmeier, Karl-Heinz; Neubauer, Fritz M.
1997-01-01
We review observations of nonlinear plasma waves detected by interplanetary spacecraft. For this paper we will focus primarily on the phase-steepened properties of such waves. Plasma waves at comet Giacobini-Zinner measured by the International Cometary Explorer (ICE), at comets Halley and Grigg-Skjellerup measured by Giotto, and interplanetary Alfven waves measured by Ulysses, will be discussed and intercompared.
Joannin, Colas; Chouvion, Benjamin; Thouverez, Fabrice; Ousty, Jean-Philippe; Mbaye, Moustapha
2017-01-01
This paper presents an extension to classic component mode synthesis methods to compute the steady-state forced response of nonlinear and dissipative structures. The procedure makes use of the nonlinear complex modes of each substructure, computed by means of a modified harmonic balance method, in order to build a reduced-order model easily solved by standard iterative solvers. The proposed method is applied to a mistuned cyclic structure subjected to dry friction forces, and proves particularly suitable for the study of such systems with high modal density and non-conservative nonlinearities.
Non-linear states of a positive or negative refraction index material in a cavity with feedback
Mártin, D. A.; Hoyuelos, M.
2010-06-01
We study a system composed by a cavity with plane mirrors containing a positive or negative refraction index material with third order effective electric and magnetic non-linearities. The aim of the work is to present a general picture of possible non-linear states in terms of the relevant parameters of the system. The parameters are the ones that appear in a reduced description that has the form of the Lugiato-Lefever equation. This equation is obtained from two coupled non-linear Schrödinger equations for the electric and magnetic field amplitudes.
Directory of Open Access Journals (Sweden)
Guowei Cai
2014-01-01
Full Text Available As to strong nonlinearity of doubly fed induction generators (DFIG and uncertainty of its model, a novel rotor current controller with nonlinearity and robustness is proposed to enhance fault ride-though (FRT capacities of grid-connected DFIG. Firstly, the model error, external disturbances, and the uncertain factors were estimated by constructing extended state observer (ESO so as to achieve linearization model, which is compensated dynamically from nonlinear model. And then rotor current controller of DFIG is designed by using terminal sliding mode variable structure control theory (TSMC. The controller has superior dynamic performance and strong robustness. The simulation results show that the proposed control approach is effective.
Nonlinear evolution of drift instabilities
Energy Technology Data Exchange (ETDEWEB)
Lee, W.W.; Krommes, J.A.; Oberman, C.R.; Smith, R.A.
1984-01-01
The nonlinear evolution of collisionless drift instabilities in a shear-free magnetic field has been studied by means of gyrokinetic particle simulation as well as numerical integration of model mode-coupling equations. The purpose of the investigation is to identify relevant nonlinear mechanisms responsible for the steady-state drift wave fluctuations. It is found that the saturation of the instability is mainly caused by the nonlinear E x B convection of the resonant electrons and their associated velocity space nonlinearity. The latter also induces energy exchange between the competing modes, which, in turn, gives rise to enhanced diffusion. The nonlinear E x B convection of the ions, which contributes to the nonlinear frequency shift, is also an important ingredient for the saturation.
A hierarchical state space approach to affective dynamics
Lodewyckx, Tom; Tuerlinckx, Francis; Kuppens, Peter; Allen, Nicholas; Sheeber, Lisa
2010-01-01
Linear dynamical system theory is a broad theoretical framework that has been applied in various research areas such as engineering, econometrics and recently in psychology. It quantifies the relations between observed inputs and outputs that are connected through a set of latent state variables. State space models are used to investigate the dynamical properties of these latent quantities. These models are especially of interest in the study of emotion dynamics, with the system representing the evolving emotion components of an individual. However, for simultaneous modeling of individual and population differences, a hierarchical extension of the basic state space model is necessary. Therefore, we introduce a Bayesian hierarchical model with random effects for the system parameters. Further, we apply our model to data that were collected using the Oregon adolescent interaction task: 66 normal and 67 depressed adolescents engaged in a conflict interaction with their parents and second-to-second physiological and behavioral measures were obtained. System parameters in normal and depressed adolescents were compared, which led to interesting discussions in the light of findings in recent literature on the links between cardiovascular processes, emotion dynamics and depression. We illustrate that our approach is flexible and general: The model can be applied to any time series for multiple systems (where a system can represent any entity) and moreover, one is free to focus on whatever component of the versatile model. PMID:21516216
Advancing brain-machine interfaces: moving beyond linear state space models.
