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.
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.
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
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...
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)
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...
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.
Energy decay of a variable-coefficient wave equation with nonlinear time-dependent localized damping
Directory of Open Access Journals (Sweden)
Jieqiong Wu
2015-09-01
Full Text Available We study the energy decay for the Cauchy problem of the wave equation with nonlinear time-dependent and space-dependent damping. The damping is localized in a bounded domain and near infinity, and the principal part of the wave equation has a variable-coefficient. We apply the multiplier method for variable-coefficient equations, and obtain an energy decay that depends on the property of the coefficient of the damping term.
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.
Delay-Dependent Observers for Uncertain Nonlinear Time-Delay Systems
Directory of Open Access Journals (Sweden)
Dongmei Yan
2013-05-01
Full Text Available This paper is concerned with the observer design problem for a class of discrete-time uncertain nonlinear systems with time-varying delay. The nonlinearities are assumed to satisfy global Lipschitz conditions which appear in both the state and measurement equations. The uncertainties are assumed to be time-varying but norm-bounded. Two Luenberger-like observers are proposed. One is delay observer and the other is delay-free observer. The delay observer which has an internal time delay is applicable when the time delay is known. The delay-free observer which does not use delayed information is especially applicable when the time delay is not known explicitly. Delay-dependent conditions for the existences of these two observers are derived based on Lyapunpv functional approach. Based on these conditions, the observer gains are obtained using the cone complementarity linearization algorithm. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.
Zaheer, Muhammad Hamad; Rehan, Muhammad; Mustafa, Ghulam; Ashraf, Muhammad
2014-11-01
This paper proposes a novel state feedback delay-range-dependent control approach for chaos synchronization in coupled nonlinear time-delay systems. The coupling between two systems is esteemed to be nonlinear subject to time-lags. Time-varying nature of both the intrinsic and the coupling delays is incorporated to broad scope of the present study for a better-quality synchronization controller synthesis. Lyapunov-Krasovskii (LK) functional is employed to derive delay-range-dependent conditions that can be solved by means of the conventional linear matrix inequality (LMI)-tools. The resultant control approach for chaos synchronization of the master-slave time-delay systems considers non-zero lower bound of the intrinsic as well as the coupling time-delays. Further, the delay-dependent synchronization condition has been established as a special case of the proposed LK functional treatment. Furthermore, a delay-range-dependent condition, independent of the delay-rate, has been provided to address the situation when upper bound of the delay-derivative is unknown. A robust state feedback control methodology is formulated for synchronization of the time-delay chaotic networks against the L2 norm bounded perturbations by minimizing the L2 gain from the disturbance to the synchronization error. Numerical simulation results are provided for the time-delay chaotic networks to show effectiveness of the proposed delay-range-dependent chaos synchronization methodologies. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.
Third-order nonlinear and linear time-dependent dynamical diffraction of X-rays in crystals.
Balyan, Minas K
2016-07-01
For the first time the third-order nonlinear time-dependent Takagi's equations of X-rays in crystals are obtained and investigated. The third-order nonlinear and linear time-dependent dynamical diffraction of X-rays spatially restricted in the diffraction plane pulses in crystals is investigated theoretically. A method of solving the linear and the third-order nonlinear time-dependent Takagi's equations is proposed. Based on this method, results of analytical and numerical calculations for both linear and nonlinear diffraction cases are presented and compared.
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.
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.
Nonlinear Behaviors of Tail Dependence and Cross-Correlation of Financial Time Series Model
Directory of Open Access Journals (Sweden)
Wei Deng
2014-01-01
Full Text Available Nonlinear behaviors of tail dependence and cross-correlation of financial time series are reproduced and investigated by stochastic voter dynamic system. The voter process is a continuous-time Markov process and is one of the interacting dynamic systems. The tail dependence of return time series for pairs of Chinese stock markets and the proposed financial models is studied by copula analysis, in an attempt to detect and illustrate the existence of relevant correlation relationships. Further, the multifractality of cross-correlations for return series is studied by multifractal detrended cross-correlation analysis, which indicates the analogous cross-correlations and some fractal characters for both actual data and simulative data and provides an intuitive evidence for market inefficiency.
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...
