Baldi, Marco
2010-01-01
We present a complete numerical study of cosmological models with a time dependent coupling between the dark energy component driving the present accelerated expansion of the Universe and the Cold Dark Matter (CDM) fluid. Depending on the functional form of the coupling strength, these models show a range of possible intermediate behaviors between the standard LCDM background evolution and the widely studied case of interacting dark energy models with a constant coupling. These different background evolutions play a crucial role in the growth of cosmic structures, and determine strikingly different effects of the coupling on the internal dynamics of nonlinear objects. By means of a suitable modification of the cosmological N-body code GADGET-2 we have performed a series of high-resolution N-body simulations of structure formation in the context of interacting dark energy models with variable couplings. Depending on the type of background evolution, the halo density profiles are found to be either less or more...
Energy Technology Data Exchange (ETDEWEB)
Cruz, Hans, E-mail: hans@ciencias.unam.mx [Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apartado Postal 70-543, 04510 México DF (Mexico); Schuch, Dieter [Institut für Theoretische Physik, JW Goethe-Universität Frankfurt am Main, Max-von-Laue-Str. 1, D-60438 Frankfurt am Main (Germany); Castaños, Octavio, E-mail: ocasta@nucleares.unam.mx [Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apartado Postal 70-543, 04510 México DF (Mexico); Rosas-Ortiz, Oscar [Physics Department, Cinvestav, A. P. 14-740, 07000 México D. F. (Mexico)
2015-09-15
The sensitivity of the evolution of quantum uncertainties to the choice of the initial conditions is shown via a complex nonlinear Riccati equation leading to a reformulation of quantum dynamics. This sensitivity is demonstrated for systems with exact analytic solutions with the form of Gaussian wave packets. In particular, one-dimensional conservative systems with at most quadratic Hamiltonians are studied.
Finite time extinction for nonlinear fractional evolution equations and related properties.
Jesus Ildefonso Diaz; Teresa Pierantozzi; Luis Vazquez
2016-01-01
The finite time extinction phenomenon (the solution reaches an equilibrium after a finite time) is peculiar to certain nonlinear problems whose solutions exhibit an asymptotic behavior entirely different from the typical behavior of solutions associated to linear problems. The main goal of this work is twofold. Firstly, we extend some of the results known in the literature to the case in which the ordinary time derivative is considered jointly with a fractional time differentiation. Secondly,...
Time-evolution of quantum systems via a complex nonlinear Riccati equation. II. Dissipative systems
Cruz, Hans; Schuch, Dieter; Castaños, Octavio; Rosas-Ortiz, Oscar
2016-10-01
In our former contribution (Cruz et al., 2015), we have shown the sensitivity to the choice of initial conditions in the evolution of Gaussian wave packets via the nonlinear Riccati equation. The formalism developed in the previous work is extended to effective approaches for the description of dissipative quantum systems. By means of simple examples we show the effects of the environment on the quantum uncertainties, correlation function, quantum energy contribution and tunnelling currents. We prove that the environmental parameter γ is strongly related with the sensitivity to the choice of initial conditions.
Soliton solutions of some nonlinear evolution equations with time-dependent coefficients
Indian Academy of Sciences (India)
Hitender Kumar; Anand Malik; Fakir Chand
2013-02-01
In this paper, we obtain exact soliton solutions of the modified KdV equation, inho-mogeneous nonlinear Schrödinger equation and (, ) equation with variable coefficients using solitary wave ansatz. The constraint conditions among the time-dependent coefficients turn out as necessary conditions for the solitons to exist. Numerical simulations for dark and bright soliton solutions for the mKdV equation are also given.
Finite time extinction for nonlinear fractional evolution equations and related properties
Directory of Open Access Journals (Sweden)
Jesus Ildefonso Diaz
2016-08-01
Full Text Available The finite time extinction phenomenon (the solution reaches an equilibrium after a finite time is peculiar to certain nonlinear problems whose solutions exhibit an asymptotic behavior entirely different from the typical behavior of solutions associated to linear problems. The main goal of this work is twofold. Firstly, we extend some of the results known in the literature to the case in which the ordinary time derivative is considered jointly with a fractional time differentiation. Secondly, we consider the limit case when only the fractional derivative remains. The latter is the most extraordinary case, since we prove that the finite time extinction phenomenon still appears, even with a non-smooth profile near the extinction time.
Nonlinear evolution equations in QCD
Stasto, A. M.
2004-01-01
The following lectures are an introduction to the phenomena of partonic saturation and nonlinear evolution equations in Quantum Chromodynamics. After a short introduction to the linear evolution, the problems of unitarity bound and parton saturation are discussed. The nonlinear Balitsky-Kovchegov evolution equation in the high energy limit is introduced, and the progress towards the understanding of the properties of its solution is reviewed. We discuss the concepts of the saturation scale, g...
On a Nonlinear Model in Adiabatic Evolutions
Sun, Jie; Lu, Song-Feng
2016-08-01
In this paper, we study a kind of nonlinear model of adiabatic evolution in quantum search problem. As will be seen here, for this problem, there always exists a possibility that this nonlinear model can successfully solve the problem, while the linear model can not. Also in the same setting, when the overlap between the initial state and the final stare is sufficiently large, a simple linear adiabatic evolution can achieve O(1) time efficiency, but infinite time complexity for the nonlinear model of adiabatic evolution is needed. This tells us, it is not always a wise choice to use nonlinear interpolations in adiabatic algorithms. Sometimes, simple linear adiabatic evolutions may be sufficient for using. Supported by the National Natural Science Foundation of China under Grant Nos. 61402188 and 61173050. The first author also gratefully acknowledges the support from the China Postdoctoral Science Foundation under Grant No. 2014M552041
Nonlinear Evolution of Ferroelectric Domains
Institute of Scientific and Technical Information of China (English)
WeiLU; Dai－NingFANG; 等
1997-01-01
The nonlinear evolution of ferroelectric domains is investigated in the paper and amodel is proposed which can be applied to numerical computation.Numerical results show that the model can accurately predict some nonlinear behavior and consist with those experimental results.
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.
Nonsmooth analysis of doubly nonlinear evolution equations
Mielke, Alexander; Savare', Giuseppe
2011-01-01
In this paper we analyze a broad class of abstract doubly nonlinear evolution equations in Banach spaces, driven by nonsmooth and nonconvex energies. We provide some general sufficient conditions, on the dissipation potential and the energy functional,for existence of solutions to the related Cauchy problem. We prove our main existence result by passing to the limit in a time-discretization scheme with variational techniques. Finally, we discuss an application to a material model in finite-strain elasticity.
Nonlinear forecasting of intertidal shoreface evolution
Grimes, D. J.; Cortale, N.; Baker, K.; McNamara, D. E.
2015-10-01
Natural systems dominated by sediment transport are notoriously difficult to forecast. This is particularly true along the ocean coastline, a region that draws considerable human attention as economic investment and infrastructure are threatened by both persistent, long-term and acute, event driven processes (i.e., sea level rise and storm damage, respectively). Forecasting the coastline's evolution over intermediate time (daily) and space (tens of meters) scales is hindered by the complexity of sediment transport and hydrodynamics, and limited access to the detailed local forcing that drives fast scale processes. Modern remote sensing systems provide an efficient, economical means to collect data within these regions. A solar-powered digital camera installation is used to capture the coast's evolution, and machine learning algorithms are implemented to extract the shoreline and estimate the daily mean intertidal coastal profile. Methods in nonlinear time series forecasting and genetic programming applied to these data corroborate that coastal morphology at these scales is predominately driven by nonlinear internal dynamics, which partially mask external forcing signatures. Results indicate that these forecasting techniques achieve nontrivial predictive skill for spatiotemporal forecast of the upper coastline profile (as much as 43% of variance in data explained for one day predictions). This analysis provides evidence that societally relevant coastline forecasts can be achieved without knowing the forcing environment or the underlying dynamical equations that govern coastline evolution.
Nonlinear Evolution of Alfvenic Wave Packets
Buti, B.; Jayanti, V.; Vinas, A. F.; Ghosh, S.; Goldstein, M. L.; Roberts, D. A.; Lakhina, G. S.; Tsurutani, B. T.
1998-01-01
Alfven waves are a ubiquitous feature of the solar wind. One approach to studying the evolution of such waves has been to study exact solutions to approximate evolution equations. Here we compare soliton solutions of the Derivative Nonlinear Schrodinger evolution equation (DNLS) to solutions of the compressible MHD equations.
Saturation at low x and nonlinear evolution
Stasto, A. M.
2002-01-01
In this talk the results of the analytical and numerical analysis of the nonlinear Balitsky-Kovchegov equation are presented. The characteristic BFKL diffusion into infrared regime is suppressed by the generation of the saturation scale. We identify the scaling and linear regimes for the solution. We also study the impact of subleading corrections onto the nonlinear evolution.
Femtosecond nonlinear polarization evolution based on cascade quadratic nonlinearities.
Liu, X; Ilday, F O; Beckwitt, K; Wise, F W
2000-09-15
We experimentally demonstrate that one can exploit nonlinear phase shifts produced in type I phase-mismatched second-harmonic generation to produce intensity-dependent polarization evolution with 100-fs pulses. An amplitude modulator based on nonlinear polarization rotation provides passive amplitude-modulation depth of up to ~50%. Applications of the amplitude and phase modulations to mode locking of femtosecond bulk and fiber lasers are promising and are discussed.
Directory of Open Access Journals (Sweden)
Jia Hui Ong
2016-07-01
Full Text Available Parameter searching is one of the most important aspects in getting favorable results in optimization problems. It is even more important if the optimization problems are limited by time constraints. In a limited time constraint problems, it is crucial for any algorithms to get the best results or near-optimum results. In a previous study, Differential Evolution (DE has been found as one of the best performing algorithms under time constraints. As this has help in answering which algorithm that yields results that are near-optimum under a limited time constraint. Hence to further enhance the performance of DE under time constraint evaluation, a throughout parameter searching for population size, mutation constant and f constant have been carried out. CEC 2015 Global Optimization Competition’s 15 scalable test problems are used as test suite for this study. In the previous study the same test suits has been used and the results from DE will be use as the benchmark for this study since it shows the best results among the previous tested algorithms. Eight different populations size are used and they are 10, 30, 50, 100, 150, 200, 300, and 500. Each of these populations size will run with mutation constant of 0.1 until 0.9 and from 0.1 until 0.9. It was found that population size 100, Cr = 0.9, F=0.5 outperform the benchmark results. It is also observed from the results that good higher Cr around 0.8 and 0.9 with low F around 0.3 to 0.4 yields good results for DE under time constraints evaluation
Nonlinear Evolution of Aggregates with Inextensible Constraints
Institute of Scientific and Technical Information of China (English)
Ming－XiangCHEN; WeiYANG; 等
1996-01-01
Crystalline and semicrystalline polymers are formed as aggregates of grains with evolving inextensible axes.This inextensible constratint leads to texture evolution under large plastic deformation.This paper reveals the nonlinear texture evolution of crystalline polymers under axi-symmetric straining.
Nonlinear evolution of parallel propagating Alfven waves: Vlasov - MHD simulation
Nariyuki, Y; Kumashiro, T; Hada, T
2009-01-01
Nonlinear evolution of circularly polarized Alfv\\'en waves are discussed by using the recently developed Vlasov-MHD code, which is a generalized Landau-fluid model. The numerical results indicate that as far as the nonlinearity in the system is not so large, the Vlasov-MHD model can validly solve time evolution of the Alfv\\'enic turbulence both in the linear and nonlinear stages. The present Vlasov-MHD model is proper to discuss the solar coronal heating and solar wind acceleration by Alfve\\'n waves propagating from the photosphere.
Time Evolution in Dynamical Spacetimes
Tiemblo, A
1996-01-01
We present a gauge--theoretical derivation of the notion of time, suitable to describe the Hamiltonian time evolution of gravitational systems. It is based on a nonlinear coset realization of the Poincaré group, implying the time component of the coframe to be invariant, and thus to represent a metric time. The unitary gauge fixing of the boosts gives rise to the foliation of spacetime along the time direction. The three supressed degrees of freedom correspond to Goldstone--like fields, whereas the remaining time component is a Higgs--like boson.
Time evolution in the presence of gravity
Pulido, A; Tresguerres, R; Pulido, Antonio; Tiemblo, Alfredo; Tresguerres, Romualdo
2001-01-01
We present a suggestion on the interpretation of canonical time evolution when gravitation is present, based on the nonlinear gauge approach to gravity. Essentially, our proposal consists of an internal-time concept, with the time variable taken from the dynamical fields characteristic of the nonlinear realization of the internal time-translational symmetry. Physical time evolution requires the latter symmetry to be broken. After disregarding other breaking mechanisms, we appeal to the Jordan-Brans-Dicke action, conveniently interpreted, to achieve that goal. We show that nontrivial time evolution follows, the special relativistic limit being recovered in the absence of gravity.
Csizmadia, Peter; Racz, Istvan
2013-01-01
A new numerical method is introduced to study the problem of time evolution of generic non-linear dynamical systems in four-dimensional spacetimes. It is assumed that the time level surfaces are foliated by a one-parameter family of codimension two compact surfaces with no boundary and which are conformal to a Riemannian manifold C. The method is based on the use of a multipole expansion determined uniquely by the induced metric structure on C. The approach is fully spectral in the angular directions. The dynamics in the complementary 1+1 Lorentzian spacetime is followed by making use of a fourth order finite differencing scheme with adaptive mesh refinement. In checking the reliability of the introduced new method the evolution of a massless scalar field on a fixed Kerr spacetime is investigated. In particular, the angular distribution of the evolving field in to be superradiant scattering is studied. The primary aim was to check the validity of some of the recent arguments claiming that the Penrose process,...
Nonlinear evolution of whistler wave modulational instability
DEFF Research Database (Denmark)
Karpman, V.I.; Lynov, Jens-Peter; Michelsen, Poul;
1995-01-01
The nonlinear evolution of the modulational instability of whistler waves coupled to fast magnetosonic waves (FMS) and to slow magnetosonic waves (SMS) is investigated. Results from direct numerical solutions in two spatial dimensions agree with simplified results from a set of ordinary different......The nonlinear evolution of the modulational instability of whistler waves coupled to fast magnetosonic waves (FMS) and to slow magnetosonic waves (SMS) is investigated. Results from direct numerical solutions in two spatial dimensions agree with simplified results from a set of ordinary...
Evolution Of Nonlinear Waves in Compressing Plasma
Energy Technology Data Exchange (ETDEWEB)
P.F. Schmit, I.Y. Dodin, and N.J. Fisch
2011-05-27
Through particle-in-cell simulations, the evolution of nonlinear plasma waves is examined in one-dimensional collisionless plasma undergoing mechanical compression. Unlike linear waves, whose wavelength decreases proportionally to the system length L(t), nonlinear waves, such as solitary electron holes, conserve their characteristic size {Delta} during slow compression. This leads to a substantially stronger adiabatic amplification as well as rapid collisionless damping when L approaches {Delta}. On the other hand, cessation of compression halts the wave evolution, yielding a stable mode.
Time Series with Tailored Nonlinearities
Raeth, C
2015-01-01
It is demonstrated how to generate time series with tailored nonlinearities by inducing well- defined constraints on the Fourier phases. Correlations between the phase information of adjacent phases and (static and dynamic) measures of nonlinearities are established and their origin is explained. By applying a set of simple constraints on the phases of an originally linear and uncor- related Gaussian time series, the observed scaling behavior of the intensity distribution of empirical time series can be reproduced. The power law character of the intensity distributions being typical for e.g. turbulence and financial data can thus be explained in terms of phase correlations.
Predicting Nonlinear Time Series
1993-12-01
response becomes R,(k) = f (Y FV,(k)) (2.4) where Wy specifies the weight associated with the output of node i to the input of nodej in the next layer and...interconnections for each of these previous nodes. 18 prr~~~o• wfe :t iam i -- ---- --- --- --- Figure 5: Delay block for ATNN [9] Thus, nodej receives the...computed values, aj(tn), and dj(tn) denotes the desired output of nodej at time in. In this thesis, the weights and time delays update after each input
Nonlinear evolution of the modulational instability of whistler waves
DEFF Research Database (Denmark)
Karpman, V.I.; Hansen, F.R.; Huld, T.
1990-01-01
The nonlinear evolution of the modulational instability of whistler waves coupled to fast magnetosonic waves is investigated in two spatial dimensions by numerical simulations. The long time evolution of the modulational instability shows a quasirecurrent behavior with a slow spreading...... of the energy, originally confined to the lowest wave numbers, to larger and larger wave numbers resulting in an apparently chaotic or random wave field. © 1990 The American Physical Society...
TAYLOR EXPANSION METHOD FOR NONLINEAR EVOLUTION EQUATIONS
Institute of Scientific and Technical Information of China (English)
HE Yin-nian
2005-01-01
A new numerical method of integrating the nonlinear evolution equations, namely the Taylor expansion method, was presented. The standard Galerkin method can be viewed as the 0-th order Taylor expansion method; while the nonlinear Galerkin method can be viewed as the 1-st order modified Taylor expansion method. Moreover, the existence of the numerical solution and its convergence rate were proven. Finally, a concrete example,namely, the two-dimensional Navier-Stokes equations with a non slip boundary condition,was provided. The result is that the higher order Taylor expansion method is of the higher convergence rate under some assumptions about the regularity of the solution.
The nonlinear evolution of modes on unstable stratified shear layers
Blackaby, Nicholas; Dando, Andrew; Hall, Philip
1993-06-01
The nonlinear development of disturbances in stratified shear flows (having a local Richardson number of value less than one quarter) is considered. Such modes are initially fast growing but, like related studies, we assume that the viscous, non-parallel spreading of the shear layer results in them evolving in a linear fashion until they reach a position where their amplitudes are large enough and their growth rates have diminished sufficiently so that amplitude equations can be derived using weakly nonlinear and non-equilibrium critical-layer theories. Four different basic integro-differential amplitude equations are possible, including one due to a novel mechanism; the relevant choice of amplitude equation, at a particular instance, being dependent on the relative sizes of the disturbance amplitude, the growth rate of the disturbance, its wavenumber, and the viscosity of the fluid. This richness of choice of possible nonlinearities arises mathematically from the indicial Frobenius roots of the governing linear inviscid equation (the Taylor-Goldstein equation) not, in general, differing by an integer. The initial nonlinear evolution of a mode will be governed by an integro-differential amplitude equations with a cubic nonlinearity but the resulting significant increase in the size of the disturbance's amplitude leads on to the next stage of the evolution process where the evolution of the mode is governed by an integro-differential amplitude equations with a quintic nonlinearity. Continued growth of the disturbance amplitude is expected during this stage, resulting in the effects of nonlinearity spreading to outside the critical level, by which time the flow has become fully nonlinear.
3-D nonlinear evolution of MHD instabilities
Energy Technology Data Exchange (ETDEWEB)
Bateman, G.; Hicks, H. R.; Wooten, J. W.
1977-03-01
The nonlinear evolution of ideal MHD internal instabilities is investigated in straight cylindrical geometry by means of a 3-D initial-value computer code. These instabilities are characterized by pairs of velocity vortex cells rolling off each other and helically twisted down the plasma column. The cells persist until the poloidal velocity saturates at a few tenths of the Alfven velocity. The nonlinear phase is characterized by convection around these essentially fixed vortex cells. For example, the initially centrally peaked temperature profile is convected out and around to form an annulus of high temperature surrounding a small region of lower temperature. Weak, centrally localized instabilities do not alter the edge of the plasma. Strong, large-scale instabilities, resulting from a stronger longitudinal equilibrium current, drive the plasma against the wall. After three examples of instability are analyzed in detail, the numerical methods and their verification are discussed.
DYNAMIC BIFURCATION OF NONLINEAR EVOLUTION EQUATIONS
Institute of Scientific and Technical Information of China (English)
MA TIAN; WANG SHOUHONG
2005-01-01
The authors introduce a notion of dynamic bifurcation for nonlinear evolution equations, which can be called attractor bifurcation. It is proved that as the control parameter crosses certain critical value, the system bifurcates from a trivial steady state solution to an attractor with dimension between m and m + 1, where m + 1 is the number of eigenvalues crossing the imaginary axis. The attractor bifurcation theory presented in this article generalizes the existing steady state bifurcations and the Hopf bifurcations. It provides a unified point of view on dynamic bifurcation and can be applied to many problems in physics and mechanics.
Nonlinear Evolution of Magnetic Islands in the Magnetopause Current Sheet
Institute of Scientific and Technical Information of China (English)
XianminWANG; ZuyinPU
1996-01-01
Nonlinear evolution of magnetic islands produced by time-dependent magnetic reconnection in the magnetopause current sheet is studied.It is shown that the magnetic islands are unstable against the interference from external disturbances.Their structure can be destroyed by medium and small-scale solar wind turbulences,leading to stochastic magnetic reconnection and the formation of irregular small0scale structures in magnetospheric boundary regions.
Some new solutions of nonlinear evolution equations with variable coefficients
Virdi, Jasvinder Singh
2016-05-01
We construct the traveling wave solutions of nonlinear evolution equations (NLEEs) with variable coefficients arising in physics. Some interesting nonlinear evolution equations are investigated by traveling wave solutions which are expressed by the hyperbolic functions, the trigonometric functions and rational functions. The applied method will be used in further works to establish more entirely new solutions for other kinds of such nonlinear evolution equations with variable coefficients arising in physics.
Nonlinear time series modelling: an introduction
Simon M. Potter
1999-01-01
Recent developments in nonlinear time series modelling are reviewed. Three main types of nonlinear models are discussed: Markov Switching, Threshold Autoregression and Smooth Transition Autoregression. Classical and Bayesian estimation techniques are described for each model. Parametric tests for nonlinearity are reviewed with examples from the three types of models. Finally, forecasting and impulse response analysis is developed.
Common large innovations across nonlinear time series
Ph.H.B.F. Franses (Philip Hans); R. Paap (Richard)
2002-01-01
textabstractWe propose a multivariate nonlinear econometric time series model, which can be used to examine if there is common nonlinearity across economic variables. The model is a multivariate censored latent effects autoregression. The key feature of this model is that nonlinearity appears as sep
Time Series Forecasting A Nonlinear Dynamics Approach
Sello, S
1999-01-01
The problem of prediction of a given time series is examined on the basis of recent nonlinear dynamics theories. Particular attention is devoted to forecast the amplitude and phase of one of the most common solar indicator activity, the international monthly smoothed sunspot number. It is well known that the solar cycle is very difficult to predict due to the intrinsic complexity of the related time behaviour and to the lack of a succesful quantitative theoretical model of the Sun magnetic cycle. Starting from a previous recent work, we checked the reliability and accuracy of a forecasting model based on concepts of nonlinear dynamical systems applied to experimental time series, such as embedding phase space,Lyapunov spectrum,chaotic behaviour. The model is based on a locally hypothesis of the behaviour on the embedding space, utilizing an optimal number k of neighbour vectors to predict the future evolution of the current point with the set of characteristic parameters determined by several previous paramet...
Exact Travelling Wave Solutions to a Coupled Nonlinear Evolution Equation[
Institute of Scientific and Technical Information of China (English)
HUANGDing-Jiang; ZHANGHong-Qing
2004-01-01
By using an improved hyperbola function method, several types of exact travelling wave solutions to a coupled nonlinear evolution equation are obtained, which include kink-shaped soliton solutions, bell-shaped soliton solutions, envelop solitary wave solutions, and new solitary waves. The method can be applied to other nonlinear evolution equations in mathematical physics.
Exact Travelling Wave Solutions to a Coupled Nonlinear Evolution Equation
Institute of Scientific and Technical Information of China (English)
HUANG Ding-Jiang; ZHANG Hong-Qing
2004-01-01
By using an improved hyperbola function method, several types of exact travelling wave solutions to a coupled nonlinear evolution equation are obtained, which include kink-shaped soliton solutions, bell-shaped soliton solutions, envelop solitary wave solutions, and new solitary waves. The method can be applied to other nonlinear evolution equations in mathematical physics.
Finite Volume Evolution Galerkin Methods for Nonlinear Hyperbolic Systems
Lukáčová-Medvid'ová, M.; Saibertová, J.; Warnecke, G.
2002-12-01
We present new truly multidimensional schemes of higher order within the frame- work of finite volume evolution Galerkin (FVEG) methods for systems of nonlinear hyperbolic conservation laws. These methods couple a finite volume formulation with approximate evolution operators. The latter are constructed using the bicharacteristics of the multidimensional hyperbolic system, such that all of the infinitely many directions of wave propagation are taken into account. Following our previous results for the wave equation system, we derive approximate evolution operators for the linearized Euler equations. The integrals along the Mach cone and along the cell interfaces are evaluated exactly, as well as by means of numerical quadratures. The influence of these numerical quadratures will be discussed. Second-order resolution is obtained using a conservative piecewise bilinear recovery and the midpoint rule approximation for time integration. We prove error estimates for the finite volume evolution Galerkin scheme for linear systems with constant coefficients. Several numerical experiments for the nonlinear. Euler equations, which confirm the accuracy and good multidimensional behavior of the FVEG schemes, are presented as well.
On Models of Nonlinear Evolution Paths in Adiabatic Quantum Algorithms
Institute of Scientific and Technical Information of China (English)
SUN Jie; LU Song-Feng; Samuel L.Braunstein
2013-01-01
In this paper,we study two different nonlinear interpolating paths in adiabatic evolution algorithms for solving a particular class of quantum search problems where both the initial and final Hamiltonian are one-dimensional projector Hamiltonians on the corresponding ground state.If the overlap between the initial state and final state of the quantum system is not equal to zero,both of these models can provide a constant time speedup over the usual adiabatic algorithms by increasing some another corresponding "complexity".But when the initial state has a zero overlap with the solution state in the problem,the second model leads to an infinite time complexity of the algorithm for whatever interpolating functions being applied while the first one can still provide a constant running time.However,inspired by a related reference,a variant of the first model can be constructed which also fails for the problem when the overlap is exactly equal to zero if we want to make up the "intrinsic" fault of the second model — an increase in energy.Two concrete theorems are given to serve as explanations why neither of these two models can improve the usual adiabatic evolution algorithms for the phenomenon above.These just tell us what should be noted when using certain nonlinear evolution paths in adiabatic quantum algorithms for some special kind of problems.
Lectures on nonlinear evolution equations initial value problems
Racke, Reinhard
2015-01-01
This book mainly serves as an elementary, self-contained introduction to several important aspects of the theory of global solutions to initial value problems for nonlinear evolution equations. The book employs the classical method of continuation of local solutions with the help of a priori estimates obtained for small data. The existence and uniqueness of small, smooth solutions that are defined for all values of the time parameter are investigated. Moreover, the asymptotic behavior of the solutions is described as time tends to infinity. The methods for nonlinear wave equations are discussed in detail. Other examples include the equations of elasticity, heat equations, the equations of thermoelasticity, Schrödinger equations, Klein-Gordon equations, Maxwell equations and plate equations. To emphasize the importance of studying the conditions under which small data problems offer global solutions, some blow-up results are briefly described. Moreover, the prospects for corresponding initial-boundary value p...
ERROR ESTIMATES FOR THE TIME DISCRETIZATION FOR NONLINEAR MAXWELL'S EQUATIONS
Institute of Scientific and Technical Information of China (English)
Marián Slodi(c)ka; Ján Bu(s)a Jr.
2008-01-01
This paper is devoted to the study of a nonlinear evolution eddy current model of the type (б)tB(H) +▽×(▽×H) = 0 subject to homogeneous Dirichlet boundary conditions H×v = 0 and a given initial datum. Here, the magnetic properties of a soft ferromagnet are linked by a nonlinear material law described by B(H). We apply the backward Euler method for the time discretization and we derive the error estimates in suitable function spaces. The results depend on the nonlinearity of B(H).
Approximate viability for nonlinear evolution inclusions with application to controllability
Directory of Open Access Journals (Sweden)
Omar Benniche
2016-12-01
Full Text Available We investigate approximate viability for a graph with respect to fully nonlinear quasi-autonomous evolution inclusions. As application, an approximate null controllability result is given.
Analysis on the effect of nonlinear polarization evolution in nonlinear amplifying loop mirror
Institute of Scientific and Technical Information of China (English)
Feng Qu; Xiaoming Liu; Pu Zhang; Xubiao Jiang; Hongming Zhang; Minyu Yao
2005-01-01
By considering the cross phase modulation (XPM) between the two orthogonal poparization components,the nonlinear birefringence and nonlinear polarization evolution (NPE) in highly-nonlinear fiber (HNLF),as well as the unequal evolutions of the state of polarization (SOP) between the clockwise (CW) and counter-clockwise (CCW) waves in a nonlinear amplifying loop mirror (NALM) are analyzed. It is pointed out that the traditional cosine expression is no longer valid for the power transmission of NALM due to uncompleted interference under the high power condition. The analytical expression considering NPE effect is derived, and the experimental result is presented.
New travelling wave solutions for nonlinear stochastic evolution equations
Indian Academy of Sciences (India)
Hyunsoo Kim; Rathinasamy Sakthivel
2013-06-01
The nonlinear stochastic evolution equations have a wide range of applications in physics, chemistry, biology, economics and finance from various points of view. In this paper, the (′/)-expansion method is implemented for obtaining new travelling wave solutions of the nonlinear (2 + 1)-dimensional stochastic Broer–Kaup equation and stochastic coupled Korteweg–de Vries (KdV) equation. The study highlights the significant features of the method employed and its capability of handling nonlinear stochastic problems.
Extension of Variable Separable Solutions for Nonlinear Evolution Equations
Institute of Scientific and Technical Information of China (English)
JIA Hua-Bing; ZHANG Shun-Li; XU Wei; ZHU Xiao-Ning; WANG Yong-Mao; LOU Sen-Yue
2008-01-01
We give the generalized definitions of variable separable solutions to nonlinear evolution equations, and characterize the relation between the functional separable solution and the derivative-dependent functional separablecation, we classify the generalized nonlinear diffusion equations that admit special functional separable solutions and obtain some exact solutions to the resulting equations.
A variational approach to nonlinear evolution equations in optics
Indian Academy of Sciences (India)
D Anderson; M Lisak; A Berntson
2001-11-01
A tutorial review is presented of the use of direct variational methods based on RayleighRitz optimization for ﬁnding approximate solutions to various nonlinear evolution equations. The practical application of the approach is demonstrated by some illustrative examples in connection with the nonlinear Schrödinger equation.
Prolongation Structure of Semi-discrete Nonlinear Evolution Equations
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
Based on noncommutative differential calculus, we present a theory of prolongation structure for semi-discrete nonlinear evolution equations. As an illustrative example, a semi-discrete model of the nonlinear Schr(o)dinger equation is discussed in terms of this theory and the corresponding Lax pairs are also given.
Direct approach for solving nonlinear evolution and two-point boundary value problems
Indian Academy of Sciences (India)
Jonu Lee; Rathinasamy Sakthivel
2013-12-01
Time-delayed nonlinear evolution equations and boundary value problems have a wide range of applications in science and engineering. In this paper, we implement the differential transform method to solve the nonlinear delay differential equation and boundary value problems. Also, we present some numerical examples including time-delayed nonlinear Burgers equation to illustrate the validity and the great potential of the differential transform method. Numerical experiments demonstrate the use and computational efﬁciency of the method. This method can easily be applied to many nonlinear problems and is capable of reducing the size of computational work.
Discrete-time nonlinear sliding mode controller
African Journals Online (AJOL)
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: Discrete-time delay system, Sliding mode control, nonlinear sliding ... The concept of the sliding mode control in recent years has drawn the ...... His area of interest is dc-dc converters, electrical vehicle and distributed generation application.
Directory of Open Access Journals (Sweden)
E. M. E. Zayed
2014-01-01
Full Text Available We apply the generalized projective Riccati equations method to find the exact traveling wave solutions of some nonlinear evolution equations with any-order nonlinear terms, namely, the nonlinear Pochhammer-Chree equation, the nonlinear Burgers equation and the generalized, nonlinear Zakharov-Kuznetsov equation. This method presents wider applicability for handling many other nonlinear evolution equations in mathematical physics.
The non-linear evolution of edge localized modes
Energy Technology Data Exchange (ETDEWEB)
Wenninger, Ronald
2013-01-09
Edge localized modes (ELMs) are instabilities in the edge of tokamak plasmas in the high confinement regime (H-mode). Without them the edge transport in ordinary H-mode plasmas is too low to establish a stationary situation. However in a future device large unmitigated ELMs are believed to cause divertor power flux densities far in excess of tolerable material limits. Hence the size of energy loss per ELM and the resulting ELM frequency must be controlled. To proceed in understanding how the ELM size is determined and how ELM mitigation methods work it is necessary to characterize the non-linear evolution of pedestal erosion. In order to achieve this experimental data is compared to the results of ELM simulations with the code JOREK (reduced MHD, non-linear) applying a specially developed synthetic magnetic diagnostic. The experimental data are acquired by several fast sampling diagnostics at the experiments ASDEX Upgrade and TCV at a large number of toroidal/poloidal positions. A central element of the presented work is the detailed characterization of dominant magnetic perturbations during ELMs. These footprints of the instability can be observed most intensely in close temporal vicinity to the onset of pedestal erosion. Dominant magnetic perturbations are caused by current perturbations located at or inside the last closed flux surface. In ASDEX Upgrade under certain conditions dominant magnetic perturbations like other H-mode edge instabilities display a similarity to solitons. Furthermore - as expected - they are often observed to be correlated to a perturbation of electron temperature. In TCV it is possible to characterize the evolution of the toroidal structure of dominant magnetic perturbations. Between growing above the level of background fluctuations and the maximum perturbation level for all time instance a similar toroidal structure is observed. This rigid mode-structure is an indication for non-linear coupling. Most frequently the dominant toroidal
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.
Discrete time learning control in nonlinear systems
Longman, Richard W.; Chang, Chi-Kuang; Phan, Minh
1992-01-01
In this paper digital learning control methods are developed primarily for use in single-input, single-output nonlinear dynamic systems. Conditions for convergence of the basic form of learning control based on integral control concepts are given, and shown to be satisfied by a large class of nonlinear problems. It is shown that it is not the gross nonlinearities of the differential equations that matter in the convergence, but rather the much smaller nonlinearities that can manifest themselves during the short time interval of one sample time. New algorithms are developed that eliminate restrictions on the size of the learning gain, and on knowledge of the appropriate sign of the learning gain, for convergence to zero error in tracking a feasible desired output trajectory. It is shown that one of the new algorithms can give guaranteed convergence in the presence of actuator saturation constraints, and indicate when the requested trajectory is beyond the actuator capabilities.
Single and multi-solitary wave solutions to a class of nonlinear evolution equations
Wang, Deng-Shan; Li, Hongbo
2008-07-01
In this paper, an effective discrimination algorithm is presented to deal with equations arising from physical problems. The aim of the algorithm is to discriminate and derive the single traveling wave solutions of a large class of nonlinear evolution equations. Many examples are given to illustrate the algorithm. At the same time, some factorization technique are presented to construct the traveling wave solutions of nonlinear evolution equations, such as Camassa-Holm equation, Kolmogorov-Petrovskii-Piskunov equation, and so on. Then a direct constructive method called multi-auxiliary equations expansion method is described to derive the multi-solitary wave solutions of nonlinear evolution equations. Finally, a class of novel multi-solitary wave solutions of the (2+1)-dimensional asymmetric version of the Nizhnik-Novikov-Veselov equation are given by three direct methods. The algorithm proposed in this paper can be steadily applied to some other nonlinear problems.
Directory of Open Access Journals (Sweden)
Yongquan Zhou
2013-01-01
Full Text Available In view of the traditional numerical method to solve the nonlinear equations exist is sensitive to initial value and the higher accuracy of defects. This paper presents an invasive weed optimization (IWO algorithm which has population diversity with the heuristic global search of differential evolution (DE algorithm. In the iterative process, the global exploration ability of invasive weed optimization algorithm provides effective search area for differential evolution; at the same time, the heuristic search ability of differential evolution algorithm provides a reliable guide for invasive weed optimization. Based on the test of several typical nonlinear equations and a circle packing problem, the results show that the differential evolution invasive weed optimization (DEIWO algorithm has a higher accuracy and speed of convergence, which is an efficient and feasible algorithm for solving nonlinear systems of equations.
New traveling wave solutions for nonlinear evolution equations
Energy Technology Data Exchange (ETDEWEB)
El-Wakil, S.A. [Theoretical Research Group, Physics Department, Faculty of Science, Mansoura University, 35516 Mansoura (Egypt); Madkour, M.A. [Theoretical Research Group, Physics Department, Faculty of Science, Mansoura University, 35516 Mansoura (Egypt); Abdou, M.A. [Theoretical Research Group, Physics Department, Faculty of Science, Mansoura University, 35516 Mansoura (Egypt)]. E-mail: m_abdou_eg@yahoo.com
2007-06-11
The generalized Jacobi elliptic function expansion method is used with a computerized symbolic computation for constructing the new exact traveling wave solutions. The validity and reliability of the method is tested by its applications on a class of nonlinear evolution equations of special interest in mathematical physics. As a result, many exact traveling wave solutions are obtained which include the kink-shaped solutions, bell-shaped solutions, singular solutions and periodic solutions. The method is straightforward and concise, and it can also be applied to other nonlinear evolution equations in mathematical physics.
The Nonlinear Evolution of Galaxy Intrinsic Alignments
Lee, Jounghun; Pen, Ue-Li
2007-01-01
The non-Gaussian contribution to the intrinsic halo spin alignments is analytically modeled and numerically detected. Assuming that the growth of non-Gaussianity in the density fluctuations caused the tidal field to have nonlinear-order effect on the orientations of the halo angular momentum, we model the intrinsic halo spin alignments as a linear scaling of the density correlations on large scales, which is different from the previous quadratic-scaling model based on the linear tidal torque ...
Factorizing the time evolution operator
Quijas, P C G
2006-01-01
There is a widespread belief in the quantum physical community, and in textbooks used to teach Quantum Mechanics, that it is a difficult task to apply the time evolution operator on an initial wave function. That is to say, because the hamiltonian operator generally is the sum of two operators, then it is a difficult task to apply the time evolution operator on an initial wave function, because it implies to apply terms like (A+B)^n. A possible solution of this problem is to factorize the time evolution operator and then apply successively the individual exponential operator on the initial wave function. However, the exponential operator does not directly factorize. In this work we present useful ways to factorizing the time evolution operator when the argument of the exponential is a sum of two operators which obey specific commutation relations. Then, we apply the exponential operator as an evolution operator for the case of elementary unidimensional potentials, like the harmonic oscillator. Also, we argue ...
Nonlinear evolution of density and flow perturbations on a Bjorken background
Brouzakis, Nikolaos; Tetradis, Nikolaos; Wiedemann, Urs Achim
2015-01-01
Density perturbations and their dynamic evolution from early to late times can be used for an improved understanding of interesting physical phenomena both in cosmology and in the context of heavy-ion collisions. We discuss the spectrum and bispectrum of these perturbations around a longitudinally expanding fireball after a heavy-ion collision. The time-evolution equations couple the spectrum and bispectrum to each other, as well as to higher-order correlation functions through nonlinear terms. A non-trivial bispectrum is thus always generated, even if absent initially. For initial conditions corresponding to a model of independent sources, we discuss the linear and nonlinear evolution is detail. We show that, if the initial conditions are sufficiently smooth for fluid dynamics to be applicable, the nonlinear effects are relatively small.
Nonlinear evolution of density and flow perturbations on a Bjorken background
Brouzakis, Nikolaos; Floerchinger, Stefan; Tetradis, Nikolaos; Wiedemann, Urs Achim
2015-03-01
Density perturbations and their dynamic evolution from early to late times can be used for an improved understanding of interesting physical phenomena both in cosmology and in the context of heavy-ion collisions. We discuss the spectrum and bispectrum of these perturbations around a longitudinally expanding fireball after a heavy-ion collision. The time-evolution equations couple the spectrum and bispectrum to each other, as well as to higher-order correlation functions through nonlinear terms. A nontrivial bispectrum is thus always generated, even if absent initially. For initial conditions corresponding to a model of independent sources, we discuss the linear and nonlinear evolution in detail. We show that, if the initial conditions are sufficiently smooth for fluid dynamics to be applicable, the nonlinear effects are relatively small.
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.
Some Nonlinear Dynamic Inequalities on Time Scales
Indian Academy of Sciences (India)
Wei Nian Li; Weihong Sheng
2007-11-01
The aim of this paper is to investigate some nonlinear dynamic inequalities on time scales, which provide explicit bounds on unknown functions. The inequalities given here unify and extend some inequalities in (B G Pachpatte, On some new inequalities related to a certain inequality arising in the theory of differential equation, J. Math. Anal. Appl. 251 (2000) 736--751).
Some Nonlinear Integral Inequalities on Time Scales
Directory of Open Access Journals (Sweden)
Li Wei Nian
2007-01-01
Full Text Available The purpose of this paper is to investigate some nonlinear integral inequalities on time scales. Our results unify and extend some continuous inequalities and their corresponding discrete analogues. The theoretical results are illustrated by a simple example at the end of this paper.
Dimensional reduction of nonlinear time delay systems
Directory of Open Access Journals (Sweden)
M. S. Fofana
2005-01-01
infinite-dimensional problem without the assumption of small time delay. This dimensional reduction is illustrated in this paper with the delay versions of the Duffing and van der Pol equations. For both nonlinear delay equations, transcendental characteristic equations of linearized stability are examined through Hopf bifurcation. The infinite-dimensional nonlinear solutions of the delay equations are decomposed into stable and centre subspaces, whose respective dimensions are determined by the linearized stability of the transcendental equations. Linear semigroups, infinitesimal generators, and their adjoint forms with bilinear pairings are the additional candidates for the infinite-dimensional reduction.
Nonlinear Analysis of Physiological Time Series
Institute of Scientific and Technical Information of China (English)
MENG Qing-fang; PENG Yu-hua; XUE Yu-li; HAN Min
2007-01-01
Abstract.The heart rate variability could be explained by a low-dimensional governing mechanism. There has been increasing interest in verifying and understanding the coupling between the respiration and the heart rate. In this paper we use the nonlinear detection method to detect the nonlinear deterministic component in the physiological time series by a single variable series and two variables series respectively, and use the conditional information entropy to analyze the correlation between the heart rate, the respiration and the blood oxygen concentration. The conclusions are that there is the nonlinear deterministic component in the heart rate data and respiration data, and the heart rate and the respiration are two variables originating from the same underlying dynamics.
Nonlinear refraction and reflection travel time tomography
Zhang, Jiahua; ten Brink, U.S.; Toksoz, M.N.
1998-01-01
We develop a rapid nonlinear travel time tomography method that simultaneously inverts refraction and reflection travel times on a regular velocity grid. For travel time and ray path calculations, we apply a wave front method employing graph theory. The first-arrival refraction travel times are calculated on the basis of cell velocities, and the later refraction and reflection travel times are computed using both cell velocities and given interfaces. We solve a regularized nonlinear inverse problem. A Laplacian operator is applied to regularize the model parameters (cell slownesses and reflector geometry) so that the inverse problem is valid for a continuum. The travel times are also regularized such that we invert travel time curves rather than travel time points. A conjugate gradient method is applied to minimize the nonlinear objective function. After obtaining a solution, we perform nonlinear Monte Carlo inversions for uncertainty analysis and compute the posterior model covariance. In numerical experiments, we demonstrate that combining the first arrival refraction travel times with later reflection travel times can better reconstruct the velocity field as well as the reflector geometry. This combination is particularly important for modeling crustal structures where large velocity variations occur in the upper crust. We apply this approach to model the crustal structure of the California Borderland using ocean bottom seismometer and land data collected during the Los Angeles Region Seismic Experiment along two marine survey lines. Details of our image include a high-velocity zone under the Catalina Ridge, but a smooth gradient zone between. Catalina Ridge and San Clemente Ridge. The Moho depth is about 22 km with lateral variations. Copyright 1998 by the American Geophysical Union.
NEW EXACT TRAVELLING WAVE SOLUTIONS TO THREE NONLINEAR EVOLUTION EQUATIONS
Institute of Scientific and Technical Information of China (English)
Sirendaoreji
2004-01-01
Based on the computerized symbolic computation, some new exact travelling wave solutions to three nonlinear evolution equations are explicitly obtained by replacing the tanhξ in tanh-function method with the solutions of a new auxiliary ordinary differential equation.
EXACT SOLITARY WAVE SOLUTIONS OF THETWO NONLINEAR EVOLUTION EQUATIONS
Institute of Scientific and Technical Information of China (English)
ZhuYanjuan; ZhangChunhua
2005-01-01
The solitary wave solutions of the combined KdV-mKdV-Burgers equation and the Kolmogorov-Petrovskii-Piskunov equation are obtained by means of the direct algebra method, which can be generalized to deal with high dimensional nonlinear evolution equations.
BOUNDARY LAYER AND VANISHING DIFFUSION LIMIT FOR NONLINEAR EVOLUTION EQUATIONS
Institute of Scientific and Technical Information of China (English)
彭艳
2014-01-01
In this paper, we consider an initial-boundary value problem for some nonlinear evolution equations with damping and diffusion. The main purpose is to investigate the boundary layer effect and the convergence rates as the diffusion parameterαgoes to zero.
The Peridic Wave Solutions for Two Nonlinear Evolution Equations
Institute of Scientific and Technical Information of China (English)
ZHANG Jin-Liang; WANG Ming-Liang; CHENG Dong-Ming; FANG Zong-De
2003-01-01
By using the F-expansion method proposed recently, the periodic wave solutions expressed by Jacobielliptic functions for two nonlinear evolution equations are derived. In the limit cases, the solitary wave solutions andthe other type of traveling wave solutions for the system are obtained.
Stable Solution of Nonlinear Age-structuredForest Evolution System
Institute of Scientific and Technical Information of China (English)
WANGDing-jiang; ZHAOTing-fang
2004-01-01
This paper studies the dynamical behavior of a class of total area dependent nonlinear age-structured forest evolution model. We give the problem of equal value for the forest system, and discuss the stable solution of system. We obtained the necessary and sufficient conditions for there exists the stable solution.
Time Series Forecasting: A Nonlinear Dynamics Approach
Sello, Stefano
1999-01-01
The problem of prediction of a given time series is examined on the basis of recent nonlinear dynamics theories. Particular attention is devoted to forecast the amplitude and phase of one of the most common solar indicator activity, the international monthly smoothed sunspot number. It is well known that the solar cycle is very difficult to predict due to the intrinsic complexity of the related time behaviour and to the lack of a succesful quantitative theoretical model of the Sun magnetic cy...
A Hierarchy of New Nonlinear Evolution Equations Associated with a 3 × 3 Matrix Spectral Problem
Institute of Scientific and Technical Information of China (English)
GENG Xian-Guo; LI Fang
2009-01-01
A 3 × 3 matrix spectral problem with three potentials and the corresponding hierarchy of new nonlinear evolution equations are proposed. Generalized Hamiltonian structures for the hierarchy of nonlinear evolution equations are derived with the aid of trace identity.