Rouse, Adam G; Schieber, Marc H
2015-01-01
Advances in recent years have dramatically improved output control by Brain-Machine Interfaces (BMIs). Such devices nevertheless remain robotic and limited in their movements compared to normal human motor performance. Most current BMIs rely on transforming recorded neural activity to a linear state space composed of a set number of fixed degrees of freedom. Here we consider a variety of ways in which BMI design might be advanced further by applying non-linear dynamics observed in normal motor behavior. We consider (i) the dynamic range and precision of natural movements, (ii) differences between cortical activity and actual body movement, (iii) kinematic and muscular synergies, and (iv) the implications of large neuronal populations. We advance the hypothesis that a given population of recorded neurons may transmit more useful information than can be captured by a single, linear model across all movement phases and contexts. We argue that incorporating these various non-linear characteristics will be an important next step in advancing BMIs to more closely match natural motor performance.
A nonlinear optimization approach for disturbance rejection in flexible space structures
Parlos, Alexander G.; Sunkel, John W.
1990-01-01
In this paper the design of an active control law for the rejection of persistent disturbances in large space structures is presented. The control system design approach is based on a deterministic model of the disturbances, with a model-based-compensator (MBC) structure, optimizing the magnitude of the disturbance that the structure can tolerate without violating certain predetermined constraints. In addition to closed-loop stability, the explicit treatment of state, control and control rate constraints, such as structural displacement, control actuator effort, and compensator time guarantees that the final design will exhibit desired performance characteristics. The technique is applied for the vibration damping of a simple two bay truss structure which is subjected to persistent disturbances, such as shuttle docking. Preliminary results indicate that the proposed control system can reject considerable persistent disturbances by utilizing most of the available control, while limiting the structural displacements to within desired tolerances. Further work, however, for incorporating additional design criteria, such as compensator robustness to be traded-off against performance specifications, is warranted.
Institute of Scientific and Technical Information of China (English)
Su Shi-Lei; Wang Yuan; Guo Qi; Wang Hong-Fu; Zhang Shou
2012-01-01
We propose a protocol to generate a four-photon polarization-entangled cluster state with cross-Kerr nonlinearity by using the interference of polarized photons. The protocol is based on optical elements,cross-Kerr nonlinearity,and homodyne measurement,therefore it is feasible with current experimental technology.The success probability of our protocol is optimal,this property makes our protocol more efficient than others in the applications of quantum communication.
Population dynamics of an Arctiid caterpillar-tachinid parasitoid system using state-space models.
Karban, Richard; de Valpine, Perry
2010-05-01
1. Population dynamics of insect host-parasitoid systems are important in many natural and managed ecosystems and have inspired much ecological theory. However, ecologists have a limited knowledge about the relative strengths of species interactions, abiotic effects and density dependence in natural host-parasitoid dynamics. Statistical time-series analyses would be more informative by incorporating multiple factors, measurement error and noisy dynamics. 2. We use a novel maximum likelihood and model-selection analysis of a state-space model for host-parasitoid dynamics to examine 21 years of annual census data for woolly bear caterpillars (Platyprepia virginalis) and their locally host-specific tachinid parasitoids (Thelaira americana). 3. Caterpillar densities varied by three orders of magnitude and were driven by density dependence and precipitation from the previous March but not detectably by parasitoids, despite variable and sometimes high (>50%) parasitism. 4. Fly fluctuations, as estimated from per cent parasitism, were affected by density dependence and precipitation from the previous July. There was marginal evidence that host abundance drives fly fluctuations as a generic linear effect but no evidence for classical Nicholson-Bailey coupling. 5. The state-space model analysis includes new methods for likelihood calculation and allows a balanced consideration of effect magnitude and statistical significance in a nonlinear model with multiple alternative explanatory variables.