Analytic approach to nonlinear hydrodynamic instabilities driven by time-dependent accelerations
Energy Technology Data Exchange (ETDEWEB)
Mikaelian, K O
2009-09-28
We extend our earlier model for Rayleigh-Taylor and Richtmyer-Meshkov instabilities to the more general class of hydrodynamic instabilities driven by a time-dependent acceleration g(t) . Explicit analytic solutions for linear as well as nonlinear amplitudes are obtained for several g(t)'s by solving a Schroedinger-like equation d{sup 2}{eta}/dt{sup 2} - g(t)kA{eta} = 0 where A is the Atwood number and k is the wavenumber of the perturbation amplitude {eta}(t). In our model a simple transformation k {yields} k{sub L} and A {yields} A{sub L} connects the linear to the nonlinear amplitudes: {eta}{sup nonlinear} (k,A) {approx} (1/k{sub L})ln{eta}{sup linear} (k{sub L}, A{sub L}). The model is found to be in very good agreement with direct numerical simulations. Bubble amplitudes for a variety of accelerations are seen to scale with s defined by s = {integral} {radical}g(t)dt, while spike amplitudes prefer scaling with displacement {Delta}x = {integral}[{integral}g(t)dt]dt.
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.
Towards time-dependent current-density-functional theory in the non-linear regime.
Escartín, J M; Vincendon, M; Romaniello, P; Dinh, P M; Reinhard, P-G; Suraud, E
2015-02-28
Time-Dependent Density-Functional Theory (TDDFT) is a well-established theoretical approach to describe and understand irradiation processes in clusters and molecules. However, within the so-called adiabatic local density approximation (ALDA) to the exchange-correlation (xc) potential, TDDFT can show insufficiencies, particularly in violently dynamical processes. This is because within ALDA the xc potential is instantaneous and is a local functional of the density, which means that this approximation neglects memory effects and long-range effects. A way to go beyond ALDA is to use Time-Dependent Current-Density-Functional Theory (TDCDFT), in which the basic quantity is the current density rather than the density as in TDDFT. This has been shown to offer an adequate account of dissipation in the linear domain when the Vignale-Kohn (VK) functional is used. Here, we go beyond the linear regime and we explore this formulation in the time domain. In this case, the equations become very involved making the computation out of reach; we hence propose an approximation to the VK functional which allows us to calculate the dynamics in real time and at the same time to keep most of the physics described by the VK functional. We apply this formulation to the calculation of the time-dependent dipole moment of Ca, Mg and Na2. Our results show trends similar to what was previously observed in model systems or within linear response. In the non-linear domain, our results show that relaxation times do not decrease with increasing deposited excitation energy, which sets some limitations to the practical use of TDCDFT in such a domain of excitations.
Time-dependent density functional theory for nonlinear properties of open-shell systems.
Rinkevicius, Zilvinas; Jha, Prakash Chandra; Oprea, Corneliu I; Vahtras, Olav; Agren, Hans
2007-09-21
This paper presents response theory based on a spin-restricted Kohn-Sham formalism for computation of time-dependent and time-independent nonlinear properties of molecules with a high spin ground state. The developed approach is capable to handle arbitrary perturbations and constitutes an efficient procedure for evaluation of electric, magnetic, and mixed properties. Apart from presenting the derivation of the proposed approach, we show results from illustrating calculations of static and dynamic hyperpolarizabilities of small Si(3n+1)H(6n+3) (n=0,1,2) clusters which mimic Si(111) surfaces with dangling bond defects. The results indicate that the first hyperpolarizability tensor components of Si(3n+1)H(6n+3) have an ordering compatible with the measurements of second harmonic generation in SiO2/Si(111) interfaces and, therefore, support the hypothesis that silicon surface defects with dangling bonds are responsible for this phenomenon. The results exhibit a strong dependence on the quality of basis set and exchange-correlation functional, showing that an appropriate set of diffuse functions is required for reliable predictions of the first hyperpolarizability of open-shell compounds.