The chaotic effects in a nonlinear QCD evolution equation
Zhu, Wei; Shen, Zhenqi; Ruan, Jianhong
2016-10-01
The corrections of gluon fusion to the DGLAP and BFKL equations are discussed in a united partonic framework. The resulting nonlinear evolution equations are the well-known GLR-MQ-ZRS equation and a new evolution equation. Using the available saturation models as input, we find that the new evolution equation has the chaos solution with positive Lyapunov exponents in the perturbative range. We predict a new kind of shadowing caused by chaos, which blocks the QCD evolution in a critical small x range. The blocking effect in the evolution equation may explain the Abelian gluon assumption and even influence our expectations to the projected Large Hadron Electron Collider (LHeC), Very Large Hadron Collider (VLHC) and the upgrade (CppC) in a circular e+e- collider (SppC).
Institute of Scientific and Technical Information of China (English)
胡业民; 胡希伟
2001-01-01
Numerical analyses for the nonlinear evolutions of stimulated Raman scattering (SRS) and stimulated Brillouin scattering (SBS) processes are given. Various effects of the second- and third-order nonlinear susceptibilities on the SRS and SBS processes are studied. The nonlinear evolutions of SRS and SBS processes are atfected more efficiently than their linear growth rates by the nonlinear susceptibility.
Nonlinear evolution of large-scale structure in the universe
Energy Technology Data Exchange (ETDEWEB)
Frenk, C.S.; White, S.D.M.; Davis, M.
1983-08-15
Using N-body simulations we study the nonlinear development of primordial density perturbation in an Einstein--de Sitter universe. We compare the evolution of an initial distribution without small-scale density fluctuations to evolution from a random Poisson distribution. These initial conditions mimic the assumptions of the adiabatic and isothermal theories of galaxy formation. The large-scale structures which form in the two cases are markedly dissimilar. In particular, the correlation function xi(r) and the visual appearance of our adiabatic (or ''pancake'') models match better the observed distribution of galaxies. This distribution is characterized by large-scale filamentary structure. Because the pancake models do not evolve in a self-similar fashion, the slope of xi(r) steepens with time; as a result there is a unique epoch at which these models fit the galaxy observations. We find the ratio of cutoff length to correlation length at this time to be lambda/sub min//r/sub 0/ = 5.1; its expected value in a neutrino dominated universe is 4(..cap omega..h)/sup -1/ (H/sub 0/ = 100h km s/sup -1/ Mpc/sup -1/). At early epochs these models predict a negligible amplitude for xi(r) and could explain the lack of measurable clustering in the Ly..cap alpha.. absorption lines of high-redshift quasars. However, large-scale structure in our models collapses after z = 2. If this collapse precedes galaxy formation as in the usual pancake theory, galaxies formed uncomfortably recently. The extent of this problem may depend on the cosmological model used; the present series of experiments should be extended in the future to include models with ..cap omega..<1.
Time evolution of cascade decay
Boyanovsky, Daniel
2014-01-01
We study non-perturbatively the time evolution of cascade decay for generic fields $\\pi \\rightarrow \\phi_1\\phi_2\\rightarrow \\phi_2\\chi_1\\chi_2$ and obtain the time dependence of amplitudes and populations for the resonant and final states. We analyze in detail the different time scales and the manifestation of unitary time evolution in the dynamics of production and decay of resonant intermediate and final states. The probability of occupation (population) ``flows'' as a function of time from the initial to the final states. When the decay width of the parent particle $\\Gamma_\\pi$ is much larger than that of the intermediate resonant state $\\Gamma_{\\phi_1}$ there is a ``bottleneck'' in the flow, the population of resonant states builds up to a maximum at $t^* = \\ln[\\Gamma_\\pi/\\Gamma_{\\phi_1}]/(\\Gamma_\\pi-\\Gamma_{\\phi_1})$ nearly saturating unitarity and decays to the final state on the longer time scale $1/\\Gamma_{\\phi_1}$. As a consequence of the wide separation of time scales in this case the cascade decay ...
Dynamics of Nonlinear Time-Delay Systems
Lakshmanan, Muthusamy
2010-01-01
Synchronization of chaotic systems, a patently nonlinear phenomenon, has emerged as a highly active interdisciplinary research topic at the interface of physics, biology, applied mathematics and engineering sciences. In this connection, time-delay systems described by delay differential equations have developed as particularly suitable tools for modeling specific dynamical systems. Indeed, time-delay is ubiquitous in many physical systems, for example due to finite switching speeds of amplifiers in electronic circuits, finite lengths of vehicles in traffic flows, finite signal propagation times in biological networks and circuits, and quite generally whenever memory effects are relevant. This monograph presents the basics of chaotic time-delay systems and their synchronization with an emphasis on the effects of time-delay feedback which give rise to new collective dynamics. Special attention is devoted to scalar chaotic/hyperchaotic time-delay systems, and some higher order models, occurring in different bran...
Shallow water modal evolution due to nonlinear internal waves
Badiey, Mohsen; Wan, Lin; Luo, Jing
2017-09-01
Acoustic modal behavior is reported for an L-shape hydrophone array during the passage of a strong nonlinear internal wave packet. Acoustic track is nearly parallel to the front of nonlinear internal waves. Through modal decomposition at the vertical array, acoustic modes are identified. Modal evolution along the horizontal array then is examined during a passing internal wave. Strong intensity fluctuations of individual modes are observed before and during the internal waves packet passes the fixed acoustic track showing a detailed evolution of the waveguide modal behavior. Acoustic refraction created either uneven distribution of modal energy over the horizontal array or additional returns observable at the entire L-shape array. Acoustic ray-mode simulations are used to phenomenologically explain the observed modal behavior.
Time evolution of quantum fractals
Wojcik; Bialynicki-Birula; Zyczkowski
2000-12-11
We propose a general construction of wave functions of arbitrary prescribed fractal dimension, for a wide class of quantum problems, including the infinite potential well, harmonic oscillator, linear potential, and free particle. The box-counting dimension of the probability density P(t)(x) = |Psi(x,t)|(2) is shown not to change during the time evolution. We prove a universal relation D(t) = 1+Dx/2 linking the dimensions of space cross sections Dx and time cross sections D(t) of the fractal quantum carpets.
Time Evolution of Quantum Fractals
Wójcik, D; Zyczkowski, K; Wojcik, Daniel; Bialynicki-Birula, Iwo; Zyczkowski, Karol
2000-01-01
We propose a general construction of wave functions of arbitrary prescribed fractal dimension, for a wide class of quantum problems, including the infinite potential well, harmonic oscillator, linear potential and free particle. The box-counting dimension of the probability density $P_t(x)=|\\Psi(x,t)|^2$ is shown not to change during the time evolution. We prove a universal relation $D_t=1+D_x/2$ linking the dimensions of space cross-sections $D_x$ and time cross-sections $D_t$ of the fractal quantum carpets.
Solitary wave solutions to nonlinear evolution equations in mathematical physics
Indian Academy of Sciences (India)
Anwar Ja’afar Mohamad Jawad; M Mirzazadeh; Anjan Biswas
2014-10-01
This paper obtains solitons as well as other solutions to a few nonlinear evolution equations that appear in various areas of mathematical physics. The two analytical integrators that are applied to extract solutions are tan–cot method and functional variable approaches. The soliton solutions can be used in the further study of shallow water waves in (1+1) as well as (2+1) dimensions.
Modified constrained differential evolution for solving nonlinear global optimization problems
2013-01-01
Nonlinear optimization problems introduce the possibility of multiple local optima. The task of global optimization is to find a point where the objective function obtains its most extreme value while satisfying the constraints. Some methods try to make the solution feasible by using penalty function methods, but the performance is not always satisfactory since the selection of the penalty parameters for the problem at hand is not a straightforward issue. Differential evolut...
Travelling wave solutions for ( + 1)-dimensional nonlinear evolution equations
Indian Academy of Sciences (India)
Jonu Lee; Rathinasamy Sakthivel
2010-10-01
In this paper, we implement the exp-function method to obtain the exact travelling wave solutions of ( + 1)-dimensional nonlinear evolution equations. Four models, the ( + 1)-dimensional generalized Boussinesq equation, ( + 1)-dimensional sine-cosine-Gordon equation, ( + 1)-double sinh-Gordon equation and ( + 1)-sinh-cosinh-Gordon equation, are used as vehicles to conduct the analysis. New travelling wave solutions are derived.
Energy Technology Data Exchange (ETDEWEB)
Zhang, H. [Univ. of Texas, Austin, TX (United States). Dept. of Mathematics
1994-10-01
In this paper the author considers a nonlinear evolution problem denoted in the paper as P. Problem (P) arises in the study of thermal evaporation of atoms and molecules from locally heated surface regions (spikes) invoked as one of several mechanisms of ion-bombardment-induced particle emission (sputtering). Then in the case of particle-induced evaporation, the Stefan-Boltzman law of heat loss by radiation is replaced by some activation law describing the loss of heat by evaporation. The equation in P is the so-called degenerate diffusion problem, which has been extensively studied in recent years. However, when dealing with the nonlinear flux boundary condition, {beta}({center_dot}) is usually assumed to be monotene. The purpose of this paper is to provide a general theory for problem P under a different assumption on {beta}({center_dot}), i.e., Lipschitz continuity instead of monotonicity. The main idea of the proof used here is to choose an appropriate test function from the corresponding linearized dual space of the solution. The similar idea has been used by many authors, e.g., Aronson, Crandall and Peletier, Bertsch and Hilhorst and Friedman. The author follows the proof of Bertsch and Hilhorst. The paper is organized as follows. They begin by stating the precise assumptions on the functions involved in P and by defining a weak solution. Then, in Section 2 they prove the existence of the solution by the method of parabolic regularization. The uniqueness is proved in Section 3. Finally, they study the large time behavior of the solution in Section 4.
Black-hole universe: time evolution.
Yoo, Chul-Moon; Okawa, Hirotada; Nakao, Ken-ichi
2013-10-18
Time evolution of a black hole lattice toy model universe is simulated. The vacuum Einstein equations in a cubic box with a black hole at the origin are numerically solved with periodic boundary conditions on all pairs of faces opposite to each other. Defining effective scale factors by using the area of a surface and the length of an edge of the cubic box, we compare them with that in the Einstein-de Sitter universe. It is found that the behavior of the effective scale factors is well approximated by that in the Einstein-de Sitter universe. In our model, if the box size is sufficiently larger than the horizon radius, local inhomogeneities do not significantly affect the global expansion law of the Universe even though the inhomogeneity is extremely nonlinear.
Nonlinear time dependent behaviour of epoxy resins
Marotzke, C.; Feldmann, T.
2016-07-01
The nonlinear behaviour of epoxy resins is studied on standard tensile tests. A strain field measurement system is applied (Aramis) in order to monitor local strains. The residual strain is measured by recovering the specimens for up to 68 hours after unloading. The time span the specimen is exposed to load has a large influence on the creeping process and the residual strain after recovering. This is studied by comparison of instantaneous unloading with keeping the specimen under permanent load for thirty minutes. It is shown that moderate differences in the initial strain can lead to large differences in the creep behaviour as well as in the residual strain.
Forecasting with nonlinear time series models
DEFF Research Database (Denmark)
Kock, Anders Bredahl; Teräsvirta, Timo
and two versions of a simple artificial neural network model. Techniques for generating multi-period forecasts from nonlinear models recursively are considered, and the direct (non-recursive) method for this purpose is mentioned as well. Forecasting with com- plex dynamic systems, albeit less frequently...... applied to economic fore- casting problems, is briefly highlighted. A number of large published studies comparing macroeconomic forecasts obtained using different time series models are discussed, and the paper also contains a small simulation study comparing recursive and direct forecasts in a partic...
Measuring nonlinear behavior in time series data
Wai, Phoong Seuk; Ismail, Mohd Tahir
2014-12-01
Stationary Test is an important test in detect the time series behavior since financial and economic data series always have missing data, structural change as well as jumps or breaks in the data set. Moreover, stationary test is able to transform the nonlinear time series variable to become stationary by taking difference-stationary process or trend-stationary process. Two different types of hypothesis testing of stationary tests that are Augmented Dickey-Fuller (ADF) test and Kwiatkowski-Philips-Schmidt-Shin (KPSS) test are examine in this paper to describe the properties of the time series variables in financial model. Besides, Least Square method is used in Augmented Dickey-Fuller test to detect the changes of the series and Lagrange multiplier is used in Kwiatkowski-Philips-Schmidt-Shin test to examine the properties of oil price, gold price and Malaysia stock market. Moreover, Quandt-Andrews, Bai-Perron and Chow tests are also use to detect the existence of break in the data series. The monthly index data are ranging from December 1989 until May 2012. Result is shown that these three series exhibit nonlinear properties but are able to transform to stationary series after taking first difference process.
Modelling of nonlinear shoaling based on stochastic evolution equations
DEFF Research Database (Denmark)
Kofoed-Hansen, Henrik; Rasmussen, Jørgen Hvenekær
1998-01-01
A one-dimensional stochastic model is derived to simulate the transformation of wave spectra in shallow water including generation of bound sub- and super-harmonics, near-resonant triad wave interaction and wave breaking. Boussinesq type equations with improved linear dispersion characteristics...... are recast into evolution equations for the complex amplitudes, and serve as the underlying deterministic model. Next, a set of evolution equations for the cumulants is derived. By formally introducing the well-known Gaussian closure hypothesis, nonlinear evolution equations for the power spectrum...... and bispectrum are derived. A simple description of depth-induced wave breaking is incorporated in the model equations, assuming that the total rate of dissipation may be distributed in proportion to the spectral energy density on each discrete frequency. The proposed phase-averaged model is compared...
Linear and Nonlinear Evolution and Diffusion Layer Selection in Electrokinetic Instability
Demekhin, E A; Polyanskikh, S V
2011-01-01
In the present work fournontrivial stages of electrokinetic instability are identified by direct numerical simulation (DNS) of the full Nernst-Planck-Poisson-Stokes (NPPS) system: i) The stage of the influence of the initial conditions (milliseconds); ii) 1D self-similar evolution (milliseconds-seconds); iii) The primary instability of the self-similar solution (seconds); iv) The nonlinear stage with secondary instabilities. The self-similar character of evolution at intermediately large times is confirmed. Rubinstein and Zaltzman instability and noise-driven nonlinear evolution to over-limiting regimes in ion-exchange membranes are numerically simulated and compared with theoretical and experimental predictions. The primary instability which happens during this stage is found to arrest self-similar growth of the diffusion layer and specifies its characteristic length as was first experimentally predicted by Yossifon and Chang (PRL 101, 254501 (2008)). A novel principle for the characteristic wave number sele...
Analytic treatment of nonlinear evolution equations using ﬁrst integral method
Indian Academy of Sciences (India)
Ahmet Bekir; Ömer Ünsal
2012-07-01
In this paper, we show the applicability of the ﬁrst integral method to combined KdV-mKdV equation, Pochhammer–Chree equation and coupled nonlinear evolution equations. The power of this manageable method is conﬁrmed by applying it for three selected nonlinear evolution equations. This approach can also be applied to other nonlinear differential equations.
On the Nonlinear Evolution of Cosmic Web: Lagrangian Dynamics Revisited
Wang, Xin
2014-01-01
We investigate the nonlinear evolution of cosmic morphologies of the large-scale structure by examining the Lagrangian dynamics of various tensors of a cosmic fluid element, including the velocity gradient tensor, the Hessian matrix of the gravitational potential as well as the deformation tensor. Instead of the eigenvalue representation, the first two tensors, which associate with the "kinematic" and "dynamical" cosmic web classification algorithm respectively, are studied in a more convenient parameter space. These parameters are defined as the rotational invariant coefficients of the characteristic equation of the tensor. In the nonlinear local model (NLM) where the magnetic part of Weyl tensor vanishes, these invariants are fully capable of characterizing the dynamics. Unlike the Zeldovich approximation (ZA), where various morphologies do not change before approaching a one-dimensional singularity, the sheets in NLM are unstable for both overdense and underdense perturbations. While it has long been known...
Nonlinear evolution operators and semigroups applications to partial differential equations
Pavel, Nicolae H
1987-01-01
This research monograph deals with nonlinear evolution operators and semigroups generated by dissipative (accretive), possibly multivalued operators, as well as with the application of this theory to partial differential equations. It shows that a large class of PDE's can be studied via the semigroup approach. This theory is not available otherwise in the self-contained form provided by these Notes and moreover a considerable part of the results, proofs and methods are not to be found in other books. The exponential formula of Crandall and Liggett, some simple estimates due to Kobayashi and others, the characterization of compact semigroups due to Brézis, the proof of a fundamental property due to Ursescu and the author and some applications to PDE are of particular interest. Assuming only basic knowledge of functional analysis, the book will be of interest to researchers and graduate students in nonlinear analysis and PDE, and to mathematical physicists.
Institute of Scientific and Technical Information of China (English)
2008-01-01
Using functional derivative technique in quantum field theory, the algebraic dy-namics approach for solution of ordinary differential evolution equations was gen-eralized to treat partial differential evolution equations. The partial differential evo-lution equations were lifted to the corresponding functional partial differential equations in functional space by introducing the time translation operator. The functional partial differential evolution equations were solved by algebraic dynam-ics. The algebraic dynamics solutions are analytical in Taylor series in terms of both initial functions and time. Based on the exact analytical solutions, a new nu-merical algorithm—algebraic dynamics algorithm was proposed for partial differ-ential evolution equations. The difficulty of and the way out for the algorithm were discussed. The application of the approach to and computer numerical experi-ments on the nonlinear Burgers equation and meteorological advection equation indicate that the algebraic dynamics approach and algebraic dynamics algorithm are effective to the solution of nonlinear partial differential evolution equations both analytically and numerically.
Institute of Scientific and Technical Information of China (English)
WANG Shundin; ZHANG Hua
2008-01-01
Using functional derivative technique In quantum field theory,the algebraic dy-namics approach for solution of ordinary differential evolution equations was gen-eralized to treat partial differential evolution equations.The partial differential evo-lution equations were lifted to the corresponding functional partial differential equations in functional space by Introducing the time translation operator.The functional partial differential evolution equations were solved by algebraic dynam-ics.The algebraic dynamics solutions are analytical In Taylor series In terms of both initial functions and time.Based on the exact analytical solutions,a new nu-merical algorithm-algebraic dynamics algorithm was proposed for partial differ-ential evolution equations.The difficulty of and the way out for the algorithm were discussed.The application of the approach to and computer numerical experi-ments on the nonlinear Burgers equation and meteorological advection equation indicate that the algebraic dynamics approach and algebraic dynamics algorithm are effective to the solution of nonlinear partial differential evolution equations both analytically and numerically.
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.
Nonconvex evolution inclusions generated by time-dependent subdifferential operators
Directory of Open Access Journals (Sweden)
Kate Arseni-Benou
1999-01-01
Full Text Available We consider nonlinear nonconvex evolution inclusions driven by time-varying subdifferentials ∂ϕ(t,x without assuming that ϕ(t,. is of compact type. We show the existence of extremal solutions and then we prove a strong relaxation theorem. Moreover, we show that under a Lipschitz condition on the orientor field, the solution set of the nonconvex problem is path-connected in C(T,H. These results are applied to nonlinear feedback control systems to derive nonlinear infinite dimensional versions of the bang-bang principle. The abstract results are illustrated by two examples of nonlinear parabolic problems and an example of a differential variational inequality.
Nonlinear time reversal of classical waves: experiment and model.
Frazier, Matthew; Taddese, Biniyam; Xiao, Bo; Antonsen, Thomas; Ott, Edward; Anlage, Steven M
2013-12-01
We consider time reversal of electromagnetic waves in a closed, wave-chaotic system containing a discrete, passive, harmonic-generating nonlinearity. An experimental system is constructed as a time-reversal mirror, in which excitations generated by the nonlinearity are gathered, time-reversed, transmitted, and directed exclusively to the location of the nonlinearity. Here we show that such nonlinear objects can be purely passive (as opposed to the active nonlinearities used in previous work), and we develop a higher data rate exclusive communication system based on nonlinear time reversal. A model of the experimental system is developed, using a star-graph network of transmission lines, with one of the lines terminated by a model diode. The model simulates time reversal of linear and nonlinear signals, demonstrates features seen in the experimental system, and supports our interpretation of the experimental results.
Grammatical Immune System Evolution for reverse engineering nonlinear dynamic Bayesian models.
McKinney, B A; Tian, D
2008-01-01
An artificial immune system algorithm is introduced in which nonlinear dynamic models are evolved to fit time series of interacting biomolecules. This grammar-based machine learning method learns the structure and parameters of the underlying dynamic model. In silico immunogenetic mechanisms for the generation of model-structure diversity are implemented with the aid of a grammar, which also enforces semantic constraints of the evolved models. The grammar acts as a DNA repair polymerase that can identify recombination and hypermutation signals in the antibody (model) genome. These signals contain information interpretable by the grammar to maintain model context. Grammatical Immune System Evolution (GISE) is applied to a nonlinear system identification problem in which a generalized (nonlinear) dynamic Bayesian model is evolved to fit biologically motivated artificial time-series data. From experimental data, we use GISE to infer an improved kinetic model for the oxidative metabolism of 17beta-estradiol (E(2)), the parent hormone of the estrogen metabolism pathway.
Integrable nonlinear evolution partial differential equations in 4 + 2 and 3 + 1 dimensions.
Fokas, A S
2006-05-19
The derivation and solution of integrable nonlinear evolution partial differential equations in three spatial dimensions has been the holy grail in the field of integrability since the late 1970s. The celebrated Korteweg-de Vries and nonlinear Schrödinger equations, as well as the Kadomtsev-Petviashvili (KP) and Davey-Stewartson (DS) equations, are prototypical examples of integrable evolution equations in one and two spatial dimensions, respectively. Do there exist integrable analogs of these equations in three spatial dimensions? In what follows, I present a positive answer to this question. In particular, I first present integrable generalizations of the KP and DS equations, which are formulated in four spatial dimensions and which have the novelty that they involve complex time. I then impose the requirement of real time, which implies a reduction to three spatial dimensions. I also present a method of solution.
Long-term evolution of strongly nonlinear internal solitary waves in a rotating channel
Directory of Open Access Journals (Sweden)
J. C. Sánchez-Garrido
2009-09-01
Full Text Available The evolution of internal solitary waves (ISWs propagating in a rotating channel is studied numerically in the framework of a fully-nonlinear, nonhydrostatic numerical model. The aim of modelling efforts was the investigation of strongly-nonlinear effects, which are beyond the applicability of weakly nonlinear theories. Results reveal that small-amplitude waves and sufficiently strong ISWs evolve differently under the action of rotation. At the first stage of evolution an initially two-dimensional ISW transforms according to the scenario described by the rotation modified Kadomtsev-Petviashvili equation, namely, it starts to evolve into a Kelvin wave (with exponential decay of the wave amplitude across the channel with front curved backwards. This transition is accompanied by a permanent radiation of secondary Poincaré waves attached to the leading wave. However, in a strongly-nonlinear limit not all the energy is transmitted to secondary radiated waves. Part of it returns to the leading wave as a result of nonlinear interactions with secondary Kelvin waves generated in the course of time. This leads to the formation of a slowly attenuating quasi-stationary system of leading Kelvin waves, capable of propagating for several hundreds hours as a localized wave packet.
Instability of coupled geostrophic density fronts and its nonlinear evolution
Scherer, Emilie; Zeitlin, Vladimir
Instability of coupled density fronts, and its fully nonlinear evolution are studied within the idealized reduced-gravity rotating shallow-water model. By using the collocation method, we benchmark the classical stability results on zero potential vorticity (PV) fronts and generalize them to non-zero PV fronts. In both cases, we find a series of instability zones intertwined with the stability regions along the along-front wavenumber axis, the most unstable modes being long wave. We then study the nonlinear evolution of the unstable modes with the help of a high-resolution well-balanced finite-volume numerical scheme by initializing it with the unstable modes found from the linear stability analysis. The most unstable long-wave mode evolves as follows: after a couple of inertial periods, the coupled fronts are pinched at some location and a series of weakly connected co-rotating elliptic anticyclonic vortices is formed, thus totally changing the character of the flow. The characteristics of these vortices are close to known rodon lens solutions. The shorter-wave unstable modes from the next instability zones are strongly concentrated in the frontal regions, have sharp gradients, and are saturated owing to dissipation without qualitatively changing the flow pattern.
Linear and Nonlinear Evolution of Disturbances in Supersonic Streamwise Vortices
Khorrami, Mehdi R.; Chang, Chau-Lyan; Wie, Yong-Sun
1997-11-01
Effective control of compressible streamwise vortices play a significant role in both external and internal aerodynamics. In this study, evolution of disturbances in a supersonic vortex is studied by using quasi-cylindrical linear stability analysis and parabolized stability equations (PSE)footnote M. R. Malik and C.-L. Chang, AIAA Paper 97-0758. formulation. Appropriate mean-flow profilesfootnote M. K. Smart, I. M. Kalkhoran, and J. Bentson, AIAA Paper 94-2576. suitable for stability analysis were identified and modeled successfully. Using linear stability analysis, the stability characteristics of axisymmetric vortices were mapped thoroughly. The results indicate that viscosity has very little effect while increasing Mach number significantly stabilizes the disturbance. Linear PSE analysis shows that the effect of streamwise mean flow variation is small for the case considered here. Nonlinear evolution of helical modes is also studied by using PSE. The growth of the disturbances results in the appearance of coherent large scale motion and significant mean flow distortion in the axial velocity and temperature fields. In the end, nonlinear effects tend to stabilize the vortex.
Effects of Interaction Between Gravitation and Nonlinear Electrodynamics On Scalar Field Evolution
Institute of Scientific and Technical Information of China (English)
CHEN Ju-Hua; WANG Yong-Jiu
2011-01-01
In this paper we investigate the scalar field evolution in the dyadosphere spacetime by using the third-order WKB approximation.We find that the coupling term between the gravitation and the nonlinear electrodynamics makes the scalar field decay more quickly and it also makes the scalar field oscillate more slowly.On the other words, this coupling term takes effect on the scalar field evolution as a damping factor.At the same time these effects become more obvious for the scalar field with higher angle quantum number.
Stability of planar diffusion wave for nonlinear evolution equation
Institute of Scientific and Technical Information of China (English)
无
2012-01-01
It is known that the one-dimensional nonlinear heat equation ut = f(u)x1x1,f'(u) 0,u(±∞,t) = u±,u+ = u_ has a unique self-similar solution u(x1/1+t).In multi-dimensional space,u(x1/1+t) is called a planar diffusion wave.In the first part of the present paper,it is shown that under some smallness conditions,such a planar diffusion wave is nonlinearly stable for the nonlinear heat equation:ut-△f(u) = 0,x ∈ Rn.The optimal time decay rate is obtained.In the second part of this paper,it is further shown that this planar diffusion wave is still nonlinearly stable for the quasilinear wave equation with damping:utt + utt+ △f(u) = 0,x ∈ Rn.The time decay rate is also obtained.The proofs are given by an elementary energy method.
A Direct Algebraic Method in Finding Particular Solutions to Some Nonlinear Evolution Equations
Institute of Scientific and Technical Information of China (English)
LIUChun-Ping; CHENJian-Kang; CAIFan
2004-01-01
Firstly, a direct algebraic method and a routine way in finding traveling wave solutions to nonlinear evolution equations are explained. And then some new exact solutions for some evolution equations are obtained by using the method.
Multiple scales analysis and travelling wave solutions for KdV type nonlinear evolution equations
Ayhan, Burcu; Ozer, M. Naci; Bekir, Ahmet
2017-01-01
Nonlinear evolution equations are the mathematical models of problems that arise in many field of science. These equations has become an important field of study in applied mathematics in recent years. We apply exact solution methods and multiple scale method which is known as a perturbation method to nonlinear evolution equations. Using exact solution methods we get travelling wave solutions expressed by hyperbolic functions, trigonometric functions and rational functions. Also we derive Nonlinear Schrödinger (NLS) type equations from Korteweg-de Vries (KdV) type nonlinear evolution equations and we get approximate solutions for KdV type equations using multiple scale method. The proposed methods are direct and effective and can be used for many nonlinear evolution equations. It is shown that these methods provide a powerful mathematical tool to solve nonlinear evolution equations in mathematical physics.
An Improved Differential Evolution Trained Neural Network Scheme for Nonlinear System Identification
Institute of Scientific and Technical Information of China (English)
Bidyadhar Subudhi; Debashisha Jena
2009-01-01
This paper prescnts an improved nonlinear system identification scheme using differential evolution (DE), neural network (NN) and Levenberg Marquardt algorithm (LM). With a view to achieve better convergence of NN weights optimization during the training, the DE and LM are used in a combined framework to train the NN. We present the convergence analysis of the DE and demonstrate the efficacy of the proposed improved system identification algorithm by exploiting the combined DE and LM training of the NN and suitably implementing it together with other system identification methods, namely NN and DE+NN on a numbcr of examples including a practical case study. The identification rcsults obtained through a series of simulation studies of these methods on different nonlinear systems demonstrate that the proposed DE and LM trained NN approach to nonlinear system identification can yield better identification results in terms of time of convergence and less identification error.
Nonlinear evolution of tidally forced inertial waves in rotating fluid bodies
Favier, B; Baruteau, C; Ogilvie, G I
2014-01-01
We perform one of the first studies into the nonlinear evolution of tidally excited inertial waves in a uniformly rotating fluid body, exploring a simplified model of the fluid envelope of a planet (or the convective envelope of a solar-type star) subject to the gravitational tidal perturbations of an orbiting companion. Our model contains a perfectly rigid spherical core, which is surrounded by an envelope of incompressible uniform density fluid. The corresponding linear problem was studied in previous papers which this work extends into the nonlinear regime, at moderate Ekman numbers (the ratio of viscous to Coriolis accelerations). By performing high-resolution numerical simulations, using a combination of pseudo-spectral and spectral element methods, we investigate the effects of nonlinearities, which lead to time-dependence of the flow and the corresponding dissipation rate. Angular momentum is deposited non-uniformly, leading to the generation of significant differential rotation in the initially unifor...
Combined forecasts from linear and nonlinear time series models
N. Terui (Nobuhiko); H.K. van Dijk (Herman)
1999-01-01
textabstractCombined forecasts from a linear and a nonlinear model are investigated for time series with possibly nonlinear characteristics. The forecasts are combined by a constant coefficient regression method as well as a time varying method. The time varying method allows for a locally (non)line
Time-Dependent Mean-Field Games with Logarithmic Nonlinearities
Gomes, Diogo A.
2015-10-06
In this paper, we prove the existence of classical solutions for time-dependent mean-field games with a logarithmic nonlinearity and subquadratic Hamiltonians. Because the logarithm is unbounded from below, this nonlinearity poses substantial mathematical challenges that have not been addressed in the literature. Our result is proven by recurring to a delicate argument which combines Lipschitz regularity for the Hamilton-Jacobi equation with estimates for the nonlinearity in suitable Lebesgue spaces. Lipschitz estimates follow from an application of the nonlinear adjoint method. These are then combined with a priori bounds for solutions of the Fokker-Planck equation and a concavity argument for the nonlinearity.
Explicit Traveling Wave Solutions to Nonlinear Evolution Equations
Institute of Scientific and Technical Information of China (English)
Linghai ZHANG
2011-01-01
First of all,some technical tools are developed. Then the author studies explicit traveling wave solutions to nonlinear dispersive wave equations,nonlinear dissipative dispersive wave equations,nonlinear convection equations,nonlinear reaction diffusion equations and nonlinear hyperbolic equations,respectively.
Multi-soliton rational solutions for some nonlinear evolution equations
Directory of Open Access Journals (Sweden)
Osman Mohamed S.
2016-01-01
Full Text Available The Korteweg-de Vries equation (KdV and the (2+ 1-dimensional Nizhnik-Novikov-Veselov system (NNV are presented. Multi-soliton rational solutions of these equations are obtained via the generalized unified method. The analysis emphasizes the power of this method and its capability of handling completely (or partially integrable equations. Compared with Hirota’s method and the inverse scattering method, the proposed method gives more general exact multi-wave solutions without much additional effort. The results show that, by virtue of symbolic computation, the generalized unified method may provide us with a straightforward and effective mathematical tool for seeking multi-soliton rational solutions for solving many nonlinear evolution equations arising in different branches of sciences.
Nonlinear Evolution of a Baroclinic Wave and Imbalanced Dissipation
Nadiga, Balasubramanya T
2015-01-01
We consider the nonlinear evolution of an unstable baroclinic wave in a regime of rotating stratified flow that is of relevance to interior circulation in the oceans and in the atmosphere---a regime characterized by small large-scale Rossby and Froude numbers, a small vertical to horizontal aspect ratio, and no bounding horizontal surfaces. Using high-resolution simulations of the non-hydrostatic Boussinesq equations and companion integrations of the balanced quasi-geostrophic equations, we present evidence for a local route to dissipation of balanced energy directly through interior turbulent cascades. Analysis of simulations presented in this study suggest that a developing baroclinic instability can lead to secondary instabilities that can cascade a small fraction of the energy forward to unbalanced scales. Mesoscale shear and strain resulting from the hydrostatic geostrophic baroclinic instability drive frontogenesis. The fronts in turn support ageostrophic secondary circulation and instabilities. These t...
Nonlinear evolution of drift instabilities in the presence of collisions
Energy Technology Data Exchange (ETDEWEB)
Federici, J.F.; Lee, W.W.; Tang, W.M.
1986-07-01
Nonlinear evolution of drift instabilities in the presence of electron-ion collisions in a shear-free slab has been studied by using gyrokinetic particle simulation techniques as well as by solving, both numerically and analytically, model mode-coupling equations. The purpose of the investigation is to determine the mechanisms responsible for the nonlinear saturation of the instability and for the ensuing steady-state transport. Such an insight is very valuable for understanding drift wave problems in more complicated geometries. The results indicate that the electron E x B convection is the dominant mechanism for saturation. It is also found that the saturation amplitude and the associated quasilinear diffusion are greatly enhanced over their collisionless values as a result of weak collisions. In the highly collisional (fluid) limit, there is an upper bound for saturation with ephi/T/sub e/ approx. = (..omega../sub l//..cap omega../sub i/)/(k/sub perpendicular/rho/sub s/)/sup 2/. The associated quasilinear diffusion, which increases with collisionality, takes the form of D/sub ql/ approx. = ..gamma../sub l//k/sub perpendicular//sup 2/, where ..omega../sub l/ and ..gamma../sub l/ are the linear frequency and growth rate, respectively. In the steady state, the diffusion process becomes stochastic in nature. The relevant mechanisms here are related to the velocity-space nonlinearities and background fluctuations. The magnitude of the diffusion at this stage can be comparable to that of quasilinear diffusion in the presence of collisions, and it remains finite even in the collisionless limit.
Nonlinear tumor evolution from dysplastic nodules to hepatocellular carcinoma.
Joung, Je-Gun; Ha, Sang Yun; Bae, Joon Seol; Nam, Jae-Yong; Gwak, Geum-Youn; Lee, Hae-Ock; Son, Dae-Soon; Park, Cheol-Keun; Park, Woong-Yang
2017-01-10
Dysplastic nodules are premalignant neoplastic nodules found in explanted livers with cirrhosis. Genetic signatures of premalignant dysplastic nodules (DNs) with concurrent hepatocellular carcinoma (HCC) may provide an insight in the molecular evolution of hepatocellular carcinogenesis. We analyzed four patients with multifocal nodular lesions and cirrhotic background by whole-exome sequencing (WES). The genomic profiles of somatic single nucleotide variations (SNV) and copy number variations (CNV) in DNs were compared to those of HCCs. The number and variant allele frequency of somatic SNVs of DNs and HCCs in each patient was identical along the progression of pathological grade. The somatic SNVs in DNs showed little conservation in HCC. Additionally, CNVs showed no conservation. Phylogenetic analysis based on SNVs and copy number profiles indicated a nonlinear segregation pattern, implying independent development of DNs and HCC in each patient. Thus, somatic mutations in DNs may be developed separately from other malignant nodules in the same liver, suggesting a nonlinear model for hepatocarcinogenesis from DNs to HCC.
Time-reversed wave mixing in nonlinear optics.
Zheng, Yuanlin; Ren, Huaijin; Wan, Wenjie; Chen, Xianfeng
2013-11-19
Time-reversal symmetry is important to optics. Optical processes can run in a forward or backward direction through time when such symmetry is preserved. In linear optics, a time-reversed process of laser emission can enable total absorption of coherent light fields inside an optical cavity of loss by time-reversing the original gain medium. Nonlinearity, however, can often destroy such symmetry in nonlinear optics, making it difficult to study time-reversal symmetry with nonlinear optical wave mixings. Here we demonstrate time-reversed wave mixings for optical second harmonic generation (SHG) and optical parametric amplification (OPA) by exploring this well-known but underappreciated symmetry in nonlinear optics. This allows us to observe the annihilation of coherent beams. Our study offers new avenues for flexible control in nonlinear optics and has potential applications in efficient wavelength conversion, all-optical computing.
Institute of Scientific and Technical Information of China (English)
唐登斌; 夏浩
2002-01-01
The nonlinear evolution problem in nonparallel boundary layer stability was studied. The relative parabolized stability equations of nonlinear nonparallel boundary layer were derived. The developed numerical method, which is very effective, was used to study the nonlinear evolution of T-S disturbance wave at finite amplitudes. Solving nonlinear equations of different modes by using predictor-corrector and iterative approach, which is uncoupled between modes, improving computational accuracy by using high order compact differential scheme, satisfying normalization condition, determining tables of nonlinear terms at different modes, and implementing stably the spatial marching, were included in this method. With different initial amplitudes, the nonlinear evolution of T-S wave was studied. The nonlinear nonparallel results of examples compare with data of direct numerical simulations (DNS) using full Navier- Stokes equations.
Evolution of Nonlinear Internal Waves in China Seas
Liu, Antony K.; Hsu, Ming-K.; Liang, Nai K.
1997-01-01
Synthetic Aperture Radar (SAR) images from ERS-I have been used to study the characteristics of internal waves of Taiwan in the East China Sea, and east of Hainan Island in the South China Sea. Rank-ordered packets of internal solitons propagating shoreward from the edge of the continental shelf were observed in the SAR images. Based on the assumption of a semidiurnal tidal origin, the wave speed can be estimated and is consistent with the internal wave theory. By using the SAR images and hydrographic data, internal waves of elevation have been identified in shallow water due to a thicker mixed layer as compared with the bottom layer on the continental shelf. The generation mechanism includes the influences of the tide and the Kuroshio intrusion across the continental shelf for the formations of elevation internal waves. The effects of water depth on the evolution of solitons and wave packets are modeled by nonlinear Kortweg-deVries (KdV) type equation and linked to satellite image observations. The numerical calculations of internal wave evolution on the continental shelf have been performed and compared with the SAR observations. For a case of depression waves in deep water, the solitons first disintegrate into dispersive wave trains and then evolve to a packet of elevation waves in the shallow water area after they pass through a turning point of approximately equal layer depths has been observed in the SAR image and simulated by numerical model.
Time Variance of the Suspension Nonlinearity
DEFF Research Database (Denmark)
Agerkvist, Finn T.; Pedersen, Bo Rohde
2008-01-01
. This paper investigates the changes in compliance the driving signal can cause, this includes low level short duration measurements of the resonance frequency as well as high power long duration measurements of the non-linearity of the suspension. It is found that at low levels the suspension softens...
Self-similar solutions for some nonlinear evolution equations: KdV, mKdV and Burgers equations
Directory of Open Access Journals (Sweden)
S.A. El-Wakil
2016-02-01
Full Text Available A method for solving three types of nonlinear evolution equations namely KdV, modified KdV and Burgers equations, with self-similar solutions is presented. The method employs ideas from symmetry reduction to space and time variables and similarity reductions for nonlinear evolution equations are performed. The obtained self-similar solutions of KdV and mKdV equations are related to Bessel and Airy functions whereas those of Burgers equation are related to the error and Hermite functions. These solutions appear as new types of solitary, shock and periodic waves. Also, the method can be applied to other nonlinear evolution equations in mathematical physics.
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.
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.
Impulsive control of nonlinear systems with time-varying delays
Institute of Scientific and Technical Information of China (English)
Yu Yong-Bin; Bao Jing-Fu; Zhang Hong-Bin; Zhong Qi-Shui; Liao Xiao-Feng; Yu Jue-Sang
2008-01-01
A whole impulsive control scheme of nonlinear systems with time-varying delays, which is an extension for impulsive control of nonlinear systems without time delay, is presented in this paper. Utilizing the Lyapunov functions and the impulsive-type comparison principles, we establish a series of different conditions under which impulsively controlled nonlinear systems with time-varying delays are asymptotically stable. Then we estimate upper bounds of impulse interval and time-varying delays for asymptotically stable control. Finally a numerical example is given to illustrate the effectiveness of the method.
Nonlinear time reversal in a wave chaotic system.
Frazier, Matthew; Taddese, Biniyam; Antonsen, Thomas; Anlage, Steven M
2013-02-01
Exploiting the time-reversal invariance and reciprocal properties of the lossless wave equation enables elegantly simple solutions to complex wave-scattering problems and is embodied in the time-reversal mirror. Here we demonstrate the implementation of an electromagnetic time-reversal mirror in a wave chaotic system containing a discrete nonlinearity. We demonstrate that the time-reversed nonlinear excitations reconstruct exclusively upon the source of the nonlinearity. As an example of its utility, we demonstrate a new form of secure communication and point out other applications.
Nonlinear analysis and prediction of time series in multiphase reactors
Liu, Mingyan
2014-01-01
This book reports on important nonlinear aspects or deterministic chaos issues in the systems of multi-phase reactors. The reactors treated in the book include gas-liquid bubble columns, gas-liquid-solid fluidized beds and gas-liquid-solid magnetized fluidized beds. The authors take pressure fluctuations in the bubble columns as time series for nonlinear analysis, modeling and forecasting. They present qualitative and quantitative non-linear analysis tools which include attractor phase plane plot, correlation dimension, Kolmogorov entropy and largest Lyapunov exponent calculations and local non-linear short-term prediction.
Asymptotics for Nonlinear Transformations of Fractionally Integrated Time Series
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The asymptotic theory for nonlinear transformations of fractionally integrated time series is developed. By the use of fractional Occupation Times Formula, various nonlinear functions of fractionally integrated series such as ARFIMA time series are studied, and the asymptotic distributions of the sample moments of such functions are obtained and analyzed. The transformations considered in this paper includes a variety of functions such as regular functions, integrable functions and asymptotically homogeneous functions that are often used in practical nonlinear econometric analysis. It is shown that the asymptotic theory of nonlinear transformations of original and normalized fractionally integrated processes is different from that of fractionally integrated processes, but is similar to the asymptotic theory of nonlinear transformations of integrated processes.
Detecting Nonlinearity in Data with Long Coherence Times
Theiler, J; Rubin, D M; Theiler, James; Linsay, Paul S.; Rubin, David M.
1993-01-01
Abstract: We consider the limitations of two techniques for detecting nonlinearity in time series. The first technique compares the original time series to an ensemble of surrogate time series that are constructed to mimic the linear properties of the original. The second technique compares the forecasting error of linear and nonlinear predictors. Both techniques are found to be problematic when the data has a long coherence time; they tend to indicate nonlinearity even for linear time series. We investigate the causes of these difficulties both analytically and with numerical experiments on ``real'' and computer-generated data. In particular, although we do see some initial evidence for nonlinear structure in the SFI dataset E, we are inclined to dismiss this evidence as an artifact of the long coherence time.
Discrete-time inverse optimal control for nonlinear systems
Sanchez, Edgar N
2013-01-01
Discrete-Time Inverse Optimal Control for Nonlinear Systems proposes a novel inverse optimal control scheme for stabilization and trajectory tracking of discrete-time nonlinear systems. This avoids the need to solve the associated Hamilton-Jacobi-Bellman equation and minimizes a cost functional, resulting in a more efficient controller. Design More Efficient Controllers for Stabilization and Trajectory Tracking of Discrete-Time Nonlinear Systems The book presents two approaches for controller synthesis: the first based on passivity theory and the second on a control Lyapunov function (CLF). Th
Losslessness of Nonlinear Stochastic Discrete-Time Systems
Directory of Open Access Journals (Sweden)
Xikui Liu
2015-01-01
Full Text Available This paper will study stochastic losslessness theory for nonlinear stochastic discrete-time systems, which are expressed by the Itô-type difference equations. A necessary and sufficient condition is developed for a nonlinear stochastic discrete-time system to be lossless. By the stochastic lossless theory, we show that a nonlinear stochastic discrete-time system can be lossless via state feedback if and only if it has relative degree 0,…,0 and lossless zero dynamics. The effectiveness of the proposed results is illustrated by a numerical example.
Solitons and periodic solutions to a couple of fractional nonlinear evolution equations
Indian Academy of Sciences (India)
M Mirzazadeh; M Eslami; Anjan Biswas
2014-03-01
This paper studies a couple of fractional nonlinear evolution equations using first integral method. These evolution equations are foam drainage equation and Klein–Gordon equation (KGE), the latter of which is considered in (2 + 1) dimensions. For the fractional evolution, the Jumarie’s modified Riemann–Liouville derivative is considered. Exact solutions to these equations are obtained.
Two Kinds of Square-Conservative Integrators for Nonlinear Evolution Equations
Institute of Scientific and Technical Information of China (English)
CHEN Jing-Bo; LIU Hong
2008-01-01
@@ Based on the Lie-group and Gauss-Legendre methods, two kinds of square-conservative integrators for squareconservative nonlinear evolution equations are presented. Lie-group based square-conservative integrators are linearly implicit, while Gauss-Legendre based square-conservative integrators are nonlinearly implicit and iterarive schemes are needed to solve the corresponding integrators. These two kinds of integrators provide natural candidates for simulating square-conservative nonlinear evolution equations in the sense that these integrators not only preserve the square-conservative properties of the continuous equations but also are nonlinearly stable.Numerical experiments are performed to test the presented integrators.
Non-linear evolution of the cosmic neutrino background
Villaescusa-Navarro, Francisco; Peña-Garay, Carlos; Viel, Matteo
2012-01-01
We investigate the non-linear evolution of the relic cosmic neutrino background by running large box-size, high resolution N-body simulations. Our set of simulations explore the properties of neutrinos in a reference $\\Lambda$CDM model with total neutrino masses between 0.05-0.60 eV in cold dark matter haloes of mass $10^{11}-10^{15}$ $h^{-1}$M$_{\\odot}$, over a redshift range $z=0-2$. We compute the halo mass function and show that it is reasonably well fitted by the Sheth-Tormen formula. More importantly, we focus on the CDM and neutrino properties of the density and peculiar velocity fields in the cosmological volume, inside and in the outskirts of virialized haloes. The dynamical state of the neutrino particles depends strongly on their momentum: whereas neutrinos in the low velocity tail behave similarly to CDM particles, neutrinos in the high velocity tail are not affected by the clustering of the underlying CDM component. We find that the neutrino (linear) unperturbed momentum distribution is modified ...
A New Generalization of Extended Tanh-Function Method for Solving Nonlinear Evolution Equations
Institute of Scientific and Technical Information of China (English)
ZHENG Xue-Dong; CHEN Yong; LI Biao; ZHANG Hong-Qing
2003-01-01
Making use of a new generalized ansatze and a proper transformation, we generalized the extended tanh-function method. Applying the generalized method with the aid of Maple, we consider some nonlinear evolution equations.As a result, we can successfully recover the previously known solitary wave solutions that had been found by the extendedtanh-function method and other more sophisticated methods. More importantly, for some equations, we also obtain othernew and more general solutions at the same time. The results include kink-profile solitary-wave solutions, bell-profilesolitary-wave solutions, periodic wave solutions, rational solutions, singular solutions and new formal solutions.