Chai, Lin; Qian, Chunjiang
2015-06-01
This paper investigates the design problem of constructing the state and output feedback stabilisation controller for a class of uncertain nonlinear systems subject to time-delay. First, a dynamic linear state feedback control law with an adaptive strategy is developed to globally stabilise the uncertain nonlinear time-delay system under a lower-triangular higher-order growth condition. Then, one more challenging problem of the adaptive output feedback stabilisation is addressed, which can globally stabilise the time-delay system when the unmeasurable states linearly grow with rate functions consisting of higher-order output.
Averaging in Parametrically Excited Systems – A State Space Formulation
Directory of Open Access Journals (Sweden)
Pfau Bastian
2016-01-01
Full Text Available Parametric excitation can lead to instabilities as well as to an improved stability behavior, depending on whether a parametric resonance or anti-resonance is induced. In order to calculate the stability domains and boundaries, the method of averaging is applied. The problem is reformulated in state space representation, which allows a general handling of the averaging method especially for systems with non-symmetric system matrices. It is highlighted that this approach can enhance the first order approximation significantly. Two example systems are investigated: a generic mechanical system and a flexible rotor in journal bearings with adjustable geometry.
H_2-Optimal Decentralized Control over Posets: A State-Space Solution for State-Feedback
Shah, Parikshit
2011-01-01
We develop a complete state-space solution to H_2-optimal decentralized control of poset-causal systems with state-feedback. Our solution is based on the exploitation of a key separability property of the problem, that enables an efficient computation of the optimal controller by solving a small number of uncoupled standard Riccati equations. Our approach gives important insight into the structure of optimal controllers, such as controller degree bounds that depend on the structure of the poset. A novel element in our state-space characterization of the controller is a remarkable pair of transfer functions, that belong to the incidence algebra of the poset, are inverses of each other, and are intimately related to prediction of the state along the different paths on the poset. The results are illustrated by a numerical example.
Energy Technology Data Exchange (ETDEWEB)
El-Hanbaly, A. M.; Sallah, M., E-mail: msallahd@mans.edu.eg [Mansoura University, Physics Department, Faculty of Science (Egypt); El-Shewy, E. K. [Taibah University Al-Madinah Al-Munawarah, Department of Physics (Saudi Arabia); Darweesh, H. F. [Mansoura University, Physics Department, Faculty of Science (Egypt)
2015-10-15
Linear and nonlinear dust-acoustic (DA) waves are studied in a collisionless, unmagnetized and dissipative dusty plasma consisting of negatively charged dust grains, Boltzmann-distributed electrons, and nonthermal ions. The normal mode analysis is used to obtain a linear dispersion relation illustrating the dependence of the wave damping rate on the carrier wave number, the dust viscosity coefficient, the ratio of the ion temperature to the electron temperatures, and the nonthermal parameter. The plasma system is analyzed nonlinearly via the reductive perturbation method that gives the KdV-Burgers equation. Some interesting physical solutions are obtained to study the nonlinear waves. These solutions are related to soliton, a combination between a shock and a soliton, and monotonic and oscillatory shock waves. Their behaviors are illustrated and shown graphically. The characteristics of the DA solitary and shock waves are significantly modified by the presence of nonthermal (fast) ions, the ratio of the ion temperature to the electron temperature, and the dust kinematic viscosity. The topology of the phase portrait and the potential diagram of the KdV-Burgers equation is illustrated, whose advantage is the ability to predict different classes of traveling wave solutions according to different phase orbits. The energy of the soliton wave and the electric field are calculated. The results in this paper can be generalized to analyze the nature of plasma waves in both space and laboratory plasma systems.