Modelling long term rockslide displacements with non-linear time-dependent relationships
De Caro, Mattia; Volpi, Giorgio; Castellanza, Riccardo; Crosta, Giovanni; Agliardi, Federico
2015-04-01
Rockslides undergoing rapid changes in behaviour pose major risks in alpine areas, and require careful characterization and monitoring both for civil protection and mitigation activities. In particular, these instabilities can undergo very slow movement with occasional and intermittent acceleration/deceleration stages of motion potentially leading to collapse. Therefore, the analysis of such instabilities remains a challenging issue. Rockslide displacements are strongly conditioned by hydrologic factors as suggested by correlations with groundwater fluctuations, snowmelt, with a frequently observed delay between perturbation and system reaction. The aim of this work is the simulation of the complex time-dependent behaviour of two case studies for which also a 2D transient hydrogeological simulation has been performed: Vajont rockslide (1960 to 1963) and the recent Mt. de La Saxe rockslide (2009 to 2012). Non-linear time-dependent constitutive relationships have been used to describe long-term creep deformation. Analyses have been performed using a "rheological-mechanical" approach that fits idealized models (e.g. viscoelastic, viscoplastic, elasto-viscoplastic, Burgers, nonlinear visco-plastic) to the experimental behaviour of specific materials by means of numerical constants. Bidimensional simulations were carried out using the finite difference code FLAC. Displacements time-series, available for the two landslides, show two superimposed deformation mechanisms: a creep process, leading to movements under "steady state" conditions (e.g. constant groundwater level), and a "dynamic" process, leading to an increase in displacement rate due to changes of external loads (e.g. groundwater level). For both cases sliding mass is considered as an elasto-plastic body subject to its self-weight, inertial and seepage forces varying with time according to water table fluctuation (due to snowmelt or changing in reservoir level) and derived from the previous hydrogeological
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.
Nonlinearity, Breaks, and Long-Range Dependence in Time-Series Models
DEFF Research Database (Denmark)
Hillebrand, Eric Tobias; Medeiros, Marcelo C.
We study the simultaneous occurrence of long memory and nonlinear effects, such as parameter changes and threshold effects, in ARMA time series models and apply our modeling framework to daily realized volatility. Asymptotic theory for parameter estimation is developed and two model building...
Institute of Scientific and Technical Information of China (English)
Li Hua-Mei
2005-01-01
By using the mapping method and an appropriate transformation, we find new exact solutions of nonlinear Gross-Pitaevskii equation with weak bias magnetic and time-dependent laser fields. The solutions obtained in this paper include Jacobian elliptic function solutions, combined Jacobian elliptic function solutions , triangular function solutions, bright and dark solitons, and soliton-like solutions.
Energy Technology Data Exchange (ETDEWEB)
Hong Qin and Ronald C. Davidson
2011-07-19
In a linear trap confining a one-component nonneutral plasma, the external focusing force is a linear function of the configuration coordinates and/or the velocity coordinates. Linear traps include the classical Paul trap and the Penning trap, as well as the newly proposed rotating-radio- frequency traps and the Mobius accelerator. This paper describes a class of self-similar nonlinear solutions of nonneutral plasma in general time-dependent linear focusing devices, with self-consistent electrostatic field. This class of nonlinear solutions includes many known solutions as special cases.
Directory of Open Access Journals (Sweden)
Brajesh Kumar Singh
2016-01-01
Full Text Available This paper deals with an analytical solution of an initial value system of time dependent linear and nonlinear partial differential equations by implementing reduced differential transform (RDT method. The effectiveness and the convergence of RDT method are tested by means of five test problems, which indicates the validity and great potential of the reduced differential transform method for solving system of partial differential equations.
Jha, Sanjeev Kumar
2015-07-21
A geostatistical framework is proposed to downscale daily precipitation and temperature. The methodology is based on multiple-point geostatistics (MPS), where a multivariate training image is used to represent the spatial relationship between daily precipitation and daily temperature over several years. Here, the training image consists of daily rainfall and temperature outputs from the Weather Research and Forecasting (WRF) model at 50 km and 10 km resolution for a twenty year period ranging from 1985 to 2004. The data are used to predict downscaled climate variables for the year 2005. The result, for each downscaled pixel, is daily time series of precipitation and temperature that are spatially dependent. Comparison of predicted precipitation and temperature against a reference dataset indicates that both the seasonal average climate response together with the temporal variability are well reproduced. The explicit inclusion of time dependence is explored by considering the climate properties of the previous day as an additional variable. Comparison of simulations with and without inclusion of time dependence shows that the temporal dependence only slightly improves the daily prediction because the temporal variability is already well represented in the conditioning data. Overall, the study shows that the multiple-point geostatistics approach is an efficient tool to be used for statistical downscaling to obtain local scale estimates of precipitation and temperature from General Circulation Models. This article is protected by copyright. All rights reserved.