Approximated Lax pairs for the reduced order integration of nonlinear evolution equations
Gerbeau, Jean-Frédéric; Lombardi, Damiano
2014-05-01
A reduced-order model algorithm, called ALP, is proposed to solve nonlinear evolution partial differential equations. It is based on approximations of generalized Lax pairs. Contrary to other reduced-order methods, like Proper Orthogonal Decomposition, the basis on which the solution is searched for evolves in time according to a dynamics specific to the problem. It is therefore well-suited to solving problems with progressive front or wave propagation. Another difference with other reduced-order methods is that it is not based on an off-line/on-line strategy. Numerical examples are shown for the linear advection, KdV and FKPP equations, in one and two dimensions.
Nonlinear Time Series Forecast Using Radial Basis Function Neural Networks
Institute of Scientific and Technical Information of China (English)
ZHENGXin; CHENTian-Lun
2003-01-01
In the research of using Radial Basis Function Neural Network (RBF NN) forecasting nonlinear time series, we investigate how the different clusterings affect the process of learning and forecasting. We find that k-means clustering is very suitable. In order to increase the precision we introduce a nonlinear feedback term to escape from the local minima of energy, then we use the model to forecast the nonlinear time series which are produced by Mackey-Glass equation and stocks. By selecting the k-means clustering and the suitable feedback term, much better forecasting results are obtained.
Shahmansouri, M.; Misra, A. P.
2016-12-01
The modulational instability (MI) and the evolution of weakly nonlinear two-dimensional (2D) Langmuir wave (LW) packets are studied in an unmagnetized collisionless plasma with weakly relativistic electron flow. By using a 2D self-consistent relativistic fluid model and employing the standard multiple-scale technique, a coupled set of Davey-Stewartson (DS)-like equations is derived, which governs the slow modulation and the evolution of LW packets in relativistic plasmas. It is found that the relativistic effects favor the instability of LW envelopes in the k - θ plane, where k is the wave number and θ ( 0 ≤ θ ≤ π ) the angle of modulation. It is also found that as the electron thermal velocity or θ increases, the growth rate of MI increases with cutoffs at higher wave numbers of modulation. Furthermore, in the nonlinear evolution of the DS-like equations, it is seen that with an effect of the relativistic flow, a Gaussian wave beam collapses in a finite time, and the collapse can be arrested when the effect of the thermal pressure or the relativistic flow is slightly relaxed. The present results may be useful to the MI and the formation of localized LW envelopes in cosmic plasmas with a relativistic flow of electrons.
Shahmansouri, M
2016-01-01
The modulational instability (MI) and the evolution of weakly nonlinear two-dimensional (2D) Langmuir wave (LW) packets are studied in an unmagnetized collisionless plasma with weakly relativistic electron flow. By using a 2D self-consistent relativistic fluid model and employing the standard multiple-scale technique, a coupled set of Davey-Stewartson (DS)-like equations is derived which governs the slow modulation and the evolution of LW packets in relativistic plasmas. It is found that the relativistic effects favor the instability of LW envelopes in the k{\\theta} plane, where k is the wave number and {\\theta} the angle of modulation. It is also found that as the electron thermal velocity or {\\theta} increases, the growth rate of MI increases with cutoffs at higher wave numbers of modulation. Furthermore, in the nonlinear evolution of the DS-like equations, it is seen that with an effect of the relativistic flow, a Gaussian wave beam collapses in a finite time, and the collapse can be arrested when the effe...
W-Stability of Multistable Nonlinear Discrete-Time Systems
Directory of Open Access Journals (Sweden)
Zhishuai Ding
2012-01-01
Full Text Available Motivated by the importance and application of discrete dynamical systems, this paper presents a new Lyapunov characterization which is an extension of conventional Lyapunov characterization for multistable discrete-time nonlinear systems. Based on a new type stability notion of W-stability introduced by D. Efimov, the estimates of solution and the Lyapunov stability theorem and converse theorem are proposed for multi-stable discrete-time nonlinear systems.
MULTISCALE HOMOGENIZATION OF NONLINEAR HYPERBOLIC EQUATIONS WITH SEVERAL TIME SCALES
Institute of Scientific and Technical Information of China (English)
Jean Louis Woukeng; David Dongo
2011-01-01
We study the multiscale homogenization of a nonlinear hyperbolic equation in a periodic setting. We obtain an accurate homogenization result. We also show that as the nonlinear term depends on the microscopic time variable, the global homogenized problem thus obtained is a system consisting of two hyperbolic equations. It is also shown that in spite of the presence of several time scales, the global homogenized problem is not a reiterated one.
Non-linear evolution of the cosmic neutrino background
Energy Technology Data Exchange (ETDEWEB)
Villaescusa-Navarro, Francisco; Viel, Matteo [INAF/Osservatorio Astronomico di Trieste, Via Tiepolo 11, 34143, Trieste (Italy); Bird, Simeon [Institute for Advanced Study, 1 Einstein Drive, Princeton, NJ, 08540 (United States); Peña-Garay, Carlos, E-mail: villaescusa@oats.inaf.it, E-mail: spb@ias.edu, E-mail: penya@ific.uv.es, E-mail: viel@oats.inaf.it [Instituto de Física Corpuscular, CSIC-UVEG, E-46071, Paterna, Valencia (Spain)
2013-03-01
We investigate the non-linear evolution of the relic cosmic neutrino background by running large box-size, high resolution N-body simulations which incorporate cold dark matter (CDM) and neutrinos as independent particle species. Our set of simulations explore the properties of neutrinos in a reference ΛCDM model with total neutrino masses between 0.05-0.60 eV in cold dark matter haloes of mass 10{sup 11}−10{sup 15} h{sup −1}M{sub s}un, over a redshift range z = 0−2. We compute the halo mass function and show that it is reasonably well fitted by the Sheth-Tormen formula, once the neutrino contribution to the total matter is removed. More importantly, we focus on the CDM and neutrino properties of the density and peculiar velocity fields in the cosmological volume, inside and in the outskirts of virialized haloes. The dynamical state of the neutrino particles depends strongly on their momentum: whereas neutrinos in the low velocity tail behave similarly to CDM particles, neutrinos in the high velocity tail are not affected by the clustering of the underlying CDM component. We find that the neutrino (linear) unperturbed momentum distribution is modified and mass and redshift dependent deviations from the expected Fermi-Dirac distribution are in place both in the cosmological volume and inside haloes. The neutrino density profiles around virialized haloes have been carefully investigated and a simple fitting formula is provided. The neutrino profile, unlike the cold dark matter one, is found to be cored with core size and central density that depend on the neutrino mass, redshift and mass of the halo, for halos of masses larger than ∼ 10{sup 13.5}h{sup −1}M{sub s}un. For lower masses the neutrino profile is best fitted by a simple power-law relation in the range probed by the simulations. The results we obtain are numerically converged in terms of neutrino profiles at the 10% level for scales above ∼ 200 h{sup −1}kpc at z = 0, and are stable with
Appropriate Algorithms for Nonlinear Time Series Analysis in Psychology
Scheier, Christian; Tschacher, Wolfgang
Chaos theory has a strong appeal for psychology because it allows for the investigation of the dynamics and nonlinearity of psychological systems. Consequently, chaos-theoretic concepts and methods have recently gained increasing attention among psychologists and positive claims for chaos have been published in nearly every field of psychology. Less attention, however, has been paid to the appropriateness of chaos-theoretic algorithms for psychological time series. An appropriate algorithm can deal with short, noisy data sets and yields `objective' results. In the present paper it is argued that most of the classical nonlinear techniques don't satisfy these constraints and thus are not appropriate for psychological data. A methodological approach is introduced that is based on nonlinear forecasting and the method of surrogate data. In artificial data sets and empirical time series we can show that this methodology reliably assesses nonlinearity and chaos in time series even if they are short and contaminated by noise.
Faster than Hermitian Time Evolution
Directory of Open Access Journals (Sweden)
Carl M. Bender
2007-12-01
Full Text Available For any pair of quantum states, an initial state $|I angle$ and afinal quantum state $|F angle$, in a Hilbert space, there are many Hamiltonians $H$ under which $|I angle$ evolves into $|F angle$. Let us impose the constraint that the difference between the largest and smallest eigenvalues of $H$, $E_{max}$ and $E_{min}$, is held fixed. We can then determine the Hamiltonian $H$ that satisfies this constraint and achieves the transformation from the initial state to the final state in the least possible time $au$. For Hermitian Hamiltonians, $au$ has a nonzero lower bound. However, amongnon-Hermitian ${cal PT}$-symmetric Hamiltonians satisfying the same energy constraint, $au$ can be made arbitrarily small without violating the time-energy uncertainty principle. The minimum value of $au$ can be made arbitrarily small because for ${cal PT}$-symmetric Hamiltonians the path from the vector $|I angle$ to the vector $|F angle$, as measured using the Hilbert-space metric appropriate for this theory, can be made arbitrarily short. The mechanism described here is similar to that in general relativity in whichthe distance between two space-time points can be made small if they are connected by a wormhole. This result may have applications in quantum computing.
Nonlinear evolution and final fate of (charged) superradiant instability
Bosch, Pablo; Lehner, Luis
2016-01-01
We describe the full nonlinear development of the superradiant instability for a charged massless scalar field, coupled to general relativity and electromagnetism, in the vicinity of a Reissner--Nordstr\\"om-AdS black hole. The presence of the negative cosmological constant provides a natural context for considering perfectly reflecting boundary conditions and studying the dynamics as the scalar field interacts repeateadly with the black hole. At early times, small superradiant perturbations grow as expected from linearized studies. Backreaction then causes the black hole to lose charge and mass until the perturbation becomes nonsuperradiant, with the final state described by a stable hairy black hole. For large gauge coupling, the instability extracts a large amount of charge per unit mass, resulting in greater entropy increase. We discuss the implications of the observed behavior for the general problem of superradiance in black hole spacetimes.
Solitary Wave and Non-traveling Wave Solutions to Two Nonlinear Evolution Equations
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
By applying the extended homogeneous balance method, we find some new explicit solutions to two nonlinear evolution equations, which include n-resonance plane solitary wave and non-traveling wave solutions.
Generalized Dromion Structures of New (2 + 1)-Dimensional Nonlinear EvolutionEquation
Institute of Scientific and Technical Information of China (English)
ZHANG Jie-Fang
2001-01-01
We derive the generalized dromions of the new (2 + 1)-dimensional nonlinear evolution equation by the arbitrary function presented in the bilinearized linear equations. The rich soliton and dromion structures for this system are released.
SIMILARITY REDUCTIONS FOR THE NONLINEAR EVOLUTION EQUATION ARISING IN THE FERMI-PASTA-ULAM PROBLEM
Institute of Scientific and Technical Information of China (English)
谢福鼎; 闫振亚; 张鸿庆
2002-01-01
Four families of similarity reductions are obtained for the nonlinear evolution equation arising in the Fermi-Pasta-Ulam problem via using both the direct method due to Clarkson and Kruskal and the improved direct method due to Lou.
Nonlinear evolution of mirror instability in the Earth's magnetosheath in pic simulations
Ahmadi, Narges
Mirror modes are large amplitude non-propagating structures frequently observed in the magnetosheath and they are generated in space plasma environments with proton temperature anisotropy of larger than one. The proton temperature anisotropy also drives the proton cyclotron instability which has larger linear growth rate than that of the mirror instability. Linear dispersion theory predicts that electron temperature anisotropy can enhance the mirror instability growth rate while leaving the proton cyclotron instability largely unaffected. Contrary to the hypothesis, electron temperature anisotropy leads to excitement of the electron whistler instability. Our results show that the electron whistler instability grows much faster than the mirror instability and quickly consumes the electron free energy, so that there is not enough electron temperature anisotropy left to significantly impact the evolution of the mirror instability. Observational studies have shown that the shape of mirror structures is related to local plasma parameters and distance to the mirror instability threshold. Mirror structures in the form of magnetic holes are observed when plasma is mirror stable or marginally mirror unstable and magnetic peaks are observed when plasma is mirror unstable. Mirror structures are created downstream of the quasi-perpendicular bow shock and they are convected toward the magnetopause. In the middle magnetosheath, where plasma is mirror unstable, mirror structures are dominated by magnetic peaks. Close to the magnetopause, plasma expansion makes the region mirror stable and magnetic peaks evolve to magnetic holes. We investigate the nonlinear evolution of mirror instability using expanding box Particle-in-Cell simulations. We change the plasma conditions by artificially enlarging the simulation box over time to make the plasma mirror stable and investigate the final nonlinear state of the mirror structures. We show that the direct nonlinear evolution of the mirror
A new application of Riccati equation to some nonlinear evolution equations
Energy Technology Data Exchange (ETDEWEB)
Geng Tao [School of Science, PO Box 122, Beijing University of Posts and Telecommunications, Beijing 100876 (China)], E-mail: taogeng@yahoo.com.cn; Shan Wenrui [School of Science, PO Box 122, Beijing University of Posts and Telecommunications, Beijing 100876 (China)
2008-03-03
By means of symbolic computation, a new application of Riccati equation is presented to obtain novel exact solutions of some nonlinear evolution equations, such as nonlinear Klein-Gordon equation, generalized Pochhammer-Chree equation and nonlinear Schroedinger equation. Comparing with the existing tanh methods and the proposed modifications, we obtain the exact solutions in the form as a non-integer power polynomial of tanh (or tan) functions by using this method, and the availability of symbolic computation is demonstrated.
Nonlinear Time Series Forecast Using Radial Basis Function Neural Networks
Institute of Scientific and Technical Information of China (English)
ZHENG Xin; CHEN Tian-Lun
2003-01-01
In the research of using Radial Basis Function Neural Network (RBF NN) forecasting nonlinear timeseries, we investigate how the different clusterings affect the process of learning and forecasting. We find that k-meansclustering is very suitable. In order to increase the precision we introduce a nonlinear feedback term to escape from thelocal minima of energy, then we use the model to forecast the nonlinear time series which are produced by Mackey-Glassequation and stocks. By selecting the k-means clustering and the suitable feedback term, much better forecasting resultsare obtained.
Multigrid Reduction in Time for Nonlinear Parabolic Problems
Energy Technology Data Exchange (ETDEWEB)
Falgout, R. D. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Manteuffel, T. A. [Univ. of Colorado, Boulder, CO (United States); O' Neill, B. [Univ. of Colorado, Boulder, CO (United States); Schroder, J. B. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2016-01-04
The need for parallel-in-time is being driven by changes in computer architectures, where future speed-ups will be available through greater concurrency, but not faster clock speeds, which are stagnant.This leads to a bottleneck for sequential time marching schemes, because they lack parallelism in the time dimension. Multigrid Reduction in Time (MGRIT) is an iterative procedure that allows for temporal parallelism by utilizing multigrid reduction techniques and a multilevel hierarchy of coarse time grids. MGRIT has been shown to be effective for linear problems, with speedups of up to 50 times. The goal of this work is the efficient solution of nonlinear problems with MGRIT, where efficient is defined as achieving similar performance when compared to a corresponding linear problem. As our benchmark, we use the p-Laplacian, where p = 4 corresponds to a well-known nonlinear diffusion equation and p = 2 corresponds to our benchmark linear diffusion problem. When considering linear problems and implicit methods, the use of optimal spatial solvers such as spatial multigrid imply that the cost of one time step evaluation is fixed across temporal levels, which have a large variation in time step sizes. This is not the case for nonlinear problems, where the work required increases dramatically on coarser time grids, where relatively large time steps lead to worse conditioned nonlinear solves and increased nonlinear iteration counts per time step evaluation. This is the key difficulty explored by this paper. We show that by using a variety of strategies, most importantly, spatial coarsening and an alternate initial guess to the nonlinear time-step solver, we can reduce the work per time step evaluation over all temporal levels to a range similar with the corresponding linear problem. This allows for parallel scaling behavior comparable to the corresponding linear problem.
Deterministic and stochastic evolution equations for fully dispersive and weakly nonlinear waves
DEFF Research Database (Denmark)
Eldeberky, Y.; Madsen, Per A.
1999-01-01
This paper presents a new and more accurate set of deterministic evolution equations for the propagation of fully dispersive, weakly nonlinear, irregular, multidirectional waves. The equations are derived directly from the Laplace equation with leading order nonlinearity in the surface boundary c...
Adaptive control method for nonlinear time-delay processes
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
Two complex properties,varying time-delay and block-oriented nonlinearity,are very common in chemical engineering processes and not easy to be controlled by routine control methods.Aimed at these two complex properties,a novel adaptive control algorithm the basis of nonlinear OFS(orthonormal functional series) model is proposed.First,the hybrid model which combines OFS and Volterra series is introduced.Then,a stable state feedback strategy is used to construct a nonlinear adaptive control algorithm that can guarantee the closed-loop stability and can track the set point curve without steady-state errors.Finally,control simulations and experiments on a nonlinear process with varying time-delay are presented.A number of experimental results validate the efficiency and superiority of this algorithm.
Nonlinear evolution of oblique waves on compressible shear layers
Goldstein, M. E.; Leib, S. J.
1989-01-01
The effects of critical-layer nonlinearity on spatially growing oblique instability waves on compressible shear layers between two parallel streams are considered. The analysis shows that mean temperature nonuniformities cause nonlinearity to occur at much smaller amplitudes than it does when the flow is isothermal. The nonlinear instability wave growth rate effects are described by an integrodifferential equation which bears some resemblance to the Landau equation, in that it involves a cubic-type nonlinearity. The numerical solutions to this equation are worked out and discussed in some detail. Inviscid solutions always end in a singularity at a finite downstream distance, but viscosity can eliminate this singularity for certain parameter ranges.
Grammatical Immune System Evolution for Reverse Engineering Nonlinear Dynamic Bayesian Models
Directory of Open Access Journals (Sweden)
B.A. McKinney
2008-01-01
Full Text Available An artificial immune system algorithm is introduced in which nonlinear dynamic models are evolved to ﬁ t time series of interacting biomolecules. This grammar-based machine learning method learns the structure and parameters of the underlying dynamic model. In silico immunogenetic mechanisms for the generation of model-structure diversity are implemented with the aid of a grammar, which also enforces semantic constraints of the evolved models. The grammar acts as a DNA repair polymerase that can identify recombination and hypermutation signals in the antibody (model genome. These signals contain information interpretable by the grammar to maintain model context. Grammatical Immune System Evolution (GISE is applied to a nonlinear system identification problem in which a generalized (nonlinear dynamic Bayesian model is evolved to ﬁ t biologically motivated artificial time-series data. From experimental data, we use GISE to infer an improved kinetic model for the oxidative metabolism of 17β-estradiol (E2, the parent hormone of the estrogen metabolism pathway.
Finite-time disturbance attenuation of nonlinear systems
Institute of Scientific and Technical Information of China (English)
MO LiPo; JIA YingMin; ZHENG ZhiMing
2009-01-01
This paper is devoted to the finite-time disturbance attenuation problem of affine nonlinear systems.Based on the finite time Lyapunov stability theory,some finite-time H_∞ performance criterions are derived.Then the state-feedback control law is designed and the structure of such a controller is investigated.Furthermore,it is shown that the H_∞ controller can also make the closed-loop system satisfy finite-time H_∞ performance for nonlinear homogeneous systems.An example is provided to demonstrate the effectiveness of the presented results.
Bifurcation and nonlinear analysis of a time-delayed thermoacoustic system
Yang, Xiaochuan; Turan, Ali; Lei, Shenghui
2017-03-01
In this paper, of primary concern is a time-delayed thermoacoustic system, viz. a horizontal Rijke tube. A continuation approach is employed to capture the nonlinear behaviour inherent to the system. Unlike the conventional approach by the Galerkin method, a dynamic system is naturally built up by discretizing the acoustic momentum and energy equations incorporating appropriate boundary conditions using a finite difference method. In addition, the interaction of Rijke tube velocity with oscillatory heat release is modeled using a modified form of King's law. A comparison of the numerical results with experimental data and the calculations reported reveals that the current approach can yield very good predictions. Moreover, subcritical Hopf bifurcations and fold bifurcations are captured with the evolution of dimensionless heat release coefficient, generic damping coefficient and time delay. Linear stability boundary, nonlinear stability boundary, bistable region and limit cycles are thus determined to gain an understanding of the intrinsic nonlinear behaviours.
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.
Nonlinear pulse propagation: a time-transformation approach.
Xiao, Yuzhe; Agrawal, Govind P; Maywar, Drew N
2012-04-01
We present a time-transformation approach for studying the propagation of optical pulses inside a nonlinear medium. Unlike the conventional way of solving for the slowly varying amplitude of an optical pulse, our new approach maps directly the input electric field to the output one, without making the slowly varying envelope approximation. Conceptually, the time-transformation approach shows that the effect of propagation through a nonlinear medium is to change the relative spacing and duration of various temporal slices of the pulse. These temporal changes manifest as self-phase modulation in the spectral domain and self-steepening in the temporal domain. Our approach agrees with the generalized nonlinear Schrödinger equation for 100 fs pulses and the finite-difference time-domain solution of Maxwell's equations for two-cycle pulses, while producing results 20 and 50 times faster, respectively.
Backstepping tracking control for nonlinear time-delay systems
Institute of Scientific and Technical Information of China (English)
Chen Weisheng; Li Junmin
2006-01-01
Two design approaches of state feedback and output feedback tracking controllers are proposed for a class of strict feedback nonlinear time-delay systems by using backstepping technique. When the states of system cannot be observed, the time-delay state observer is designed to estimate the system states. Domination method is used to deal with nonlinear time-delay function under the assumption that the nonlinear time-delay functions of systems satisfy Lipschitz condition. The global asymptotical tracking of the references signal is achieved and the bound of all signals of the resultant closed-loop system is also guaranteed. By constructing a Lyapunov-Krasoviskii functional, the stability of the closed-loop system is proved. The feasibility of the proposed approach is illustrated by a simulation example.
Nonlinear techniques for forecasting solar activity directly from its time series
Ashrafi, S.; Roszman, L.; Cooley, J.
1993-01-01
This paper presents numerical techniques for constructing nonlinear predictive models to forecast solar flux directly from its time series. This approach makes it possible to extract dynamical in variants of our system without reference to any underlying solar physics. We consider the dynamical evolution of solar activity in a reconstructed phase space that captures the attractor (strange), give a procedure for constructing a predictor of future solar activity, and discuss extraction of dynamical invariants such as Lyapunov exponents and attractor dimension.
Nonlinear Time Series Analysis via Neural Networks
Volná, Eva; Janošek, Michal; Kocian, Václav; Kotyrba, Martin
This article deals with a time series analysis based on neural networks in order to make an effective forex market [Moore and Roche, J. Int. Econ. 58, 387-411 (2002)] pattern recognition. Our goal is to find and recognize important patterns which repeatedly appear in the market history to adapt our trading system behaviour based on them.
Nonlinear evolution characteristics of the climate system on the interdecadal-centennial timescale
Institute of Scientific and Technical Information of China (English)
Gao Xin-Quan; Zhang Wen
2005-01-01
To better understand the physical mechanism of the climate change on interdecadal-centennial timescale, this paper focuses on analysing and modelling the evolution characteristics of the climate change. The method of wavelet transform is used to pick out the interdecadal timescale oscillations from long-term instrumental observations, natural proxy records, and modelling series. The modelling series derived from the most simplified nonlinear climatic model are used to identify whether modifications are concerned with some forcings such as the solar radiation on the climate system. The results show that two major oscillations exist in various observations and model series, namely the 2030a and the 60-70a timescale respectively, and these quasi-periodicities are modulated with time. Further, modelling results suggest that the originations of these oscillations are not directly linked with the periodic variation of solar radiations such as the 1-year cycle, the 11-year cycle, and others, but possibly induced by the internal nonlinear effects of the climate system. It seems that the future study on the genesis of the climate change with interdecadal-centennial timescale should focus on the internal nonlinear dynamics in the climate system.
The Nonlinear Evolution of Massive Stellar Core Collapses That ``Fizzle''
Imamura, James N.; Pickett, Brian K.; Durisen, Richard H.
2003-04-01
Core collapse in a massive rotating star may pause before nuclear density is reached, if the core contains total angular momentum J>~1049 g cm2 s-1. In such aborted or ``fizzled'' collapses, temporary equilibrium objects form that, although rapidly rotating, are secularly and dynamically stable because of the high electron fraction per baryon Ye>0.3 and the high entropy per baryon Sb/k~1-2 of the core material at neutrino trapping. These fizzled collapses are called ``fizzlers.'' In the absence of prolonged infall from the surrounding star, the evolution of fizzlers is driven by deleptonization, which causes them to contract and spin up until they either become stable neutron stars or reach the dynamic instability point for barlike modes. The barlike instability case is of current interest because the bars would be sources of gravitational wave (GW) radiation. In this paper, we use linear and nonlinear techniques, including three-dimensional hydrodynamic simulations, to study the behavior of fizzlers that have deleptonized to the point of reaching dynamic bar instability. The simulations show that the GW emission produced by bar-unstable fizzlers has rms strain amplitude r15h=10-23 to 10-22 for an observer on the rotation axis, with wave frequency of roughly 60-600 Hz. Here h is the strain and r15= (r/15 Mpc) is the distance to the fizzler in units of 15 Mpc. If the bars that form by dynamic instability can maintain GW emission at this level for 100 periods or more, they may be detectable by the Laser Interferometer Gravitational-Wave Observatory at the distance of the Virgo Cluster. They would be detectable as burst sources, defined as sources that persist for ~10 cycles or less, if they occurred in the Local Group of galaxies. The long-term behavior of the bars is the crucial issue for the detection of fizzler events. The bars present at the end of our simulations are dynamically stable but will evolve on longer timescales because of a variety of effects, such as
Nonpoint Symmetry and Reduction of Nonlinear Evolution and Wave Type Equations
Directory of Open Access Journals (Sweden)
Ivan Tsyfra
2015-01-01
Full Text Available We study the symmetry reduction of nonlinear partial differential equations with two independent variables. We propose new ansätze reducing nonlinear evolution equations to system of ordinary differential equations. The ansätze are constructed by using operators of nonpoint classical and conditional symmetry. Then we find solution to nonlinear heat equation which cannot be obtained in the framework of the classical Lie approach. By using operators of Lie-Bäcklund symmetries we construct the solutions of nonlinear hyperbolic equations depending on arbitrary smooth function of one variable too.
Time-dependent secular evolution in galaxies
Weinberg, M D
2004-01-01
Lynden-Bell & Kalnajs (1972) presented a useful formula for computing the long-range torque between spiral arms and the disk at large. The derivation uses second-order perturbation theory and assumes that the perturbation slowly grows over a very long time: the time-asymptotic limit. This formula has been widely used to predict the angular momentum transport between spiral arms and stellar bars between disks and dark-matter halos. However, this paper shows that the LBK time-asymptotic limit is not appropriate because the characteristic evolution time for galaxies is too close to the relevant dynamical times. We demonstrate that transients, not present in the time-asymptotic formula, can play a major role in the evolution for realistic astronomical time scales. A generalisation for arbitrary time dependence is presented and illustrated by the bar--halo and satellite--halo interaction. The natural time dependence in bar-driven halo evolution causes quantitative differences in the overall torque and qualitat...
Nonlinear projective filtering; 1, Application to real time series
Schreiber, T
1998-01-01
We discuss applications of nonlinear filtering of time series by locally linear phase space projections. Noise can be reduced whenever the error due to the manifold approximation is smaller than the noise in the system. Examples include the real time extraction of the fetal electrocardiogram from abdominal recordings.
Extracting Knowledge From Time Series An Introduction to Nonlinear Empirical Modeling
Bezruchko, Boris P
2010-01-01
This book addresses the fundamental question of how to construct mathematical models for the evolution of dynamical systems from experimentally-obtained time series. It places emphasis on chaotic signals and nonlinear modeling and discusses different approaches to the forecast of future system evolution. In particular, it teaches readers how to construct difference and differential model equations depending on the amount of a priori information that is available on the system in addition to the experimental data sets. This book will benefit graduate students and researchers from all natural sciences who seek a self-contained and thorough introduction to this subject.
Directory of Open Access Journals (Sweden)
Hasibun Naher
2013-03-01
Full Text Available In this article, new (G′/G-expansion method and new generalized (G′/G-expansion method is proposed to generate more general and abundant new exact traveling wave solutions of nonlinear evolution equations. The novelty and advantages of these methods is exemplified by its implementation to the KdV equation. The results emphasize the power of proposed methods in providing distinct solutions of different physical structures in nonlinear science. Moreover, these methods could be more effectively used to deal with higher dimensional and higher order nonlinear evolution equations which frequently arise in many scientific real time application fields.
General expression for linear and nonlinear time series models
Institute of Scientific and Technical Information of China (English)
Ren HUANG; Feiyun XU; Ruwen CHEN
2009-01-01
The typical time series models such as ARMA, AR, and MA are founded on the normality and stationarity of a system and expressed by a linear difference equation; therefore, they are strictly limited to the linear system. However, some nonlinear factors are within the practical system; thus, it is difficult to fit the model for real systems with the above models. This paper proposes a general expression for linear and nonlinear auto-regressive time series models (GNAR). With the gradient optimization method and modified AIC information criteria integrated with the prediction error, the parameter estimation and order determination are achieved. The model simulation and experiments show that the GNAR model can accurately approximate to the dynamic characteristics of the most nonlinear models applied in academics and engineering. The modeling and prediction accuracy of the GNAR model is superior to the classical time series models. The proposed GNAR model is flexible and effective.
An almost symmetric Strang splitting scheme for nonlinear evolution equations.
Einkemmer, Lukas; Ostermann, Alexander
2014-07-01
In this paper we consider splitting methods for the time integration of parabolic and certain classes of hyperbolic partial differential equations, where one partial flow cannot be computed exactly. Instead, we use a numerical approximation based on the linearization of the vector field. This is of interest in applications as it allows us to apply splitting methods to a wider class of problems from the sciences. However, in the situation described, the classic Strang splitting scheme, while still being a method of second order, is not longer symmetric. This, in turn, implies that the construction of higher order methods by composition is limited to order three only. To remedy this situation, based on previous work in the context of ordinary differential equations, we construct a class of Strang splitting schemes that are symmetric up to a desired order. We show rigorously that, under suitable assumptions on the nonlinearity, these methods are of second order and can then be used to construct higher order methods by composition. In addition, we illustrate the theoretical results by conducting numerical experiments for the Brusselator system and the KdV equation.
Compositional Finite-Time Stability analysis of nonlinear systems
DEFF Research Database (Denmark)
Tabatabaeipour, Mojtaba; Blanke, Mogens
2014-01-01
for the system but with bounded disturbance. Sufficient conditions for finite-time stability and finite-time boundedness of nonlinear systems as well as a computational method based on sum of squares programming to check the conditions are given. The problem of finite-time stability for a system that consists......This paper, investigates finite-time stability and finite-time boundedness for nonlinear systems with polynomial vector fields. Finite-time stability requires the states of the system to remain a given bounded set in a finite-time interval and finite-time boundedness considers the same problem...... of an interconnection of subsystems is also considered and we show how to decompose the problem into subproblems for each subsystem with coupling constraints. A solution to the problem using sum of squares programming and dual decomposition is presented. The method is demonstrated through some examples....
Exact Controllability for a Class of Nonlinear Evolution Control Systems
Institute of Scientific and Technical Information of China (English)
L¨u Yue; Li Yong
2015-01-01
In this paper, we study the exact controllability of the nonlinear control systems. The controllability results by using the monotone operator theory are es-tablished. No compactness assumptions are imposed in the main results.
Annenkov, Sergei; Shrira, Victor
2016-04-01
, we find a good agreement between our DNS-ZE results and simulations by Xiao et al (2013), both for the evolution of frequency spectra and for the directional spreading. In the long term, all three approaches demonstrate very close evolution of integral characteristics of spectra, approaching for large time the theoretical asymptotes of the self-similar stage of evolution. However, the detailed comparison of the spectral evolution shows certain notable differences. Both kinetic equations give virtually identical evolution of spectrum B, but in the case of initially nearly one-dimensional spectrum A the KE overestimates the amplitude of the spectral peak. Meanwhile, the DNS-ZE results show considerably wider spectra with less pronounced peak. There is a striking difference for the rate of spectral broadening, which is much larger for the gKE and especially for the KE, than for the DNS-ZE. We show that the rates of change of the spectra obtained with the DNS-ZE are proportional to the fourth power of nonlinearity, corresponding to the dynamical timescale of evolution, rather than the statistical timescale of both kinetic equations.
Instability of wormholes supported by a ghost scalar field: II. Nonlinear evolution
Energy Technology Data Exchange (ETDEWEB)
Gonzalez, J A; Guzman, F S; Sarbach, O [Instituto de Fisica y Matematicas, Universidad Michoacana de San Nicolas de Hidalgo, Edificio C-3, Cd. Universitaria, A P 2-82, 58040 Morelia, Michoacan (Mexico)
2009-01-07
We analyze the nonlinear evolution of spherically symmetric wormhole solutions coupled to a massless ghost scalar field using numerical methods. In a previous article, we have shown that static wormholes with these properties are unstable with respect to linear perturbations. Here, we show that depending on the initial perturbation the wormholes either expand or decay to a Schwarzschild black hole. We estimate the time scale of the expanding solutions and those collapsing to a black hole, and show that they are consistent in the regime of small perturbations with those predicted from perturbation theory. In the collapsing case, we also present a systematic study of the final black hole horizon and discuss the possibility for a luminous signal to travel from one universe to the other and back before the black hole forms. In the expanding case, the wormholes seem to undergo an exponential expansion, at least during the run time of our simulations.
Nonlinear evolution of cylindrical gravitational waves: numerical method and physical aspects
Celestino, Juliana; Rodrigues, E L
2015-01-01
General cylindrical waves are the simplest axisymmetrical gravitational waves that contain both $+$ and $\\times$ modes of polarization. In this paper, we have studied the evolution of general cylindrical gravitational waves in the realm of the characteristic scheme with a numerical code based on the Galerkin-Collocation method. The investigation consists of the numerical realization of concepts such as Bondi mass and the news functions adapted to cylindrical symmetry. The Bondi mass decays due to the presence of the news functions associated with both polarization modes. We have interpreted that each polarization mode as channels from which mass is extracted. Under this perspective, we have presented the enhancement effect of the polarization mode $+$ due to the nonlinear interaction with the mode $\\times$. After discussing the role of matter in cylindrical symmetry, we have extended the numerical code to include electromagnetic fields.
Time-reversal of nonlinear waves: Applicability and limitations
Ducrozet, G.; Fink, M.; Chabchoub, A.
2016-09-01
Time-reversal (TR) refocusing of waves is one of the fundamental principles in wave physics. Using the TR approach, time-reversal mirrors can physically create a time-reversed wave that exactly refocus back, in space and time, to its original source regardless of the complexity of the medium as if time were going backward. Laboratory experiments have proved that this approach can be applied not only in acoustics and electromagnetism, but also in the field of linear and nonlinear water waves. Studying the range of validity and limitations of the TR approach may determine and quantify its range of applicability in hydrodynamics. In this context, we report a numerical study of hydrodynamic time-reversal using a unidirectional numerical wave tank, implemented by the nonlinear high-order spectral method, known to accurately model the physical processes at play, beyond physical laboratory restrictions. The applicability of the TR approach is assessed over a variety of hydrodynamic localized and pulsating structures' configurations, pointing out the importance of high-order dispersive and particularly nonlinear effects in the refocusing of hydrodynamic stationary envelope solitons and breathers. We expect that the results may motivate similar experiments in other nonlinear dispersive media and encourage several applications with particular emphasis on the field of ocean engineering.
Nonlinear light behaviors near phase transition in non-parity-time-symmetric complex waveguides
Nixon, Sean
2016-01-01
Many classes of non-parity-time (PT) symmetric waveguides with arbitrary gain and loss distributions still possess all-real linear spectrum or exhibit phase transition. In this article, nonlinear light behaviors in these complex waveguides are probed analytically near a phase transition. Using multi-scale perturbation methods, a nonlinear ordinary differential equation (ODE) is derived for the light's amplitude evolution. This ODE predicts that the first class of these non-PT-symmetric waveguides support continuous families of solitons and robust amplitude-oscillating solutions both above and below phase transition, in close analogy with PT-symmetric systems. For the other classes of waveguides, the light's intensity always amplifies under the effect of nonlinearity even if the waveguide is below phase transition. These analytical predictions are confirmed by direct computations of the full system.
LEARNING GRANGER CAUSALITY GRAPHS FOR MULTIVARIATE NONLINEAR TIME SERIES
Institute of Scientific and Technical Information of China (English)
Wei GAO; Zheng TIAN
2009-01-01
An information theory method is proposed to test the. Granger causality and contemporaneous conditional independence in Granger causality graph models. In the graphs, the vertex set denotes the component series of the multivariate time series, and the directed edges denote causal dependence, while the undirected edges reflect the instantaneous dependence. The presence of the edges is measured by a statistics based on conditional mutual information and tested by a permutation procedure. Furthermore, for the existed relations, a statistics based on the difference between general conditional mutual information and linear conditional mutual information is proposed to test the nonlinearity. The significance of the nonlinear test statistics is determined by a bootstrap method based on surrogate data. We investigate the finite sample behavior of the procedure through simulation time series with different dependence structures, including linear and nonlinear relations.
Robust stability of discrete-time nonlinear system with time-delay
Institute of Scientific and Technical Information of China (English)
LIU Xin-ge; WU Min
2005-01-01
The robustly asymptotical stability problem for discrete-time nonlinear systems with time-delay was investigated. Positive definite matrix are constructed through Lyapunov functional. With the identity transform, property of matrix inverse and S-procedure, a new sufficient condition independent of the size of time-delay for robust stability of discrete-time nonlinear systems with time-delay is established. With Schur complement, another equivalent sufficient condition for robust stability of discrete-time nonlinear systems with time-delay is given. Finally, a sufficient condition dependent on the size of time-delay for robust stability of discrete-time nonlinear systems with time-delay is obtained. A unified approach is used to cast the robust stability problem into a convex optimization involving linear matrix inequalities.
Non-linear power law approach for spatial and temporal pattern analysis of salt marsh evolution
Taramelli, A.; Cornacchia, L.; Valentini, E.; Bozzeda, F.
2013-11-01
Many complex systems on the Earth surface show non-equilibrium fluctuations, often determining the spontaneous evolution towards a critical state. In this context salt marshes are characterized by complex patterns both in geomorphological and ecological features, which often appear to be strongly correlated. A striking feature in salt marshes is vegetation distribution, which can self-organize in patterns over time and space. Self-organized patchiness of vegetation can often give rise to power law relationships in the frequency distribution of patch sizes. In cases where the whole distribution does not follow a power law, the variance of scale in its tail may often be disregarded. To this end, the research aims at how changes in the main climatic and hydrodynamic variables may influence such non-linearity, and how numerical thresholds can describe this. Since it would be difficult to simultaneously monitor the presence and typology of vegetation and channel sinuosity through in situ data, and even harder to analyze them over medium to large time-space scales, remote sensing offers the ability to analyze the scale invariance of patchiness distributions. Here, we focus on a densely vegetated and channelized salt marsh (Scheldt estuary Belgium-the Netherlands) by means of the sub-pixel analysis on satellite images to calculate the non-linearity in the values of the power law exponents due to the variance of scale. The deviation from power laws represents stochastic conditions under climate drivers that can be hybridized on the basis of a fuzzy Bayesian generative algorithm. The results show that the hybrid approach is able to simulate the non-linearity inherent to the system and clearly show the existence of a link between the autocorrelation level of the target variable (i.e. size of vegetation patches), due to its self-organization properties, and the influence exerted on it by the external drivers (i.e. climate and hydrology). Considering the results of the
Time shift of pulses due to dispersion slope and nonlinearity
Energy Technology Data Exchange (ETDEWEB)
Marcuse, D.; Menyuk, C.R.; Holzloehner, R.
1999-12-01
The authors show that the time delay of optical pulses traveling in long fibers is influenced by the dispersion slope and the fiber nonlinearity. Consequently, one or more new pulses that are inserted by add-drop operations into a pulse train that has already traveled a long distance may shift relative to the old pulses. This time shift delays the initial pulses more than the newly inserted ones, so that the newly inserted pulses can leave their time frames, leading to errors.
Nonlinear evolution of oblique whistler waves in radiation belts
Sharma, R. P.; Nandal, P.; Yadav, N.; Sharma, Swati
2017-02-01
Magnetic power spectrum and formation of coherent structures have been investigated in the present work applicable to Van Allen radiation belt. The nonlinear interaction of high frequency oblique whistler wave and low frequency magnetosonic wave has been investigated. Simulation was performed of the coupled equation of these two waves. The nonlinear interaction of these waves leads to the formation of the localized structures. These resulting localized structures are of complex nature. The associated magnetic power spectrum has also been studied. Dispersive nonlinear processes account for the high frequency part of the spectrum. The resulting magnetic power spectrum shows a scaling of k^{ - 4.5}. The energy transfer process from injection scales to smaller scales is explained by the results.
Invariant Subspaces of the Two-Dimensional Nonlinear Evolution Equations
Directory of Open Access Journals (Sweden)
Chunrong Zhu
2016-11-01
Full Text Available In this paper, we develop the symmetry-related methods to study invariant subspaces of the two-dimensional nonlinear differential operators. The conditional Lie–Bäcklund symmetry and Lie point symmetry methods are used to construct invariant subspaces of two-dimensional differential operators. We first apply the multiple conditional Lie–Bäcklund symmetries to derive invariant subspaces of the two-dimensional operators. As an application, the invariant subspaces for a class of two-dimensional nonlinear quadratic operators are provided. Furthermore, the invariant subspace method in one-dimensional space combined with the Lie symmetry reduction method and the change of variables is used to obtain invariant subspaces of the two-dimensional nonlinear operators.
Stability of Nonlinear Stochastic Discrete-Time Systems
2013-01-01
This paper studies the stability for nonlinear stochastic discrete-time systems. First of all, several definitions on stability are introduced, such as stability, asymptotical stability, and pth moment exponential stability. Moreover, using the method of the Lyapunov functionals, some efficient criteria for stochastic stability are obtained. Some examples are presented to illustrate the effectiveness of the proposed theoretical results.
Global Format for Conservative Time Integration in Nonlinear Dynamics
DEFF Research Database (Denmark)
Krenk, Steen
2014-01-01
The widely used classic collocation-based time integration procedures like Newmark, Generalized-alpha etc. generally work well within a framework of linear problems, but typically may encounter problems, when used in connection with essentially nonlinear structures. These problems are overcome in...
Time-Reversal of Nonlinear Waves - Applicability and Limitations
Ducrozet, G; Chabchoub, A
2016-01-01
Time-reversal (TR) refocusing of waves is one of fundamental principles in wave physics. Using the TR approach, "Time-reversal mirrors" can physically create a time-reversed wave that exactly refocus back, in space and time, to its original source regardless of the complexity of the medium as if time were going backwards. Lately, laboratory experiments proved that this approach can be applied not only in acoustics and electromagnetism but also in the field of linear and nonlinear water waves. Studying the range of validity and limitations of the TR approach may determine and quantify its range of applicability in hydrodynamics. In this context, we report a numerical study of hydrodynamic TR using a uni-directional numerical wave tank, implemented by the nonlinear high-order spectral method, known to accurately model the physical processes at play, beyond physical laboratory restrictions. The applicability of the TR approach is assessed over a variety of hydrodynamic localized and pulsating structures' configu...
Probing material nonlinearity at various depths by time reversal mirrors
Payan, C.; Ulrich, T. J.; Le Bas, P. Y.; Griffa, M.; Schuetz, P.; Remillieux, M. C.; Saleh, T. A.
2014-04-01
In this Letter, the time reversal mirror is used to focus elastic energy at a prescribed location and to analyze the amplitude dependence of the focus signal, thus providing the nonlinearity of the medium. By varying the frequency content of the focused waveforms, the technique can be used to probe the surface, by penetrating to a depth defined by the wavelength of the focused waves. The validity of this concept is shown in the presence of gradual and distributed damage in concrete by comparing actual results with a reference nonlinear measurement and X ray tomography images.
Probing material nonlinearity at various depths by time reversal mirrors
Energy Technology Data Exchange (ETDEWEB)
Payan, C. [LMA UPR CNRS 7051, Aix Marseille Université, 31 Chemin Joseph Aiguier, 13402 Marseille (France); Ulrich, T. J.; Le Bas, P. Y.; Remillieux, M. C. [Los Alamos National Laboratory, EES-17, Los Alamos, New Mexico 87545 (United States); Griffa, M.; Schuetz, P. [Swiss Federal Laboratories for Materials Science and Technology (EMPA), Überlandstrasse 129, 8600 Dübendorf (Switzerland); Saleh, T. A. [Los Alamos National Laboratory, MST-16, Los Alamos, New Mexico 87545 (United States)
2014-04-07
In this Letter, the time reversal mirror is used to focus elastic energy at a prescribed location and to analyze the amplitude dependence of the focus signal, thus providing the nonlinearity of the medium. By varying the frequency content of the focused waveforms, the technique can be used to probe the surface, by penetrating to a depth defined by the wavelength of the focused waves. The validity of this concept is shown in the presence of gradual and distributed damage in concrete by comparing actual results with a reference nonlinear measurement and X ray tomography images.
Nonlinear Time Series Prediction Using Chaotic Neural Networks
Institute of Scientific and Technical Information of China (English)
LI KePing; CHEN TianLun
2001-01-01
A nonlinear feedback term is introduced into the evaluation equation of weights of the backpropagation algorithm for neural network, the network becomes a chaotic one. For the purpose of that we can investigate how the different feedback terms affect the process of learning and forecasting, we use the model to forecast the nonlinear time series which is produced by Makey-Glass equation. By selecting the suitable feedback term, the system can escape from the local minima and converge to the global minimum or its approximate solutions, and the forecasting results are better than those of backpropagation algorithm.``
Nonlinear transformation on the transfer entropy of financial time series
Wu, Zhenyu; Shang, Pengjian
2017-09-01
Transfer entropy (TE) now is widely used in the data mining and economic field. However, TE itself demands that time series intend to be stationary and meet Markov condition. Naturally, we are interested in investigating the effect of the nonlinear transformation of the two series on the TE. Therefore, the paper is designed to study the TE of five nonlinear ;volatile; transformations based on the data which are generated by the linear modeling and the logistic maps modeling, as well as the dataset that come from financial markets. With only one of the TE of nonlinear transformations fluctuating around the TE of original series, the TE of others all have increased with different degrees.
Elements of nonlinear time series analysis and forecasting
De Gooijer, Jan G
2017-01-01
This book provides an overview of the current state-of-the-art of nonlinear time series analysis, richly illustrated with examples, pseudocode algorithms and real-world applications. Avoiding a “theorem-proof” format, it shows concrete applications on a variety of empirical time series. The book can be used in graduate courses in nonlinear time series and at the same time also includes interesting material for more advanced readers. Though it is largely self-contained, readers require an understanding of basic linear time series concepts, Markov chains and Monte Carlo simulation methods. The book covers time-domain and frequency-domain methods for the analysis of both univariate and multivariate (vector) time series. It makes a clear distinction between parametric models on the one hand, and semi- and nonparametric models/methods on the other. This offers the reader the option of concentrating exclusively on one of these nonlinear time series analysis methods. To make the book as user friendly as possible...