Approximate Bayesian Computation by Subset Simulation using hierarchical state-space models
Vakilzadeh, Majid K.; Huang, Yong; Beck, James L.; Abrahamsson, Thomas
2017-02-01
A new multi-level Markov Chain Monte Carlo algorithm for Approximate Bayesian Computation, ABC-SubSim, has recently appeared that exploits the Subset Simulation method for efficient rare-event simulation. ABC-SubSim adaptively creates a nested decreasing sequence of data-approximating regions in the output space that correspond to increasingly closer approximations of the observed output vector in this output space. At each level, multiple samples of the model parameter vector are generated by a component-wise Metropolis algorithm so that the predicted output corresponding to each parameter value falls in the current data-approximating region. Theoretically, if continued to the limit, the sequence of data-approximating regions would converge on to the observed output vector and the approximate posterior distributions, which are conditional on the data-approximation region, would become exact, but this is not practically feasible. In this paper we study the performance of the ABC-SubSim algorithm for Bayesian updating of the parameters of dynamical systems using a general hierarchical state-space model. We note that the ABC methodology gives an approximate posterior distribution that actually corresponds to an exact posterior where a uniformly distributed combined measurement and modeling error is added. We also note that ABC algorithms have a problem with learning the uncertain error variances in a stochastic state-space model and so we treat them as nuisance parameters and analytically integrate them out of the posterior distribution. In addition, the statistical efficiency of the original ABC-SubSim algorithm is improved by developing a novel strategy to regulate the proposal variance for the component-wise Metropolis algorithm at each level. We demonstrate that Self-regulated ABC-SubSim is well suited for Bayesian system identification by first applying it successfully to model updating of a two degree-of-freedom linear structure for three cases: globally
Yothers, Mitchell P; Bumm, Lloyd A
2016-01-01
We have developed a real-space method to correct distortion due to thermal drift and piezoelectric actuator nonlinearities on scanning tunneling microscope images using Matlab. The method uses the known structures typically present in high-resolution atomic and molecularly-resolved images as an internal standard. Each image feature (atom or molecule) is first identified in the image. The locations of each feature's nearest neighbors (NNs) are used to measure the local distortion at that location. The local distortion map across the image is simultaneously fit to our distortion model, which includes thermal drift in addition to piezoelectric actuator hysteresis and creep. The image coordinates of the features and image pixels are corrected using an inverse transform from the distortion model. We call this technique the thermal-drift, hysteresis, and creep transform (DHCT). Performing the correction in real space allows defects, domain boundaries, and step edges to be excluded with a spatial mask. Additional re...
Homotopy deform method for reproducing kernel space for nonlinear boundary value problems
Indian Academy of Sciences (India)
MIN-QIANG XU; YING-ZHEN LIN
2016-10-01
In this paper, the combination of homotopy deform method (HDM) and simplified reproducing kernel method (SRKM) is introduced for solving the boundary value problems (BVPs) of nonlinear differential equations. The solution methodology is based on Adomian decomposition and reproducing kernel method (RKM). By the HDM, the nonlinear equations can be converted into a series of linear BVPs. After that, the simplified reproducing kernel method, which not only facilitates the reproducing kernel but also avoids the time-consuming Schmidt orthogonalization process, is proposed to solve linear equations. Some numerical test problems including ordinary differential equations and partial differential equations are analysed to illustrate the procedure and confirm the performance of the proposed method. The results faithfully reveal that our algorithm is considerably accurate and effective as expected.
Effect of joint damping and joint nonlinearity on the dynamics of space structures
Bowden, Mary; Dugundji, John
1988-01-01
Analyses of the effect of linear joint characteristics on the vibrations of a free-free, three-joint beam model show that increasing joint damping increases resonant frequencies and increases modal damping but only to the point where the joint gets 'locked up' by damping. This behavior is different from that predicted by modeling joint damping as proportional damping. Nonlinear analyses of the three-joint model with cubic springs at the joints show all the classical single DOF nonlinear response behavior at each resonance of the multiple DOF system: nondoubling of response for a doubling of forcing amplitude, multiple solutions, jump behavior, and resonant frequency shifts. These properties can be concisely quantified by characteristic backbone curves, which show the locus of resonant peaks for increasing forcing amplitude.
EXISTENCE OF SOLUTIONS OF A FAMILY OF NONLINEAR BOUNDARY VALUE PROBLEMS IN L2-SPACES
Institute of Scientific and Technical Information of China (English)
WeiLi; ZhouHaiyun
2005-01-01
By using the perturbation results of sums of ranges of accretive mappings of Calvert and Gupta (1978),the abstract results on the existence of solutions of a family of nonlinear boundary value problems in L2 (Ω) are studied. The equation discussed in this paper and the methods used here are extension and complement to the corresponding results of Wei Li and He Zhen's previous papers. Especially,some new techniques are used in this paper.