Nonlinear Evolution of the Ion-Ion Beam Instability
DEFF Research Database (Denmark)
Pécseli, Hans; Trulsen, J.
1982-01-01
The criterion for the existence of vortexlike ion phase-space configurations, as obtained by a standard pseudopotential method, is found to coincide with the criterion for the linear instability for two (cold) counterstreaming ion beams. A nonlinear equation is derived, which demonstrates...
STUDY ON EXACT ANALYTICAL SOLUTIONS FOR TWO SYSTEMS OF NONLINEAR EVOLUTION EQUATIONS
Institute of Scientific and Technical Information of China (English)
闫振亚; 张鸿庆
2001-01-01
The homogeneous balance method was improved and applied to two systems of nonlinear evolution equations. As a result, several families of exact analytic solutions are derived by some new ansatzs. These solutions contain Wang's and Zhang's results and other new types of analytical solutions, such as rational fraction solutions and periodic solutions. The way can also be applied to solve more nonlinear partial differential equations.
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
A trial equation method to nonlinear evolution equation with rank inhomogeneous is given. As applications, the exact traveling wave solutions to some higher-order nonlinear equations such as generalized Boussinesq equation,generalized Pochhammer-Chree equation, KdV-Burgers equation, and KS equation and so on, are obtained. Among these, some results are new. The proposed method is based on the idea of reduction of the order of ODE. Some mathematical details of the proposed method are discussed.
Directory of Open Access Journals (Sweden)
Hasibun Naher
2014-10-01
Full Text Available In this article, new extension of the generalized and improved (G′/G-expansion method is proposed for constructing more general and a rich class of new exact traveling wave solutions of nonlinear evolution equations. To demonstrate the novelty and motivation of the proposed method, we implement it to the Korteweg-de Vries (KdV equation. The new method is oriented toward the ease of utilize and capability of computer algebraic system and provides a more systematic, convenient handling of the solution process of nonlinear equations. Further, obtained solutions disclose a wider range of applicability for handling a large variety of nonlinear partial differential equations.
Institute of Scientific and Technical Information of China (English)
WANG Mei-Jiao; WANG Qi
2006-01-01
In this work, by means of a new more general ansatz and the symbolic computation system Maple, we extend the Riccati equation rational expansion method [Chaos, Solitons & Fractals 25 (2005) 1019] to uniformly construct a series of stochastic nontravelling wave solutions for nonlinear stochastic evolution equation. To illustrate the effectiveness of our method, we take the stochastic mKdV equation as an example, and successfully construct some new and more general solutions including a series of rational formal nontraveling wave and coefficient functions' soliton-like solutions and trigonometric-like function solutions. The method can also be applied to solve other nonlinear stochastic evolution equation or equations.
Rogue waves and rational solutions of a (3+1)-dimensional nonlinear evolution equation
Energy Technology Data Exchange (ETDEWEB)
Zhaqilao,, E-mail: zhaqilao@imnu.edu.cn
2013-12-06
A simple symbolic computation approach for finding the rogue waves and rational solutions to the nonlinear evolution equation is proposed. It turns out that many rational solutions with real and complex forms of a (3+1)-dimensional nonlinear evolution equation are obtained. Some features of rogue waves and rational solutions are graphically discussed. -- Highlights: •A simple symbolic computation approach for finding the rational solutions to the NEE is proposed. •Some rogue waves and rational solutions with real and complex forms of a (3+1)-D NEE are obtained. •Some features of rogue waves are graphically discussed.
Global Existence and Uniqueness of Solutions to Evolution p-Laplacian Systems with Nonlinear Sources
Institute of Scientific and Technical Information of China (English)
WEI Yingjie; GAO Wenjie
2013-01-01
This paper presents the global existence and uniqueness of the initial and boundary value problem to a system of evolution p-Laplacian equations coupled with general nonlinear terms.The authors use skills of inequality estimation and the method of regularization to construct a sequence of approximation solutions,hence obtain the global existence of solutions to a regularized system.Then the global existence of solutions to the system of evolution p-Laplacian equations is obtained with the application of a standard limiting process.The uniqueness of the solution is proven when the nonlinear terms are local Lipschitz continuous.
Travelling Wave Solutions to a Special Type of Nonlinear Evolution Equation
Institute of Scientific and Technical Information of China (English)
XU Gui-Qiong; LI Zhi-Bin
2003-01-01
A unified approach is presented for finding the travelling wave solutions to one kind of nonlinear evolution equation by introducing a concept of "rank". The key idea of this method is to make use of the arbitrariness of the manifold in Painleve analysis. We selected a new expansion variable and thus obtained a rich variety of travelling wave solutions to nonlinear evolution equation, which covered solitary wave solutions, periodic wave solutions, Weierstrass elliptic function solutions, and rational solutions. Three illustrative equations are investigated by this means, and abundant travelling wave solutions are obtained in a systematic way. In addition, some new solutions are firstly reported here.
Nonlinear behaviors of parity-time-symmetric lasers
Yang, Jianke
2016-01-01
We propose a time-dependent partial differential equation model to investigate the dynamical behavior of the parity-time (PT) symmetric laser during the nonlinear stage of its operation. This model incorporates physical effects such as the refractive index distribution, dispersion, material loss, nonlinear gain saturation and self-phase modulation. We show that when the loss is weak, multiple stable steady states and time-periodic states of light exist above the lasing threshold, rendering the laser multi-mode. However, when the loss is strong, only a single stable steady state of broken PT symmetry exists for a wide range of the gain amplitude, rendering the laser single-mode. These results reveal the important role the loss plays in maintaining the single-mode operation of PT lasers.
Decoherence in time evolution of bound entanglement
Sun, Z; Sun, C P; Wang, X; Sun, Zhe; Wang, Xiaoguang
2007-01-01
We study a dynamic process of disentanglement by considering the time evolution of bound entanglement for a quantum open system, two qutrits coupling to a common environment. Here, the initial quantum correlations of the two qutrits are characterized by the bound entanglement. In order to show the universality of the role of environment on bound entanglement, both bosonic and spin environments are considered. We found that the bound entanglement displays collapses and revivals, and it can be stable against small temperature and time change. The thermal fluctuation effects on bound entanglement are also considered.
Randomness in Sequence Evolution Increases over Time.
Directory of Open Access Journals (Sweden)
Guangyu Wang
Full Text Available The second law of thermodynamics states that entropy, as a measure of randomness in a system, increases over time. Although studies have investigated biological sequence randomness from different aspects, it remains unknown whether sequence randomness changes over time and whether this change consists with the second law of thermodynamics. To capture the dynamics of randomness in molecular sequence evolution, here we detect sequence randomness based on a collection of eight statistical random tests and investigate the randomness variation of coding sequences with an application to Escherichia coli. Given that core/essential genes are more ancient than specific/non-essential genes, our results clearly show that core/essential genes are more random than specific/non-essential genes and accordingly indicate that sequence randomness indeed increases over time, consistent well with the second law of thermodynamics. We further find that an increase in sequence randomness leads to increasing randomness of GC content and longer sequence length. Taken together, our study presents an important finding, for the first time, that sequence randomness increases over time, which may provide profound insights for unveiling the underlying mechanisms of molecular sequence evolution.
Design and Control of Nonlinear Mechanical Systems for Minimum Time
Directory of Open Access Journals (Sweden)
J.B. Cardoso
2008-01-01
Full Text Available This paper presents an integrated methodology for optimal design and control of nonlinear flexible mechanical systems, including minimum time problems. This formulation is implemented in an optimum design code and it is applied to the nonlinear behavior dynamic response. Damping and stiffness characteristics plus control driven forces are considered as decision variables. A conceptual separation between time variant and time invariant design parameters is presented, this way including the design space into the control space and considering the design variables as control variables not depending on time. By using time integrals through all the derivations, design and control problems are unified. In the optimization process we can use both types of variables simultaneously or by interdependent levels. For treating minimum time problems, a unit time interval is mapped onto the original time interval, then treating equally time variant and time invariant problems. The dynamic response and its sensitivity are discretized via space-time finite elements, and may be integrated either by at-once integration or step-by-step. Adjoint system approach is used to calculate the sensitivities.
Integrable nonlinear parity-time symmetric optical oscillator
Hassan, Absar U; Miri, Mohammad-Ali; Khajavikhan, Mercedeh; Christodoulides, Demetrios N
2016-01-01
The nonlinear dynamics of a balanced parity-time symmetric optical microring arrangement are analytically investigated. By considering gain and loss saturation effects, the pertinent conservation laws are explicitly obtained in the Stokes domain-thus establishing integrability. Our analysis indicates the existence of two regimes of oscillatory dynamics and frequency locking, both of which are analogous to those expected in linear parity-time symmetric systems. Unlike other saturable parity time symmetric systems considered before, the model studied in this work first operates in the symmetric regime and then enters the broken parity-time phase.
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.
Soliton solutions to a few fractional nonlinear evolution equations in shallow water wave dynamics
Mirzazadeh, Mohammad; Ekici, Mehmet; Sonmezoglu, Abdullah; Ortakaya, Sami; Eslami, Mostafa; Biswas, Anjan
2016-05-01
This paper studies a few nonlinear evolution equations that appear with fractional temporal evolution and fractional spatial derivatives. These are Benjamin-Bona-Mahoney equation, dispersive long wave equation and Nizhnik-Novikov-Veselov equation. The extended Jacobi's elliptic function expansion method is implemented to obtain soliton and other periodic singular solutions to these equations. In the limiting case, when the modulus of ellipticity approaches zero or unity, these doubly periodic functions approach solitary waves or shock waves or periodic singular solutions emerge.
Small x nonlinear evolution with impact parameter and the structure function data
Berger, Jeffrey
2011-01-01
Nonlinear evolution at small values of Bjorken x is evaluated numerically using the dipole framework with impact parameter dependence. Confinement effects are modeled by including masses into the evolution. Sensitivity of the predictions due to different prescriptions of the cuts on large dipole sizes is investigated. Running coupling effects are taken into account in this analysis. Finally, a comparison with the inclusive data from HERA on the structure functions F2 and FL is performed.
Analyzing the Dynamics of Nonlinear Multivariate Time Series Models
Institute of Scientific and Technical Information of China (English)
DenghuaZhong; ZhengfengZhang; DonghaiLiu; StefanMittnik
2004-01-01
This paper analyzes the dynamics of nonlinear multivariate time series models that is represented by generalized impulse response functions and asymmetric functions. We illustrate the measures of shock persistences and asymmetric effects of shocks derived from the generalized impulse response functions and asymmetric function in bivariate smooth transition regression models. The empirical work investigates a bivariate smooth transition model of US GDP and the unemployment rate.
Time inversion, Self-similar evolution, and Issue of time
Datta, D P
2001-01-01
We investigate the question, "how does time flow?" and show that time may change by inversions as well. We discuss its implications to a simple class of linear systems. Instead of introducing any unphysical behaviour, inversions can lead to a new multi- time scale evolutionary path for the linear system exhibiting late time stochastic fluctuations. We explain how stochastic behaviour is injected into the linear system as a combined effect of an uncertainty in the definition of inversion and the irrationality of the golden mean number. We also give an ansatz for the nonlinear stochastic behaviour of (fractal) time which facilitates us to estimate the late and short time limits of a two-time correlation function relevant for the stochastic fluctuations in linear systems. These fluctuations are shown to enjoy generic 1/f spectrum. The implicit functional definition of the fractal time is shown to satisfy the differential equation dx=dt. We also discuss the relevance of intrinsic time in the present formalism, st...
A procedure to construct exact solutions of nonlinear evolution equations
Indian Academy of Sciences (India)
Adem Cengiz Çevikel; Ahmet Bekir; Mutlu Akar; Sait San
2012-09-01
In this paper, we implemented the functional variable method for the exact solutions of the Zakharov-Kuznetsov-modified equal-width (ZK-MEW), the modified Benjamin-Bona-Mohany (mBBM) and the modified kdV-Kadomtsev-Petviashvili (kdV-KP) equation. By using this scheme, we found some exact solutions of the above-mentioned equation. The obtained solutions include solitary wave solutions, periodic wave solutions and combined formal solutions. The functional variable method presents a wider-applicability for handling nonlinear wave equations.
The nonlinear evolution of inviscid Goertler vortices in three-dimensional boundary layers
Blackaby, Nicholas; Dando, Andrew; Hall, Philip
1995-09-01
The nonlinear development of inviscid Gortler vortices in a three-dimensional boundary layer is considered. We do not follow the classical approach of weakly nonlinear stability problems and consider a mode which has just become unstable. Instead we extend the method of Blackaby, Dando, and Hall (1992), which considered the closely related nonlinear development of disturbances in stratified shear flows. The Gortler modes we consider are initially fast growing and we assume, following others, that boundary-layer spreading results in them evolving in a linear fashion until they reach a stage where their amplitudes are large enough and their growth rates have diminished sufficiently so that amplitude equations can be derived using weakly nonlinear and non-equilibrium critical-layer theories. From the work of Blackaby, Dando and Hall (1993) is apparent, given the range of parameters for the Gortler problem, that there are three possible nonlinear integro-differential evolution equations for the disturbance amplitude. These are a cubic due to viscous effects, a cubic which corresponds to the novel mechanism investigated in this previous paper, and a quintic. In this paper we shall concentrate on the two cubic integro-differential equations and in particular, on the one due to the novel mechanism as this will be the first to affect a disturbance. It is found that the consideration of a spatial evolution problem as opposed to temporal (as was considered in Blackaby, Dando, and Hall, 1992) causes a number of significant changes to the evolution equations.
A Novel Method for Nonlinear Time Series Forecasting of Time-Delay Neural Network
Institute of Scientific and Technical Information of China (English)
JIANG Weijin; XU Yuhui
2006-01-01
Based on the idea of nonlinear prediction of phase space reconstruction, this paper presented a time delay BP neural network model, whose generalization capability was improved by Bayesian regularization.Furthermore, the model is applied to forecast the import and export trades in one industry.The results showed that the improved model has excellent generalization capabilities, which not only learned the historical curve, but efficiently predicted the trend of business.Comparing with common evaluation of forecasts, we put on a conclusion that nonlinear forecast can not only focus on data combination and precision improvement, it also can vividly reflect the nonlinear characteristic of the forecasting system.While analyzing the forecasting precision of the model, we give a model judgment by calculating the nonlinear characteristic value of the combined serial and original serial, proved that the forecasting model can reasonably catch' the dynamic characteristic of the nonlinear system which produced the origin serial.
Directory of Open Access Journals (Sweden)
Berezovskaya Faina S
2004-09-01
Full Text Available Abstract Background The size distribution of gene families in a broad range of genomes is well approximated by a generalized Pareto function. Evolution of ensembles of gene families can be described with Birth, Death, and Innovation Models (BDIMs. Analysis of the properties of different versions of BDIMs has the potential of revealing important features of genome evolution. Results In this work, we extend our previous analysis of stochastic BDIMs. In addition to the previously examined rational BDIMs, we introduce potentially more realistic logistic BDIMs, in which birth/death rates are limited for the largest families, and show that their properties are similar to those of models that include no such limitation. We show that the mean time required for the formation of the largest gene families detected in eukaryotic genomes is limited by the mean number of duplications per gene and does not increase indefinitely with the model degree. Instead, this time reaches a minimum value, which corresponds to a non-linear rational BDIM with the degree of approximately 2.7. Even for this BDIM, the mean time of the largest family formation is orders of magnitude greater than any realistic estimates based on the timescale of life's evolution. We employed the embedding chains technique to estimate the expected number of elementary evolutionary events (gene duplications and deletions preceding the formation of gene families of the observed size and found that the mean number of events exceeds the family size by orders of magnitude, suggesting a highly dynamic process of genome evolution. The variance of the time required for the formation of the largest families was found to be extremely large, with the coefficient of variation >> 1. This indicates that some gene families might grow much faster than the mean rate such that the minimal time required for family formation is more relevant for a realistic representation of genome evolution than the mean time. We
Institute of Scientific and Technical Information of China (English)
WANG Peng-Zhou; ZHANG Shun-Li
2008-01-01
We present basic theory of variable separation for (1 + 1)-dimensional nonlinear evolution equations with mixed partial derivatives. As an application, we classify equations uxt = A(u, ux)uxxx + B(u, ux) that admits derivative-dependent functional separable solutions (DDFSSs) and illustrate how to construct those DDFSSs with some examples.
Exact Solutions of Some (1+1)-Dimensional Nonlinear Evolution Equations
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
By means of the variable separation method, new exact solutions of some (1+1)-dimensional nonlinear evolution equations are obtained. Abundant localized excitations can be found by selecting corresponding arbitrary functions appropriately. Namely, the new soliton-like localized excitations and instanton-like localized excitations are presented.
Localized Excitations in a Sixth-Order (1+1)-Dimensional Nonlinear Evolution Equation
Institute of Scientific and Technical Information of China (English)
SHEN Shou-Feng
2005-01-01
In this letter, by means of the Lax pair, Darboux transformation, and variable separation approach, a new exact solution of a sixth-order (1+ 1)-dimensional nonlinear evolution equation, which includes some arbitrary functions,is obtained. Abundant new localized excitations can be found by selecting appropriate functions and they are illustrated both analytically and graphically.
Institute of Scientific and Technical Information of China (English)
CHEN Jiang; HE Hong-Sheng; YANG Kong-Qing
2005-01-01
A generalized F-expansion method is introduced and applied to (3+ 1)-dimensional Kadomstev-Petviashvili(KP) equation. As a result, some new Jacobi elliptic function solutions of the equation are found, from which the trigonometric function solutions and the solitary wave solutions can be obtained. The method can also be extended to other types of nonlinear evolution equations in mathematical physics.
The homotopic mapping solution for the solitary wave for a generalized nonlinear evolution equation
Institute of Scientific and Technical Information of China (English)
Mo Jia-Qi; Lin Su-Rong
2009-01-01
This paper studies a generalized nonlinear evolution equation. Using the homotopic mapping method,it constructs a corresponding homotopic mapping transform. Selecting a suitable initial approximation and using homotopic mapping,it obtains an approximate solution with an arbitrary degree of accuracy for the solitary wave. From the approximate solution obtained by using the homotopic mapping method,it possesses a good accuracy.
Non-Linear Evolution of Steady and Migrating Alternate Bars in a Straight Channel (abstract)
Southgate, H.N.; Crosato, A.
2013-01-01
This paper contains an analysis of a long-duration experiment that shows the evolution of alternate bars in a straight channel. The theoretical predictions are based on a weakly non-linear theory of the morphological development. Both the experiment and theory have several innovative features.
Non-Linear Evolution of Steady and Migrating Alternate Bars in a Straight Channel (abstract)
Southgate, H.N.; Crosato, A.
2013-01-01
This paper contains an analysis of a long-duration experiment that shows the evolution of alternate bars in a straight channel. The theoretical predictions are based on a weakly non-linear theory of the morphological development. Both the experiment and theory have several innovative features.
Directory of Open Access Journals (Sweden)
Yusuf Pandir
2012-01-01
Full Text Available We obtain the classification of exact solutions, including soliton, rational, and elliptic solutions, to the one-dimensional general improved Camassa Holm KP equation and KdV equation by the complete discrimination system for polynomial method. In discussion, we propose a more general trial equation method for nonlinear partial differential equations with generalized evolution.
Indian Academy of Sciences (India)
Yusuf Gurefe; Abdullah Sonmezoglu; Emine Misirli
2011-12-01
In this paper some exact solutions including soliton solutions for the KdV equation with dual power law nonlinearity and the (, ) equation with generalized evolution are obtained using the trial equation method. Also a more general trial equation method is proposed.
Nonlinear evolution of the modulational instability under weak forcing and damping
Directory of Open Access Journals (Sweden)
J. Touboul
2010-12-01
Full Text Available The evolution of modulational instability, or Benjamin-Feir instability is investigated within the framework of the two-dimensional fully nonlinear potential equations, modified to include wind forcing and viscous dissipation. The wind model corresponds to the Miles' theory. The introduction of dissipation in the equations is briefly discussed. Evolution of this instability in the presence of damping was considered by Segur et al. (2005a and Wu et al. (2006. Their results were extended theoretically by Kharif et al. (2010 who considered wind forcing and viscous dissipation within the framework of a forced and damped nonlinear Schrödinger equation. The marginal stability curve derived from the fully nonlinear numerical simulations coincides with the curve obtained by Kharif et al. (2010 from a linear stability analysis. Furthermore, it is found that the presence of wind forcing promotes the occurrence of a permanent frequency-downshifting without invoking damping due to breaking wave phenomenon.
Directory of Open Access Journals (Sweden)
S. S. Motsa
2014-01-01
Full Text Available This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs. The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature.
Motsa, S S; Magagula, V M; Sibanda, P
2014-01-01
This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs). The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature.
Nonlinear and Perturbative Evolution of Distorted Black Holes; 2, Odd-parity Modes
Baker, J; Campanelli, M; Loustó, C O; Seidel, E; Takahashi, R
2000-01-01
We compare the fully nonlinear and perturbative evolution of nonrotating black holes with odd-parity distortions utilizing the perturbative results to interpret the nonlinear results. This introduction of the second polarization (odd-parity) mode of the system, and the systematic use of combined techniques brings us closer to the goal of studying more complicated systems like distorted, rotating black holes, such as those formed in the final inspiral stage of two black holes. The nonlinear evolutions are performed with the 3D parallel code for Numerical Relativity, {Cactus}, and an independent axisymmetric code, {Magor}. The linearized calculation is performed in two ways: (a) We treat the system as a metric perturbation on Schwarzschild, using the Regge-Wheeler equation to obtain the waveforms produced. (b) We treat the system as a curvature perturbation of a Kerr black hole (but here restricted to the case of vanishing rotation parameter a) and evolve it with the Teukolsky equation The comparisons of the wa...
Institute of Scientific and Technical Information of China (English)
ZHANG Ying-Yue; YANG Qiu-Ying; CHEN Tian-Lun
2007-01-01
We introduce a modified small-world network adding new links with nonlinearly preferential connection instead of adding randomly, then we apply Bak-Sneppen (BS) evolution model on this network. We study several important structural properties of our network such as the distribution of link-degree, the maximum link-degree, and the length of the shortest path. We further argue several dynamical characteristics of the model such as the important critical value fc, the f0 avalanche, and the mutating condition, and find that those characteristics show particular behaviors.
Discrete-Time Approximation for Nonlinear Continuous Systems with Time Delays
Directory of Open Access Journals (Sweden)
Bemri H’mida
2016-05-01
Full Text Available This paper is concerned with the discretization of nonlinear continuous time delay systems. Our approach is based on Taylor-Lie series. The main idea aims to minimize the effect of the delay and neglects the importance of nonlinear parameter by the linearization of the system study in an attempt to make its handling and easier programming as possible. We investigate a new method based on the development of new theoretical methods for the time discretization of nonlinear systems with time delay .The performance of these proposed discretization methods was validated by doing the numerical simulation using a nonlinear system with state delay. Some illustrative examples are given to show the effectiveness of the obtained results.
The Nonlinear Dynamics of Time Dependent Subcritical Baroclinic Currents
Pedlosky, J.; Flierl, G. R.
2006-12-01
The nonlinear dynamics of baroclinically unstable waves in a time dependent zonal shear flow is considered in the framework of the two-layer Phillips model on the beta plane. In most cases considered in this study the amplitude of the shear is well below the critical value of the steady shear version of the model. Nevertheless, the time dependent problem in which the shear oscillates periodically is unstable, and the unstable waves grow to substantial amplitudes, in some cases with strongly nonlinear and turbulent characteristics. For very small values of the shear amplitude in the presence of dissipation an analytical, asymptotic theory predicts a self-sustained wave whose amplitude undergoes a nonlinear oscillation whose period is amplitude dependent. There is a sensitive amplitude dependence of the wave on the frequency of the oscillating shear when the shear amplitude is small. This behavior is also found in a truncated model of the dynamics, and that model is used to examine larger shear amplitudes. When there is a mean value of the shear in addition to the oscillating component, but such that the total shear is still subcritical, the resulting nonlinear states exhibit a rectified horizontal buoyancy flux with a nonzero time average as a result of the instability of the oscillating shear. For higher, still subcritical, values of the shear we have detected a symmetry breaking in which a second cross-stream mode is generated through an instability of the unstable wave although this second mode would by itself be stable on the basic time dependent current. For shear values that are substantially subcritical but of order of the critical shear, calculations with a full quasi-geostrophic numerical model reveal a turbulent flow generated by the instability. If the beta effect is disregarded the inviscid, linear problem is formally stable. However, our calculations show that a small degree of nonlinearity is enough to destabilize the flow leading to large amplitude
Nonlinear time-series-based adaptive control applications
Mohler, R. R.; Rajkumar, V.; Zakrzewski, R. R.
1991-01-01
A control design methodology based on a nonlinear time-series reference model is presented. It is indicated by highly nonlinear simulations that such designs successfully stabilize troublesome aircraft maneuvers undergoing large changes in angle of attack as well as large electric power transients due to line faults. In both applications, the nonlinear controller was significantly better than the corresponding linear adaptive controller. For the electric power network, a flexible AC transmission system with series capacitor power feedback control is studied. A bilinear autoregressive moving average reference model is identified from system data, and the feedback control is manipulated according to a desired reference state. The control is optimized according to a predictive one-step quadratic performance index. A similar algorithm is derived for control of rapid changes in aircraft angle of attack over a normally unstable flight regime. In the latter case, however, a generalization of a bilinear time-series model reference includes quadratic and cubic terms in angle of attack.
Lie algebras for time evolution with applications from chaos studies to spintronics
Wendler, Tim G.; Berrondo, Manuel; Beus, Ty; Sayer, Ryan T.; van Huele, Jean-Francois S.
2012-10-01
We illustrate the power of Lie algebras in computing the time evolution of quantum systems with time-dependent physical parameters. By factorizing the quantum mechanical time evolution operator and using the linear independence of the Lie algebra generators, we reduce the operator equations to systems of coupled ordinary differential equations of scalar functions applicable to a variety of dynamical systems. We use the results to explore the possibility of detecting chaos in quantum nonlinear oscillators based on criteria from classical chaos studies and to follow spin currents in time-dependent spin-orbit coupled media.
Universal and integrable nonlinear evolution systems of equations in 2+1 dimensions
Energy Technology Data Exchange (ETDEWEB)
Maccari, A. [Technical Institute G. Cardano, Piazza della Resistenza 1, 00015 Monterotondo, Rome (Italy)
1997-08-01
Integrable systems of nonlinear partial differential equations (PDEs) are obtained from integrable equations in 2+1 dimensions, by means of a reduction method of broad applicability based on Fourier expansion and spatio{endash}temporal rescalings, which is asymptotically exact in the limit of weak nonlinearity. The integrability by the spectral transform is explicitly demonstrated, because the corresponding Lax pairs have been derived, applying the same reduction method to the Lax pair of the initial equation. These systems of nonlinear PDEs are likely to be of applicative relevance and have a {open_quotes}universal{close_quotes} character, inasmuch as they may be derived from a very large class of nonlinear evolution equations with a linear dispersive part. {copyright} {ital 1997 American Institute of Physics.}
Blind speech source separation via nonlinear time-frequency masking
Institute of Scientific and Technical Information of China (English)
XU Shun; CHEN Shaorong; LIU Yulin
2008-01-01
Aim at the underdetermined convolutive mixture model, a blind speech source separation method based on nonlinear time-frequency masking was proposed, where the approximate W-disjoint orthogonality (W-DO) property among independent speech signals in time-frequency domain is utilized. In this method, the observation mixture signal from multimicrophones is normalized to be independent of frequency in the time-frequency domain at first, then the dynamic clustering algorithm is adopted to obtain the active source information in each time-frequency slot, a nonlinear function via deflection angle from the cluster center is selected for time-frequency masking, finally the blind separation of mixture speech signals can be achieved by inverse STFT (short-time Fourier transformation). This method can not only solve the problem of frequency permutation which may be met in most classic frequency-domain blind separation techniques, but also suppress the spatial direction diffusion of the separation matrix. The simulation results demonstrate that the proposed separation method is better than the typical BLUES method, the signal-noise-ratio gain (SNRG) increases 1.58 dB averagely.
Nonlinear triple-point problems on time scales
Directory of Open Access Journals (Sweden)
Douglas R. Anderson
2004-04-01
Full Text Available We establish the existence of multiple positive solutions to the nonlinear second-order triple-point boundary-value problem on time scales, $$displaylines{ u^{Delta abla}(t+h(tf(t,u(t=0, cr u(a=alpha u(b+delta u^Delta(a,quad eta u(c+gamma u^Delta(c=0 }$$ for $tin[a,c]subsetmathbb{T}$, where $mathbb{T}$ is a time scale, $eta, gamma, deltage 0$ with $Beta+gamma>0$, $0
Time evolution of Wikipedia network ranking
Eom, Young-Ho; Benczúr, András; Shepelyansky, Dima L
2013-01-01
We study the time evolution of ranking and spectral properties of the Google matrix of English Wikipedia hyperlink network during years 2003 - 2011. The statistical properties of ranking of Wikipedia articles via PageRank and CheiRank probabilities, as well as the matrix spectrum, are shown to be stabilized for 2007 - 2011. A special emphasis is done on ranking of Wikipedia personalities and universities. We show that PageRank selection is dominated by politicians while 2DRank, which combines PageRank and CheiRank, gives more accent on personalities of arts. The Wikipedia PageRank of universities recovers 80 percents of top universities of Shanghai ranking during the considered time period.
Time evolution of Wikipedia network ranking
Eom, Young-Ho; Frahm, Klaus M.; Benczúr, András; Shepelyansky, Dima L.
2013-12-01
We study the time evolution of ranking and spectral properties of the Google matrix of English Wikipedia hyperlink network during years 2003-2011. The statistical properties of ranking of Wikipedia articles via PageRank and CheiRank probabilities, as well as the matrix spectrum, are shown to be stabilized for 2007-2011. A special emphasis is done on ranking of Wikipedia personalities and universities. We show that PageRank selection is dominated by politicians while 2DRank, which combines PageRank and CheiRank, gives more accent on personalities of arts. The Wikipedia PageRank of universities recovers 80% of top universities of Shanghai ranking during the considered time period.
Nonlinear shot noise, memory systems, and all-time hit parades
Eliazar, Iddo; Klafter, Joseph
2006-07-01
Consider the evolution of a memory system ‘fed’ by an external event-process. New memories are continuously recorded by the system. Simultaneously, the recollection of old memories continuously fades away. Thus, at a given time epoch the memory system ranks all past events according to present importance-magnitudes attributed to them. Illustratively, the memory system is an all-time hit parade run continuously in time. Motivated by a recently-introduced nonlinear shot noise system-model [I. Eliazar, J. Klafter, Physica A, in press (titled: non-linear shot noise: Lévy, Noah, & Joseph).], we explore a memory system-model in which: (i) the external events follow an arbitrary time-homogeneous Poisson point process; and (ii) the ‘fading’ of memories is governed by an arbitrary nonlinear differential-equation dynamics. A Poissonian analysis of the model is conducted, addressing questions such as: How do memories get constructed and degraded? How does the memory process evolve? What is its stationary structure? What is its correlation structure? In addition, a Poissonian eigenvalue problem, arising in this context, is studied.
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.
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.
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.
Prescott, Aaron M.; Abel, Steven M.
2016-12-01
The rational design of network behavior is a central goal of synthetic biology. Here, we combine in silico evolution with nonlinear dimensionality reduction to redesign the responses of fixed-topology signaling networks and to characterize sets of kinetic parameters that underlie various input-output relations. We first consider the earliest part of the T cell receptor (TCR) signaling network and demonstrate that it can produce a variety of input-output relations (quantified as the level of TCR phosphorylation as a function of the characteristic TCR binding time). We utilize an evolutionary algorithm (EA) to identify sets of kinetic parameters that give rise to: (i) sigmoidal responses with the activation threshold varied over 6 orders of magnitude, (ii) a graded response, and (iii) an inverted response in which short TCR binding times lead to activation. We also consider a network with both positive and negative feedback and use the EA to evolve oscillatory responses with different periods in response to a change in input. For each targeted input-output relation, we conduct many independent runs of the EA and use nonlinear dimensionality reduction to embed the resulting data for each network in two dimensions. We then partition the results into groups and characterize constraints placed on the parameters by the different targeted response curves. Our approach provides a way (i) to guide the design of kinetic parameters of fixed-topology networks to generate novel input-output relations and (ii) to constrain ranges of biological parameters using experimental data. In the cases considered, the network topologies exhibit significant flexibility in generating alternative responses, with distinct patterns of kinetic rates emerging for different targeted responses.
Nonlinear asymmetric tearing mode evolution in cylindrical geometry
Teng, Q.; Ferraro, N.; Gates, D. A.; Jardin, S. C.; White, R. B.
2016-10-01
The growth of a tearing mode is described by reduced MHD equations. For a cylindrical equilibrium, tearing mode growth is governed by the modified Rutherford equation, i.e., the nonlinear Δ'(w ) . For a low beta plasma without external heating, Δ'(w ) can be approximately described by two terms, Δ'ql(w ), ΔA'(w ) [White et al., Phys. Fluids 20, 800 (1977); Phys. Plasmas 22, 022514 (2015)]. In this work, we present a simple method to calculate the quasilinear stability index Δql' rigorously, for poloidal mode number m ≥2 . Δql' is derived by solving the outer equation through the Frobenius method. Δ'ql is composed of four terms proportional to: constant Δ'0 , w, w ln w , and w2. ΔA' is proportional to the asymmetry of island that is roughly proportional to w. The sum of Δql' and ΔA' is consistent with the more accurate expression calculated perturbatively [Arcis et al., Phys. Plasmas 13, 052305 (2006)]. The reduced MHD equations are also solved numerically through a 3D MHD code M3D-C1 [Jardin et al., Comput. Sci. Discovery 5, 014002 (2012)]. The analytical expression of the perturbed helical flux and the saturated island width agree with the simulation results. It is also confirmed by the simulation that the ΔA' has to be considered in calculating island saturation.
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.
Hybrid discretization method for time-delay nonlinear systems
Energy Technology Data Exchange (ETDEWEB)
Zhang, Zheng [Xi' an Jiaotong University, Xi' an (China); Zhang, Yuanliang; Kil Chong, To [Chonbuk National University, Jeonju (Korea, Republic of); Kostyukova, Olga [3Institute of Mathematics National Academy of Science of Belarus, Minsk (Belarus)
2010-03-15
A hybrid discretization scheme that combines the virtues of the Taylor series and Matrix exponential integration methods is proposed. In the algorithm, each sampling time interval is divided into two subintervals to be considered according to the time delay and sampling period. The algorithm is not too expensive computationally and lends itself to be easily inserted into large simulation packages. The mathematical structure of the new discretization scheme is explored and described in detail. The performance of the proposed discretization procedure is evaluated by employing case studies. Various input signals, sampling rates, and time-delay values are considered to test the proposed method. The results demonstrate that the proposed discretization scheme is better than previous Taylor series method for nonlinear time-delay systems, especially when a large sampling period is inevitable
Evolutions of matter-wave bright soliton with spatially modulated nonlinearity
Institute of Scientific and Technical Information of China (English)
Yongshan Cheng; Fei Liu
2009-01-01
The evolution characteristics of a matter-wave bright soliton are investigated by means of the variational approach in the presence of spatially varying nonlinearity.It is found that the atom density envelope of the soliton is changed as a result of the spatial variation of the s-wave scattering length.The stable soliton can exist in appropriate initial conditions.The movement of the soliton depends on the sign and value of the coefficient of spatially modulated nonlinearity.These theoretical predictions are confirmed by the full numerical simulations of the one-dimensional Gross-Pitaevskii equation.
Experimental investigation of the nonlinear evolution of an impurity-driven drift wave
Energy Technology Data Exchange (ETDEWEB)
Allen, G.R.; Yamada, M.; Rewoldt, G.; Tang, W.M.
1982-04-01
An impurity-driven drift wave is observed to be destabilized by the reversed density gradient of a singly-ionized heavy-impurity-ion population in a Q-machine plasma. The evolution of the instability is investigated as it progresses from the initial linear exponential growth phase, into a nonlinear saturated state, whereupon strong radially outward anomalous diffusion is observed. The relationship between the anomalous diffusion coefficient and the wave amplitude is in agreement with estimates obtained from the nonlinear drift-wave turbulence theory of Dupree.
Nonlinear evolution equations associated with the chiral-field spectral problem
Energy Technology Data Exchange (ETDEWEB)
Bruschi, M.; Ragnisco, O. (Istituto Nazionale di Fisica Nucleare, Roma (Italy); Dipt. di Fisica, Univ. Rome (Italy))
1985-08-11
In this paper we derive and investigate the class of nonlinear evolution equations (NEEs) associated with the linear problem psisub(x) = lambdaApsi. It turns out that many physically interesting NEEs pertain to this class: for instance, the chiral-field equation, the nonlinear Klein-Gordon equations, the Heisenberg and Papanicolau spin chain models, the modified Boussinesq equation, the Wadati-Konno-Ichikawa equations, etc. We display also the Baecklund transformations for such a class and exploit them to derive in a special case the one-soliton solution.
Institute of Scientific and Technical Information of China (English)
YAN Zhen-Ya
2004-01-01
A Weierstrass elliptic function expansion method and its algorithm are developed in this paper. The method changes the problem solving nonlinear evolution equations into another one solving the correspondingsystem of nonlinear algebraic equations. With the aid of symbolic computation (e.g. Maple), the method is applied to the combined KdV-mKdV equation and (2+1)-dimensional coupled Davey-Stewartson equation. As a consequence, many new types of doubly periodic solutions are obtained in terms of the Weierstrass elliptic function. Jacobi elliptic function solutions and solitary wave solutions are also given as simple limits of doubly periodic solutions.
Institute of Scientific and Technical Information of China (English)
YANZhen-Ya
2004-01-01
A Weierstrass elliptic function expansion method and its algorithm are developed in this paper. The method changes the problem solving nonlinear evolution equations into another one solving the corresponding system of nonlinear algebraic equations. With the aid of symbolic computation (e.g. Maple), the method is applied to the combined KdV-mKdV equation and (2+1)-dimensional coupled Davey-Stewartson equation. As a consequence, many new types of doubly periodic solutions are obtained in terms of the Weierstrass elliptic function. Jacobi elliptic function solutions and solitary wave solutions are also given as simple limits of doubly periodic solutions.
Real-Time Implementation of Nonlinear Optical Processing Functions.
1986-09-30
demonstrating that the memory is nonlinear and selective. The recording medium could be replaced with real-time media such as photorefractive crystals. Thicker...recording media Fi4 4. Schematic of experiment that d,.non* trated ,,pera have the added advantage of higher angular selectiv- "" . e e r aity. thus... geometrica snapes in contact ’A,.n a c-:’:ser ’Figure 51a’ ., and a spher:cal 4:verg.ng reference -eam Upion :"um’latlon of t -" c-’gram by the object beam
Reaching a consensus: a discrete nonlinear time-varying case
Saburov, M.; Saburov, K.
2016-07-01
In this paper, we have considered a nonlinear protocol for a structured time-varying and synchronous multi-agent system. By means of cubic triple stochastic matrices, we present an opinion sharing dynamics of the multi-agent system as a trajectory of a non-homogeneous system of cubic triple stochastic matrices. We show that the multi-agent system eventually reaches to a consensus if either of the following two conditions is satisfied: (1) every member of the group people has a positive subjective distribution on the given task after some revision steps or (2) all entries of some cubic triple stochastic matrix are positive.
Directory of Open Access Journals (Sweden)
Florian Hartig
Full Text Available If two species exhibit different nonlinear responses to a single shared resource, and if each species modifies the resource dynamics such that this favors its competitor, they may stably coexist. This coexistence mechanism, known as relative nonlinearity of competition, is well understood theoretically, but less is known about its evolutionary properties and its prevalence in real communities. We address this challenge by using adaptive dynamics theory and individual-based simulations to compare community stabilization and evolutionary stability of species that coexist by relative nonlinearity. In our analysis, evolution operates on the species' density-compensation strategies, and we consider a trade-off between population growth rates at high and low resource availability. We confirm previous findings that, irrespective of the particular model of density dependence, there are many combinations of overcompensating and undercompensating density-compensation strategies that allow stable coexistence by relative nonlinearity. However, our analysis also shows that most of these strategy combinations are not evolutionarily stable and will be outcompeted by an intermediate density-compensation strategy. Only very specific trade-offs lead to evolutionarily stable coexistence by relative nonlinearity. As we find no reason why these particular trade-offs should be common in nature, we conclude that the sympatric evolution and evolutionary stability of relative nonlinearity, while possible in principle, seems rather unlikely. We speculate that this may, at least in part, explain why empirical demonstrations of this coexistence mechanism are rare, noting, however, that the difficulty to detect relative nonlinearity in the field is an equally likely explanation for the current lack of empirical observations, and that our results are limited to communities with non-overlapping generations and constant resource supply. Our study highlights the need for
Hartig, Florian; Münkemüller, Tamara; Johst, Karin; Dieckmann, Ulf
2014-01-01
If two species exhibit different nonlinear responses to a single shared resource, and if each species modifies the resource dynamics such that this favors its competitor, they may stably coexist. This coexistence mechanism, known as relative nonlinearity of competition, is well understood theoretically, but less is known about its evolutionary properties and its prevalence in real communities. We address this challenge by using adaptive dynamics theory and individual-based simulations to compare community stabilization and evolutionary stability of species that coexist by relative nonlinearity. In our analysis, evolution operates on the species' density-compensation strategies, and we consider a trade-off between population growth rates at high and low resource availability. We confirm previous findings that, irrespective of the particular model of density dependence, there are many combinations of overcompensating and undercompensating density-compensation strategies that allow stable coexistence by relative nonlinearity. However, our analysis also shows that most of these strategy combinations are not evolutionarily stable and will be outcompeted by an intermediate density-compensation strategy. Only very specific trade-offs lead to evolutionarily stable coexistence by relative nonlinearity. As we find no reason why these particular trade-offs should be common in nature, we conclude that the sympatric evolution and evolutionary stability of relative nonlinearity, while possible in principle, seems rather unlikely. We speculate that this may, at least in part, explain why empirical demonstrations of this coexistence mechanism are rare, noting, however, that the difficulty to detect relative nonlinearity in the field is an equally likely explanation for the current lack of empirical observations, and that our results are limited to communities with non-overlapping generations and constant resource supply. Our study highlights the need for combining ecological and
A Decentralized Approach for Nonlinear Prediction of Time Series Data in Sensor Networks
Directory of Open Access Journals (Sweden)
Richard Cédric
2010-01-01
Full Text Available Wireless sensor networks rely on sensor devices deployed in an environment to support sensing and monitoring, including temperature, humidity, motion, and acoustic. Here, we propose a new approach to model physical phenomena and track their evolution by taking advantage of the recent developments of pattern recognition for nonlinear functional learning. These methods are, however, not suitable for distributed learning in sensor networks as the order of models scales linearly with the number of deployed sensors and measurements. In order to circumvent this drawback, we propose to design reduced order models by using an easy to compute sparsification criterion. We also propose a kernel-based least-mean-square algorithm for updating the model parameters using data collected by each sensor. The relevance of our approach is illustrated by two applications that consist of estimating a temperature distribution and tracking its evolution over time.
Non-linear macro evolution of a dc driven micro atmospheric glow discharge
Energy Technology Data Exchange (ETDEWEB)
Xu, S. F.; Zhong, X. X., E-mail: xxzhong@sjtu.edu.cn [The State Key Laboratory on Fiber Optic Local Area, Communication Networks and Advanced Optical Communication Systems, Key Laboratory for Laser Plasmas and Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240 (China)
2015-10-15
We studied the macro evolution of the micro atmospheric glow discharge generated between a micro argon jet into ambient air and static water. The micro discharge behaves similarly to a complex ecosystem. Non-linear behaviors are found for the micro discharge when the water acts as a cathode, different from the discharge when water behaves as an anode. Groups of snapshots of the micro discharge formed at different discharge currents are captured by an intensified charge-coupled device with controlled exposure time, and each group consisted of 256 images taken in succession. Edge detection methods are used to identify the water surface and then the total brightness is defined by adding up the signal counts over the area of the micro discharge. Motions of the water surface at different discharge currents show that the water surface lowers increasingly rapidly when the water acts as a cathode. In contrast, the water surface lowers at a constant speed when the water behaves as an anode. The light curves are similar to logistic growth curves, suggesting that a self-inhibition process occurs in the micro discharge. Meanwhile, the total brightness increases linearly during the same time when the water acts as an anode. Discharge-water interactions cause the micro discharge to evolve. The charged particle bomb process is probably responsible for the different behaviors of the micro discharges when the water acts as cathode and anode.
Revisiting Waiting Times in DNA evolution
Nicodeme, Pierre
2012-01-01
Transcription factors are short stretches of DNA (or $k$-mers) mainly located in promoters sequences that enhance or repress gene expression. With respect to an initial distribution of letters on the DNA alphabet, Behrens and Vingron consider a random sequence of length $n$ that does not contain a given $k$-mer or word of size $k$. Under an evolution model of the DNA, they compute the probability $\\mathfrak{p}_n$ that this $k$-mer appears after a unit time of 20 years. They prove that the waiting time for the first apparition of the $k$-mer is well approximated by $T_n=1/\\mathfrak{p}_n$. Their work relies on the simplifying assumption that the $k$-mer is not self-overlapping. They observe in particular that the waiting time is mostly driven by the initial distribution of letters. Behrens et al. use an approach by automata that relaxes the assumption related to words overlaps. Their numerical evaluations confirms the validity of Behrens and Vingron approach for non self-overlapping words, but provides up to 44...
Discrete-Time Nonlinear Control of VSC-HVDC System
Directory of Open Access Journals (Sweden)
TianTian Qian
2015-01-01
Full Text Available Because VSC-HVDC is a kind of strong nonlinear, coupling, and multi-input multioutput (MIMO system, its control problem is always attracting much attention from scholars. And a lot of papers have done research on its control strategy in the continuous-time domain. But the control system is implemented through the computer discrete sampling in practical engineering. It is necessary to study the mathematical model and control algorithm in the discrete-time domain. The discrete mathematical model based on output feedback linearization and discrete sliding mode control algorithm is proposed in this paper. And to ensure the effectiveness of the control system in the quasi sliding mode state, the fast output sampling method is used in the output feedback. The results from simulation experiment in MATLAB/SIMULINK prove that the proposed discrete control algorithm can make the VSC-HVDC system have good static, dynamic, and robust characteristics in discrete-time domain.
Institute of Scientific and Technical Information of China (English)
YANG Xu-Dong; RUAN Hang-Yu; LOU Sen-Yue
2007-01-01
A new algorithm for symbolic computation of polynomial-type conserved densities for nonlinear evolution systems is presented. The algorithm is implemented in Maple. The improved algorithm is more efficient not only in removing the redundant terms of the general form of the conserved densities but also in solving the conserved densities with the associated flux synchronously without using Euler operator. Furthermore, the program conslaw. mpl can be used to determine the preferences for a given parameterized nonlinear evolution systems. The code is tested on several well-known nonlinear evolution equations from the soliton theory.
Cycle slipping in nonlinear circuits under periodic nonlinearities and time delays
Smirnova, Vera; Proskurnikov, Anton; Utina, Natalia V.
2014-01-01
Phase-locked loops (PLL), Costas loops and other synchronizing circuits are featured by the presence of a nonlinear phase detector, described by a periodic nonlinearity. In general, nonlinearities can cause complex behavior of the system such multi-stability and chaos. However, even phase locking ma
Empirical intrinsic geometry for nonlinear modeling and time series filtering.
Talmon, Ronen; Coifman, Ronald R
2013-07-30
In this paper, we present a method for time series analysis based on empirical intrinsic geometry (EIG). EIG enables one to reveal the low-dimensional parametric manifold as well as to infer the underlying dynamics of high-dimensional time series. By incorporating concepts of information geometry, this method extends existing geometric analysis tools to support stochastic settings and parametrizes the geometry of empirical distributions. However, the statistical models are not required as priors; hence, EIG may be applied to a wide range of real signals without existing definitive models. We show that the inferred model is noise-resilient and invariant under different observation and instrumental modalities. In addition, we show that it can be extended efficiently to newly acquired measurements in a sequential manner. These two advantages enable us to revisit the Bayesian approach and incorporate empirical dynamics and intrinsic geometry into a nonlinear filtering framework. We show applications to nonlinear and non-Gaussian tracking problems as well as to acoustic signal localization.
Linear and nonlinear dynamic systems in financial time series prediction
Directory of Open Access Journals (Sweden)
Salim Lahmiri
2012-10-01
Full Text Available Autoregressive moving average (ARMA process and dynamic neural networks namely the nonlinear autoregressive moving average with exogenous inputs (NARX are compared by evaluating their ability to predict financial time series; for instance the S&P500 returns. Two classes of ARMA are considered. The first one is the standard ARMA model which is a linear static system. The second one uses Kalman filter (KF to estimate and predict ARMA coefficients. This model is a linear dynamic system. The forecasting ability of each system is evaluated by means of mean absolute error (MAE and mean absolute deviation (MAD statistics. Simulation results indicate that the ARMA-KF system performs better than the standard ARMA alone. Thus, introducing dynamics into the ARMA process improves the forecasting accuracy. In addition, the ARMA-KF outperformed the NARX. This result may suggest that the linear component found in the S&P500 return series is more dominant than the nonlinear part. In sum, we conclude that introducing dynamics into the ARMA process provides an effective system for S&P500 time series prediction.
A New Hybrid Methodology for Nonlinear Time Series Forecasting
Directory of Open Access Journals (Sweden)
Mehdi Khashei
2011-01-01
Full Text Available Artificial neural networks (ANNs are flexible computing frameworks and universal approximators that can be applied to a wide range of forecasting problems with a high degree of accuracy. However, using ANNs to model linear problems have yielded mixed results, and hence; it is not wise to apply them blindly to any type of data. This is the reason that hybrid methodologies combining linear models such as ARIMA and nonlinear models such as ANNs have been proposed in the literature of time series forecasting. Despite of all advantages of the traditional methodologies for combining ARIMA and ANNs, they have some assumptions that will degenerate their performance if the opposite situation occurs. In this paper, a new methodology is proposed in order to combine the ANNs with ARIMA in order to overcome the limitations of traditional hybrid methodologies and yield more general and more accurate hybrid models. Empirical results with Canadian Lynx data set indicate that the proposed methodology can be a more effective way in order to combine linear and nonlinear models together than traditional hybrid methodologies. Therefore, it can be applied as an appropriate alternative methodology for hybridization in time series forecasting field, especially when higher forecasting accuracy is needed.
Finite-time Lyapunov exponents in time-delayed nonlinear dynamical systems.
Kanno, Kazutaka; Uchida, Atsushi
2014-03-01
We introduce a method for the calculation of finite-time Lyapunov exponents in time-delayed nonlinear dynamical systems. We apply the method to the Mackey-Glass model with time-delayed feedback. We investigate the standard deviation of the probability distribution of the finite-time Lyapunov exponents when the finite time or the delay time is changed. It is found that the standard deviation decreases in a power-law scaling with the exponent ∼0.5 as the finite time or the delay time is increased. Similar results are obtained for the finite-time Lyapunov spectrum.
Nonlinear evolution of Airy-like beams generated by modulated waveguide arrays.
Cao, Zheng; Tan, Qinggui; Li, Xiaojun; Qi, Xinyuan
2016-08-20
We numerically study the formation of modulated waveguide generated Airy-like beams and their subsequent evolution in homogeneous medium. The results show that the Airy-like beams could be generated from narrow Gaussian beams propagating in one-dimensional transverse separation modulated unbent, cosine bent, or logarithm bent waveguide arrays, respectively. The waveguide-generated Airy-like beams maintain their characteristics when propagating without nonlinearity or under the self-defocusing nonlinearity in homogeneous medium, while the beams are distorted under the self-focusing nonlinearity. The deformation depends on the waveguide bending and the outgoing angles of the Airy-like beams. Our results provide a new way to generate and manipulate the Airy-like beam.
Energy Technology Data Exchange (ETDEWEB)
Eliasson, B., E-mail: bengt.eliasson@strath.ac.uk [SUPA, Physics Department, John Anderson Building, Strathclyde University, Glasgow G4 0NG, Scotland (United Kingdom); Lazar, M., E-mail: mlazar@tp4.rub.de [Centre for Mathematical Plasma Astrophysics, Celestijnenlaan 200B, 3001 Leuven (Belgium); Institut für Theoretische Physik, Lehrstuhl IV: Weltraum- und Astrophysik, Ruhr-Universität Bochum, 44780 Bochum (Germany)
2015-06-15
This paper presents a numerical study of the linear and nonlinear evolution of the electromagnetic electron-cyclotron (EMEC) instability in a bi-Kappa distributed plasma. Distributions with high energy tails described by the Kappa power-laws are often observed in collision-less plasmas (e.g., solar wind and accelerators), where wave-particle interactions control the plasma thermodynamics and keep the particle distributions out of Maxwellian equilibrium. Under certain conditions, the anisotropic bi-Kappa distribution gives rise to plasma instabilities creating low-frequency EMEC waves in the whistler branch. The instability saturates nonlinearly by reducing the temperature anisotropy until marginal stability is reached. Numerical simulations of the Vlasov-Maxwell system of equations show excellent agreement with the growth-rate and real frequency of the unstable modes predicted by linear theory. The wave-amplitude of the EMEC waves at nonlinear saturation is consistent with magnetic trapping of the electrons.
Evolution of nonlinear optical properties: from gold atomic clusters to plasmonic nanocrystals.
Philip, Reji; Chantharasupawong, Panit; Qian, Huifeng; Jin, Rongchao; Thomas, Jayan
2012-09-12
Atomic clusters of metals are an emerging class of extremely interesting materials occupying the intermediate size regime between atoms and nanoparticles. Here we report the nonlinear optical (NLO) characteristics of ultrasmall, atomically precise clusters of gold, which are smaller than the critical size for electronic energy quantization (∼2 nm). Our studies reveal remarkable features of the distinct evolution of the optical nonlinearity as the clusters progress in size from the nonplasmonic regime to the plasmonic regime. We ascertain that the smallest atomic clusters do not show saturable absorption at the surface plasmon wavelength of larger gold nanocrystals (>2 nm). Consequently, the third-order optical nonlinearity in these ultrasmall gold clusters exhibits a significantly lower threshold for optical power limiting. This limiting efficiency, which is superior to that of plasmonic nanocrystals, is highly beneficial for optical limiting applications.
A convective-advective balance approach for solving some nonlinear evolution equations analytically
Energy Technology Data Exchange (ETDEWEB)
Abdel Hamid, B. [United Arab Emirates Univ. (United Arab Emirates). Dept. of Mathematics and Computer Science
1999-09-01
A symbolic computation-based approach of balancing the convective and advective effects in a nonlinear evolution equation leads to a transformation that maps the nonlinear equation onto either a linear one or to a system of linear and homogeneous equations. The method is demonstrated by mapping Burgers' equation and nonlinear heat equation onto the linear heat equation. It is shown that the transformation obtained by balancing the convective-advective effects are reducible to those obtained by the Cole and Hopf through Backlund transformation. The method is also used to transform the modified KdV equation into a system of linear and homogeneous functions in the partial derivatives which leads to an exact solution. Computations in the presented approach are carried out in a straightforward way.
Indian Academy of Sciences (India)
Junchao Chen; Biao Li
2012-03-01
In this paper, an extended multiple (′/)-expansion method is proposed to seek exact solutions of nonlinear evolution equations. The validity and advantages of the proposed method is illustrated by its applications to the Sharma–Tasso–Olver equation, the sixth-order Ramani equation, the generalized shallow water wave equation, the Caudrey–Dodd–Gibbon–Sawada–Kotera equation, the sixth-order Boussinesq equation and the Hirota–Satsuma equations. As a result, various complexiton solutions consisting of hyperbolic functions, trigonometric functions, rational functions and their mixture with parameters are obtained. When some parameters are taken as special values, the known double solitary-like wave solutions are derived from the double hyperbolic function solution. In addition, this method can also be used to deal with some high-dimensional and variable coefﬁcients’ nonlinear evolution equations.
Directory of Open Access Journals (Sweden)
S. S. Motsa
2014-01-01
Full Text Available This paper presents a new application of the homotopy analysis method (HAM for solving evolution equations described in terms of nonlinear partial differential equations (PDEs. The new approach, termed bivariate spectral homotopy analysis method (BISHAM, is based on the use of bivariate Lagrange interpolation in the so-called rule of solution expression of the HAM algorithm. The applicability of the new approach has been demonstrated by application on several examples of nonlinear evolution PDEs, namely, Fisher’s, Burgers-Fisher’s, Burger-Huxley’s, and Fitzhugh-Nagumo’s equations. Comparison with known exact results from literature has been used to confirm accuracy and effectiveness of the proposed method.
Barker, Adrian J
2016-01-01
We perform global two-dimensional hydrodynamical simulations of Keplerian discs with free eccentricity over thousands of orbital periods. Our aim is to determine the validity of secular theory in describing the evolution of eccentric discs, and to explore their nonlinear evolution for moderate eccentricities. Linear secular theory is found to correctly predict the structure and precession rates of discs with small eccentricities. However, discs with larger eccentricities (and eccentricity gradients) are observed to precess faster (retrograde relative to the orbital motion), at a rate that depends on their eccentricities (and eccentricity gradients). We derive analytically a nonlinear secular theory for eccentric gas discs, which explains this result as a modification of the pressure forces whenever eccentric orbits in a disc nearly intersect. This effect could be particularly important for highly eccentric discs produced in tidal disruption events, or for narrow gaseous rings; it might also play a role in cau...
Design of Nonlinear Circuits: The Linear Time-Varying Approach
Kuijstermans, F.C.M.
2003-01-01
Over the last years the ever-growing demand for higher performance has led to much interest in using nonlinear circuit concepts for electronic circuit design. For this we have to deal with analysis and synthesis of dynamic nonlinear circuits. This thesis proposes to handle the nonlinear design
Design of Nonlinear Circuits: The Linear Time-Varying Approach
Kuijstermans, F.C.M.
2003-01-01
Over the last years the ever-growing demand for higher performance has led to much interest in using nonlinear circuit concepts for electronic circuit design. For this we have to deal with analysis and synthesis of dynamic nonlinear circuits. This thesis proposes to handle the nonlinear design comp
Nonlinear wave evolution in VLASOV plasma: a lie-transform analysis
Energy Technology Data Exchange (ETDEWEB)
Cary, J.R.
1979-08-01
Nonlinear wave evolution in Vlasov plasma is analyzed using the Lie transform, a powerful mathematical tool which is applicable to Hamiltonian systems. The first part of this thesis is an exposition of the Lie transform. Dewar's general Lie transform theory is explained and is used to construct Deprit's Lie transform perturbation technique. The basic theory is illustrated by simple examples.
Bi-Hamiltonian Structure of a Third-Order Nonlinear Evolution Equation on Plane Curve Motions
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
In the present paper, we identify the integrability of the third-order nonlinear evolution equation ut = (1/2)((uxx + u)-2)x in a Hamiltonian viewpoint. We prove that the recursion operator obtained by S. Yu. Sakovich is hereditary, and then deduce a bi-Hamiltonian structure of the equation by using some decomposition of the hereditary operator. A hierarchy associated to the equation is also shown.
Application of Exp-function method for nonlinear evolution equations with variable coefficients
Energy Technology Data Exchange (ETDEWEB)
El-Wakil, S.A.; Madkour, M.A. [Theoretical Research Group, Physics Department, Faculty of Science, Mansoura University, 35516 Mansoura (Egypt); Abdou, M.A. [Theoretical Research Group, Physics Department, Faculty of Science, Mansoura University, 35516 Mansoura (Egypt); Faculty of Education for Girls, Physics Department, King Kahlid University, Bisha, Kingdom Saudi Arabia (Saudi Arabia)], E-mail: m_abdou_eg@yahoo.com
2007-09-10
In this Letter, the Exp-function method with the aid of symbolic computational system Maple is used to obtain generalized solitary solutions and periodic solutions of a generalized Zakharov-Kuznetsov equation with variable coefficients. It is shown that the Exp-function method, with the help of symbolic computation, provides a powerful mathematical tool for solving other nonlinear evolution equations arising in mathematical physics.
Non-linear macro evolution of a dc driven micro atmospheric glow discharge
Xu, Shaofeng
2015-01-01
We studied the macro evolution of the micro atmospheric glow discharge generated between a micro argon jet into ambient air and static water. The micro discharge behaves similarly to a complex ecosystem. Non-linear behaviors are found for the micro discharge when the water acts as a cathode, different from the discharge when water behaves as an anode. Groups of snapshots of the micro discharge formed at different discharge currents are captured by an intensified charge-coupled device with controlled exposure time, and each group consisted of 256 images taken in succession. Edge detection methods are used to identify the water surface and then the total brightness is defined by adding up the signal counts over the area of the micro discharge. Motions of the water surface at different discharge currents show that the water surface lowers increasingly rapidly when the water acts as a cathode. In contrast, the water surface lowers at a constant speed when the water behaves as an anode. The light curves are simila...
Directory of Open Access Journals (Sweden)
Fei Chen
2013-01-01
Full Text Available This paper deals with the finite-time stabilization problem for discrete-time Markov jump nonlinear systems with time delays and norm-bounded exogenous disturbance. The nonlinearities in different jump modes are parameterized by neural networks. Subsequently, a linear difference inclusion state space representation for a class of neural networks is established. Based on this, sufficient conditions are derived in terms of linear matrix inequalities to guarantee stochastic finite-time boundedness and stochastic finite-time stabilization of the closed-loop system. A numerical example is illustrated to verify the efficiency of the proposed technique.
Nonlinear Time Series Analysis in Earth Sciences - Potentials and Pitfalls
Kurths, Jürgen; Donges, Jonathan F.; Donner, Reik V.; Marwan, Norbert; Zou, Yong
2010-05-01
The application of methods of nonlinear time series analysis has a rich tradition in Earth sciences and has enabled substantially new insights into various complex processes there. However, some approaches and findings have been controversially discussed over the last decades. One reason is that they are often bases on strong restrictions and their violation may lead to pitfalls and misinterpretations. Here, we discuss three general concepts of nonlinear dynamics and statistical physics, synchronization, recurrence and complex networks and explain how to use them for data analysis. We show that the corresponding methods can be applied even to rather short and non-stationary data which are typical in Earth sciences. References Marwan, N., Romano, M., Thiel, M., Kurths, J.: Recurrence plots for the analysis of complex systems, Physics Reports 438, 237-329 (2007) Arenas, A., Diaz-Guilera, A., Kurths, J., Moreno, Y., Zhou, C.: Synchronization in complex networks, Physics Reports 469, 93-153 (2008) Marwan, N., Donges, J.F., Zou, Y., Donner, R. and Kurths, J., Phys. Lett. A 373, 4246 (2009) Donges, J.F., Zou, Y., Marwan, N. and Kurths, J. Europhys. Lett. 87, 48007 (2009) Donner, R., Zou, Y., Donges, J.F., Marwan, N. and Kurths, J., Phys. Rev. E 81, 015101(R) (2010)
Nonlinear Aerodynamics-Structure Time Simulation for HALE Aircraft Design/Analysis Project
National Aeronautics and Space Administration — Time simulation of a nonlinear aerodynamics model (NA) developed at Virginia Tech coupled with a nonlinear structure model (NS) is proposed as a design/analysis...
Sahadevan, R.; Prakash, P.
2017-01-01
We show how invariant subspace method can be extended to time fractional coupled nonlinear partial differential equations and construct their exact solutions. Effectiveness of the method has been illustrated through time fractional Hunter-Saxton equation, time fractional coupled nonlinear diffusion system, time fractional coupled Boussinesq equation and time fractional Whitman-Broer-Kaup system. Also we explain how maximal dimension of the time fractional coupled nonlinear partial differential equations can be estimated.
Ouari, Kamel; Rekioua, Toufik; Ouhrouche, Mohand
2014-01-01
In order to make a wind power generation truly cost-effective and reliable, an advanced control techniques must be used. In this paper, we develop a new control strategy, using nonlinear generalized predictive control (NGPC) approach, for DFIG-based wind turbine. The proposed control law is based on two points: NGPC-based torque-current control loop generating the rotor reference voltage and NGPC-based speed control loop that provides the torque reference. In order to enhance the robustness of the controller, a disturbance observer is designed to estimate the aerodynamic torque which is considered as an unknown perturbation. Finally, a real-time simulation is carried out to illustrate the performance of the proposed controller.
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.
Chen, Yong; Yan, Zhenya
2017-01-01
The effect of derivative nonlinearity and parity-time-symmetric (PT -symmetric) potentials on the wave propagation dynamics is explored in the derivative nonlinear Schrödinger equation, where the physically interesting Scarf-II and harmonic-Hermite-Gaussian potentials are chosen. We study numerically the regions of unbroken and broken linear PT -symmetric phases and find some stable bright solitons of this model in a wide range of potential parameters even though the corresponding linear PT -symmetric phases are broken. The semielastic interactions between particular bright solitons and exotic incident waves are illustrated such that we find that particular nonlinear modes almost keep their shapes after interactions even if the exotic incident waves have evidently been changed. Moreover, we exert the adiabatic switching on PT -symmetric potential parameters such that a stable nonlinear mode with the unbroken linear PT -symmetric phase can be excited to another stable nonlinear mode belonging to the broken linear PT -symmetric phase.
Institute of Scientific and Technical Information of China (English)
赵应桥; 朱鹤元; 刘建华; 孙迭篪; 李富铭
1997-01-01
A time-resolved cross-phase modulation method combined with a modified nonlinear Schrodinger equation is used to study the effects of nonlinear response time on the propagation of ultrashort pulses in nonlinear dispersion media. Evolution of cross-phase modulation spectrum with the different time delay between the probe pulse and pump pulse is simulated using split-step Fourier method. It is shown that both normal self-frequency-shift-red-shift and abnormal self-frequency-shift-blue-shift can occur in the frequency domain for the probe pulse, and a satisfactory theoretical interpretation is given.
Global Format for Conservative Time Integration in Nonlinear Dynamics
DEFF Research Database (Denmark)
Krenk, Steen
2014-01-01
equivalent static load steps, easily implemented in existing computer codes. The paper considers two aspects: representation of nonlinear internal forces in a form that implies energy conservation, and the option of an algorithmic damping with the purpose of extracting energy from undesirable high...... over the time step. This explicit formula is exact for structures with internal energy in the form of a polynomial in the displacement components of degree four. A fully general form follows by introducing an additional term based on a secant representation of the internal energy. The option......-frequency parts of the response. The energy conservation property is developed in two steps. First a fourth-order representation of the internal energy increment is obtained in terms of the mean value of the associated internal forces and an additional term containing the increment of the tangent stiffness matrix...
On Hamiltonian realization of time-varying nonlinear systems
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
This paper Investigates Hamiltonian realization of time-varying nonlinear (TVN) systems, and proposes a number of new methods for the problem. It is shown that every smooth TVN system can be expressed as a generalized Hamiltonian system if the origin is the equilibrium of the system. If the Jacooian matrix of a TVN system is nonsingu-lar, the system has a generalized Hamiltonian realization whose structural matrix and Hamiltonian function are given explicitly. For the case that the Jacobian matrix is singular, this paper provides a constructive decomposition method, and then proves that a TVN system has a generalized Hamiltonian realization if its Jacobian matrix has a nonsingular main diagonal block. Furthermore, some sufficient (necessary and sufficient) conditions for dissipative Hamiltonian realization of TVN systems are also presented in this paper.
Mohanty, Pratap Ranjan; Panda, Anup Kumar
2016-11-01
This paper is concerned to performance improvement of boost PFC converter under large random load fluctuation, ensuring unity power factor (UPF) at source end and regulated voltage at load side. To obtain such performance, a nonlinear controller based on dynamic evolution path theory is designed and its robustness is examined under both heavy and light loading condition. In this paper, %THD and zero-cross-over dead-zone of input current is significantly reduced. Also, very less response time of input current and output voltage to that of load and reference variation is remarked. A simulation model of proposed system is designed and it is realized using dSPACE 1104 signal processor for a 390VDC, 500W prototype. The relevant experimental and simulation waveforms are presented.
Institute of Scientific and Technical Information of China (English)
Wu Xuesong; Gao Wenjie; Cao Jianwen
2011-01-01
In this paper, the authors discuss the global existence and blow-up of the solution to an evolution ρ-Laplace system with nonlinear sources and nonlinear boundary condition. The authors first establish the local existence of solutions, then give a necessary and sufficient condition on the global existence of the positive solution.
Nonlinear Time Series Analysis of White Dwarf Light Curves
Jevtic, N.; Zelechoski, S.; Feldman, H.; Peterson, C.; Schweitzer, J.
2001-12-01
We use nonlinear time series analysis methods to examine the light intensity curves of white dwarf PG1351+489 obtained by the Whole Earth Telescope (WET). Though these methods were originally introduced to study chaotic systems, when a clear signature of determinism is found for the process generating an observable and it couples the active degrees of freedom of the system, then the notion of phase space provides a framework for exploring the system dynamics of nonlinear systems in general. With a pronounced single frequency, its harmonics and other frequencies of lower amplitude on a broadband background, the PG1351 light curve lends itself to the use of time delay coordinates. Our phase space reconstruction yields a triangular, toroidal three-dimensional shape. This differs from earlier results of a circular toroidal representation. We find a morphological similarity to a magnetic dynamo model developed for fast rotators that yields a union of both results: the circular phase space structure for the ascending portion of the cycle, and the triangular structure for the declining portion. The rise and fall of the dynamo cycle yield both different phase space representations and different correlation dimensions. Since PG1351 is known to have no significant fields, these results may stimulate the observation of light curves of known magnetic white dwarfs for comparison. Using other data obtained by the WET, we compare the phase space reconstruction of DB white dwarf PG1351 with that of GD 358 which has a more complex power spectrum. We also compare these results with those for PG1159. There is some general similarity between the results of the phase space reconstruction for the DB white dwarfs. As expected, the difference between the results for the DB white dwarfs and PG1159 is great.
A nonlinear correlation function for selecting the delay time in dynamical reconstructions
Aguirre, Luis Antonio
1995-02-01
Numerical results discussed in this paper suggest that a function which detects nonlinear correlations in time series usually indicates shorter correlation times than the linear autocorrelation function which is often used for this purpose. The nonlinear correlation function can also detect changes in the data which cannot be distinguished by the linear counterpart. This affects a number of approaches for the selection of the delay time used in the reconstruction of nonlinear dynamics from a single time series based on time delay coordinates.
Transient evolution of a photon gas in the nonlinear QED vacuum
Energy Technology Data Exchange (ETDEWEB)
Wu, S Q; Hartemann, F V
2011-10-04
Thermally induced vacuum polarization stemming from QED radiative corrections to the electromagnetic field equations is studied. The physical behavior of thermal radiation, in the nonlinear QED vacuum first described by Heisenberg and Euler, is a problem of some theoretical importance in view of its relation to the cosmic microwave background (CMB), early universe evolution, and Hawking-Unruh radiation. The questions of evolution toward equilibrium, stability, and invariance of thermal radiation under such conditions are of great interest. Our analysis presents novel aspects associated with photon-photon scattering in a photon gas in the framework of quantum kinetic theory. Within the context of the Euler-Heisenberg theory, we show that a homogeneous, isotropic photon gas with arbitrary spectral distribution function evolves toward an equilibrium state with a Bose-Einstein distribution. The transient evolution toward equilibrium of a gas of photons undergoing photon-photon scattering is studied in detail via the Boltzmann transport equation.
Complexity Variability Assessment of Nonlinear Time-Varying Cardiovascular Control
Valenza, Gaetano; Citi, Luca; Garcia, Ronald G.; Taylor, Jessica Noggle; Toschi, Nicola; Barbieri, Riccardo
2017-01-01
The application of complex systems theory to physiology and medicine has provided meaningful information about the nonlinear aspects underlying the dynamics of a wide range of biological processes and their disease-related aberrations. However, no studies have investigated whether meaningful information can be extracted by quantifying second-order moments of time-varying cardiovascular complexity. To this extent, we introduce a novel mathematical framework termed complexity variability, in which the variance of instantaneous Lyapunov spectra estimated over time serves as a reference quantifier. We apply the proposed methodology to four exemplary studies involving disorders which stem from cardiology, neurology and psychiatry: Congestive Heart Failure (CHF), Major Depression Disorder (MDD), Parkinson’s Disease (PD), and Post-Traumatic Stress Disorder (PTSD) patients with insomnia under a yoga training regime. We show that complexity assessments derived from simple time-averaging are not able to discern pathology-related changes in autonomic control, and we demonstrate that between-group differences in measures of complexity variability are consistent across pathologies. Pathological states such as CHF, MDD, and PD are associated with an increased complexity variability when compared to healthy controls, whereas wellbeing derived from yoga in PTSD is associated with lower time-variance of complexity. PMID:28218249
Complexity Variability Assessment of Nonlinear Time-Varying Cardiovascular Control
Valenza, Gaetano; Citi, Luca; Garcia, Ronald G.; Taylor, Jessica Noggle; Toschi, Nicola; Barbieri, Riccardo
2017-02-01
The application of complex systems theory to physiology and medicine has provided meaningful information about the nonlinear aspects underlying the dynamics of a wide range of biological processes and their disease-related aberrations. However, no studies have investigated whether meaningful information can be extracted by quantifying second-order moments of time-varying cardiovascular complexity. To this extent, we introduce a novel mathematical framework termed complexity variability, in which the variance of instantaneous Lyapunov spectra estimated over time serves as a reference quantifier. We apply the proposed methodology to four exemplary studies involving disorders which stem from cardiology, neurology and psychiatry: Congestive Heart Failure (CHF), Major Depression Disorder (MDD), Parkinson’s Disease (PD), and Post-Traumatic Stress Disorder (PTSD) patients with insomnia under a yoga training regime. We show that complexity assessments derived from simple time-averaging are not able to discern pathology-related changes in autonomic control, and we demonstrate that between-group differences in measures of complexity variability are consistent across pathologies. Pathological states such as CHF, MDD, and PD are associated with an increased complexity variability when compared to healthy controls, whereas wellbeing derived from yoga in PTSD is associated with lower time-variance of complexity.
McKinney, B. A.; Crowe, J. E., Jr.; Voss, H. U.; Crooke, P. S.; Barney, N.; Moore, J. H.
2006-02-01
We introduce a grammar-based hybrid approach to reverse engineering nonlinear ordinary differential equation models from observed time series. This hybrid approach combines a genetic algorithm to search the space of model architectures with a Kalman filter to estimate the model parameters. Domain-specific knowledge is used in a context-free grammar to restrict the search space for the functional form of the target model. We find that the hybrid approach outperforms a pure evolutionary algorithm method, and we observe features in the evolution of the dynamical models that correspond with the emergence of favorable model components. We apply the hybrid method to both artificially generated time series and experimentally observed protein levels from subjects who received the smallpox vaccine. From the observed data, we infer a cytokine protein interaction network for an individual’s response to the smallpox vaccine.
Evolution of Channels Draining Mount St. Helens: Linking Non-Linear and Rapid, Threshold Responses
Simon, A.
2010-12-01
The catastrophic eruption of Mount St. Helens buried the valley of the North Fork Toutle River (NFT) to a depth of up to 140 m. Initial integration of a new drainage network took place episodically by the “filling and spilling” (from precipitation and seepage) of depressions formed during emplacement of the debris avalanche deposit. Channel incision to depths of 20-30 m occurred in the debris avalanche and extensive pyroclastic flow deposits, and headward migration of the channel network followed, with complete integration taking place within 2.5 years. Downstream reaches were converted from gravel-cobble streams with step-pool sequences to smoothed, infilled channels dominated by sand-sized materials. Subsequent channel evolution was dominated by channel widening with the ratio of changes in channel width to changes in channel depth ranging from about 60 to 100. Widening resulted in significant adjustment of hydraulic variables that control sediment-transport rates. For a given discharge over time, flow depths were reduced, relative roughness increased and flow velocity and boundary shear stress decreased non-linearly. These changes, in combination with coarsening of the channel bed with time resulted in systematically reduced rates of degradation (in upstream reaches), aggradation (in downstream reaches) and sediment-transport rates through much of the 1990s. Vertical adjustments were, therefore, easy to characterize with non-linear decay functions with bed-elevation attenuating with time. An empirical model of bed-level response was then created by plotting the total dimensionless change in elevation against river kilometer for both initial and secondary vertical adjustments. High magnitude events generated from the generated from upper part of the mountain, however, can cause rapid (threshold) morphologic changes. For example, a rain-on-snow event in November 2006 caused up to 9 m of incision along a 6.5 km reach of Loowit Creek and the upper NFT. The event
Nonlinear time-domain modeling of balanced-armature receivers
DEFF Research Database (Denmark)
Jensen, Joe; Agerkvist, Finn T.; Harte, James
2011-01-01
Nonlinear distortion added by the loudspeaker in a hearing aid lowers the signal-to-noise ratio and may degrade the hearing aid user's ability to understand speech. The balancedarmature- type loudspeakers, predominantly used in hearing aids, are inherently nonlinear devices, as any displacement o...
Feijoo, David; Konotop, Vladimir V
2016-01-01
We analyze a system of three two-dimensional nonlinear Schr\\"odinger equations coupled by linear terms and with the cubic-quintic (focusing-defocusing) nonlinearity. We consider two versions of the model: conservative and parity-time ($\\mathcal{PT}$) symmetric. These models describe triple-core nonlinear optical waveguides, with balanced gain and losses in the $\\mathcal{PT}$-symmetric case. We obtain families of soliton solutions and discuss their stability. The latter study is performed using a linear stability analysis and checked with direct numerical simulations of the evolutional system of equations. Stable solitons are found in the conservative and $\\mathcal{PT}$-symmetric cases. Interactions and collisions between the conservative and $\\mathcal{PT}$-symmetric solitons are briefly investigated, as well.
Shemer, Lev; Sergeeva, Anna; Liberzon, Dan
2010-12-01
Results of extensive experiments on propagation of unidirectional nonlinear random waves in a large wave tank are presented. The nonlinearity of the wavefield determined by the characteristic wave amplitude and the dominant wave length was retained constant in various series of experimental runs. In each experimental series, initial spectra of different shape and/or width were considered. Every series contained sufficient number of independent realizations to ensure reliable statistics. Evolution of various statistical parameters along the tank was investigated. It is demonstrated that the spectrum width plays an important role in the evolution of the random wavefield and strongly affects the variation of the wave spectrum as well as of parameters that characterize the deviation of the wavefield statistics from that corresponding to the Gaussian distribution. In particular, in a random wavefield that initially contains independent free harmonics within a narrow spectrum, extremely steep waves appear more often in the process of evolutions than predicted by a Rayleigh distribution, while for wider initial wave spectra the probability of those waves decreases sharply and is well below the Rayleigh values.
AUTO-EXTRACTING TECHNIQUE OF DYNAMIC CHAOS FEATURES FOR NONLINEAR TIME SERIES
Institute of Scientific and Technical Information of China (English)
CHEN Guo
2006-01-01
The main purpose of nonlinear time series analysis is based on the rebuilding theory of phase space, and to study how to transform the response signal to rebuilt phase space in order to extract dynamic feature information, and to provide effective approach for nonlinear signal analysis and fault diagnosis of nonlinear dynamic system. Now, it has already formed an important offset of nonlinear science. But, traditional method cannot extract chaos features automatically, and it needs man's participation in the whole process. A new method is put forward, which can implement auto-extracting of chaos features for nonlinear time series. Firstly, to confirm time delay τ by autocorrelation method; Secondly, to compute embedded dimension m and correlation dimension D;Thirdly, to compute the maximum Lyapunov index λmax; Finally, to calculate the chaos degree Dch of features extracting has important meaning to fault diagnosis of nonlinear system based on nonlinear chaos features. Examples show validity of the proposed method.
Carasso, Alfred S
2013-01-01
Identifying sources of ground water pollution, and deblurring nanoscale imagery as well as astronomical galaxy images, are two important applications involving numerical computation of parabolic equations backward in time. Surprisingly, very little is known about backward continuation in nonlinear parabolic equations. In this paper, an iterative procedure originating in spectroscopy in the 1930's, is adapted into a useful tool for solving a wide class of 2D nonlinear backward parabolic equations. In addition, previously unsuspected difficulties are uncovered that may preclude useful backward continuation in parabolic equations deviating too strongly from the linear, autonomous, self adjoint, canonical model. This paper explores backward continuation in selected 2D nonlinear equations, by creating fictitious blurred images obtained by using several sharp images as initial data in these equations, and capturing the corresponding solutions at some positive time T. Successful backward continuation from t=T to t = 0, would recover the original sharp image. Visual recognition provides meaningful evaluation of the degree of success or failure in the reconstructed solutions. Instructive examples are developed, illustrating the unexpected influence of certain types of nonlinearities. Visually and statistically indistinguishable blurred images are presented, with vastly different deblurring results. These examples indicate that how an image is nonlinearly blurred is critical, in addition to the amount of blur. The equations studied represent nonlinear generalizations of Brownian motion, and the blurred images may be interpreted as visually expressing the results of novel stochastic processes.
Non-linear time series extreme events and integer value problems
Turkman, Kamil Feridun; Zea Bermudez, Patrícia
2014-01-01
This book offers a useful combination of probabilistic and statistical tools for analyzing nonlinear time series. Key features of the book include a study of the extremal behavior of nonlinear time series and a comprehensive list of nonlinear models that address different aspects of nonlinearity. Several inferential methods, including quasi likelihood methods, sequential Markov Chain Monte Carlo Methods and particle filters, are also included so as to provide an overall view of the available tools for parameter estimation for nonlinear models. A chapter on integer time series models based on several thinning operations, which brings together all recent advances made in this area, is also included. Readers should have attended a prior course on linear time series, and a good grasp of simulation-based inferential methods is recommended. This book offers a valuable resource for second-year graduate students and researchers in statistics and other scientific areas who need a basic understanding of nonlinear time ...
Traveling wave solutions of nonlinear evolution equations via the enhanced (G′/G-expansion method
Directory of Open Access Journals (Sweden)
Kamruzzaman Khan
2014-07-01
Full Text Available In this article, an enhanced (G′/G-expansion method is suggested to find the traveling wave solutions for the modified Korteweg de-Vries (mKDV equation. Abundant traveling wave solutions are derived, which are expressed by the hyperbolic and trigonometric functions involving several parameters. The efficiency of this method for finding these exact solutions has been demonstrated. It is shown that the proposed method is effective and can be used for many other nonlinear evolution equations (NLEEs in mathematical physics.
Infinitely-many conservation laws for two (2+1)-dimensional nonlinear evolution equations in fluids
Indian Academy of Sciences (India)
Yan Jiang; Bo Tian; Pan Wang; Kun Su
2014-07-01
In this paper, a method that can be used to construct the infinitely-many conservation laws with the Lax pair is generalized from the (1+1)-dimensional nonlinear evolution equations (NLEEs) to the (2+1)-dimensional ones. Besides, we apply that method to the Kadomtsev– Petviashvili (KP) and Davey–Stewartson equations in fluids, and respectively obtain their infinitelymany conservation laws with symbolic computation. Based on that method, we can also construct the infinitely-many conservation laws for other multidimensional NLEEs possessing the Lax pairs, including the cylindrical KP, modified KP and (2+1)-dimensional Gardner equations, in fluids, plasmas, optical fibres and Bose–Einstein condensates.
Differential Evolution-Based PID Control of Nonlinear Full-Car Electrohydraulic Suspensions
Directory of Open Access Journals (Sweden)
Jimoh O. Pedro
2013-01-01
Full Text Available This paper presents a differential-evolution- (DE- optimized, independent multiloop proportional-integral-derivative (PID controller design for full-car nonlinear, electrohydraulic suspension systems. The multiloop PID control stabilises the actuator via force feedback and also improves the system performance. Controller gains are computed using manual tuning and through DE optimization to minimise a performance index, which addresses suspension travel, road holding, vehicle handling, ride comfort, and power consumption constraints. Simulation results showed superior performance of the DE-optimized PID-controlled active vehicle suspension system (AVSS over the manually tuned PID-controlled AVSS and the passive vehicle suspension system (PVSS.
A THIRD-ORDER BOUSSINESQ MODEL APPLIED TO NONLINEAR EVOLUTION OF SHALLOW-WATER WAVES
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
The conventional Boussinesq model is extended to the third order in dispersion and nonlinearity. The new equations are shown to possess better linear dispersion characteristics. For the evolution of periodic waves over a constant depth, the computed wave envelops are spatially aperiodic and skew. The model is then applied to the study of wave focusing by a topographical lens and the results are compared with Whalin's (1971) experimental data as well as some previous results from the conventional Boussinesq model. Encouragingly, improved agreement with Whalin's experimental data is found.
TRAVELLING WAVE SOLUTIONS OF NONLINEAR EVOLUTION EQUATIONS BY USING SYMBOLIC COMPUTATION
Institute of Scientific and Technical Information of China (English)
FanEngui
2001-01-01
Abstract. A Riccati equation involving a parameter and symbolic computation are used to uni-formly construct the different forms of travelling wave solutions for nonlinear evolution equa-tions. It is shown that the sign of the parameter can be applied in judging the existence of vari-ous forms of travelling wave solutions. An efficiency of this method is demonstrated on some e-quations,which include Burgers-Huxley equation,Caudrey-Dodd-Gibbon-Kawada equation,gen-eralized Benjamin-Bona-Mahony equation and generalized Fisher equation.
Canonical structure of evolution equations with non-linear dispersive terms
Indian Academy of Sciences (India)
B Talukdar; J Shamanna; S Ghosh
2003-07-01
The inverse problem of the variational calculus for evolution equations characterized by non-linear dispersive terms is analysed with a view to clarify why such a system does not follow from Lagrangians. Conditions are derived under which one could construct similar equations which admit a Lagrangian representation. It is shown that the system of equations thus obtained can be Hamiltonized by making use of the Dirac’s theory of constraints. The speciﬁc results presented refer to the third- and ﬁfth-order equations of the so-called distinguished subclass.
Nonlinear dynamics of wind waves: multifractal phase/time effects
Directory of Open Access Journals (Sweden)
R. H. Mellen
1994-01-01
Full Text Available In addition to the bispectral coherence method, phase/time analysis of analytic signals is another promising avenue for the investigation of phase effects in wind waves. Frequency spectra of phase fluctuations obtained from both sea and laboratory experiments follow an F-β power law over several decades, suggesting that a fractal description is appropriate. However, many similar natural phenomena have been shown to be multifractal. Universal multifractals are quantified by two additional parameters: the Lévy index 0 α 2 for the type of multifractal and the co-dimension 0 C1 1 for intermittence. The three parameters are a full statistical measure the nonlinear dynamics. Analysis of laboratory flume data is reported here and the results indicate that the phase fluctuations are 'hard multifractal' (α > 1. The actual estimate is close to the limiting value α = 2, which is consistent with Kolmogorov's lognormal model for turbulent fluctuations. Implications for radar and sonar backscattering from the sea surface are briefly considered.
Assessing Spontaneous Combustion Instability with Nonlinear Time Series Analysis
Eberhart, C. J.; Casiano, M. J.
2015-01-01
Considerable interest lies in the ability to characterize the onset of spontaneous instabilities within liquid propellant rocket engine (LPRE) combustion devices. Linear techniques, such as fast Fourier transforms, various correlation parameters, and critical damping parameters, have been used at great length for over fifty years. Recently, nonlinear time series methods have been applied to deduce information pertaining to instability incipiency hidden in seemingly stochastic combustion noise. A technique commonly used in biological sciences known as the Multifractal Detrended Fluctuation Analysis has been extended to the combustion dynamics field, and is introduced here as a data analysis approach complementary to linear ones. Advancing, a modified technique is leveraged to extract artifacts of impending combustion instability that present themselves a priori growth to limit cycle amplitudes. Analysis is demonstrated on data from J-2X gas generator testing during which a distinct spontaneous instability was observed. Comparisons are made to previous work wherein the data were characterized using linear approaches. Verification of the technique is performed by examining idealized signals and comparing two separate, independently developed tools.
Time-domain seismic reliability of nonlinear structures
Indian Academy of Sciences (India)
Achintya Haldar; Jungwon Huh; Ali Mehrabian
2006-08-01
A novel reliability analysis technique is presented to estimate the reliability of real structural systems. Its unique feature is that the dynamic loadings can be applied in time domain. It is a nonlinear stochastic ﬁnite element logarithm combined with the response surface method (RSM). It generates the response surface around the most probable failure point and incorporates information of the distribution of the random variables in the RSM formulation. It is veriﬁed using the Monte Carlo simulation technique, and is found to be very efﬁcient and accurate. Most sources of nonlinearlity and uncertainty can be explicitly incorporated in the formulation. The ﬂexibility of connections, represented by moment-relative rotation $(M–\\theta )$ curves, is addressed. After the Northridge earthquake of 1994, several improved steel connections were proposed. Structural Sesimic Design Associates (SSDA) tested several full-scale proprietory slotted web beam–column connections. The authors suggested $(M–\\theta )$ curves for this connection using actual test data. Behaviours of steel frames, assuming the connections are fully restrained, partially restrained, consisting of pre- and post-Northridge connections are evaluated and compared. Desirable features of the post-Northridge connections observed during testing are analytically conﬁrmed. Laterally weak steel frame is then strengthened with concrete shear walls. Capabilities and the advanced nature of the method are demonstrated with the help of realistic examples.
The self-similar, non-linear evolution of rotating magnetic flux ropes
Directory of Open Access Journals (Sweden)
C. J. Farrugia
Full Text Available We study, in the ideal MHD approximation, the non-linear evolution of cylindrical magnetic flux tubes differentially rotating about their symmetry axis. Our force balance consists of inertial terms, which include the centrifugal force, the gradient of the axial magnetic pressure, the magnetic pinch force and the gradient of the gas pressure. We employ the "separable" class of self-similar magnetic fields, defined recently. Taking the gas to be a polytrope, we reduce the problem to a single, ordinary differential equation for the evolution function. In general, two regimes of evolution are possible; expansion and oscillation. We investigate the specific effect rotation has on these two modes of evolution. We focus on critical values of the flux rope parameters and show that rotation can suppress the oscillatory mode. We estimate the critical value of the angular velocity Ω_{crit}, above which the magnetic flux rope always expands, regardless of the value of the initial energy. Studying small-amplitude oscillations of the rope, we find that torsional oscillations are superimposed on the rotation and that they have a frequency equal to that of the radial oscillations. By setting the axial component of the magnetic field to zero, we study small-amplitude oscillations of a rigidly rotating pinch. We find that the frequency of oscillation ω is inversely proportional to the angular velocity of rotation Ω; the product ωΩbeing proportional to the inverse square of the Alfvén time. The period of large-amplitude oscillations of a rotating flux rope of low beta increases exponentially with the energy of the equivalent 1D oscillator. With respect to large-amplitude oscillations of a non-rotating flux rope, the only change brought about by rotation is to introduce a multiplicative factor greater than unity, which further increases the period. This multiplicative factor depends on the ratio of the azimuthal speed to the Alfvén speed
Bartelmann, Matthias; Berg, Daniel; Kozlikin, Elena; Lilow, Robert; Viermann, Celia
2014-01-01
We calculate the power spectrum of density fluctuations in the statistical non-equilibrium field theory for classical, microscopic degrees of freedom to first order in the interaction potential. We specialise our result to cosmology by choosing appropriate initial conditions and propagators and show that the non-linear growth of the density power spectrum found in numerical simulations of cosmic structure evolution is reproduced well to redshift zero and for arbitrary wave numbers. The main difference of our approach to ordinary cosmological perturbation theory is that we do not perturb a dynamical equation for the density contrast. Rather, we transport the initial phase-space distribution of a canonical particle ensemble forward in time and extract any collective information from it at the time needed. Since even small perturbations of particle trajectories can lead to large fluctuations in density, our approach allows to reach high density contrast already at first order in the perturbations of the particle...
Non-linear Imaging using an Experimental Synthetic Aperture Real Time Ultrasound Scanner
DEFF Research Database (Denmark)
Rasmussen, Joachim; Du, Yigang; Jensen, Jørgen Arendt
2011-01-01
This paper presents the first non-linear B-mode image of a wire phantom using pulse inversion attained via an experimental synthetic aperture real-time ultrasound scanner (SARUS). The purpose of this study is to implement and validate non-linear imaging on SARUS for the further development of new...... non-linear techniques. This study presents non-linear and linear B-mode images attained via SARUS and an existing ultrasound system as well as a Field II simulation. The non-linear image shows an improved spatial resolution and lower full width half max and -20 dB resolution values compared to linear...
Neural network-based H∞ filtering for nonlinear systems with time-delays
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
A novel H∞ design methodology for a neural network-based nonlinear filtering scheme is addressed.Firstly,neural networks are employed to approximate the nonlinearities.Next,the nonlinear dynamic system is represented by the mode-dependent linear difference inclusion (LDI).Finally,based on the LDI model,a neural network-based nonlinear filter (NNBNF) is developed to minimize the upper bound of H∞ gain index of the estimation error under some linear matrix inequality (LMI) constraints.Compared with the existing nonlinear filters,NNBNF is time-invariant and numerically tractable.The validity and applicability of the proposed approach are successfully demonstrated in an illustrative example.
Erratum for the time-like evolution in QCDNUM
Botje, M
2016-01-01
A recent comparison of the evolution programs QCDNUM and APFEL showed a discrepancy in the time-like evolution of the singlet fragmentation function at NLO. It was found that the splitting functions of this evolution were wrongly assigned in QCDNUM, and also that the fragmentation functions were not correctly matched at the flavour thresholds. These errors are corrected in a new release of the program.
Coward, Adrian V.; Papageorgiou, Demetrios T.; Smyrlis, Yiorgos S.