State space approach to single molecule localization in fluorescence microscopy.
Vahid, Milad R; Chao, Jerry; Kim, Dongyoung; Ward, E Sally; Ober, Raimund J
2017-03-01
Single molecule super-resolution microscopy enables imaging at sub-diffraction-limit resolution by producing images of subsets of stochastically photoactivated fluorophores over a sequence of frames. In each frame of the sequence, the fluorophores are accurately localized, and the estimated locations are used to construct a high-resolution image of the cellular structures labeled by the fluorophores. Many methods have been developed for localizing fluorophores from the images. The majority of these methods comprise two separate steps: detection and estimation. In the detection step, fluorophores are identified. In the estimation step, the locations of the identified fluorophores are estimated through an iterative approach. Here, we propose a non-iterative state space-based localization method which combines the detection and estimation steps. We demonstrate that the estimated locations obtained from the proposed method can be used as initial conditions in an estimation routine to potentially obtain improved location estimates. The proposed method models the given image as the frequency response of a multi-order system obtained with a balanced state space realization algorithm based on the singular value decomposition of a Hankel matrix. The locations of the poles of the resulting system determine the peak locations in the frequency domain, and the locations of the most significant peaks correspond to the single molecule locations in the original image. The performance of the method is validated using both simulated and experimental data.
Iterative feedback tuning of uncertain state space systems
Directory of Open Access Journals (Sweden)
J. K. Huusom
2010-09-01
Full Text Available Iterative Feedback Tuning is a purely data driven tuning algorithm for optimizing control parameters based on closed loop data. The algorithm is designed to produce an unbiased estimate of the performance cost function gradient for iteratively improving the control parameters to achieve optimal loop performance. This tuning method has been developed for systems based on a transfer function representation. This paper presents a state feedback control system with a state observer and its transfer function equivalent in terms of input output dynamics. It is shown how the parameters in the closed loop state space system can be tuned by Iterative Feedback Tuning utilizing this equivalent representation. A simulation example illustrates that the tuning converges to the known analytical solution for the feedback control gain and to the Kalman gain in the state observer. In case of parametric uncertainty, different choices of tuning parameters are investigated. It is shown that the data driven tuning method produces optimal performance for convex problems when it is the model parameter estimates in the observer that are tuned.
Nonlinear effect of elastic vortexlike motion on the dynamic stress state of solids
Shilko, Evgeny V.; Grinyaev, Yurii V.; Popov, Mikhail V.; Popov, Valentin L.; Psakhie, Sergey G.
2016-05-01
We present a theoretical analysis of the dynamic stress-strain state of regions in a solid body that are involved in a collective elastic vortexlike motion. It is shown that the initiation of elastic vortexlike motion in the material is accompanied by the appearance of dilatancy and equivalent strain, the magnitudes of which are proportional to the square of the ratio of linear velocity on the periphery of the elastic vortex to the velocity of longitudinal elastic waves (P wave). Under conditions of dynamic loading the described dynamic effects are able to initiate inelastic deformation or destruction of the material at loading speeds of a few percent of the P -wave speed. The obtained analytical estimates suggest that dynamic nonlinear strains can make a significant contribution in a number of widely studied nonlinear dynamic phenomena in solids. Among them are the effect of acoustic (dynamic) dilatancy in solids and granular media, which leads to the generation of longitudinal elastic waves by transverse waves [V. Tournat et al., Phys. Rev. Lett. 92, 085502 (2004), 10.1103/PhysRevLett.92.085502] and the formation of an array of intense "hot spots" (reminiscent of shear-induced hydrodynamic instabilities in fluids) in adiabatic shear bands [P. R. Guduru et al., Phys. Rev. E 64, 036128 (2001), 10.1103/PhysRevE.64.036128].