1994-01-01
In this paper the nonlinear stability of two-phase core-annular flow in a pipe is examined when the acting pressure gradient is modulated by time harmonic oscillations and viscosity stratification and interfacial tension is present. An exact solution of the Navier-Stokes equations is used as the background state to develop an asymptotic theory valid for thin annular layers, which leads to a novel nonlinear evolution describing the spatio-temporal evolution of the interface. The evolution equation is an extension of the equation found for constant pressure gradients and generalizes the Kuramoto-Sivashinsky equation with dispersive effects found by Papageorgiou, Maldarelli & Rumschitzki, Phys. Fluids A 2(3), 1990, pp. 340-352, to a similar system with time periodic coefficients. The distinct regimes of slow and moderate flow are considered and the corresponding evolution is derived. Certain solutions are described analytically in the neighborhood of the first bifurcation point by use of multiple scales asymptotics. Extensive numerical experiments, using dynamical systems ideas, are carried out in order to evaluate the effect of the oscillatory pressure gradient on the solutions in the presence of a constant pressure gradient.
Directory of Open Access Journals (Sweden)
Mingzhu Song
2016-01-01
Full Text Available We address the problem of globally asymptotic stability for a class of stochastic nonlinear systems with time-varying delays. By the backstepping method and Lyapunov theory, we design a linear output feedback controller recursively based on the observable linearization for a class of stochastic nonlinear systems with time-varying delays to guarantee that the closed-loop system is globally asymptotically stable in probability. In particular, we extend the deterministic nonlinear system to stochastic nonlinear systems with time-varying delays. Finally, an example and its simulations are given to illustrate the theoretical results.
IDENTIFICATION OF NONLINEAR DYNAMIC SYSTEMS:TIME-FREQUENCY FILTERING AND SKELETON CURVES
Institute of Scientific and Technical Information of China (English)
王丽丽; 张景绘
2001-01-01
The nonlinear behavior varying with the instantaneous response was analyzed through the joint time-frequency analysis method for a class of S. D. O . F nonlinear system.A masking operator on definite regions is defined and two theorems are presented. Based on these, the nonlinear system is modeled with a special time-varying linear one, called the generalized skeleton linear system ( GSLS ). The frequency skeleton curve and the damping skeleton curve are defined to describe the main feature of the non-linearity as well. More over, an identification method is proposed through the skeleton curves and the time frequency filtering technique.
Global exponential stabilisation of a class of nonlinear time-delay systems
Benabdallah, Amel; Echi, Nadhem
2016-12-01
This paper deals with the state and output feedback stabilisation problems for a family of nonlinear time-delay systems satisfying some relaxed triangular-type condition. The delay is supposed to be constant. Parameter-dependent control laws are used to compensate for the nonlinearities. Based on the Lyapunov-Krasovskii functionals, global exponential stability of the closed-loop systems is achieved. Finally, an extension to nonlinear time-varying delay systems is given.
Spin Evolution of Accreting Neutron Stars: Nonlinear Development of the R-mode Instability
Bondarescu, Ruxandra; Wasserman, Ira
2007-01-01
The nonlinear saturation of the r-mode instability and its effects on the spin evolution of Low Mass X-ray Binaries (LMXBs) are modeled using the triplet of modes at the lowest parametric instability threshold. We solve numerically the coupled equations for the three mode amplitudes in conjunction with the spin and temperature evolution equations. We observe that very quickly the mode amplitudes settle into quasi-stationary states. Once these states are reached, the mode amplitudes can be found algebraically and the system of equations is reduced from eight to two equations: spin and temperature evolution. Eventually, the system may reach thermal equilibrium and either (1) undergo a cyclic evolution with a frequency change of at most 10%, (2) evolve toward a full equilibrium state in which the accretion torque balances the gravitational radiation emission, or (3) enter a thermogravitational runaway on a very long timescale of about $10^6$ years. Alternatively, a faster thermal runaway (timescale of about 100 ...
A unified nonlinear stochastic time series analysis for climate science
Moon, Woosok; Wettlaufer, John S.
2017-03-01
Earth’s orbit and axial tilt imprint a strong seasonal cycle on climatological data. Climate variability is typically viewed in terms of fluctuations in the seasonal cycle induced by higher frequency processes. We can interpret this as a competition between the orbitally enforced monthly stability and the fluctuations/noise induced by weather. Here we introduce a new time-series method that determines these contributions from monthly-averaged data. We find that the spatio-temporal distribution of the monthly stability and the magnitude of the noise reveal key fingerprints of several important climate phenomena, including the evolution of the Arctic sea ice cover, the El Nio Southern Oscillation (ENSO), the Atlantic Nio and the Indian Dipole Mode. In analogy with the classical destabilising influence of the ice-albedo feedback on summertime sea ice, we find that during some time interval of the season a destabilising process operates in all of these climate phenomena. The interaction between the destabilisation and the accumulation of noise, which we term the memory effect, underlies phase locking to the seasonal cycle and the statistical nature of seasonal predictability.
A unified nonlinear stochastic time series analysis for climate science
Moon, Woosok; Wettlaufer, John S.
2017-01-01
Earth’s orbit and axial tilt imprint a strong seasonal cycle on climatological data. Climate variability is typically viewed in terms of fluctuations in the seasonal cycle induced by higher frequency processes. We can interpret this as a competition between the orbitally enforced monthly stability and the fluctuations/noise induced by weather. Here we introduce a new time-series method that determines these contributions from monthly-averaged data. We find that the spatio-temporal distribution of the monthly stability and the magnitude of the noise reveal key fingerprints of several important climate phenomena, including the evolution of the Arctic sea ice cover, the El Nio Southern Oscillation (ENSO), the Atlantic Nio and the Indian Dipole Mode. In analogy with the classical destabilising influence of the ice-albedo feedback on summertime sea ice, we find that during some time interval of the season a destabilising process operates in all of these climate phenomena. The interaction between the destabilisation and the accumulation of noise, which we term the memory effect, underlies phase locking to the seasonal cycle and the statistical nature of seasonal predictability. PMID:28287128
Hornsby, William A; Buchholz, Rico; Grosshauser, Stefan; Weikl, Arne; Zarzoso, David; Casson, Francis J; Poli, Emanuele; Peeters, Artur G
2015-01-01
The non-linear evolution of a magnetic island is studied using the Vlasov gyro-kinetic code GKW. The interaction of electromagnetic turbulence with a self-consistently growing magnetic island, generated by a tearing unstable $\\Delta' > 0$ current profile, is considered. The turbulence is able to seed the magnetic island and bypass the linear growth phase by generating structures that are approximately an ion gyro-radius in width. The non-linear evolution of the island width and its rotation frequency, after this seeding phase, is found to be modified and is dependent on the value of the plasma beta and equilibrium pressure gradients. At low values of beta the island evolves largely independent of the turbulence, while at higher values the interaction has a dramatic effect on island growth, causing the island to grow exponentially at the growth rate of its linear phase, even though the island is larger than linear theory validity. The turbulence forces the island to rotate in the ion-diamagnetic direction as o...
Ryu, D; Frank, A I; Ryu, Dongsu; Frank, Adam
2000-01-01
We investigate through high resolution 3D simulations the nonlinear evolution of compressible magnetohydrodynamic flows subject to the Kelvin-Helmholtz instability. We confirm in 3D flows the conclusion from our 2D work that even apparently weak magnetic fields embedded in Kelvin-Helmholtz unstable plasma flows can be fundamentally important to nonlinear evolution of the instability. In fact, that statement is strengthened in 3D by this work, because it shows how field line bundles can be stretched and twisted in 3D as the quasi-2D Cat's Eye vortex forms out of the hydrodynamical motions. In our simulations twisting of the field may increase the maximum field strength by more than a factor of two over the 2D effect. If, by these developments, the Alfv\\'en Mach number of flows around the Cat's Eye drops to unity or less, our simulations suggest magnetic stresses will eventually destroy the Cat's Eye and cause the plasma flow to self-organize into a relatively smooth and apparently stable flow that retains memo...
Application of the green function formalism to nonlinear evolution of the low gain FEL oscillator
Energy Technology Data Exchange (ETDEWEB)
Shvets, G. [Princeton Plasma Physics Lab., NJ (United States); Wurtele, J.S.; Gardent, D. [Massachusetts Institute of Technology, Cambridge, MA (United States)] [and others
1995-12-31
A matrix formalism for the optical pulse evolution in the frequency domain, is applied to the nonlinear regime of operation. The formalism was previously developed for studies of the linear evolution of the low-gain FEL oscillator with an arbitrary shape of the electron beam. By varying experimentally controllable parameters, such as cavity detunning and cavity losses, different regimes of operation of the FEL oscillator, such as a steady state saturation and limit cycle saturation, are studied numerically. It is demonstrated that the linear supermodes, numerically obtained from the matrix formalism, provide an appropriate framework for analyzing the periodic change in the output power in the limit cycle regime. The frequency of this oscillation is related to the frequencies of the lowest-order linear supermodes. The response of the output radiation to periodic variation of the electron energy is studied. It is found that the response is enhanced when the frequency of the energy variation corresponds to the difference of per-pass phase advances of the lowest linear supermodes. Finally, various nonlinear models are tested to capture the steady state saturation and limit cycle variation of the EM field in the oscillator cavity.
A note on the time evolution of generalized coherent states
Stone, Michael
2000-01-01
I consider the time evolution of generalized coherent states based on non-standard fiducial vectors, and show that only for a restricted class of fiducial vectors does the associated classical motion determine the quantum evolution of the states. I discuss some consequences of this for path integral representations.
Entropy, biological evolution and the psychological arrow of time
Heinrich, Torsten; Päs, Heinrich
2014-01-01
We argue that in Universes where future and past differ only by the entropy content a psychological arrow of time pointing in the direction of entropy increase can arise from natural selection in biological evolution. We show that this effect can be demonstrated in very simple toy computer simulations of evolution in an entropy increasing or decreasing environment.
Prandtl-Ishlinskii hysteresis models for complex time dependent hysteresis nonlinearities
Al Janaideh, M.; Krejčí, P
2012-01-01
We introduce a new class of time dependent hysteresis models by combining the time dependent Prandtl–Ishlinskii model with functional nonlinearities. This combination improves the capability of the time dependent Prandtl–Ishlinskii model to characterize a class of complex time dependent hysteresis nonlinearities in smart actuators. The analytical inversion for the proposed time dependent hysteresis model is also presented in order to extend the inversion algorithm of the inverse time dependen...
2010-09-30
Hyperfast Modeling of Nonlinear Ocean Waves A. R. Osborne Dipartimento di Fisica Generale, Università di Torino Via Pietro Giuria 1, 10125...PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) Universit?i Torino,Dipartimento di Fisica Generale,Via Pietro Giuria 1,10125 Torino, Italy, 8. PERFORMING
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 neural architecture for nonlinear adaptive filtering of time series
DEFF Research Database (Denmark)
Hoffmann, Nils; Larsen, Jan
1991-01-01
A neural architecture for adaptive filtering which incorporates a modularization principle is proposed. It facilitates a sparse parameterization, i.e. fewer parameters have to be estimated in a supervised training procedure. The main idea is to use a preprocessor which determines the dimension...... of the input space and can be designed independently of the subsequent nonlinearity. Two suggestions for the preprocessor are presented: the derivative preprocessor and the principal component analysis. A novel implementation of fixed Volterra nonlinearities is given. It forces the boundedness...
Sir Clive Granger’s contributions to nonlinear time series and econometrics
DEFF Research Database (Denmark)
Terasvirta, Timo
Clive Granger had a wide range of reseach interests and has worked in a number of areas. In this work the focus is on his contributions to nonlinear time series models and modelling. Granger's contributions to a few other aspects of nonlinearity are reviewed as well.......Clive Granger had a wide range of reseach interests and has worked in a number of areas. In this work the focus is on his contributions to nonlinear time series models and modelling. Granger's contributions to a few other aspects of nonlinearity are reviewed as well....
Global adaptive output feedback control for a class of nonlinear time-delay systems.
Zhai, Jun-yong; Zha, Wen-ting
2014-01-01
This paper addresses the problem of global output feedback control for a class of nonlinear time-delay systems. The nonlinearities are dominated by a triangular form satisfying linear growth condition in the unmeasurable states with an unknown growth rate. With a change of coordinates, a linear-like controller is constructed, which avoids the repeated derivatives of the nonlinearities depending on the observer states and the dynamic gain in backstepping approach and therefore, simplifies the design procedure. Using the idea of universal control, we explicitly construct a universal-type adaptive output feedback controller which globally regulates all the states of the nonlinear time-delay systems.
System Identification for Nonlinear FOPDT Model with Input-Dependent Dead-Time
DEFF Research Database (Denmark)
Sun, Zhen; Yang, Zhenyu
2011-01-01
. In order to identify these parameters in an online manner, the considered system is discretized at first. Then, the nonlinear FOPDT identification problem is formulated as a stochastic Mixed Integer Non-Linear Programming problem, and an identification algorithm is proposed by combining the Branch......An on-line iterative method of system identification for a kind of nonlinear FOPDT system is proposed in the paper. The considered nonlinear FOPDT model is an extension of the standard FOPDT model by means that its dead time depends on the input signal and the other parameters are time dependent...
Applied Time Domain Stability Margin Assessment for Nonlinear Time-Varying Systems
Kiefer, J. M.; Johnson, M. D.; Wall, J. H.; Dominguez, A.
2016-01-01
The baseline stability margins for NASA's Space Launch System (SLS) launch vehicle were generated via the classical approach of linearizing the system equations of motion and determining the gain and phase margins from the resulting frequency domain model. To improve the fidelity of the classical methods, the linear frequency domain approach can be extended by replacing static, memoryless nonlinearities with describing functions. This technique, however, does not address the time varying nature of the dynamics of a launch vehicle in flight. An alternative technique for the evaluation of the stability of the nonlinear launch vehicle dynamics along its trajectory is to incrementally adjust the gain and/or time delay in the time domain simulation until the system exhibits unstable behavior. This technique has the added benefit of providing a direct comparison between the time domain and frequency domain tools in support of simulation validation. This technique was implemented by using the Stability Aerospace Vehicle Analysis Tool (SAVANT) computer simulation to evaluate the stability of the SLS system with the Adaptive Augmenting Control (AAC) active and inactive along its ascent trajectory. The gains for which the vehicle maintains apparent time-domain stability defines the gain margins, and the time delay similarly defines the phase margin. This method of extracting the control stability margins from the time-domain simulation is relatively straightforward and the resultant margins can be compared to the linearized system results. The sections herein describe the techniques employed to extract the time-domain margins, compare the results between these nonlinear and the linear methods, and provide explanations for observed discrepancies. The SLS ascent trajectory was simulated with SAVANT and the classical linear stability margins were evaluated at one second intervals. The linear analysis was performed with the AAC algorithm disabled to attain baseline stability
On the ?2-stability of time-varying linear and nonlinear discrete-time MIMO systems
Institute of Scientific and Technical Information of China (English)
Y.V.VENKATESH
2014-01-01
New conditions are derived for the 2-stability of time-varying linear and nonlinear discrete-time multiple-input multiple-output (MIMO) systems, having a linear time time-invariant block with the transfer function Γ(z), in negative feedback with a matrix of periodic/aperiodic gains A(k),k =0,1,2,. . . and a vector of certain classes of non-monotone/monotone nonlinearitiesϕ( · ), without restrictions on their slopes and also not requiring path-independence of their line integrals. The stability conditions, which are derived in the frequency domain, have the following features: i) They involve the positive definiteness of the real part (as evaluated on |z| = 1) of the product of Γ(z) and a matrix multiplier function of z. ii) For periodic A(k), one class of multiplier functions can be chosen so as to impose no constraint on the rate of variations A(k), but for aperiodic A(k), which allows a more general multiplier function, constraints are imposed on certain global averages of the generalized eigenvalues of (A(k+1),A(k)),k=1,2,. . . . iii) They are distinct from and less restrictive than recent results in the literature.
On Reduced Time Evolution for Initially Correlated Pure States
Aniello, P; Marmo, G; Ventriglia, F; Vitale, P
2009-01-01
A new method to deal with reduced dynamics of open systems by means of the Schr\\"odinger equation is presented. It allows one to consider the reduced time evolution for correlated and uncorrelated initial conditions.
Large Time Asymptotics for Solutions of Nonlinear Partial Differential Equations
Sachdev, PL
2010-01-01
A large number of physical phenomena are modeled by nonlinear partial differential equations, subject to appropriate initial/boundary conditions. This title presents the constructive mathematical techniques. It deals with the asymptotic methods which include self-similarity, balancing argument, and matched asymptotic expansions
Grigoryeva, Lyudmila; Henriques, Julie; Larger, Laurent; Ortega, Juan-Pablo
2014-07-01
Reservoir computing is a recently introduced machine learning paradigm that has already shown excellent performances in the processing of empirical data. We study a particular kind of reservoir computers called time-delay reservoirs that are constructed out of the sampling of the solution of a time-delay differential equation and show their good performance in the forecasting of the conditional covariances associated to multivariate discrete-time nonlinear stochastic processes of VEC-GARCH type as well as in the prediction of factual daily market realized volatilities computed with intraday quotes, using as training input daily log-return series of moderate size. We tackle some problems associated to the lack of task-universality for individually operating reservoirs and propose a solution based on the use of parallel arrays of time-delay reservoirs. Copyright © 2014 Elsevier Ltd. All rights reserved.
Hashemi, Mahnaz; Ghaisari, Jafar; Askari, Javad
2015-07-01
This paper investigates an adaptive controller for a class of Multi Input Multi Output (MIMO) nonlinear systems with unknown parameters, bounded time delays and in the presence of unknown time varying actuator failures. The type of considered actuator failure is one in which some inputs may be stuck at some time varying values where the values, times and patterns of the failures are unknown. The proposed approach is constructed based on a backstepping design method. The boundedness of all the closed-loop signals is guaranteed and the tracking errors are proved to converge to a small neighborhood of the origin. The proposed approach is employed for a double inverted pendulums benchmark and a chemical reactor system. The simulation results show the effectiveness of the proposed method.
Nonlinear Analysis of Spur Gear Pair with Time-varying Mesh Stiffness
Rao T. V. V. L. N.; Awang M.; Lias M. R.; Rani A. M. A.
2014-01-01
This study presents nonlinear analysis of single degree of freedom spur gear pair with time-varying mesh stiffness. The backlash is approximated using nonlinear term. The periodic steady-state solutions of the nonlinear system are obtained by closed-form expressions using the method of multiple scales. The stability and forced vibration response of the gear system are analyzed. The effect of mesh stiffness variation on the amplitude parameter of nondimensional dynamic transmission error for p...
PERFORMANCE EVALUATION: LITERATURE REVIEW AND TIME EVOLUTION.
Directory of Open Access Journals (Sweden)
Pintea Mirela-Oana
2012-07-01
Full Text Available Performance evaluation of an economic entity requires approaching several criteria, such as industry and economic entity type, managerial and entrepreneurial strategy, competitive environment, human and material resources available, using a system of appropriate performance indicators for this purpose.The exigencies of communication occurred on the growing number of phenomena that marked the global economy in recent decades (internationalization and relocation of business crises and turmoil in financial markets, demand performance measurement to be made in a comprehensive way by financial and non-financial criteria. Indicators are measures of performance used by management to measure, report and improve performance of the economic entity. The relationship between indicators and management is ensured by the existence of performance measurement systems. Studies to date indicate that economic entities using balanced performance measurement systems as a key management tool registered superior performance compared to entities not using such systems. This study attempts to address the issue of performance evaluation by presenting opinions of different authors concerning the process of performance measurement and to present, after revising the literature, the evolution of the performance evaluation systems. We tried to do this literature review because sustainable development and, therefore, globalization require new standards of performance that exceeds the economic field, both for domestic companies as well as international ones. So, these standards should be integrated into corporate strategy development to ensure sustainability of activities undertaken by harmonizing the economic, social and environmental objectives. To assess the performance of economic entities it is required that performance evaluation to be done with a balanced multidimensional system, including both financial ratios and non-financial indicators in order to reduce the limits of
Time-Periodic Solution of a 2D Fourth-Order Nonlinear Parabolic Equation
Indian Academy of Sciences (India)
Xiaopeng Zhao; Changchun Liu
2014-08-01
By using the Galerkin method, we study the existence and uniqueness of time-periodic generalized solutions and time-periodic classical solutions to a fourth-order nonlinear parabolic equation in 2D case.
Nonlinear Time Reversal Acoustic Method of Friction Stir Weld Assessment Project
National Aeronautics and Space Administration — The goal of the project is demonstration of the feasibility of Friction Stir Weld (FSW) assessment by novel Nonlinear Time Reversal Acoustic (TRA) method. Time...
Continuous neural identifier for uncertain nonlinear systems with time delays in the input signal.
Alfaro-Ponce, M; Argüelles, A; Chairez, I
2014-12-01
Time-delay systems have been successfully used to represent the complexity of some dynamic systems. Time-delay is often used for modeling many real systems. Among others, biological and chemical plants have been described using time-delay terms with better results than those models that have not consider them. However, getting those models represented a challenge and sometimes the results were not so satisfactory. Non-parametric modeling offered an alternative to obtain suitable and usable models. Continuous neural networks (CNN) have been considered as a real alternative to provide models over uncertain non-parametric systems. This article introduces the design of a specific class of non-parametric model for uncertain time-delay system based on CNN considering the so-called delayed learning laws analysis. The convergence analysis as well as the learning laws were produced by means of a Lyapunov-Krasovskii functional. Three examples were developed to demonstrate the effectiveness of the modeling process forced by the identifier proposed in this study. The first example was a simple nonlinear model used as benchmark example. The second example regarded the human immunodeficiency virus dynamic behavior is used to show the performance of the suggested non-parametric identifier based on CNN for no fictitious neither academic models. Finally, a third example describing the evolution of hepatitis B virus served to test the identifier presented in this study and was also useful to provide evidence of its superior performance against a non-delayed identifier based on CNN.
Misra, A P
2010-01-01
We consider the nonlinear propagation of electrostatic wave packets in an ultra-relativistic (UR) degenerate dense electron-ion plasma, whose dynamics is governed by the nonlocal two-dimensional nonlinear Schroedinger-like equations. The coupled set of equations are then used to study the modulational instability (MI) of a uniform wave train to an infinitesimal perturbation of multi-dimensional form. The condition for the MI is obtained, and it is shown that the nondimensional parameter, $\\beta\\propto\\lambda_C n_0^{1/3}$ (where $\\lambda_C$ is the reduced Compton wavelength and $n_0$ is the particle number density), associated with the UR pressure of degenerate electrons, shifts the stable (unstable) regions at $n_{0}\\sim10^{30}$ cm$^{-3}$ to unstable (stable) ones at higher densities, i.e. $n_{0}\\gtrsim7\\times10^{33}$. It is also found that higher the values of $n_{0}$, the lower is the growth rate of MI with cut-offs at lower wave numbers of modulation. Furthermore, the dynamical evolution of the wave packet...
Directory of Open Access Journals (Sweden)
Meng-Meng Jiang
2016-01-01
Full Text Available Under the weaker assumption on nonlinear functions, the adaptive finite-time stabilization of more general high-order nonlinear systems with dynamic and parametric uncertainties is solved in this paper. To solve this problem, finite-time input-to-state stability (FTISS is used to characterize the unmeasured dynamic uncertainty. By skillfully combining Lyapunov function, sign function, backstepping, and finite-time input-to-state stability approaches, an adaptive state feedback controller is designed to guarantee high-order nonlinear systems are globally finite-time stable.
Flowing with Time: a New Approach to Nonlinear Cosmological Perturbations
Pietroni, Massimo
2008-01-01
Nonlinear effects are crucial in order to compute the cosmological matter power spectrum to the accuracy required by future generation surveys. Here, a new approach is presented, in which the power spectrum and the bispectrum are obtained -at any redshift and for any momentum scale- by integrating a coupled system of differential equations. The solution of the equations corresponds, in perturbation theory, to the summation of an infinite class of corrections. Compared to other resummation frameworks, the scheme discussed here is particularly suited to cosmologies other than LambdaCDM, such as those based on modifications of gravity and those containing massive neutrinos. As a first application, we compute the Baryonic Acoustic Oscillation feature of the power spectrum, and compare the results with perturbation theory, the halo model, and N-body simulations. The density-velocity and velocity-velocity power spectra are also computed, showing that they are much less contaminated by nonlinearities than the densit...
Exact control of parity-time symmetry in periodically modulated nonlinear optical couplers
Yang, Baiyuan; Hu, QiangLin; Yu, XiaoGuang
2016-01-01
We propose a mechanism for realization of exact control of parity-time (PT) symmetry by using a periodically modulated nonlinear optical coupler with balanced gain and loss. It is shown that for certain appropriately chosen values of the modulation parameters, we can construct a family of exact analytical solutions for the two-mode equations describing the dynamics of such nonlinear couplers. These exact solutions give explicit examples that allow us to precisely manipulate the system from nonlinearity-induced symmetry breaking to PT symmetry, thus providing an analytical approach to the all-optical signal control in nonlinear PT-symmetric structures.
Nonlinear time series theory, methods and applications with R examples
Douc, Randal; Stoffer, David
2014-01-01
FOUNDATIONSLinear ModelsStochastic Processes The Covariance World Linear Processes The Multivariate Cases Numerical Examples ExercisesLinear Gaussian State Space Models Model Basics Filtering, Smoothing, and Forecasting Maximum Likelihood Estimation Smoothing Splines and the Kalman Smoother Asymptotic Distribution of the MLE Missing Data Modifications Structural Component Models State-Space Models with Correlated Errors Exercises Beyond Linear ModelsNonlinear Non-Gaussian Data Volterra Series Expansion Cumulants and Higher-Order Spectra Bilinear Models Conditionally Heteroscedastic Models Thre
Recurrence for discrete time unitary evolutions
Grünbaum, F A; Werner, A H; Werner, R F
2012-01-01
We consider quantum dynamical systems specified by a unitary operator U and an initial state vector \\phi. In each step the unitary is followed by a projective measurement checking whether the system has returned to the initial state. We call the system recurrent if this eventually happens with probability one. We show that recurrence is equivalent to the absence of an absolutely continuous part from the spectral measure of U with respect to \\phi. We also show that in the recurrent case the expected first return time is an integer or infinite, for which we give a topological interpretation. A key role in our theory is played by the first arrival amplitudes, which turn out to be the (complex conjugated) Taylor coefficients of the Schur function of the spectral measure. On the one hand, this provides a direct dynamical interpretation of these coefficients; on the other hand it links our definition of first return times to a large body of mathematical literature.
Wideband nonlinear time reversal seismo-acoustic method for landmine detection.
Sutin, Alexander; Libbey, Brad; Fillinger, Laurent; Sarvazyan, Armen
2009-04-01
Acoustic and seismic waves provide a method to localize compliant mines by vibrating the top plate and a thin soil layer above the mine. This vibration is mostly linear, but also includes a small nonlinear deviation. The main goal of this paper is to introduce a method of processing that uses phase-inversion to observe nonlinear effects in a wide frequency band. The method extracts a nonlinear part of surface velocity from two similar broadcast signals of opposite sign by summing and cancelling the linear components and leaving the nonlinear components. This phase-inversion method is combined with time reversal focusing to provide increased seismic vibration and enhance the nonlinear effect. The experiments used six loudspeakers in a wood box placed over sand in which inert landmines were buried. The nonlinear surface velocity of the sand with a mine compared to the sand without a mine was greater as compared to a linear technique.
Directory of Open Access Journals (Sweden)
Mourad Kchaou
2017-01-01
Full Text Available This paper addresses the problem of sliding mode control (SMC design for a class of uncertain switched descriptor systems with state delay and nonlinear input. An integral sliding function is designed and an adaptive sliding mode controller for the reaching motion is then synthesised such that the trajectories of the resulting closed-loop system can be driven onto a prescribed sliding surface and maintained there for all subsequent times. Moreover, based on a new Lyapunov-Krasovskii functional, a delay-dependent sufficient condition is established such that the admissibility as well as the H∞ performance requirement of the sliding mode dynamics can be guaranteed in the presence of time delay, external disturbances, and nonlinear input which comprises dead-zones and/or sector nonlinearities. The major contributions of this paper of this approach include (i the closed-loop system exhibiting strong robustness against nonlinear dynamics and (ii the control scheme enjoying the chattering-free characteristic. Finally, two representative examples are given to illustrate the theoretical developments.
DEFF Research Database (Denmark)
Nielsen, Søren R. K.; Peng, Yongbo; Sichani, Mahdi Teimouri
2016-01-01
The paper deals with the response and reliability analysis of hysteretic or geometric nonlinear uncertain dynamical systems of arbitrary dimensionality driven by stochastic processes. The approach is based on the probability density evolution method proposed by Li and Chen (Stochastic dynamics...... of structures, 1st edn. Wiley, London, 2009; Probab Eng Mech 20(1):33–44, 2005), which circumvents the dimensional curse of traditional methods for the determination of non-stationary probability densities based on Markov process assumptions and the numerical solution of the related Fokker–Planck and Kolmogorov......–Feller equations. The main obstacle of the method is that a multi-dimensional convolution integral needs to be carried out over the sample space of a set of basic random variables, for which reason the number of these need to be relatively low. In order to handle this problem an approach is suggested, which...
Holzwarth, V R
2003-01-01
Observations of magnetically active close binaries with orbital periods of a few days reveal the existence of starspots at preferred longitudes (with respect to the direction of the companion star). We numerically investigate the non-linear dynamics and evolution of magnetic flux tubes in the convection zoneof a fast-rotating component of a close binary system and explore whether the tidal effects are able to generate non-uniformities in the surface distribution of erupting flux tubes. Assuming a synchronised system with a rotation period of two days and consisting of two solar-type components, both the tidal force and the deviation of the stellar structure from spherical shape are considered in lowest-order perturbation theory. The magnetic field is initially stored in the form of toroidal magnetic flux rings within the stably stratified overshoot region beneath the convection zone. Once the field has grown sufficiently strong, instabilities initiate the formation of rising flux loops, which rise through the...
Michaelian, Karo
2013-01-01
The most important thermodynamic work performed by life today is the dissipation of the solar photon flux into heat through organic pigments in water. From this thermodynamic perspective, biological evolution is thus just the dispersal of organic pigments and water throughout Earth's surface, while adjusting the gases of Earth's atmosphere to allow the most intense part of the solar spectrum to penetrate the atmosphere and reach the surface to be intercepted by these pigments. The covalent bonding of atoms in organic pigments provides excited levels compatible with the energies of these photons. Internal conversion through vibrational relaxation to the ground state of these excited molecules when in water leads to rapid dissipation of the solar photons into heat, and this is the major source of entropy production on Earth. A non-linear irreversible thermodynamic analysis shows that the proliferation of organic pigments on Earth is a direct consequence of the pigments catalytic properties in dissipating the so...
Nonlinear evolution of cylindrical gravitational waves: Numerical method and physical aspects
Celestino, Juliana; de Oliveira, H. P.; Rodrigues, E. L.
2016-05-01
General cylindrical waves are the simplest axisymmetrical gravitational waves that contain both + and × modes of polarization. In this paper, we have studied the evolution of general cylindrical gravitational waves in the realm of the characteristic scheme with a numerical code based on the Galerkin-Collocation method. The investigation consists of the numerical realization of concepts such as Bondi mass and the news functions adapted to cylindrical symmetry. The Bondi mass decays due to the presence of the news functions associated with both polarization modes. We have interpreted each polarization mode as channels from which mass is extracted. Under this perspective, we have presented the enhancement effect of the polarization mode + due to the nonlinear interaction with the mode ×. After discussing the role of matter in cylindrical symmetry, we have extended the numerical code to include electromagnetic fields.
H∞ Control for Nonlinear Stochastic Systems with Time-Delay and Multiplicative Noise
Directory of Open Access Journals (Sweden)
Ming Gao
2015-01-01
Full Text Available This paper studies the infinite horizon H∞ control problem for a general class of nonlinear stochastic systems with time-delay and multiplicative noise. The exponential/asymptotic mean square H∞ control design of delayed nonlinear stochastic systems is presented by solving Hamilton-Jacobi inequalities. Two numerical examples are provided to show the effectiveness of the proposed design method.
Analysis of nonlinear systems with time varying inputs and its application to gain scheduling
Directory of Open Access Journals (Sweden)
J.-T. Lim
1996-01-01
Full Text Available An analytical framework for analysis of a class of nonlinear systems with time varying inputs is presented. It is shown that the trajectories of the transformed nonlinear systems are uniformly bounded with an ultimate bound under certain conditions shown in this paper. The result obtained is useful for applications, in particular, analysis and design of gain scheduling.
OSCILLATION FOR NONLINEAR SECOND-ORDER DYNAMIC EQUATIONS ON TIME SCALES
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
Through the use of generalized Riccati transformation techniques, we establish some oscillation criteria for one type of nonlinear dynamic equation on time scales. Several examples, including a semilinear dynamic equation and a nonlinear Emden-Fowler dynamic equation, are also given to illustrate these criteria and to improve the results obtained in some references.
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.
Absolute stability of nonlinear systems with time delays and applications to neural networks
Directory of Open Access Journals (Sweden)
Xinzhi Liu
2001-01-01
Full Text Available In this paper, absolute stability of nonlinear systems with time delays is investigated. Sufficient conditions on absolute stability are derived by using the comparison principle and differential inequalities. These conditions are simple and easy to check. In addition, exponential stability conditions for some special cases of nonlinear delay systems are discussed. Applications of those results to cellular neural networks are presented.
Long-time asymptotics for the defocusing integrable discrete nonlinear Schr\\"odinger equation
YAMANE, HIDESHI
2011-01-01
We investigate the long-time asymptotics for the defocusing integrable discrete nonlinear Schr\\"odinger equation by means of the Deift-Zhou nonlinear steepest descent method. The leading term is a sum of two terms that oscillate with decay of order $t^{-1/2}$.
Long-time asymptotics for the defocusing integrable discrete nonlinear Schrödinger equation
YAMANE, HIDESHI
2014-01-01
We investigate the long-time asymptotics for the defocusing integrable discrete nonlinear Schrödinger equation of Ablowitz-Ladik by means of the inverse scattering transform and the Deift-Zhou nonlinear steepest descent method. The leading part is a sum of two terms that oscillate with decay of order $t^{-1/2}$.
Finite time blow-up for a wave equation with a nonlocal nonlinearity
Fino, Ahmad; Georgiev, Vladimir
2010-01-01
In this article, we study the local existence of solutions for a wave equation with a nonlocal in time nonlinearity. Moreover, a blow-up results are proved under some conditions on the dimensional space, the initial data and the nonlinear forcing term.
Analysis of Nonlinear Discrete Time Active Control System with Boring Chatter
Directory of Open Access Journals (Sweden)
Shujing Wu
2014-03-01
Full Text Available In this work we study the design and analysis for nonlinear discrete time active control system with boring charter. It is shown that most analysis result for continuous time nonlinear system can be extended to the discrete time case. In previous studies, a method of nonlinear Model Following Control System (MFCS was proposed by Okubo (1985. In this study, the method of nonlinear MFCS will be extended to nonlinear discrete time system with boring charter. Nonlinear systems which are dealt in this study have the property of norm constraints ║ƒ (v (k║&le&alpha+&betaβ║v (k║&gamma, where &alpha&ge0, &beta&ge0, 0&le&gamma&le1. When 0&le&gamma&le1. It is easy to extend the method to discrete time systems. But in the case &gamma = 1 discrete time systems, the proof becomes difficult. In this case, a new criterion is proposed to ensure that internal states are stable. We expect that this method will provide a useful tool in areas related to stability analysis and design for nonlinear discrete time systems as well.
Nonlinear evolution of subsonic and supersonic disturbances on a compressible free shear layer
Leib, S. J.
1991-01-01
The effects of a nonlinear-nonequilibrium-viscous critical layer on the spatial evolution of subsonic and supersonic instability modes on a compressible free shear layer is considered. It is shown that the instability wave amplitude is governed by an integrodifferential equation with cubic-type nonlinearity. Numerical and asymptotic solutions to this equation show that the amplitude either ends in a singularity at a finite downstream distance or reaches an equilibrium value, depending on the Prandtl number, viscosity law, viscous parameter and a real parameter which is determined by the linear inviscid stability theory. A necessary condition for the existence of the equilibrium solution is derived, and whether or not this condition is met is determined numerically for a wide range of physical parameters including both subsonic and supersonic disturbances. it is found that no equilibrium solution exists for the subsonic modes unless the temperature ratio of the low-to-high-speed streams exceeds a critical value, while equilibrium solutions for the most rapidly growing supersonic mode exist over most of the parameter range examined.
Time evolution of superradiant instabilities for charged black holes in a cavity
Degollado, Juan Carlos
2013-01-01
Frequency domain studies have recently demonstrated that charged scalar fields exhibit fast growing superradiant instabilities when interacting with charged black holes in a cavity. Here, we present a time domain analysis of the long time evolution of test charged scalar field configurations on the Reissner-Nordstr\\"om background, with or without a mirror-like boundary condition. Initial data is taken to be either a Gaussian wave packet or a regularised (near the horizon) quasi-bound state. Then, Fourier transforming the data obtained in the evolution confirms the results obtained in the frequency domain analysis, in particular for the fast growing modes. We show that spherically symmetric (l=0) modes have even faster growth rates than the l=1 modes for `small' field charge. Thus, our study confirms that this setup is particularly promising for considering the non-linear development of the superradiant instability, since the fast growth makes the signal overcome the numerical error that dominates for small gr...
Castaños, Octavio; Schuch, Dieter; Rosas-Ortiz, Oscar
2013-02-01
Based on the Gaussian wave packet solution for the harmonic oscillator and the corresponding creation and annihilation operators, a generalization is presented that also applies for wave packets with time-dependent width as they occur for systems with different initial conditions, time-dependent frequency or in contact with a dissipative environment. In all these cases, the corresponding coherent states, position and momentum uncertainties and quantum mechanical energy contributions can be obtained in the same form if the creation and annihilation operators are expressed in terms of a complex variable that fulfils a nonlinear Riccati equation which determines the time-evolution of the wave packet width. The solutions of this Riccati equation depend on the physical system under consideration and on the (complex) initial conditions and have close formal similarities with general superpotentials leading to isospectral potentials in supersymmetric quantum mechanics. The definition of the generalized creation and annihilation operator is also in agreement with a factorization of the operator corresponding to the Ermakov invariant that exists in all cases considered.
Synthesis of nonlinear discrete control systems via time-delay affine Takagi-Sugeno fuzzy models.
Chang, Wen-Jer; Chang, Wei
2005-04-01
The affine Takagi-Sugeno (TS) fuzzy model played a more important role in nonlinear control because it can be used to approximate the nonlinear systems more than the homogeneous TS fuzzy models. Besides, it is known that the time delays exist in physical systems and the previous works did not consider the time delay effects in the analysis of affine TS fuzzy models. Hence a parallel distributed compensation based fuzzy controller design issue for discrete time-delay affine TS fuzzy models is considered in this paper. The time-delay effect is considered in the discrete affine TS fuzzy models and the stabilization issue is developed for the nonlinear time-delay systems. Finally, a numerical simulation for a time-delayed nonlinear truck-trailer system is given to show the applications of the present approach.
Pola, Giordano; Di Benedetto, Maria Domenica
2010-01-01
Time-delay systems are an important class of dynamical systems that provide a solid mathematical framework to deal with many application domains of interest. In this paper we focus on nonlinear control systems with unknown and time-varying delay signals and we propose one approach to the control design of such systems, which is based on the construction of symbolic models. Symbolic models are abstract descriptions of dynamical systems in which one symbolic state and one symbolic input correspond to an aggregate of states and an aggregate of inputs. We first introduce the notion of incremental input-delay-to-state stability and characterize it by means of Liapunov-Krasovskii functionals. We then derive sufficient conditions for the existence of symbolic models that are shown to be alternating approximately bisimilar to the original system. Further results are also derived which prove the computability of the proposed symbolic models in a finite number of steps.
Dynamic structure evolution of time-dependent network
Zhang, Beibei; Zhou, Yadong; Xu, Xiaoyan; Wang, Dai; Guan, Xiaohong
2016-08-01
In this paper, we research the long-voided problem of formulating the time-dependent network structure evolution scheme, it focus not only on finding new emerging vertices in evolving communities and new emerging communities over the specified time range but also formulating the complex network structure evolution schematic. Previous approaches basically applied to community detection on time static networks and thus failed to consider the potentially crucial and useful information latently embedded in the dynamic structure evolution process of time-dependent network. To address these problems and to tackle the network non-scalability dilemma, we propose the dynamic hierarchical method for detecting and revealing structure evolution schematic of the time-dependent network. In practice and specificity, we propose an explicit hierarchical network evolution uncovering algorithm framework originated from and widely expanded from time-dependent and dynamic spectral optimization theory. Our method yields preferable results compared with previous approaches on a vast variety of test network data, including both real on-line networks and computer generated complex networks.
Adaptive robust stabilisation for a class of uncertain nonlinear time-delay dynamical systems
Wu, Hansheng
2013-02-01
The problem of adaptive robust stabilisation is considered for a class of uncertain nonlinear dynamical systems with multiple time-varying delays. It is assumed that the upper bounds of the nonlinear delayed state perturbations are unknown and that the time-varying delays are any non-negative continuous and bounded functions which do not require that their derivatives have to be less than one. In particular, it is only required that the nonlinear uncertainties, which can also include time-varying delays, are bounded in any non-negative nonlinear functions which are not required to be known for the system designer. For such a class of uncertain nonlinear time-delay systems, a new method is presented whereby a class of continuous memoryless adaptive robust state feedback controllers with a rather simpler structure is proposed. It is also shown that the solutions of uncertain nonlinear time-delay systems can be guaranteed to be uniformly exponentially convergent towards a ball which can be as small as desired. Finally, as an application, an uncertain nonlinear time-delay ecosystem with two competing species is given to demonstrate the validity of the results.
Evolution of perturbed dynamical systems: analytical computation with time independent accuracy
Gurzadyan, A. V.; Kocharyan, A. A.
2016-12-01
An analytical method for investigation of the evolution of dynamical systems with independent on time accuracy is developed for perturbed Hamiltonian systems. The error-free estimation using of computer algebra enables the application of the method to complex multi-dimensional Hamiltonian and dissipative systems. It also opens principal opportunities for the qualitative study of chaotic trajectories. The performance of the method is demonstrated on perturbed two-oscillator systems. It can be applied to various non-linear physical and astrophysical systems, e.g. to long-term planetary dynamics.
Evolution of perturbed dynamical systems: analytical computation with time independent accuracy
Energy Technology Data Exchange (ETDEWEB)
Gurzadyan, A.V. [Russian-Armenian (Slavonic) University, Department of Mathematics and Mathematical Modelling, Yerevan (Armenia); Kocharyan, A.A. [Monash University, School of Physics and Astronomy, Clayton (Australia)
2016-12-15
An analytical method for investigation of the evolution of dynamical systems with independent on time accuracy is developed for perturbed Hamiltonian systems. The error-free estimation using of computer algebra enables the application of the method to complex multi-dimensional Hamiltonian and dissipative systems. It also opens principal opportunities for the qualitative study of chaotic trajectories. The performance of the method is demonstrated on perturbed two-oscillator systems. It can be applied to various non-linear physical and astrophysical systems, e.g. to long-term planetary dynamics. (orig.)
Evolution of perturbed dynamical systems: analytical computation with time independent accuracy
Gurzadyan, A V
2016-01-01
An analytical method for investigation of the evolution of dynamical systems {\\it with independent on time accuracy} is developed for perturbed Hamiltonian systems. The error-free estimation using of computer algebra enables the application of the method to complex multi-dimensional Hamiltonian and dissipative systems. It also opens principal opportunities for the qualitative study of chaotic trajectories. The performance of the method is demonstrated on perturbed two-oscillator systems. It can be applied to various non-linear physical and astrophysical systems, e.g. to the long-term planetary dynamics.
EXISTENCE OF TIME PERIODIC SOLUTIONS FOR A DAMPED GENERALIZED COUPLED NONLINEAR WAVE EQUATIONS
Institute of Scientific and Technical Information of China (English)
房少梅; 郭柏灵
2003-01-01
The time periodic solution problem of damped generalized coupled nonlinear wave equations with periodic boundary condition was studied. By using the Galerkin method to construct the approximating sequence of time periodic solutions, a priori estimate and Laray-Schauder fixed point theorem to prove the convergence of the approximate solutions, the existence of time periodic solutions for a damped generalized coupled nonlinear wave equations can be obtained.
Faes, Luca; Zhao, He; Chon, Ki H; Nollo, Giandomenico
2009-03-01
We propose a method to extend to time-varying (TV) systems the procedure for generating typical surrogate time series, in order to test the presence of nonlinear dynamics in potentially nonstationary signals. The method is based on fitting a TV autoregressive (AR) model to the original series and then regressing the model coefficients with random replacements of the model residuals to generate TV AR surrogate series. The proposed surrogate series were used in combination with a TV sample entropy (SE) discriminating statistic to assess nonlinearity in both simulated and experimental time series, in comparison with traditional time-invariant (TIV) surrogates combined with the TIV SE discriminating statistic. Analysis of simulated time series showed that using TIV surrogates, linear nonstationary time series may be erroneously regarded as nonlinear and weak TV nonlinearities may remain unrevealed, while the use of TV AR surrogates markedly increases the probability of a correct interpretation. Application to short (500 beats) heart rate variability (HRV) time series recorded at rest (R), after head-up tilt (T), and during paced breathing (PB) showed: 1) modifications of the SE statistic that were well interpretable with the known cardiovascular physiology; 2) significant contribution of nonlinear dynamics to HRV in all conditions, with significant increase during PB at 0.2 Hz respiration rate; and 3) a disagreement between TV AR surrogates and TIV surrogates in about a quarter of the series, suggesting that nonstationarity may affect HRV recordings and bias the outcome of the traditional surrogate-based nonlinearity test.
Matsas, V J; Richardson, D J; Newson, T P; Payne, D N
1993-03-01
A full characterization of a self-starting, passively mode-locked soliton ring fiber laser in terms of its various modes of mode-locked operation, cavity length, and type of fiber used is presented. Direct evidence, based on state-of-polarization measurements, that nonlinear polarization evolution is the responsible mode-locking mechanism is also given.
Energy Technology Data Exchange (ETDEWEB)
Liu Chunping
2003-06-02
Using a direct algebraic method, more new exact solutions of the Kolmogorov-Petrovskii-Piskunov equation are presented by formula form. Then a theorem concerning the relation between the kink-type solution and the kink-bell-type solution of nonlinear evolution equations is given. Finally, the applications of the theorem to several well-known equations in physics are also discussed.
Nonlinear Time Series Model for Shape Classification Using Neural Networks
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
A complex nonlinear exponential autoregressive (CNEAR) model for invariant feature extraction is developed for recognizing arbitrary shapes on a plane. A neural network is used to calculate the CNEAR coefficients. The coefficients, which constitute the feature set, are proven to be invariant to boundary transformations such as translation, rotation, scale and choice of starting point in tracing the boundary. The feature set is then used as the input to a complex multilayer perceptron (C-MLP) network for learning and classification. Experimental results show that complicated shapes can be accurately recognized even with the low-order model and that the classification method has good fault tolerance when noise is present.