Directory of Open Access Journals (Sweden)
A.M. Elnaggar
2016-01-01
Full Text Available An analysis of primary, superharmonic of order five, and subharmonic of order one-three resonances for non-linear s.d.o.f. system with two distinct time-delays under an external excitation is investigated. The method of multiple scales is used to determine two first order ordinary differential equations which describe the modulation of the amplitudes and the phases. Steady-state solutions and their stabilities in each resonance are studied. Numerical results are obtained by using the Software of Mathematica, which presented in a group of figures. The effect of the feedback gains and time-delays on the non-linear response of the system is discussed and it is found that: an appropriate feedback can enhance the control performance. A suitable choice of the feedback gains and time-delays can enlarge the critical force amplitude, and reduce the peak amplitude of the response (or peak amplitude of the free oscillation term for the case of primary resonance (superharmonic resonance. Furthermore, a proper feedback can eliminate saddle-node bifurcation, thereby eliminating jump and hysteresis phenomena taking place in the corresponding uncontrolled system. For subharmonic resonance, an adequate feedback can reduce the regions of subharmonic resonance response.
Surface Gap Soliton Ground States for the Nonlinear Schr\\"{o}dinger Equation
Dohnal, Tomáš; Reichel, Wolfgang
2010-01-01
We consider the nonlinear Schr\\"{o}dinger equation $(-\\Delta +V(x))u = \\Gamma(x) |u|^{p-1}u$, $x\\in \\R^n$ with $V(x) = V_1(x) \\chi_{\\{x_1>0\\}}(x)+V_2(x) \\chi_{\\{x_10\\}}(x)+\\Gamma_2(x) \\chi_{\\{x_1<0\\}}(x)$ and with $V_1, V_2, \\Gamma_1, \\Gamma_2$ periodic in each coordinate direction. This problem describes the interface of two periodic media, e.g. photonic crystals. We study the existence of ground state $H^1$ solutions (surface gap soliton ground states) for $0<\\min \\sigma(-\\Delta +V)$. Using a concentration compactness argument, we provide an abstract criterion for the existence based on ground state energies of each periodic problem (with $V\\equiv V_1, \\Gamma\\equiv \\Gamma_1$ and $V\\equiv V_2, \\Gamma\\equiv \\Gamma_2$) as well as a more practical criterion based on ground states themselves. Examples of interfaces satisfying these criteria are provided. In 1D it is shown that, surprisingly, the criteria can be reduced to conditions on the linear Bloch waves of the operators $-\\tfrac{d^2}{dx^2} +V_1(x)$ an...
Perspectives for quantum state engineering via high non-linearity in a double-EIT regime
Paternostro, M; Ham, B S
2003-01-01
We analyse the possibilities for quantum state engineering offered by a model for Kerr-type non-linearity enhanced by electromagnetically induced transparency (EIT), which was recently proposed by Petrosyan and Kurizki [{\\sl Phys. Rev. A} {\\bf 65}, 33833 (2002)]. We go beyond the semiclassical treatment and derive a quantum version of the model with both a full Hamiltonian approach and an analysis in terms of dressed states. The preparation of an entangled coherent state via a cross-phase modulation effect is demonstrated. We briefly show that the violation of locality for such an entangled coherent state is robust against low detection efficiency. Finally, we investigate the possibility of a bi-chromatic photon blockade realized via the interaction of a low density beam of atoms with a bi-modal electromagnetic cavity which is externally driven. We show the effectiveness of the blockade effect even when more than a single atom is inside the cavity. The possibility to control two different cavity modes allows ...
Directory of Open Access Journals (Sweden)
Hideki Gotoh
2014-10-01
Full Text Available Optical nonlinear effects are examined using a two-color micro-photoluminescence (micro-PL method in a coherently coupled exciton-biexciton system in a single quantum dot (QD. PL and photoluminescence excitation spectroscopy (PLE are employed to measure the absorption spectra of the exciton and biexciton states. PLE for Stokes and anti-Stokes PL enables us to clarify the nonlinear optical absorption properties in the lowest exciton and biexciton states. The nonlinear absorption spectra for excitons exhibit asymmetric shapes with peak and dip structures, and provide a distinct contrast to the symmetric dip structures of conventional nonlinear spectra. Theoretical analyses with a density matrix method indicate that the nonlinear spectra are caused not by a simple coherent interaction between the exciton and biexciton states but by coupling effects among exciton, biexciton and continuum states. These results indicate that Fano quantum interference effects appear in exciton-biexciton systems at QDs and offer important insights into their physics.