Neural-network-based approximate output regulation of discrete-time nonlinear systems.
Lan, Weiyao; Huang, Jie
2007-07-01
The existing approaches to the discrete-time nonlinear output regulation problem rely on the offline solution of a set of mixed nonlinear functional equations known as discrete regulator equations. For complex nonlinear systems, it is difficult to solve the discrete regulator equations even approximately. Moreover, for systems with uncertainty, these approaches cannot offer a reliable solution. By combining the approximation capability of the feedforward neural networks (NNs) with an online parameter optimization mechanism, we develop an approach to solving the discrete nonlinear output regulation problem without solving the discrete regulator equations explicitly. The approach of this paper can be viewed as a discrete counterpart of our previous paper on approximately solving the continuous-time nonlinear output regulation problem.
Time Delay Evolution of Five Active Galactic Nuclei
Indian Academy of Sciences (India)
A. Kovačević; L. Č. Popović; A. I. Shapovalova; D. Ilić; A. N. Burenkov; V. H. Chavushyan
2015-12-01
Here we investigate light curves of the continuum and emission lines of five type 1 active galactic nuclei (AGN) from our monitoring campaign, to test time-evolution of their time delays. Using both modeled and observed AGN light curves, we apply Gaussian kernel-based estimator to capture variation of local patterns of their time evolving delays. The largest variations of time delays of all objects occur in the period when continuum or emission lines luminosity is the highest. However, Gaussian kernel-based method shows instability in the case of NGC 5548, 3C 390.3, E1821+643 and NGC 4051 possibly due to numerical discrepancies between damped random walk (DRW) time scale of light curves and sliding time windows of the method. The temporal variations of time lags of Arp 102B can correspond to the real nature of the time lag evolution.
On the time delay evolution of five Active Galactic Nuclei
Kovacevic, Andjelka; Shapovalova, Alla I; Ilic, Dragana; Burenkov, Aleksandr N; Chavushyan, Vahram H
2015-01-01
Here we investigate light curves of the continuum and emission lines of five type 1 active galactic nuclei (AGN) from our monitoring campaign, to test time-evolution of their time delays.Using both modeled and observed AGN light curves we apply Gaussian-kernel based estimator to capture variation of local patterns of their time evolving delays. The largest variations of time delays of all objects occur in the period when continuum or emission lines luminosity is the highest. However, Gaussian kernel based method shows instability in the case of NGC 5548, 3C 390.3, E1821+643 and NGC 4051 possible due to numerical discrepancies between Damped Random Walk (DRW) time scale of light curves and sliding time windows of the method. The temporal variations of time lags of Arp 102B can correspond to the real nature of the time lag evolution.
Institute of Scientific and Technical Information of China (English)
顾成奎; 王正欧; 孙雅明
2003-01-01
A new method for identifying nonlinear time-varying systems with unknown structure is presented. The method extends the application area of basis sequence identification. The essential idea is to utilize the learning and nonlinear approximating ability of neural networks to model the non-linearity of the system, characterize time-varying dynamics of the system by the time-varying parametric vector of the network, then the parametric vector of the network is approximated by a weighted sum of known basis sequences. Because of black-box modeling ability of neural networks, the presented method can identify nonlinear time-varying systems with unknown structure. In order to improve the real-time capability of the algorithm, the neural network is trained by a simple fast learning algorithm based on local least squares presented by the authors. The effectiveness and the performance of the method are demonstrated by some simulation results.
Castro López, R.; Sun, Guo-Hua; Camacho-Nieto, O.; Yáñez-Márquez, C.; Dong, Shi-Hai
2017-09-01
We present analytical matter-wave solutions to a generalized Gross-Pitaevskii (GGP) equation with several new time and space varying nonlinearity coefficients and external fields. This is realized by taking a suitable similarity transformation to the GGP equation which makes the original partial differential equation into a stationary and ordinary differential equation. We report a few families of analytical solutions of the GGP equation with several new time and space varying nonlinearity interactions, in which some physically relevant soliton solutions are found. The profile features of the evolution wave functions depend on the different choices of the composite functions ξ.
Ajaev; Davis
2000-02-01
Directional solidification of a dilute binary alloy in a Hele-Shaw cell is modeled by a long-wave nonlinear evolution equation with zero flux and contact-angle conditions at the walls. The basic steady-state solution and its linear stability criteria are found analytically, and the nonlinear system is solved numerically. Concave-down (toward the solid) interfaces under physically realistic conditions are found to be more unstable than the planar front. Weakly nonlinear analysis indicates that subcritical bifurcation is promoted, the domain of modulational instability is expanded and transition to three-dimensional patterns is delayed due to the contact-angle condition. In the strongly nonlinear regime fully three-dimensional steady-state solutions are found whose characteristic amplitude is larger than that for the two-dimensional problem. In the subcritical regime secondary bifurcation to stable solutions is promoted.
Time evolution of the wave equation using rapid expansion method
Pestana, Reynam C.
2010-07-01
Forward modeling of seismic data and reverse time migration are based on the time evolution of wavefields. For the case of spatially varying velocity, we have worked on two approaches to evaluate the time evolution of seismic wavefields. An exact solution for the constant-velocity acoustic wave equation can be used to simulate the pressure response at any time. For a spatially varying velocity, a one-step method can be developed where no intermediate time responses are required. Using this approach, we have solved for the pressure response at intermediate times and have developed a recursive solution. The solution has a very high degree of accuracy and can be reduced to various finite-difference time-derivative methods, depending on the approximations used. Although the two approaches are closely related, each has advantages, depending on the problem being solved. © 2010 Society of Exploration Geophysicists.
Time rescaling and pattern formation in biological evolution.
Igamberdiev, Abir U
2014-09-01
Biological evolution is analyzed as a process of continuous measurement in which biosystems interpret themselves in the environment resulting in changes of both. This leads to rescaling of internal time (heterochrony) followed by spatial reconstructions of morphology (heterotopy). The logical precondition of evolution is the incompleteness of biosystem's internal description, while the physical precondition is the uncertainty of quantum measurement. The process of evolution is based on perpetual changes in interpretation of information in the changing world. In this interpretation the external biospheric gradients are used for establishment of new features of organization. It is concluded that biological evolution involves the anticipatory epigenetic changes in the interpretation of genetic symbolism which cannot generally be forecasted but can provide canalization of structural transformations defined by the existing organization and leading to predictable patterns of form generation.
The nonlinear evolution of rogue waves generated by means of wave focusing technique
Hu, HanHong; Ma, Ning
2011-01-01
Generating the rogue waves in offshore engineering is investigated, first of all, to forecast its occurrence to protect the offshore structure from being attacked, to study the mechanism and hydrodynamic properties of rouge wave experimentally as well as the rouge/structure interaction for the structure design. To achieve these purposes demands an accurate wave generation and calculation. In this paper, we establish a spatial domain model of fourth order nonlinear Schrödinger (NLS) equation for describing deep-water wave trains in the moving coordinate system. In order to generate rogue waves in the experimental tank efficiently, we take care that the transient water wave (TWW) determines precisely the concentration of time/place. First we simulate the three-dimensional wave using TWW in the numerical tank and modeling the deepwater basin with a double-side multi-segmented wave-maker in Shanghai Jiao Tong University (SJTU) under the linear superposing theory. To discuss its nonlinearity for guiding the experiment, we set the TWW as the initial condition of the NLS equation. The differences between the linear and nonlinear simulations are presented. Meanwhile, the characteristics of the transient water wave, including water particle velocity and wave slope, are investigated, which are important factors in safeguarding the offshore structures.
Non-linear time series analysis: methods and applications to atrial fibrillation.
Hoekstra, B P; Diks, C G; Allessie, M A; Degoede, J
2001-01-01
We apply methods from non-linear statistical time series analysis to characterize electrograms of atrial fibrillation. These are based on concepts originating from the theory of non-linear dynamical systems and use the empirical reconstruction density in reconstructed phase space. Application of these methods is not restricted to deterministic chaos but is valid in a general time series context. We illustrate this by applying three recently proposed non-linear time series methods to fibrillation electrograms: 1) a test for time reversibility in atrial electrograms during paroxysmal atrial fibrillation in patients; 2) a test to detect differences in the dynamical behaviour during the pharmacological conversion of sustained atrial fibrillation in instrumented conscious goats; 3) a test for general Granger causality to identify couplings and information transport in the atria during fibrillation. We conclude that a characterization of the dynamics via the reconstruction density offers a useful framework for the non-linear analysis of electrograms of atrial fibrillation.
Oscillation Criteria for Fourth-Order Nonlinear Dynamic Equations on Time Scales
Directory of Open Access Journals (Sweden)
Xin Wu
2013-01-01
Full Text Available We establish some new oscillation criteria for nonlinear dynamic equation of the form on an arbitrary time scale with , where are positive rd-continuous functions. An example illustrating the importance of our result is included.
STABILIZATION OF NONLINEAR TIME-VARYING SYSTEMS: A CONTROL LYAPUNOV FUNCTION APPROACH
Institute of Scientific and Technical Information of China (English)
Zhongping JIANG; Yuandan LIN; Yuan WANG
2009-01-01
This paper presents a control Lyapunov function approach to the global stabilization problem for general nonlinear and time-varying systems. Explicit stabilizing feedback control laws are proposed based on the method of control Lyapunov functions and Sontag's universal formula.
Nonlinear system identification NARMAX methods in the time, frequency, and spatio-temporal domains
Billings, Stephen A
2013-01-01
Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains describes a comprehensive framework for the identification and analysis of nonlinear dynamic systems in the time, frequency, and spatio-temporal domains. This book is written with an emphasis on making the algorithms accessible so that they can be applied and used in practice. Includes coverage of: The NARMAX (nonlinear autoregressive moving average with exogenous inputs) modelThe orthogonal least squares algorithm that allows models to be built term by
Directory of Open Access Journals (Sweden)
Yan Che
2012-01-01
Full Text Available The estimation problem is investigated for a class of stochastic nonlinear systems with distributed time-varying delays and missing measurements. The considered distributed time-varying delays, stochastic nonlinearities, and missing measurements are modeled in random ways governed by Bernoulli stochastic variables. The discussed nonlinearities are expressed by the statistical means. By using the linear matrix inequality method, a sufficient condition is established to guarantee the mean-square stability of the estimation error, and then the estimator parameters are characterized by the solution to a set of LMIs. Finally, a simulation example is exploited to show the effectiveness of the proposed design procedures.
Rogue Waves of Nonlinear Schrödinger Equation with Time-Dependent Linear Potential Function
Directory of Open Access Journals (Sweden)
Ni Song
2016-01-01
Full Text Available The rogue waves of the nonlinear Schrödinger equation with time-dependent linear potential function are investigated by using the similarity transformation in this paper. The first-order and second-order rogue waves solutions are obtained and the nonlinear dynamic behaviors of these solutions are discussed in detail. In addition, the amplitudes of the rogue waves under the effect of the gravity field and external magnetic field changing with the time are analyzed by using numerical simulation. The results can be used to study the matter rogue waves in the Bose-Einstein condensates and other fields of nonlinear science.
Determining the input dimension of a neural network for nonlinear time series prediction
Institute of Scientific and Technical Information of China (English)
张胜; 刘红星; 高敦堂; 都思丹
2003-01-01
Determining the input dimension of a feed-forward neural network for nonlinear time series prediction plays an important role in the modelling.The paper first summarizes the current methods for determining the input dimension of the neural network.Then inspired by the fact that the correlation dimension of a nonlinear dynamic system is the mostimportant feature of it,the paper presents a new idea that the input dimension of the neural network for nonlinear time series prediction can be taken as an integer just greater than or equal to the correlation dimension.Finally,some wlidation examples and results are given.
Fatigue damage localization using time-domain features extracted from nonlinear Lamb waves
Hong, Ming; Su, Zhongqing; Lu, Ye; Cheng, Li
2014-03-01
Nonlinear guided waves are sensitive to small-scale fatigue damage that may hardly be identified by traditional techniques. A characterization method for fatigue damage is established based on nonlinear Lamb waves in conjunction with the use of a piezoelectric sensor network. Theories on nonlinear Lamb waves for damage detection are first introduced briefly. Then, the ineffectiveness of using pure frequency-domain information of nonlinear wave signals for locating damage is discussed. With a revisit to traditional gross-damage localization techniques based on the time of flight, the idea of using temporal signal features of nonlinear Lamb waves to locate fatigue damage is introduced. This process involves a time-frequency analysis that enables the damage-induced nonlinear signal features, which are either undiscernible in the original time history or uninformative in the frequency spectrum, to be revealed. Subsequently, a finite element modeling technique is employed, accounting for various sources of nonlinearities in a fatigued medium. A piezoelectric sensor network is configured to actively generate and acquire probing Lamb waves that involve damageinduced nonlinear features. A probability-based diagnostic imaging algorithm is further proposed, presenting results in diagnostic images intuitively. The approach is experimentally verified on a fatigue-damaged aluminum plate, showing reasonably good accuracy. Compared to existing nonlinear ultrasonics-based inspection techniques, this approach uses a permanently attached sensor network that well accommodates automated online health monitoring; more significantly, it utilizes time-domain information of higher-order harmonics from time-frequency analysis, and demonstrates a great potential for quantitative characterization of small-scale damage with improved localization accuracy.
Time-Resolved Nonlinear Absorptive Properties of Phenyleneethynylenes.
Slepkov, A. D.; Hegmann, F. A.; Tykwinski, R. R.; Marsden, J. A.; Miller, J. J.; Haley, M. M.
2004-03-01
Conjugated organic chromophores of varying polar symmetries are attractive candidate materials for two-photon absorption (TPA) applications. Central to the realization of useful TPA chromophores is a combination of optimized functionalization and special geometry. Phenyleneethynylene molecular scaffolds are small but heavily conjugated systems that display strong two-photon absorption. Furthermore, using optimized synthetic routes, the three-dimensional organization of these molecules can be conveniently controlled. The ultrafast two-photon and excited-state absorption of three substituted molecules display complex temporal behaviour. The nonlinear response of these materials depends drastically on the donor-acceptor symmetry about the central core. Understanding these trends impacts both on designing materials with desirable TPA properties and on understanding the electronic landscape in functionalized organic materials.
A polynomial criterion for adaptive stabilizability of discrete-time nonlinear systems
Li, Chanying; Xie, Liang-Liang; Guo, Lei
2006-01-01
In this paper, we will investigate the maximum capability of adaptive feedback in stabilizing a basic class of discrete-time nonlinear systems with both multiple unknown parameters and bounded noises. We will present a complete proof of the polynomial criterion for feedback capability as stated in "Robust stability of discrete-time adaptive nonlinear control" (C. Li, L.-L. Xie. and L. Guo, IFAC World Congress, Prague, July 3-8, 2005), by providing both the necessity and sufficiency analyze...
Discussion of Some Problems About Nonlinear Time Series Prediction Using v-Support Vector Machine
Institute of Scientific and Technical Information of China (English)
GAO Cheng-Feng; CHEN Tian-Lun; NAN Tian-Shi
2007-01-01
Some problems in using v-support vector machine (v-SVM) for the prediction of nonlinear time series are discussed. The problems include selection of various net parameters, which affect the performance of prediction, mixture of kernels, and decomposition cooperation linear programming v-SVM regression, which result in improvements of the algorithm. Computer simulations in the prediction of nonlinear time series produced by Mackey-Glass equation and Lorenz equation provide some improved results.
Estimation in continuous-time stochastic| volatility models using nonlinear filters
DEFF Research Database (Denmark)
Nielsen, Jan Nygaard; Vestergaard, M.; Madsen, Henrik
2000-01-01
Presents a correction to the authorship of the article 'Estimation in Continuous-Time Stochastic Volatility Models Using Nonlinear Filters,' published in the periodical 'International Journal of Theoretical and Applied Finance,' Vol. 3, No. 2., pp. 279-308.......Presents a correction to the authorship of the article 'Estimation in Continuous-Time Stochastic Volatility Models Using Nonlinear Filters,' published in the periodical 'International Journal of Theoretical and Applied Finance,' Vol. 3, No. 2., pp. 279-308....
Noise-correlation-time-mediated localization in random nonlinear dynamical systems
Cabrera, J L; De la Rubia, F J; Cabrera, Juan L.
1999-01-01
We investigate the behavior of the residence times density function for different nonlinear dynamical systems with limit cycle behavior and perturbed parametrically with a colored noise. We present evidence that underlying the stochastic resonancelike behavior with the noise correlation time, there is an effect of optimal localization of the system trajectories in the phase space. This phenomenon is observed in systems with different nonlinearities, suggesting a degree of universality.
An improved impulsive control approach to nonlinear systems with time-varying delays
Institute of Scientific and Technical Information of China (English)
Zhang Hua-Guang; Fu Jie; Ma Tie-Dong; Tong Shao-Cheng
2009-01-01
A scheme for the impulsive control of nonlinear systems with time-varying delays is investigated in this paper. Based on the Lyapunov-like stability theorem for impulsive functional differential equations (FDEs), some sufficient conditions are presented to guarantee the uniform asymptotic stability of impulsively controlled nonlinear systems with time-varying delays. These conditions are more effective and less conservative than those obtained. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed method.
Oscillation of Second-order Nonlinear Dynamic Equation on Time Scales
Institute of Scientific and Technical Information of China (English)
YANG Jia-shan
2013-01-01
The oscillation for a class of second order nonlinear variable delay dynamic equation on time scales with nonlinear neutral term and damping term was discussed in this article.By using the generalized Riccati technique,integral averaging technique and the time scales theory,some new sufficient conditions for oscillation of the equation are proposed.These results generalize and extend many known results for second order dynamic equations.Some examples are given to illustrate the main results of this article.
Quantum Dynamics in Classical Time Evolution of Correlation Functions
Wetterich, C
1997-01-01
The time-dependence of correlation functions under the influence of cla= ssical equations of motion is described by an exact evolution equation. For conservative systems thermodynamic equilibrium is a fixed point of these equations. We show that this fixed point is not universally stable, since infinitely many conserved correlation functions obstruct the approach to equilibrium. Equilibrium can therefore be reached at most for suitably av= eraged quantities or for subsystems, similar to quantum statistics. The classica= l time evolution of correlation functions shows many dynamical features of quant= um mechanics.
Institute of Scientific and Technical Information of China (English)
HAO Dong-shan; L(U) Jian
2005-01-01
The evolution of the electron phase orbits based on the multi-photon nonlinear Compton scattering with the high power laser-plasma is discussed by using Kroll-Morton-Rosenbluth theory. The random evolution of the un-captured electron phase orbits from periodicity to non-periodicity is found after the energy has been exchanged between the electron and photons. With the increase of the absorbed photon number n by an electron,this evolution will be more and more intense, while which is rapidly decreased with the enhancement of the collision non-flexibility ξ and their initial speeds of the electrons and photons, but this evolution is lower than that in the high power laser field. When the electrons are captured by the laser field, the evolution is finished, and the electrons will stably transport,and the photons don't provide the energy for these electrons any more.
Nonlinear Spinor field in isotropic space-time and dark energy models
Saha, Bijan
2016-01-01
Within the scope of isotropic FRW cosmological model the role of nonlinear spinor field in the evolution of the Universe is studied. It is found that unlike in anisotropic cosmological models in the present case the spinor field does not possess nontrivial non-diagonal components of energy-momentum tensor. The spinor description of different matter was given and evolution of the Universe corresponding to these source is illustrated. In the framework of a three fluid system the utility of spinor description of matter is established.
Finite-time H∞ filtering for non-linear stochastic systems
Hou, Mingzhe; Deng, Zongquan; Duan, Guangren
2016-09-01
This paper describes the robust H∞ filtering analysis and the synthesis of general non-linear stochastic systems with finite settling time. We assume that the system dynamic is modelled by Itô-type stochastic differential equations of which the state and the measurement are corrupted by state-dependent noises and exogenous disturbances. A sufficient condition for non-linear stochastic systems to have the finite-time H∞ performance with gain less than or equal to a prescribed positive number is established in terms of a certain Hamilton-Jacobi inequality. Based on this result, the existence of a finite-time H∞ filter is given for the general non-linear stochastic system by a second-order non-linear partial differential inequality, and the filter can be obtained by solving this inequality. The effectiveness of the obtained result is illustrated by a numerical example.
Time Evolution in the external field problem of Quantum Electrodynamics
Lazarovici, Dustin
2013-01-01
A general problem of quantum field theories is the fact that the free vacuum and the vacuum for an interacting theory belong to different, non-equivalent representations of the canonical (anti-)commutation relations. In the external field problem of QED, we encounter this problem in the form that the Dirac time evolution for an external field with non-vanishing magnetic components will not satisfy the Shale-Stinespring condition, known to be necessary and sufficient for the existence of an implementation on the fermionic Fock space. Therefore, a second quantization of the time evolution in the usual way is impossible. In this thesis, we present several rigorous approaches to QED with time-dependent, external fields and analyze in what sense a time evolution can exist in the second quantized theory. We study different constructions of the fermionic Fock space and prove their equivalence. We study and compare the results of Deckert et. al. (2010), where the time evolution is realized as unitary transformations ...
Nonlinear evolution of multi-helicity neo-classical tearing modes in rotating tokamak plasmas
Wei, Lai; Wang, Zheng-Xiong; Wang, Jialei; Yang, Xuefeng
2016-10-01
Plasma perturbations from the core and/or boundary regions of tokamaks can provide seed islands for the excitation of neo-classical tearing modes (NTMs) with negative {{ Δ }\\prime} , where {{ Δ }\\prime} is the linear instability parameter of the classical tearing mode. In this work, by means of reduced magnetohydrodynamic simulations, we numerically investigate the nonlinear evolution of multi-helicity NTMs in rotating tokamak plasmas with these two types of plasma perturbations with different boundary conditions. In the first case of initial plasma perturbations from the core region with a zero boundary condition, the meta-stable property of seed-island triggered NTM with negative {{ Δ }\\prime} is verified in the single helicity simulation. Nevertheless in the multiple helicity simulation, this seed-island triggered NTM with negative {{ Δ }\\prime} can be suppressed by a spontaneous NTM with positive {{ Δ }\\prime} through the competitive interaction between NTMs with different helicities. If a fixed poloidal rotation is taken into account in the first case, two different helicity NTMs could coexist in the saturation stage, which is different qualitatively from the process without plasma rotation. In the second case of initial plasma perturbations from the boundary region with a nonzero boundary condition, as the amplitude of plasma perturbations on the boundary increases, the mode with negative {{ Δ }\\prime} gradually changes from the driven-reconnection state to the NTM state, accompanied by an enhancement of magnetic island width in the single helicity simulation. Nevertheless in the multi-helicity simulation, the spontaneous NTM with positive {{ Δ }\\prime} can make the driven-reconnection triggered NTM with negative {{ Δ }\\prime} transfer from the NTM state back to the driven-reconnection state again. The underlying mechanism behind these transitions is analyzed step by step. Effects of fixed and unfixed poloidal rotations on the nonlinear
Unifying time evolution and optimization with matrix product states
Haegeman, Jutho; Lubich, Christian; Oseledets, Ivan; Vandereycken, Bart; Verstraete, Frank
2016-10-01
We show that the time-dependent variational principle provides a unifying framework for time-evolution methods and optimization methods in the context of matrix product states. In particular, we introduce a new integration scheme for studying time evolution, which can cope with arbitrary Hamiltonians, including those with long-range interactions. Rather than a Suzuki-Trotter splitting of the Hamiltonian, which is the idea behind the adaptive time-dependent density matrix renormalization group method or time-evolving block decimation, our method is based on splitting the projector onto the matrix product state tangent space as it appears in the Dirac-Frenkel time-dependent variational principle. We discuss how the resulting algorithm resembles the density matrix renormalization group (DMRG) algorithm for finding ground states so closely that it can be implemented by changing just a few lines of code and it inherits the same stability and efficiency. In particular, our method is compatible with any Hamiltonian for which ground-state DMRG can be implemented efficiently. In fact, DMRG is obtained as a special case of our scheme for imaginary time evolution with infinite time step.
Ayhan, Burcu; Özer, M. Naci; Bekir, Ahmet
2016-08-01
In this article, we applied the method of multiple scales for Korteweg-de Vries (KdV) type equations and we derived nonlinear Schrödinger (NLS) type equations. So we get a relation between KdV type equations and NLS type equations. In addition, exact solutions were found for KdV type equations. The ( G'} over G )-expansion methods and the ( {G'} over G, {1 over G}} )-expansion methods were proposed to establish new exact solutions for KdV type differential equations. We obtained periodic and hyperbolic function solutions for these equations. These methods are very effective for getting travelling wave solutions of nonlinear evolution equations (NEEs).
Islam, Md Shafiqul; Khan, Kamruzzaman; Akbar, M Ali; Mastroberardino, Antonio
2014-10-01
The purpose of this article is to present an analytical method, namely the improved F-expansion method combined with the Riccati equation, for finding exact solutions of nonlinear evolution equations. The present method is capable of calculating all branches of solutions simultaneously, even if multiple solutions are very close and thus difficult to distinguish with numerical techniques. To verify the computational efficiency, we consider the modified Benjamin-Bona-Mahony equation and the modified Korteweg-de Vries equation. Our results reveal that the method is a very effective and straightforward way of formulating the exact travelling wave solutions of nonlinear wave equations arising in mathematical physics and engineering.
Time-domain Adaptive Compensation Algorithm for Distortion of Nonlinear Amplifiers
Ding, Yuanming; Sun, Lianming; Sano, Akira
A new time-domain adaptive predistortion scheme is proposed to compensate nonlinearity of high power amplifiers (HPA) in OFDM systems. A Hammerstein model is adopted to approximate the input-output nonlinear distortion of HPA by using complex power series followed by linear dynamical distortion. According to the Hammerstein model structure, the compensation input to HPA is adaptively given in an on-line manner so that the linearization from the predistorter input to the HPA output can be attained even if the nonlinear input-output relation of HPA is uncertain and changeable. The effectiveness of the proposed adaptive scheme is validated through numerical simulations.
Nonlinear Analysis of Spur Gear Pair with Time-varying Mesh Stiffness
Directory of Open Access Journals (Sweden)
Rao T. V. V. L. N.
2014-07-01
Full Text Available This study presents nonlinear analysis of single degree of freedom spur gear pair with time-varying mesh stiffness. The backlash is approximated using nonlinear term. The periodic steady-state solutions of the nonlinear system are obtained by closed-form expressions using the method of multiple scales. The stability and forced vibration response of the gear system are analyzed. The effect of mesh stiffness variation on the amplitude parameter of nondimensional dynamic transmission error for primary resonance is presented. The closed-form solutions in terms of mesh stiffness variations provide design guidelines for dynamic analysis of spur gear.
Determining the minimum embedding dimension of nonlinear time series based on prediction method
Institute of Scientific and Technical Information of China (English)
Bian Chun-Hua; Ning Xin-Bao
2004-01-01
Determining the embedding dimension of nonlinear time series plays an important role in the reconstruction of nonlinear dynamics. The paper first summarizes the current methods for determining the embedding dimension.Then, inspired by the fact that the optimum modelling dimension of nonlinear autoregressive (NAR) prediction model can characterize the embedding feature of the dynamics, the paper presents a new idea that the optimum modelling dimension of the NAR model can be taken as the minimum embedding dimension. Some validation examples and results are given and the present method shows its advantage for short data series.
Evolution of nonlinear internal waves in the East and South China Seas
Liu, Antony K.; Chang, Y. Steve; Hsu, Ming-K.; Liang, Nai K.
1998-04-01
Synthetic Aperture Radar (SAR) images from ERS-I have been used to study the characteristics of internal waves northeast and south of Taiwan in the East China Sea, and east of Hainan Island in the South China Sea. Rank-ordered packets of internal solitons propagating shoreward from the edge of the continental shelf were observed in the SAR images. On the basis of the assumption of a semidiurnal tidal origin, the wave speed can be estimated and is consistent with the internal wave theory. By using the SAR images and hydrographic data, internal waves of elevation have been identified in shallow water by a thicker mixed layer as compared with the bottom layer on the continental shelf. The generation mechanism includes the influences of the tide and the Kuroshio intrusion across the continental shelf for the formations of elevation internal waves. The effects of water depth on the evolution of solitons and wave packets are modeled by the nonlinear Kortweg-deVries (KdV) type equation and linked to satellite image observations. The numerical calculations of internal wave evolution on the continental shelf have been performed and compared with the SAR observations. For a case of depression waves in deep water, the solitons first disintegrate into dispersive wave trains and then evolve to a packet of elevation waves in the shallow water area after they pass through a "turning point" of approximately equal layer depths that has been observed in the SAR image and simulated by the numerical model. The importance of the dissipation effect in the coastal area is also discussed and demonstrated.
Nonlinear detection of paleoclimate-variability transitions possibly related to human evolution.
Donges, Jonathan F; Donner, Reik V; Trauth, Martin H; Marwan, Norbert; Schellnhuber, Hans-Joachim; Kurths, Jürgen
2011-12-20
Potential paleoclimatic driving mechanisms acting on human evolution present an open problem of cross-disciplinary scientific interest. The analysis of paleoclimate archives encoding the environmental variability in East Africa during the past 5 Ma has triggered an ongoing debate about possible candidate processes and evolutionary mechanisms. In this work, we apply a nonlinear statistical technique, recurrence network analysis, to three distinct marine records of terrigenous dust flux. Our method enables us to identify three epochs with transitions between qualitatively different types of environmental variability in North and East Africa during the (i) Middle Pliocene (3.35-3.15 Ma B.P.), (ii) Early Pleistocene (2.25-1.6 Ma B.P.), and (iii) Middle Pleistocene (1.1-0.7 Ma B.P.). A deeper examination of these transition periods reveals potential climatic drivers, including (i) large-scale changes in ocean currents due to a spatial shift of the Indonesian throughflow in combination with an intensification of Northern Hemisphere glaciation, (ii) a global reorganization of the atmospheric Walker circulation induced in the tropical Pacific and Indian Ocean, and (iii) shifts in the dominating temporal variability pattern of glacial activity during the Middle Pleistocene, respectively. A reexamination of the available fossil record demonstrates statistically significant coincidences between the detected transition periods and major steps in hominin evolution. This result suggests that the observed shifts between more regular and more erratic environmental variability may have acted as a trigger for rapid change in the development of humankind in Africa.
Effect of reduction time on third order optical nonlinearity of reduced graphene oxide
Sreeja, V. G.; Vinitha, G.; Reshmi, R.; Anila, E. I.; Jayaraj, M. K.
2017-04-01
We report the influence of reduction time on structural, linear and nonlinear optical properties of reduced graphene oxide (rGO) thin films synthesized by spin coating method. We observed that the structural, linear and nonlinear optical properties can be tuned with reduction time in GO is due to the increased structural ordering because of the restoration of sp2 carbon atoms with the time of reduction. The nonlinear absorption studies by open aperture Z-scan technique exhibited a saturable absorption. The nonlinear refraction studies showed the self de focusing nature of rGO by closed aperture Z scan technique. The nonlinear absorption coefficient and saturation intensity varies with the time for reduction of GO which is attributed to the depletion of valence band and the conduction band filling effect. Our results emphasize duration for reduction of GO dependent optical nonlinearity of rGO thin films to a great extent and explore its applications Q switched mode locking laser systems for generating ultra short laser pulses and in optical sensors. The rGO coated films were characterized by X-Ray diffraction method (XRD), Fourier transform infrared spectroscopy (FTIR), Raman spectroscopy, UV-Vis absorption spectroscopy (UV-Vis), Photoluminescence (PL) and Scanning electron microscope (SEM) measurements.
Nonlinear response to a click in a time-domain model of the mammalian ear.
Meaud, Julien; Lemons, Charlsie
2015-07-01
In this paper, a state-space implementation of a previously developed frequency-domain model of the cochlea is coupled to a lumped parameter model of the middle ear. After validation of the time-domain model by comparison of its steady-state response to results obtained with a frequency-domain formulation, the nonlinear response of the cochlea to clicks is investigated. As observed experimentally, a compressive nonlinearity progressively develops within the first few cycles of the response of the basilar membrane (BM). Furthermore, a time-frequency analysis shows that the instantaneous frequency of the BM response to a click progressively approaches the characteristic frequency. This phenomenon, called glide, is predicted at all stimulus intensities, as in experiments. In typical experiments with sensitive animals, the click response is characterized by a long ringing and the response envelope includes several lobes. In order to achieve similar results, inhomogeneities are introduced in the cochlear model. Simulations demonstrate the strong link between characteristics of the frequency response, such as dispersion and frequency-dependent nonlinearity, and characteristics of the time-domain response, such as the glide and a time-dependent nonlinearity. The progressive buildup of cochlear nonlinearity in response to a click is shown to be a consequence of the glide and of frequency-dependent nonlinearity.
LS-based discrete-time adaptive nonlinear control——Feasibility and limitations
Institute of Scientific and Technical Information of China (English)
郭雷; 魏晨Institute of Systems Science; Chinese Academy of Sciences; Beijing 100080; China
1996-01-01
Global stability and instability of a class of discrete-time adaptive nonlinear control systems are investigated.The systems to be controlled are assumed to be linear in unknown parameters but nonlinear in dynamics which are characterizEd by a nonlinear function f(x).It is shown that in the scalar parameter case,when the standard least-squares (LS) method is used in estimation,the certainty equivalence adaptive control is globally stable whenever f(x) has a growth rate |f(x)| =0(||x||b) with b<8.Moreover,in the case where b≥8,it is also shown that the dosed-loop adaptive control system does not have global stability in general.Both the results found and the new analytical methods introduced may be regarded as a basic step for further study of discrete-time adaptive nonlinear control systems.
Real-Time Onboard Global Nonlinear Aerodynamic Modeling from Flight Data
Brandon, Jay M.; Morelli, Eugene A.
2014-01-01
Flight test and modeling techniques were developed to accurately identify global nonlinear aerodynamic models onboard an aircraft. The techniques were developed and demonstrated during piloted flight testing of an Aermacchi MB-326M Impala jet aircraft. Advanced piloting techniques and nonlinear modeling techniques based on fuzzy logic and multivariate orthogonal function methods were implemented with efficient onboard calculations and flight operations to achieve real-time maneuver monitoring and analysis, and near-real-time global nonlinear aerodynamic modeling and prediction validation testing in flight. Results demonstrated that global nonlinear aerodynamic models for a large portion of the flight envelope were identified rapidly and accurately using piloted flight test maneuvers during a single flight, with the final identified and validated models available before the aircraft landed.
Stability analysis of nonlinear systems by multiple time scaling. [using perturbation methods
Morino, L.
1974-01-01
The asymptotic solution for the transient analysis of a general nonlinear system in the neighborhood of the stability boundary was obtained by using the multiple-time-scaling asymptotic-expansion method. The nonlinearities are assumed to be of algebraic nature. Terms of order epsilon to the 3rd power (where epsilon is the order of amplitude of the unknown) are included in the solution. The solution indicates that there is always a limit cycle which is stable (unstable) and exists above (below) the stability boundary if the nonlinear terms are stabilizing (destabilizing). Extension of the solution to include fifth order nonlinear terms is also presented. Comparisons with harmonic balance and with multiple-time-scaling solution of panel flutter equations are also included.
On invariant analysis of some time fractional nonlinear systems of partial differential equations. I
Singla, Komal; Gupta, R. K.
2016-10-01
An investigation of Lie point symmetries for systems of time fractional partial differential equations including Ito system, coupled Burgers equations, coupled Korteweg de Vries equations, Hirota-Satsuma coupled KdV equations, and coupled nonlinear Hirota equations has been done. Using the obtained symmetries, each one of the systems is reduced to the nonlinear system of fractional ordinary differential equations involving Erdélyi-Kober fractional differential operator depending on a parameter α.
Solving Nonlinear Time Delay Control Systems by Fourier series
Directory of Open Access Journals (Sweden)
Mohammad Hadi Farahi
2014-06-01
Full Text Available In this paper we present a method to find the solution of time-delay optimal control systems using Fourier series. The method is based upon expanding various time functions in the system as their truncated Fourier series. Operational matrices of integration and delay are presented and are utilized to reduce the solution of time-delay control systems to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.
Non-smooth finite-time stabilization for a class of nonlinear systems
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
In this paper, global finite-time stabilization problem for a large class of nonlinear control systems is considered. An iterative design approach is given based on Lyapunov function. The finite time stabilizing control laws are constructed in the form of continuous but non-smooth time-invariant feedback.
Indian Academy of Sciences (India)
Wenjun Liu; Kewang Chen
2013-09-01
In this paper, we implemented the functional variable method and the modified Riemann–Liouville derivative for the exact solitary wave solutions and periodic wave solutions of the time-fractional Klein–Gordon equation, and the time-fractional Hirota–Satsuma coupled KdV system. This method is extremely simple but effective for handling nonlinear time-fractional differential equations.
Energy Technology Data Exchange (ETDEWEB)
Schüler, D.; Alonso, S.; Bär, M. [Physikalisch-Technische Bundesanstalt, Abbestrasse 2-12, 10587 Berlin (Germany); Torcini, A. [CNR-Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi - Via Madonna del Piano 10, I-50019 Sesto Fiorentino (Italy); INFN Sez. Firenze, via Sansone 1, I-50019 Sesto Fiorentino (Italy)
2014-12-15
Pattern formation often occurs in spatially extended physical, biological, and chemical systems due to an instability of the homogeneous steady state. The type of the instability usually prescribes the resulting spatio-temporal patterns and their characteristic length scales. However, patterns resulting from the simultaneous occurrence of instabilities cannot be expected to be simple superposition of the patterns associated with the considered instabilities. To address this issue, we design two simple models composed by two asymmetrically coupled equations of non-conserved (Swift-Hohenberg equations) or conserved (Cahn-Hilliard equations) order parameters with different characteristic wave lengths. The patterns arising in these systems range from coexisting static patterns of different wavelengths to traveling waves. A linear stability analysis allows to derive a two parameter phase diagram for the studied models, in particular, revealing for the Swift-Hohenberg equations, a co-dimension two bifurcation point of Turing and wave instability and a region of coexistence of stationary and traveling patterns. The nonlinear dynamics of the coupled evolution equations is investigated by performing accurate numerical simulations. These reveal more complex patterns, ranging from traveling waves with embedded Turing patterns domains to spatio-temporal chaos, and a wide hysteretic region, where waves or Turing patterns coexist. For the coupled Cahn-Hilliard equations the presence of a weak coupling is sufficient to arrest the coarsening process and to lead to the emergence of purely periodic patterns. The final states are characterized by domains with a characteristic length, which diverges logarithmically with the coupling amplitude.
Approach in Theory of Nonlinear Evolution Equations: The Vakhnenko-Parkes Equation
Directory of Open Access Journals (Sweden)
V. O. Vakhnenko
2016-01-01
Full Text Available A variety of methods for examining the properties and solutions of nonlinear evolution equations are explored by using the Vakhnenko equation (VE as an example. The VE, which arises in modelling the propagation of high-frequency waves in a relaxing medium, has periodic and solitary traveling wave solutions some of which are loop-like in nature. The VE can be written in an alternative form, known as the Vakhnenko-Parkes equation (VPE, by a change of independent variables. The VPE has an N-soliton solution which is discussed in detail. Individual solitons are hump-like in nature whereas the corresponding solution to the VE comprises N-loop-like solitons. Aspects of the inverse scattering transform (IST method, as applied originally to the KdV equation, are used to find one- and two-soliton solutions to the VPE even though the VPE’s spectral equation is third-order and not second-order. A Bäcklund transformation for the VPE is used to construct conservation laws. The standard IST method for third-order spectral problems is used to investigate solutions corresponding to bound states of the spectrum and to a continuous spectrum. This leads to N-soliton solutions and M-mode periodic solutions, respectively. Interactions between these types of solutions are investigated.
On Robust Stability of a Class of Uncertain Nonlinear Systems with Time-Varying Delay
Institute of Scientific and Technical Information of China (English)
NIAN Xiao-hong
2002-01-01
The problem of robust stability of a class of uncertain nonlinear dynamical systems with time-delay is considered. Based on the assumption that the nominal system is stable, some sufficient conditions onrobust stability of uncertain nonlinear dynamical systems with time-delay are derived. Some analytical methods and a type of Lyapunov functional are used to investigate such sufficient conditions. The results obtained in this paper are applicable to perturbed time-delay systems with unbounded time-varying delay.Some previous results are improved and a numerical example is given to demonstrate the validity of our results.
DEFF Research Database (Denmark)
Tatu, Aditya Jayant
defined subspace, the N-links bicycle chain space, i.e. the space of curves with equidistant neighboring landmark points. This in itself is a useful shape space for medical image analysis applications. The Histogram of Gradient orientation based features are many in number and are widely used......This thesis deals with two unrelated issues, restricting curve evolution to subspaces and computing image patches in the equivalence class of Histogram of Gradient orientation based features using nonlinear projection methods. Curve evolution is a well known method used in various applications like...... specific requirements like shape priors or a given data model, and due to limitations of the computer, the computed curve evolution forms a path in some finite dimensional subspace of the space of curves. We give methods to restrict the curve evolution to a finite dimensional linear or implicitly defined...
Scheduling jobs with time-resource tradeoff via nonlinear programming
Grigoriev, Alexander; Uetz, Marc
2009-01-01
We consider a scheduling problem where the processing time of any job is dependent on the usage of a discrete renewable resource, e.g. personnel. An amount of $k$ units of that resource can be allocated to the jobs at any time, and the more of that resource is allocated to a job, the smaller its pro
Nonlinear analysis of a simple model of temperature evolution in a satellite
Gaite, Jose; Pérez-Grande, Isabel
2007-01-01
We analyse a simple model of the heat transfer to and from a small satellite orbiting round a solar system planet. Our approach considers the satellite isothermal, with external heat input from the environment and from internal energy dissipation, and output to the environment as black-body radiation. The resulting nonlinear ordinary differential equation for the satellite's temperature is analysed by qualitative, perturbation and numerical methods, which show that the temperature approaches a periodic pattern (attracting limit cycle). This approach can occur in two ways, according to the values of the parameters: (i) a slow decay towards the limit cycle over a time longer than the period, or (ii) a fast decay towards the limit cycle over a time shorter than the period. In the first case, an exactly soluble average equation is valid. We discuss the consequences of our model for the thermal stability of satellites.
Nonlinear quasimodes near elliptic periodic geodesics
Albin, Pierre; Marzuola, Jeremy L; Thomann, Laurent
2011-01-01
We consider the nonlinear Schr\\"odinger equation on a compact manifold near an elliptic periodic geodesic. Using a geometric optics construction, we construct quasimodes to a nonlinear stationary problem which are highly localized near the periodic geodesic. We show the nonlinear Schr\\"odinger evolution of such a quasimode remains localized near the geodesic, at least for short times.
Energy Technology Data Exchange (ETDEWEB)
Jain, Neeraj; Büchner, Jörg [Max Planck/Princeton Center for Plasma Physics, Göttingen (Germany); Max Planck Institute for Solar System Research, Justus-Von-Liebig-Weg-3, Göttingen (Germany)
2014-07-15
Nonlinear evolution of three dimensional electron shear flow instabilities of an electron current sheet (ECS) is studied using electron-magnetohydrodynamic simulations. The dependence of the evolution on current sheet thickness is examined. For thin current sheets (half thickness =d{sub e}=c/ω{sub pe}), tearing mode instability dominates. In its nonlinear evolution, it leads to the formation of oblique current channels. Magnetic field lines form 3-D magnetic spirals. Even in the absence of initial guide field, the out-of-reconnection-plane magnetic field generated by the tearing instability itself may play the role of guide field in the growth of secondary finite-guide-field instabilities. For thicker current sheets (half thickness ∼5 d{sub e}), both tearing and non-tearing modes grow. Due to the non-tearing mode, current sheet becomes corrugated in the beginning of the evolution. In this case, tearing mode lets the magnetic field reconnect in the corrugated ECS. Later thick ECS develops filamentary structures and turbulence in which reconnection occurs. This evolution of thick ECS provides an example of reconnection in self-generated turbulence. The power spectra for both the thin and thick current sheets are anisotropic with respect to the electron flow direction. The cascade towards shorter scales occurs preferentially in the direction perpendicular to the electron flow.
Time evolution of damage in thermally induced creep rupture
Yoshioka, N.
2012-01-01
We investigate the time evolution of a bundle of fibers subject to a constant external load. Breaking events are initiated by thermally induced stress fluctuations followed by load redistribution which subsequently leads to an avalanche of breakings. We compare analytic results obtained in the mean-field limit to the computer simulations of localized load redistribution to reveal the effect of the range of interaction on the time evolution. Focusing on the waiting times between consecutive bursts we show that the time evolution has two distinct forms: at high load values the breaking process continuously accelerates towards macroscopic failure, however, for low loads and high enough temperatures the acceleration is preceded by a slow-down. Analyzing the structural entropy and the location of consecutive bursts we show that in the presence of stress concentration the early acceleration is the consequence of damage localization. The distribution of waiting times has a power law form with an exponent switching between 1 and 2 as the load and temperature are varied.
A time stepping method in analysis of nonlinear structural dynamics
Directory of Open Access Journals (Sweden)
Gholampour A. A.
2011-12-01
Full Text Available In this paper a new method is proposed for the direct time integration method for structural dynamics problems. The proposed method assumes second order variations of the acceleration at each time step. Therefore more terms in the Taylor series expansion were used compared to other methods. Because of the increase in order of variations of acceleration, this method has higher accuracy than classical methods. The displacement function is a polynomial with five constants and they are calculated using: two equations for initial conditions (from the end of previous time step, two equations for satisfying the equilibrium at both ends of the time step, and one equation for the weighted residual integration. Proposed method has higher stability and order of accuracy than the other methods.
CYCLE TIMES ASSIGNMENT OF NONLINEAR DISCRETE EVENT DYNAMIC SYSTEMS
Institute of Scientific and Technical Information of China (English)
CHEN Wende
2000-01-01
In this paper, nonautonomous models of Discrete Event Dynamic Systems (DEDS) are established by min-max function, reachability and observability are defined,the problem on cycle times assignment of DEDS, which corresponds with the important problem on poles assignment of linear systems, is studied. By Gunawardena et al.'Duality Theorem following results are obtained: Cycle times of system can be assigned under state feedback(or output feedback) if and only if system is reachable (or reachable and obserbable).
Observer-based Adaptive Iterative Learning Control for Nonlinear Systems with Time-varying Delays
Institute of Scientific and Technical Information of China (English)
Wei-Sheng Chen; Rui-Hong Li; Jing Li
2010-01-01
An observer-based adaptive iterative learning control (AILC) scheme is developed for a class of nonlinear systems with unknown time-varying parameters and unknown time-varying delays. The linear matrix inequality (LMI) method is employed to design the nonlinear observer. The designed controller contains a proportional-integral-derivative (PID) feedback term in time domain. The learning law of unknown constant parameter is differential-difference-type, and the learning law of unknown time-varying parameter is difference-type. It is assumed that the unknown delay-dependent uncertainty is nonlinearly parameterized. By constructing a Lyapunov-Krasovskii-like composite energy function (CEF), we prove the boundedness of all closed-loop signals and the convergence of tracking error. A simulation example is provided to illustrate the effectiveness of the control algorithm proposed in this paper.
Time-Dependent Nonlinear Optical Susceptibility of an Out-of-Equilibrium Soft Material
Ghofraniha, Neda; Conti, Claudio; Ruocco, Giancarlo; Zamponi, Francesco
2009-01-01
We investigate the time-dependent nonlinear optical absorption of a clay dispersion (Laponite) in an organic dye (rhodamine B) water solution displaying liquid-arrested state transition. Specifically, we determine the characteristic time τD of the nonlinear susceptibility buildup due to the Soret effect. By comparing τD with the relaxation time provided by standard dynamic light scattering measurements we report on the decoupling of the two collective diffusion times at the two very different length scales during the aging of the out-of-equilibrium system. With this demonstration experiment we also show the potentiality of nonlinear optics measurements in the study of the late stage of arrest in soft materials.
H {sub {infinity}} analysis of nonlinear stochastic time-delay systems
Energy Technology Data Exchange (ETDEWEB)
Shu Huisheng [Department of Applied Mathematics, Dong Hua University, Shanghai 200051 (China)] e-mail: hsshu@dhu.edu.cn; Wei Guoliang [Department of Applied Mathematics, Dong Hua University, Shanghai 200051 (China)
2005-10-01
In this paper, the H {sub {infinity}} analysis problem is studied for a general class of nonlinear stochastic systems with time-delay. The stochastic systems are described in terms of stochastic functional differential equations. The Razumikhin-type lemma is employed to establish sufficient conditions for the time-delay stochastic systems to be internally stable, and the H {sub {infinity}} analysis problem is studied in order to quantify the disturbance rejection attenuation level of the nonlinear stochastic time-delay system. In particular, the paper obtains the general conditions under which the L {sub 2} gain of the system is less than or equal to a given constant. Some easy-to-test criteria are also given so as to determine whether the nonlinear stochastic time-delay system under investigation is internally stable and whether it achieves certain H {sub {infinity}} performance index. Finally, illustrative examples are provided to show the usefulness of the proposed theory.
Stability for a class of nonlinear time-delay systems via Hamiltonian functional method
Institute of Scientific and Technical Information of China (English)
YANG RenMing; WANG YuZhen
2012-01-01
This paper investigates the stability of a class of nonlinear time-delay systems via Hamiltonian functional method,and proposes a number of new results on generalized Hamiltonian realization (GHR) and stability analysis for this class of systems.Firstly,the concept of GHR of general nonlinear time-delay systems is proposed,and several new GHR methods are given.Then,based on the new GHR methods obtained,the stability of time-delay systems is investigated,and several delay-dependent sufficient conditions in term of matrix inequalities are derived for the stability analysis by constructing suitable Lyapunov-Krasovskii (L-K) functionals.Finally,an illustrative example shows that the results obtained in this paper have less conservatism,and work very well in the stability analysis of some nonlinear time-delay Hamiltonian systems.
Band-phase-randomized Surrogates to assess nonlinearity in non-stationary time series
Guarin, Diego; Orozco, Alvaro
2011-01-01
Testing for nonlinearity is one of the most important preprocessing steps in nonlinear time series analysis. Typically, this is done by means of the linear surrogate data methods. But it is a known fact that the validity of the results heavily depends on the stationarity of the time series. Since most physiological signals are non-stationary, it is easy to falsely detect nonlinearity using the linear surrogate data methods. In this document, we propose a methodology to extend the procedure for generating constrained surrogate time series in order to assess nonlinearity in non-stationary data. The method is based on the band-phase-randomized surrogates, which consists (contrary to the linear surrogate data methods) in randomizing only a portion of the Fourier phases in the high frequency band. Analysis of simulated time series showed that in comparison to the linear surrogate data method, our method is able to discriminate between linear stationarity, linear non-stationary and nonlinear time series. When apply...
Real-time solution of nonlinear potential flow equations for lifting rotors
Directory of Open Access Journals (Sweden)
Jianzhe HUANG
2017-06-01
Full Text Available Analysis of rotorcraft dynamics requires solution of the rotor induced flow field. Often, the appropriate model to be used for induced flow is nonlinear potential flow theory (which is the basis of vortex-lattice methods. These nonlinear potential flow equations sometimes must be solved in real time––such as for real-time flight simulation, when observers are needed for controllers, or in preliminary design computations. In this paper, the major effects of nonlinearities on induced flow are studied for lifting rotors in low-speed flight and hover. The approach is to use a nonlinear state-space model of the induced flow based on a Galerkin treatment of the potential flow equations.
Zhong, Xiangnan; He, Haibo; Zhang, Huaguang; Wang, Zhanshan
2014-12-01
In this paper, we develop and analyze an optimal control method for a class of discrete-time nonlinear Markov jump systems (MJSs) with unknown system dynamics. Specifically, an identifier is established for the unknown systems to approximate system states, and an optimal control approach for nonlinear MJSs is developed to solve the Hamilton-Jacobi-Bellman equation based on the adaptive dynamic programming technique. We also develop detailed stability analysis of the control approach, including the convergence of the performance index function for nonlinear MJSs and the existence of the corresponding admissible control. Neural network techniques are used to approximate the proposed performance index function and the control law. To demonstrate the effectiveness of our approach, three simulation studies, one linear case, one nonlinear case, and one single link robot arm case, are used to validate the performance of the proposed optimal control method.
Naro, Daniel; Rummel, Christian; Schindler, Kaspar; Andrzejak, Ralph G.
2014-09-01
The rank-based nonlinear predictability score was recently introduced as a test for determinism in point processes. We here adapt this measure to time series sampled from time-continuous flows. We use noisy Lorenz signals to compare this approach against a classical amplitude-based nonlinear prediction error. Both measures show an almost identical robustness against Gaussian white noise. In contrast, when the amplitude distribution of the noise has a narrower central peak and heavier tails than the normal distribution, the rank-based nonlinear predictability score outperforms the amplitude-based nonlinear prediction error. For this type of noise, the nonlinear predictability score has a higher sensitivity for deterministic structure in noisy signals. It also yields a higher statistical power in a surrogate test of the null hypothesis of linear stochastic correlated signals. We show the high relevance of this improved performance in an application to electroencephalographic (EEG) recordings from epilepsy patients. Here the nonlinear predictability score again appears of higher sensitivity to nonrandomness. Importantly, it yields an improved contrast between signals recorded from brain areas where the first ictal EEG signal changes were detected (focal EEG signals) versus signals recorded from brain areas that were not involved at seizure onset (nonfocal EEG signals).
Stability analysis of a general family of nonlinear positive discrete time-delay systems
Nam, P. T.; Phat, V. N.; Pathirana, P. N.; Trinh, H.
2016-07-01
In this paper, we propose a new approach to analyse the stability of a general family of nonlinear positive discrete time-delay systems. First, we introduce a new class of nonlinear positive discrete time-delay systems, which generalises some existing discrete time-delay systems. Second, through a new technique that relies on the comparison and mathematical induction method, we establish explicit criteria for stability and instability of the systems. Three numerical examples are given to illustrate the feasibility of the obtained results.
Finite-time stabilization for a class of stochastic nonlinear systems via output feedback.
Zha, Wenting; Zhai, Junyong; Fei, Shumin; Wang, Yunji
2014-05-01
This paper investigates the problem of global finite-time stabilization in probability for a class of stochastic nonlinear systems. The drift and diffusion terms satisfy lower-triangular or upper-triangular homogeneous growth conditions. By adding one power integrator technique, an output feedback controller is first designed for the nominal system without perturbing nonlinearities. Based on homogeneous domination approach and stochastic finite-time stability theorem, it is proved that the solution of the closed-loop system will converge to the origin in finite time and stay at the origin thereafter with probability one. Two simulation examples are presented to illustrate the effectiveness of the proposed design procedure.
Adaptive neural network tracking control for a class of unknown nonlinear time-delay systems
Institute of Scientific and Technical Information of China (English)
Chen Weisheng; Li Junmin
2006-01-01
For a class of unknown nonlinear time-delay systems, an adaptive neural network (NN) control design approach is proposed. Backstepping, domination and adaptive bounding design technique are combined to construct a robust memoryless adaptive NN tracking controller. Unknown time-delay functions are approximated by NNs, such that the requirement on the nonlinear time-delay functions is relaxed. Based on Lyapunov-Krasoviskii functional, the sem-global uniformly ultimately boundedness (UUB) of all the signals in the closed-loop system is proved. The arbitrary output tracking accuracy is achieved by tuning the design parameters. The feasibility is investigated by an illustrative simulation example.
Multiple time scale based reduction scheme for nonlinear chemical dynamics
Das, D.; Ray, D. S.
2013-07-01
A chemical reaction is often characterized by multiple time scales governing the kinetics of reactants, products and intermediates. We eliminate the fast relaxing intermediates in autocatalytic reaction by transforming the original system into a new one in which the linearized part is diagonal. This allows us to reduce the dynamical system by identifying the associated time scales and subsequent adiabatic elimination of the fast modes. It has been shown that the reduced system sustains the robust qualitative signatures of the original system and at times the generic form of the return map for the chaotic system from which complex dynamics stems out in the original system can be identified. We illustrate the scheme for a three-variable cubic autocatalytic reaction and four-variable peroxidase-oxidase reaction.
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.
Hybrid time/frequency domain modeling of nonlinear components
DEFF Research Database (Denmark)
Wiechowski, Wojciech Tomasz; Lykkegaard, Jan; Bak, Claus Leth
2007-01-01
model is used as a basis for its implementation. First, the linear network part is replaced with an ideal voltage source and a time domain (EMT) simulation is performed. During the initial oscillations, harmonic content of the converter currents is calculated at every period by a fast Fourier transform...... and the periodic steady state is identified. Obtained harmonic currents are assigned to current sources and used in the frequency domain calculation in the linear network. The obtained three-phase bus voltage is then inverse Fourier transformed and assigned to the voltage source and the time domain simulation...... is performed again. This process is repeated until the change in the magnitudes and phase angles of the fundamental and low order characteristic harmonics of the bus voltage is smaller then predefined precision indexes. The method is verified against precise time domain simulation. The convergence properties...
Sasanpour, Pezhman; Shahmansouri, Afsaneh; Rashidian, Bizhan
2010-11-01
Third order nonlinear effects and its enhancement in gold nanostructures has been numerically studied. Analysis method is based on computationally solving nonlinear Maxwell's equations, considering dispersion behavior of permittivity described by Drude model and third order nonlinear susceptibility. Simulation is done by method of nonlinear finite difference time domain method, in which nonlinear equations of electric field are solved by Newton-Raphshon method. As the main outcomes of third order nonlinear susceptibility, four wave mixing and third harmonic generation terms are produced around gold nanostructures. Results of analysis on different geometries and structures show that third order nonlinearity products are more enhanced in places where electric field enhancement is occurred due to surface plasmons. Results indicates that enhancement of nonlinearities is strongly occurred in structures whose interface is dielectric. According to analysis results, nonlinear effects are highly concentrated in the vicinity of nanostructures. Hence this approach can be used in applications where localized ultraviolet light is required.
Singular perturbation methods for nonlinear dynamic systems with time delays
Energy Technology Data Exchange (ETDEWEB)
Hu, H.Y. [MOE Key Laboratory of Structure Mechanics and Control for Aircraft, Nanjing University of Aeronautics and Astronautics, 210016 Nanjing (China)], E-mail: hhyae@nuaa.edu.cn; Wang, Z.H. [MOE Key Laboratory of Structure Mechanics and Control for Aircraft, Nanjing University of Aeronautics and Astronautics, 210016 Nanjing (China)
2009-04-15
This review article surveys the recent advances in the dynamics and control of time-delay systems, with emphasis on the singular perturbation methods, such as the method of multiple scales, the method of averaging, and two newly developed methods, the energy analysis and the pseudo-oscillator analysis. Some examples are given to demonstrate the advantages of the methods. The comparisons with other methods show that these methods lead to easier computations and higher accurate prediction on the local dynamics of time-delay systems near a Hopf bifurcation.
Finite-beta effects on the nonlinear evolution of the (m = 1; n = 1) mode in tokamaks
Energy Technology Data Exchange (ETDEWEB)
Holmes, J.A.; Carreras, B.A.; Hicks, H.R.; Lynch, V.E.; Rothe, K.E.
1982-01-01
The stability and evolution of ISX-B-like plasmas are numerically studied using a reduced set of resistive magnetohydrodynamic (MHD) equations. For a sequence of equilibria stable to ideal modes, the n = 1 mode changes from a tearing branch to a pressure-driven branch as ..beta../sup p/ is increased. When this mode is unstable at low beta, it is just the (m = 1;n = 1) tearing mode. Higher n modes also become linearly unstable with increasing ..beta../sub p/; they are essentially pressure driven and have a ballooning character. For low values of beta the instability is best described as a ..beta../sub p/ distortion of the (m = 1;n = 1) tearing mode. This mode drives many other helicities through toroidal and nonlinear couplings. As ..beta../sub p/ is increased, the growth of the m = 1 island slows down in time, going from exponential to linear before reconnection occurs. If ..beta../sub p/ is large enough, the island saturates without reconnection. A broad spectrum of other modes, driven by the (m = 1;n = 1) instability, is produced. These results agree with some observed features of MHD activity in ISX-B.
Sun, Dajun D; Lee, Ping I
2015-04-06
The importance of rate of supersaturation generation on the kinetic solubility profiles of amorphous systems has recently been shown by us; however, the previous focus was limited to constant rates of supersaturation generation. The objective of the current study is to further examine the effect of nonlinear rate profiles of supersaturation generation in amorphous systems, including (1) instantaneous or infinite rate (i.e., initial degree of supersaturation), (2) first-order rate (e.g., from dissolution of amorphous drug particles), and (3) matrix diffusion regulated rate (e.g., drug release from amorphous solid dispersions (ASDs) based on cross-linked poly(2-hydroxyethyl methacrylate) (PHEMA) hydrogels), on the kinetic solubility profiles of a model poorly soluble drug indomethacin (IND) under nonsink dissolution conditions. The previously established mechanistic model taking into consideration both the crystal growth and ripening processes was extended to predict the evolution of supersaturation resulting from nonlinear rates of supersaturation generation. Our results confirm that excessively high initial supersaturation or a rapid supersaturation generation leads to a surge in maximum supersaturation followed by a rapid decrease in drug concentration owing to supersaturation-induced precipitation; however, an exceedingly low degree of supersaturation or a slow rate of supersaturation generation does not sufficiently raise the supersaturation level, which results in a lower but broader maximum kinetic solubility profile. Our experimental data suggest that an optimal area-under-the-curve of the kinetic solubility profiles exists at an intermediate initial supersaturation level for the amorphous systems studied here, which agrees well with the predicted trend. Our model predictions also support our experimental findings that IND ASD in cross-linked PHEMA exhibits a unique kinetic solubility profile because the resulting supersaturation level is governed by a matrix
Camporeale, Enrico; Zimbardo, G.
2015-01-01
We present a self-consistent Particle-in-Cell simulation of the resonant interactions between anisotropic energetic electrons and a population of whistler waves, with parameters relevant to the Earths radiation belt. By tracking PIC particles, and comparing with test-particle simulations we emphasize the importance of including nonlinear effects and time evolution in the modeling of wave-particle interactions, which are excluded in the resonant limit of quasi- linear theory routinely used in ...
Time-dependent exact solutions of the nonlinear Kompaneets equation
Energy Technology Data Exchange (ETDEWEB)
Ibragimov, N H, E-mail: nib@bth.s [Department of Mathematics and Science, Blekinge Institute of Technology, 371 79 Karlskrona (Sweden)
2010-12-17
Time-dependent exact solutions of the Kompaneets photon diffusion equation are obtained for several approximations of this equation. One of the approximations describes the case when the induced scattering is dominant. In this case, the Kompaneets equation has an additional symmetry which is used for constructing some exact solutions as group invariant solutions. (fast track communication)
Time-varying Combinations of Predictive Densities using Nonlinear Filtering
M. Billio (Monica); R. Casarin (Roberto); F. Ravazzolo (Francesco); H.K. van Dijk (Herman)
2012-01-01
textabstractWe propose a Bayesian combination approach for multivariate predictive densities which relies upon a distributional state space representation of the combination weights. Several specifications of multivariate time-varying weights are introduced with a particular focus on weight dynamics
Continuous Time Random Walks for the Evolution of Lagrangian Velocities
Dentz, Marco; Comolli, Alessandro; Borgne, Tanguy Le; Lester, Daniel R
2016-01-01
We develop a continuous time random walk (CTRW) approach for the evolution of Lagrangian velocities in steady heterogeneous flows based on a stochastic relaxation process for the streamwise particle velocities. This approach describes persistence of velocities over a characteristic spatial scale, unlike classical random walk methods, which model persistence over a characteristic time scale. We first establish the relation between Eulerian and Lagrangian velocities for both equidistant and isochrone sampling along streamlines, under transient and stationary conditions. Based on this, we develop a space continuous CTRW approach for the spatial and temporal dynamics of Lagrangian velocities. While classical CTRW formulations have non-stationary Lagrangian velocity statistics, the proposed approach quantifies the evolution of the Lagrangian velocity statistics under both stationary and non-stationary conditions. We provide explicit expressions for the Lagrangian velocity statistics, and determine the behaviors of...
Time evolution of dimethyl carbinol in water vortex rings
Omocea, Ioana-Laura; Damian, Iulia-Rodica; Simionescu, Štefan-Mugur; Bǎlan, Corneliu; Mihǎilescu, Mona
2015-02-01
The paper is concerned with the experimental study of the time evolution of a single laminar vortex ring generated at the interface between water and dimethyl carbinol. The experiments were performed by the submerged injection with a constant rate of dimethyl carbinol (isopropyl alcohol) in a water tank. The dynamics of the vortex formation was recorded at 1000 fps with a Photron Fastcam SA1 camera, equipped with a microscopic Edmund Optics objective. A symmetrical buoyant vortex ring with an elongated topology was observed at the interface between the two immiscible liquids. The analyses of the time dependence of the vortex rings disclosed three regions for the evolution of the interface: one dominated by inertia force, a transition region and a third region, dominated by buoyancy force.
Restudy on Time-Evolution of SUSY Dark Matter
Institute of Scientific and Technical Information of China (English)
FENG Tai-Fu; LI Xue-Qian; MENG Qing-Wei; REN Zhen-Yu
2002-01-01
We restudy the Lee-Weinberg time-evolution equation including the R-parity violation. We carefullyanalyze the intluence of the boundary conditions, equation of state, SUSY parameters, especially the R-parity violation,and other factors on the time-evolution of the SUSY cold dark matter. Our numerical results show that without Rparity violation, only two ranges 20 ＜ mx01 ＜ 30 GeV and 75 ＜ mx01 ＜ 110 GeV can be consistent with data, if30 ＜ mx01 ＜ 75 GeV, there must be at least two kinds of heavy particles contributing to the cold dark matter. However,with the R-parity violation, the heavy neutralino can be dark matter constituent, but it must decay and the R-parityviolation parameter is constrained by the present data.
A Time Marching Scheme for Solving Volume Integral Equations on Nonlinear Scatterers
Bagci, Hakan
2015-01-07
Transient electromagnetic field interactions on inhomogeneous penetrable scatterers can be analyzed by solving time domain volume integral equations (TDVIEs). TDVIEs are oftentimes solved using marchingon-in-time (MOT) schemes. Unlike finite difference and finite element schemes, MOT-TDVIE solvers require discretization of only the scatterers, do not call for artificial absorbing boundary conditions, and are more robust to numerical phase dispersion. On the other hand, their computational cost is high, they suffer from late-time instabilities, and their implicit nature makes incorporation of nonlinear constitutive relations more difficult. Development of plane-wave time-domain (PWTD) and FFT-based schemes has significantly reduced the computational cost of the MOT-TDVIE solvers. Additionally, latetime instability problem has been alleviated for all practical purposes with the development of accurate integration schemes and specially designed temporal basis functions. Addressing the third challenge is the topic of this presentation. I will talk about an explicit MOT scheme developed for solving the TDVIE on scatterers with nonlinear material properties. The proposed scheme separately discretizes the TDVIE and the nonlinear constitutive relation between electric field intensity and flux density. The unknown field intensity and flux density are expanded using half and full Schaubert-Wilton-Glisson (SWG) basis functions in space and polynomial temporal interpolators in time. The resulting coupled system of the discretized TDVIE and constitutive relation is integrated in time using an explicit P E(CE) m scheme to yield the unknown expansion coefficients. Explicitness of time marching allows for straightforward incorporation of the nonlinearity as a function evaluation on the right hand side of the coupled system of equations. Consequently, the resulting MOT scheme does not call for a Newton-like nonlinear solver. Numerical examples, which demonstrate the applicability
Non-Linear Wave Loads and Ship responses by a time-domain Strip Theory
DEFF Research Database (Denmark)
Xia, Jinzhu; Wang, Zhaohui; Jensen, Jørgen Juncher
1998-01-01
A non-linear time-domain strip theory for vertical wave loads and ship responses is presented. The theory is generalized from a rigorous linear time-domain strip theory representaton. The hydrodynamic memory effect due to the free surface is approximated by a higher order differential equation...
Teren, F.
1977-01-01
Minimum time accelerations of aircraft turbofan engines are presented. The calculation of these accelerations was made by using a piecewise linear engine model, and an algorithm based on nonlinear programming. Use of this model and algorithm allows such trajectories to be readily calculated on a digital computer with a minimal expenditure of computer time.
Multivariate nonlinear time series modeling of exposure and risk in road safety research
Bijleveld, F.; Commandeur, J.; Montfort, van K.; Koopman, S.J.
2010-01-01
A multivariate non-linear time series model for road safety data is presented. The model is applied in a case-study into the development of a yearly time series of numbers of fatal accidents (inside and outside urban areas) and numbers of kilometres driven by motor vehicles in the Netherlands betwee
Stability of quantized time-delay nonlinear systems : A Lyapunov-Krasowskii-functional approach
Persis, Claudio De; Mazenc, Frédéric
2009-01-01
Lyapunov-Krasowskii functionals are used to design quantized control laws for nonlinear continuous-time systems in the presence of time-invariant constant delays in the input. The quantized control law is implemented via hysteresis to avoid chattering. Under appropriate conditions, our analysis appl
Nonlinear Evolution and Final Fate of Charged Anti-de Sitter Black Hole Superradiant Instability.
Bosch, Pablo; Green, Stephen R; Lehner, Luis
2016-04-08
We describe the full nonlinear development of the superradiant instability for a charged massless scalar field coupled to general relativity and electromagnetism, in the vicinity of a Reissner-Nordström-anti-de Sitter black hole. The presence of the negative cosmological constant provides a natural context for considering perfectly reflecting boundary conditions and studying the dynamics as the scalar field interacts repeatedly with the black hole. At early times, small superradiant perturbations grow as expected from linearized studies. Backreaction then causes the black hole to lose charge and mass until the perturbation becomes nonsuperradiant, with the final state described by a stable hairy black hole. For large gauge coupling, the instability extracts a large amount of charge per unit mass, resulting in greater entropy increase. We discuss the implications of the observed behavior for the general problem of superradiance in black hole spacetimes.
Finite-time singularity in the evolution of hyperinflation episodes
Szybisz, Martin A.; Leszek Szybisz
2008-01-01
A model proposed by Sornette, Takayasu, and Zhou for describing hyperinflation regimes based on adaptive expectations expressed in terms of a power law which leads to a finite-time singularity is revisited. It is suggested to express the price index evolution explicitly in terms of the parameters introduced along the theoretical formulation avoiding any combination of them used in the original work. This procedure allows to study unambiguously the uncertainties of such parameters when an erro...
Bartelmann, Matthias; Berg, Daniel; Kozlikin, Elena; Lilow, Robert; Viermann, Celia
2014-01-01
We use the non-equlibrium statistical field theory for classical particles, recently developed by Mazenko and Das and Mazenko, together with the free generating functional we have previously derived for point sets initially correlated in phase space, to calculate the time evolution of power spectra in the free theory, i.e. neglecting particle interactions. We provide expressions taking linear and quadratic momentum correlations into account. Up to this point, the expressions are general with respect to the free propagator of the microscopic degrees of freedom. We then specialise the propagator to that expected for particles in cosmology treated within the Zel'dovich approximation and show that, to linear order in the momentum correlations, the linear growth of the cosmological power spectrum is reproduced. Quadratic momentum correlations return a first contribution to the non-linear evolution of the power spectrum, for which we derive a simple closed expression valid for arbitrary wave numbers. This expressio...
National Research Council Canada - National Science Library
Naher, Hasibun; Abdullah, Farah Aini
2013-01-01
In this article, new (G′/G)-expansion method and new generalized (G′/G)-expansion method is proposed to generate more general and abundant new exact traveling wave solutions of nonlinear evolution equations...
Regular nonlinear response of the driven Duffing oscillator to chaotic time series
Institute of Scientific and Technical Information of China (English)
YuanYe; Li Yue; Danilo P. Mandic; Yang Bao-Jun
2009-01-01
Nonlinear response of the driven Duffing oscillator to periodic or quasi-periodic signals has been well studied. In this paper, we investigate the nonlinear response of the driven Duffing oscillator to non-periodic, more specifically, chaotic time series. Through numerical simulations, we find that the driven Duffing oscillator can also show regular nonlinear response to the chaotic time series with different degree of chaos as generated by the same chaotic series generating model, and there exists a relationship between the state of the driven Duffing oscillator and the chaoticity of the input signal of the driven Duffing oscillator. One real-world and two artificial chaotic time series are used to verify the new feature of Duffing oscillator. A potential application of the new feature of Duffing oscillator is also indicated.
Tang, You-Fu; Liu, Shu-Lin; Jiang, Rui-Hong; Liu, Ying-Hui
2013-03-01
We study the correlation between detrended fluctuation analysis (DFA) and the Lempel-Ziv complexity (LZC) in nonlinear time series analysis in this paper. Typical dynamic systems including a logistic map and a Duffing model are investigated. Moreover, the influence of Gaussian random noise on both the DFA and LZC are analyzed. The results show a high correlation between the DFA and LZC, which can quantify the non-stationarity and the nonlinearity of the time series, respectively. With the enhancement of the random component, the exponent a and the normalized complexity index C show increasing trends. In addition, C is found to be more sensitive to the fluctuation in the nonlinear time series than α. Finally, the correlation between the DFA and LZC is applied to the extraction of vibration signals for a reciprocating compressor gas valve, and an effective fault diagnosis result is obtained.
Spectral functions and time evolution from the Chebyshev recursion
Wolf, F. Alexander; Justiniano, Jorge A.; McCulloch, Ian P.; Schollwöck, Ulrich
2015-03-01
We link linear prediction of Chebyshev and Fourier expansions to analytic continuation. We push the resolution in the Chebyshev-based computation of T =0 many-body spectral functions to a much higher precision by deriving a modified Chebyshev series expansion that allows to reduce the expansion order by a factor ˜1/6 . We show that in a certain limit the Chebyshev technique becomes equivalent to computing spectral functions via time evolution and subsequent Fourier transform. This introduces a novel recursive time-evolution algorithm that instead of the group operator e-i H t only involves the action of the generator H . For quantum impurity problems, we introduce an adapted discretization scheme for the bath spectral function. We discuss the relevance of these results for matrix product state (MPS) based DMRG-type algorithms, and their use within the dynamical mean-field theory (DMFT). We present strong evidence that the Chebyshev recursion extracts less spectral information from H than time evolution algorithms when fixing a given amount of created entanglement.
Sequential Monte Carlo methods for nonlinear discrete-time filtering
Bruno, Marcelo GS
2013-01-01
In these notes, we introduce particle filtering as a recursive importance sampling method that approximates the minimum-mean-square-error (MMSE) estimate of a sequence of hidden state vectors in scenarios where the joint probability distribution of the states and the observations is non-Gaussian and, therefore, closed-form analytical expressions for the MMSE estimate are generally unavailable.We begin the notes with a review of Bayesian approaches to static (i.e., time-invariant) parameter estimation. In the sequel, we describe the solution to the problem of sequential state estimation in line
Ulku, Huseyin Arda
2014-07-06
Effects of material nonlinearities on electromagnetic field interactions become dominant as field amplitudes increase. A typical example is observed in plasmonics, where highly localized fields “activate” Kerr nonlinearities. Naturally, time domain solvers are the method of choice when it comes simulating these nonlinear effects. Oftentimes, finite difference time domain (FDTD) method is used for this purpose. This is simply due to the fact that explicitness of the FDTD renders the implementation easier and the material nonlinearity can be easily accounted for using an auxiliary differential equation (J.H. Green and A. Taflove, Opt. Express, 14(18), 8305-8310, 2006). On the other hand, explicit marching on-in-time (MOT)-based time domain integral equation (TDIE) solvers have never been used for the same purpose even though they offer several advantages over FDTD (E. Michielssen, et al., ECCOMAS CFD, The Netherlands, Sep. 5-8, 2006). This is because explicit MOT solvers have never been stabilized until not so long ago. Recently an explicit but stable MOT scheme has been proposed for solving the time domain surface magnetic field integral equation (H.A. Ulku, et al., IEEE Trans. Antennas Propag., 61(8), 4120-4131, 2013) and later it has been extended for the time domain volume electric field integral equation (TDVEFIE) (S. B. Sayed, et al., Pr. Electromagn. Res. S., 378, Stockholm, 2013). This explicit MOT scheme uses predictor-corrector updates together with successive over relaxation during time marching to stabilize the solution even when time step is as large as in the implicit counterpart. In this work, an explicit MOT-TDVEFIE solver is proposed for analyzing electromagnetic wave interactions on scatterers exhibiting Kerr nonlinearity. Nonlinearity is accounted for using the constitutive relation between the electric field intensity and flux density. Then, this relation and the TDVEFIE are discretized together by expanding the intensity and flux - sing half
The effect and design of time delay in feedback control for a nonlinear isolation system
Sun, Xiuting; Xu, Jian; Fu, Jiangsong
2017-03-01
The optimum value of time delay of active control used in a nonlinear isolation system for different types of external excitation is studied in this paper. Based on the mathematical model of the nonlinear isolator with time-delayed active control, the stability, response and displacement transmissibility of the system are analyzed to obtain the standards for appropriate values of time delay and control strengths. The effects of nonlinearity and time delay on the stability and vibration response are discussed in details. For impact excitation and random excitation, the optimal value of time delay is obtained based on the vibration dissipation time via eigenvalues analysis, while for harmonic excitation, the optimal values are determined based on multiple vibration properties including natural frequency, amplitude death region and effective isolation region by the Averaging Method. This paper establishes the relationship between the parameters and vibration properties of a nonlinear isolation system which provides the guidance for optimizing time-delayed active control for different types of excitation in engineering practices.
Energy Technology Data Exchange (ETDEWEB)
Miles, A
2004-04-27
In core-collapse supernovae, strong blast waves drive interfaces susceptible to Rayleigh-Taylor (RT), Richtmyer-Meshkov (RM), and Kelvin-Helmholtz (KH) instabilities. In addition, perturbation growth can result from material expansion in large-scale velocity gradients behind the shock front. Laser-driven experiments are designed to produce a strongly shocked interface whose evolution is a scaled version of the unstable hydrogen-helium interface in core-collapse supernovae such as SN 1987A. The ultimate goal of this research is to develop an understanding of the effect of hydrodynamic instabilities and the resulting transition to turbulence on supernovae observables that remain as yet unexplained. In this dissertation, we present a computational study of unstable systems driven by high Mach number shock and blast waves. Using multi-physics radiation hydrodynamics codes and theoretical models, we consider the late nonlinear instability evolution of single mode, few mode, and multimode interfaces. We rely primarily on 2D calculations but present recent 3D results as well. For planar multimode systems, we show that compressibility effects preclude the emergence of a regime of self-similar instability growth independent of the initial conditions (IC's) by allowing for memory of the initial conditions to be retained in the mix-width at all times. The loss of transverse spectral information is demonstrated, however, along with the existence of a quasi-self-similar regime over short time intervals. Aspects of the IC's are shown to have a strong effect on the time to transition to the quasi-self-similar regime. With higher-dimensional blast waves, divergence restores the properties necessary for establishment of the self-similar state, but achieving it requires very high initial characteristic mode number and high Mach number for the incident blast wave. We point to recent stellar calculations that predict IC's we find incompatible with self-similarity, and
Energy Technology Data Exchange (ETDEWEB)
Miles, Aaron R. [Univ. of Maryland, College Park, MD (United States)
2004-01-01
In core-collapse supernovae, strong blast waves drive interfaces susceptible to Rayleigh-Taylor (RT), Richtmyer-Meshkov (RM), and Kelvin-Helmholtz (KH) instabilities. In addition, perturbation growth can result from material expansion in large-scale velocity gradients behind the shock front. Laser-driven experiments are designed to produce a strongly shocked interface whose evolution is a scaled version of the unstable hydrogen-helium interface in core-collapse supernovae such as SN 1987A. The ultimate goal of this research is to develop an understanding of the effect of hydrodynamic instabilities and the resulting transition to turbulence on supernovae observables that remain as yet unexplained. In this dissertation, we present a computational study of unstable systems driven by high Mach number shock and blast waves. Using multi-physics radiation hydrodynamics codes and theoretical models, we consider the late nonlinear instability evolution of single mode, few mode, and multimode interfaces. We rely primarily on 2D calculations but present recent 3D results as well. For planar multimode systems, we show that compressibility effects preclude the emergence of a regime of self-similar instability growth independent of the initial conditions (IC's) by allowing for memory of the initial conditions to be retained in the mix-width at all times. The loss of transverse spectral information is demonstrated, however, along with the existence of a quasi-self-similar regime over short time intervals. Aspects of the IC's are shown to have a strong effect on the time to transition to the quasi-self-similar regime. With higher-dimensional blast waves, divergence restores the properties necessary for establishment of the self-similar state, but achieving it requires very high initial characteristic mode number and high Mach number for the incident blast wave. We point to recent stellar calculations that predict IC's we find incompatible with self-similarity, and
Li, Dongfang; Zhang, Jiwei
2016-10-01
Anomalous diffusion behavior in many practical problems can be described by the nonlinear time-fractional parabolic problems on unbounded domain. The numerical simulation is a challenging problem due to the dependence of global information from time fractional operators, the nonlinearity of the problem and the unboundedness of the spacial domain. To overcome the unboundedness, conventional computational methods lead to extremely expensive costs, especially in high dimensions with a simple treatment of boundary conditions by making the computational domain large enough. In this paper, based on unified approach proposed in [25], we derive the efficient nonlinear absorbing boundary conditions (ABCs), which reformulates the problem on unbounded domain to an initial boundary value problem on bounded domain. To overcome nonlinearity, we construct a linearized finite difference scheme to solve the reduced nonlinear problem such that iterative methods become dispensable. And the stability and convergence of our linearized scheme are proved. Most important, we prove that the numerical solutions are bounded by the initial values with a constant coefficient, i.e., the constant coefficient is independent of the time. Overall, the computational cost can be significantly reduced comparing with the usual implicit schemes and a simple treatment of boundary conditions. Finally, numerical examples are given to demonstrate the efficiency of the artificial boundary conditions and theoretical results of the schemes.
Finite-time Consensus for Nonlinear Multi-agent Systems with Fixed Topologies
Shang, Yilun
2009-01-01
In this paper, we study finite-time state consensus problems for continuous nonlinear multi-agent systems. Building on the theory of finite-time Lyapunov stability, we propose sufficient criteria which guarantee the system to reach a consensus in finite time, provided that the underlying directed network contains a spanning tree. Novel finite-time consensus protocols are introduced as examples for applying the criteria. Simulations are also presented to illustrate our theoretical results.
Nonlinear effects on Turing patterns: Time oscillations and chaos
Aragón, J. L.
2012-08-08
We show that a model reaction-diffusion system with two species in a monostable regime and over a large region of parameter space produces Turing patterns coexisting with a limit cycle which cannot be discerned from the linear analysis. As a consequence, the patterns oscillate in time. When varying a single parameter, a series of bifurcations leads to period doubling, quasiperiodic, and chaotic oscillations without modifying the underlying Turing pattern. A Ruelle-Takens-Newhouse route to chaos is identified. We also examine the Turing conditions for obtaining a diffusion-driven instability and show that the patterns obtained are not necessarily stationary for certain values of the diffusion coefficients. These results demonstrate the limitations of the linear analysis for reaction-diffusion systems. © 2012 American Physical Society.
Integral sliding mode control for a class of nonlinear neutral systems with time-varying delays
Institute of Scientific and Technical Information of China (English)
Lou Xu-Yang; Cui Bao-Tong
2008-01-01
This paper focuses on sliding mode control problems for a class of nonlinear neutral systems with time-varying delays. An integral sliding surface is firstly constructed. Then it finds a useful criteria to guarantee the global stability for the nonlinear neutral systems with time-varying delays in the specified switching surface, whose condition is formulated as linear matrix inequality. The synthesized sliding mode controller guarantees the reachability of the specified sliding surface. Finally, a numerical simulation validates the effectiveness and feasibility of the proposed technique.
Wei, Song; Chen, Wen; Hon, Y. C.
2016-11-01
This paper investigates the temporal effects in the modeling of flows through porous media and particles transport. Studies will be made among the time fractional diffusion model and two classical nonlinear diffusion models. The effects of the parameters upon the mentioned models have been studied. By simulating the sub-diffusion processes and comparing the numerical results of these models under different boundary conditions, we can conclude that the time fractional diffusion model is more suitable for simulating the sub-diffusion with steady diffusion rate; whereas the nonlinear models are more appropriate for depicting the sub-diffusion under changing diffusion rate.
Observability of nonlinear dynamics: Normalized results and a time-series approach
Aguirre, Luis A.; Bastos, Saulo B.; Alves, Marcela A.; Letellier, Christophe
2008-03-01
This paper investigates the observability of nonlinear dynamical systems. Two difficulties associated with previous studies are dealt with. First, a normalized degree observability is defined. This permits the comparison of different systems, which was not generally possible before. Second, a time-series approach is proposed based on omnidirectional nonlinear correlation functions to rank a set of time series of a system in terms of their potential use to reconstruct the original dynamics without requiring the knowledge of the system equations. The two approaches proposed in this paper and a former method were applied to five benchmark systems and an overall agreement of over 92% was found.
Anderson, Kristin K.; LaGasse, Michael J.; Haus, Hermann A.; Fujimoto, James G.
1990-05-01
We describe the application of a new femtosecond measurement technique, time division interferometry, for investigating the transient nonlinear index in waveguides. This technique performs an interferometric measurement using a time division multiplexed reference pulse and achieves high sensitivity with increased immunity to acoustic and thermal parasitics. Using a tunable femtosecond laser source, direct measurements of the wavelength dependent nonresonant nonlinear index have been performed in A1GaAs waveguides. In addition, conventional pump and probe absorption measurements permit the investigation of carrier dynamics, band filling, and two photon absorption effects. Two photon absorption is found to be a potentially serious limiting effect for obtaining all optical switching.
Finite-time Consensus of Heterogeneous Multi-agent Systems with Linear and Nonlinear Dynamics
Institute of Scientific and Technical Information of China (English)
ZHU Ya-Kun; GUAN Xin-Ping; LUO Xiao-Yuan
2014-01-01
In this paper, the finite-time consensus problems of heterogeneous multi-agent systems composed of both linear and nonlinear dynamics agents are investigated. Nonlinear consensus protocols are proposed for the heterogeneous multi-agent systems. Some suﬃcient conditions for the finite-time consensus are established in the leaderless and leader-following cases. The results are also extended to the case where the communication topology is directed and satisfies a detailed balance condition on coupling weights. At last, some simulation results are given to illustrate the effectiveness of the obtained theoretical results.
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
Energy Technology Data Exchange (ETDEWEB)
Burr, T.L.
1994-04-01
This report is a primer on the analysis of both linear and nonlinear time series with applications in nuclear safeguards and nonproliferation. We analyze eight simulated and two real time series using both linear and nonlinear modeling techniques. The theoretical treatment is brief but references to pertinent theory are provided. Forecasting is our main goal. However, because our most common approach is to fit models to the data, we also emphasize checking model adequacy by analyzing forecast errors for serial correlation or nonconstant variance.
Adaptive Leader-Following Consensus for Second-Order Time-Varying Nonlinear Multiagent Systems.
Hua, Changchun; You, Xiu; Guan, Xinping
2017-06-01
The leader-following consensus problem is investigated for second-order time-varying nonlinear multiagent systems with unmodeled dynamics and unknown parameters over directed communication topology. Under the assumption that the unknown nonlinearities satisfy Lipschitz conditions with time-varying gains, a local adaptive law is introduced for the design of consensus protocol that enable all followers' state variables to consensus with that of leader asymptotically. The proposed protocols are independent of system parameters and only require the relative state information of its neighbors, and hence they are fully distributed. Simulation examples are given to illustrate the effectiveness of the theoretical results.
Energy Technology Data Exchange (ETDEWEB)
Burr, T.L.
1994-04-01
This report is a primer on the analysis of both linear and nonlinear time series with applications in nuclear safeguards and nonproliferation. We analyze eight simulated and two real time series using both linear and nonlinear modeling techniques. The theoretical treatment is brief but references to pertinent theory are provided. Forecasting is our main goal. However, because our most common approach is to fit models to the data, we also emphasize checking model adequacy by analyzing forecast errors for serial correlation or nonconstant variance.
Practical stabilization of a class of uncertain time-varying nonlinear delay systems
Institute of Scientific and Technical Information of China (English)
Bassem Ben HAMED; Mohamed Ali HAMMAMI
2009-01-01
In this paper we deal with a class of uncertain time-varying nonlinear systems with a state delay. Under some assumptions, we construct some stabilizing continuous feedback, i.e. linear and nonlinear in the state, which can guarantee global uniform exponential stability and global uniform practical convergence of the considered system. The quadratic Lyapunov function for the nominal stable system is used as a Lyapunov candidate function for the global system. The results developed in this note are applicable to a class of dynamical systems with uncertain time-delay. Our result is illustrated by a numerical example.
Nonlinear model calibration of a shear wall building using time and frequency data features
Asgarieh, Eliyar; Moaveni, Babak; Barbosa, Andre R.; Chatzi, Eleni
2017-02-01
This paper investigates the effects of different factors on the performance of nonlinear model updating for a seven-story shear wall building model. The accuracy of calibrated models using different data features and modeling assumptions is studied by comparing the time and frequency responses of the models with the exact simulated ones. Simplified nonlinear finite element models of the shear wall building are calibrated so that the misfit between the considered response data features of the models and the structure is minimized. A refined FE model of the test structure, which was calibrated manually to match the shake table test data, is used instead of the real structure for this performance evaluation study. The simplified parsimonious FE models are composed of simple nonlinear beam-column fiber elements with nonlinearity infused in them by assigning generated hysteretic nonlinear material behaviors to uniaxial stress-strain relationship of the fibers. Four different types of data features and their combinations are used for model calibration: (1) time-varying instantaneous modal parameters, (2) displacement time histories, (3) acceleration time histories, and (4) dissipated hysteretic energy. It has been observed that the calibrated simplified FE models can accurately predict the nonlinear structural response in the absence of significant modeling errors. In the last part of this study, the physics-based models are further simplified for casting into state-space formulation and a real-time identification is performed using an Unscented Kalman filter. It has been shown that the performance of calibrated state-space models can be satisfactory when reasonable modeling assumptions are used.
Frequency-domain L2-stability conditions for time-varying linear and nonlinear MIMO systems
Institute of Scientific and Technical Information of China (English)
Zhihong HUANG; Y. V. VENKATESH; Cheng XIANG; Tong Heng LEE
2014-01-01
The paper deals with the L2-stability analysis of multi-input-multi-output (MIMO) systems, governed by integral equations, with a matrix of periodic/aperiodic time-varying gains and a vector of monotone, non-monotone and quasi-monotone nonlin-earities. For nonlinear MIMO systems that are described by differential equations, most of the literature on stability is based on an application of quadratic forms as Lyapunov-function candidates. In contrast, a non-Lyapunov framework is employed here to derive new and more general L2-stability conditions in the frequency domain. These conditions have the following features:i) They are expressed in terms of the positive definiteness of the real part of matrices involving the transfer function of the linear time-invariant block and a matrix multiplier function that incorporates the minimax properties of the time-varying linear/nonlinear block. ii) For certain cases of the periodic time-varying gain, they contain, depending on the multiplier function chosen, no restrictions on the normalized rate of variation of the time-varying gain, but, for other periodic/aperiodic time-varying gains, they do. Overall, even when specialized to periodic-coefficient linear and nonlinear MIMO systems, the stability conditions are distinct from and less restrictive than recent results in the literature. No comparable results exist in the literature for aperiodic time-varying gains. Furthermore, some new stability results concerning the dwell-time problem and time-varying gain switching in linear and nonlinear MIMO systems with periodic/aperiodic matrix gains are also presented. Examples are given to illustrate a few of the stability theorems.
Time Evolution of Entanglement Entropy from Black Hole Interiors
Hartman, Thomas
2013-01-01
We compute the time-dependent entanglement entropy of a CFT which starts in relatively simple initial states. The initial states are the thermofield double for thermal states, dual to eternal black holes, and a particular pure state, dual to a black hole formed by gravitational collapse. The entanglement entropy grows linearly in time. This linear growth is directly related to the growth of the black hole interior measured along "nice" spatial slices. These nice slices probe the spacelike direction in the interior, at a fixed special value of the interior time. In the case of a two-dimensional CFT, we match the bulk and boundary computations of the entanglement entropy. We briefly discuss the long time behavior of various correlators, computed via classical geodesics or surfaces, and point out that their exponential decay comes about for similar reasons. We also present the time evolution of the wavefunction in the tensor network description.
Time evolution of entanglement entropy from black hole interiors
Hartman, Thomas; Maldacena, Juan
2013-05-01
We compute the time-dependent entanglement entropy of a CFT which starts in relatively simple initial states. The initial states are the thermofield double for thermal states, dual to eternal black holes, and a particular pure state, dual to a black hole formed by gravitational collapse. The entanglement entropy grows linearly in time. This linear growth is directly related to the growth of the black hole interior measured along "nice" spatial slices. These nice slices probe the spacelike direction in the interior, at a fixed special value of the interior time. In the case of a two-dimensional CFT, we match the bulk and boundary computations of the entanglement entropy. We briefly discuss the long time behavior of various correlators, computed via classical geodesics or surfaces, and point out that their exponential decay comes about for similar reasons. We also present the time evolution of the wavefunction in the tensor network description.
H∞ output tracking control of discrete-time nonlinear systems via standard neural network models.
Liu, Meiqin; Zhang, Senlin; Chen, Haiyang; Sheng, Weihua
2014-10-01
This brief proposes an output tracking control for a class of discrete-time nonlinear systems with disturbances. A standard neural network model is used to represent discrete-time nonlinear systems whose nonlinearity satisfies the sector conditions. H∞ control performance for the closed-loop system including the standard neural network model, the reference model, and state feedback controller is analyzed using Lyapunov-Krasovskii stability theorem and linear matrix inequality (LMI) approach. The H∞ controller, of which the parameters are obtained by solving LMIs, guarantees that the output of the closed-loop system closely tracks the output of a given reference model well, and reduces the influence of disturbances on the tracking error. Three numerical examples are provided to show the effectiveness of the proposed H∞ output tracking design approach.