Tadepalli, Siva Kumar; Krishna Rao Kandanvli, V.; Kar, Haranath
2015-11-01
A recently reported paper (Ji, X., Liu, T., Sun, Y., and Su, H. (2011), 'Stability analysis and controller synthesis for discrete linear time-delay systems with state saturation nonlinearities', International Journal of Systems Science, 42, 397-406) for the global asymptotic stability analysis and controller synthesis for a class of discrete linear time delay systems employing state saturation nonlinearities is reviewed. It is claimed in Ji, Liu, Sun and Su (2011) that a previous approach by Kandanvli and Kar (Kandanvli, V.K.R and Kar, H. (2009), 'Robust stability of discrete-time state-delayed systems with saturation nonlinearities: Linear matrix inequality approach', Signal Processing, 89, 161-173) is recovered from their approach as a special case. It is shown that this claim is not justified.
Different models of the active cochlea, and how to implement them in the state-space formalism.
Sisto, Renata; Moleti, Arturo; Paternoster, Nicolo; Botti, Teresa; Bertaccini, Daniele
2010-09-01
The state-space formalism [Elliott S. J., et al. (2007). J. Acoust. Soc. Am. 122, 2759-2771] allows one to discretize cochlear models in a straightforward matrix form and to modify the main physical properties of the cochlear model by changing the position and functional form of a few matrix elements. Feed-forward and feed-backward properties can be obtained by simply introducing off-diagonal terms in the matrixes expressing the coupling between the dynamical variables and the additional active pressure on the basilar membrane. Some theoretical issues related to different cochlear modeling choices, their implementation in a state-space scheme, and their physical consequences on the cochlear phenomenology, as predicted by numerical simulations, are discussed. Different schematizations of the active term describing the behavior of the outer hair cell's feedback mechanism, including nonlinear and nonlocal dependences on either pressure or basilar membrane displacement, are also discussed, showing their effect on some measurable cochlear properties.
Equivalence of Nonlinear Systems to Input-Output Prime Forms
Marino, R.; Respondek, W.; van der Schaft, A. J.
1994-01-01
The problem of transforming nonlinear control systems into input-output prime forms is dealt with, using state space, static state feedback, and also output space transformations. Necessary and sufficient geometric conditions for the solvability of this problem are obtained. The results obtained generalize well-known results both on feedback linearization as well as input-output decoupling of nonlinear systems. It turns out that, from a computational point of view, the output space transforma...
A Markovian state-space framework for integrating flexibility into space system design decisions
Lafleur, Jarret M.
The past decades have seen the state of the art in aerospace system design progress from a scope of simple optimization to one including robustness, with the objective of permitting a single system to perform well even in off-nominal future environments. Integrating flexibility, or the capability to easily modify a system after it has been fielded in response to changing environments, into system design represents a further step forward. One challenge in accomplishing this rests in that the decision-maker must consider not only the present system design decision, but also sequential future design and operation decisions. Despite extensive interest in the topic, the state of the art in designing flexibility into aerospace systems, and particularly space systems, tends to be limited to analyses that are qualitative, deterministic, single-objective, and/or limited to consider a single future time period. To address these gaps, this thesis develops a stochastic, multi-objective, and multi-period framework for integrating flexibility into space system design decisions. Central to the framework are five steps. First, system configuration options are identified and costs of switching from one configuration to another are compiled into a cost transition matrix. Second, probabilities that demand on the system will transition from one mission to another are compiled into a mission demand Markov chain. Third, one performance matrix for each design objective is populated to describe how well the identified system configurations perform in each of the identified mission demand environments. The fourth step employs multi-period decision analysis techniques, including Markov decision processes from the field of operations research, to find efficient paths and policies a decision-maker may follow. The final step examines the implications of these paths and policies for the primary goal of informing initial system selection. Overall, this thesis unifies state-centric concepts of