Directory of Open Access Journals (Sweden)
Hamid Reza Karimi
2009-01-01
Full Text Available The problem of stability analysis for a class of neutral systems with mixed time-varying neutral, discrete and distributed delays and nonlinear parameter perturbations is addressed. By introducing a novel Lyapunov-Krasovskii functional and combining the descriptor model transformation, the Leibniz-Newton formula, some free-weighting matrices, and a suitable change of variables, new sufficient conditions are established for the stability of the considered system, which are neutral-delay-dependent, discrete-delay-range-dependent, and distributed-delay-dependent. The conditions are presented in terms of linear matrix inequalities (LMIs and can be efficiently solved using convex programming techniques. Two numerical examples are given to illustrate the efficiency of the proposed method.
Zhang, Wei; Wang, Jun
2017-09-01
In attempt to reproduce price dynamics of financial markets, a stochastic agent-based financial price model is proposed and investigated by stochastic exclusion process. The exclusion process, one of interacting particle systems, is usually thought of as modeling particle motion (with the conserved number of particles) in a continuous time Markov process. In this work, the process is utilized to imitate the trading interactions among the investing agents, in order to explain some stylized facts found in financial time series dynamics. To better understand the correlation behaviors of the proposed model, a new time-dependent intrinsic detrended cross-correlation (TDI-DCC) is introduced and performed, also, the autocorrelation analyses are applied in the empirical research. Furthermore, to verify the rationality of the financial price model, the actual return series are also considered to be comparatively studied with the simulation ones. The comparison results of return behaviors reveal that this financial price dynamics model can reproduce some correlation features of actual stock markets.
Time-Dependent Behavior of Diabase and a Nonlinear Creep Model
Yang, Wendong; Zhang, Qiangyong; Li, Shucai; Wang, Shugang
2014-07-01
Triaxial creep tests were performed on diabase specimens from the dam foundation of the Dagangshan hydropower station, and the typical characteristics of creep curves were analyzed. Based on the test results under different stress levels, a new nonlinear visco-elasto-plastic creep model with creep threshold and long-term strength was proposed by connecting an instantaneous elastic Hooke body, a visco-elasto-plastic Schiffman body, and a nonlinear visco-plastic body in series mode. By introducing the nonlinear visco-plastic component, this creep model can describe the typical creep behavior, which includes the primary creep stage, the secondary creep stage, and the tertiary creep stage. Three-dimensional creep equations under constant stress conditions were deduced. The yield approach index (YAI) was used as the criterion for the piecewise creep function to resolve the difficulty in determining the creep threshold value and the long-term strength. The expression of the visco-plastic component was derived in detail and the three-dimensional central difference form was given. An example was used to verify the credibility of the model. The creep parameters were identified, and the calculated curves were in good agreement with the experimental curves, indicating that the model is capable of replicating the physical processes.
Towards adjoint-based inversion of time-dependent mantle convection with non-linear viscosity
Li, Dunzhu; Gurnis, Michael; Stadler, Georg
2017-01-01
We develop and study an adjoint-based inversion method for the simultaneous recovery of initial temperature conditions and viscosity parameters in time-dependent mantle convection from the current mantle temperature and historic plate motion. Based on a realistic rheological model with temperature- and strain rate-dependent viscosity, we formulate the inversion as a PDE-constrained optimization problem. The objective functional includes the misfit of surface velocity (plate motion) history, the misfit of the current mantle temperature, and a regularization for the uncertain initial condition. The gradient of this functional with respect to the initial temperature and the uncertain viscosity parameters is computed by solving the adjoint of the mantle convection equations. This gradient is used in a preconditioned quasi-Newton minimization algorithm. We study the prospects and limitations of the inversion, as well as the computational performance of the method using two synthetic problems, a sinking cylinder and a realistic subduction model. The subduction model is characterized by the migration of a ridge toward a trench whereby both plate motions and subduction evolve. The results demonstrate: (1) for known viscosity parameters, the initial temperature can be well recovered, as in previous initial condition-only inversions where the effective viscosity was given; (2) for known initial temperature, viscosity parameters can be recovered accurately, despite the existence of trade-offs due to ill-conditioning; (3) for the joint inversion of initial condition and viscosity parameters, initial condition and effective viscosity can be reasonably recovered, but the high dimension of the parameter space and the resulting ill-posedness may limit recovery of viscosity parameters.
Institute of Scientific and Technical Information of China (English)
2008-01-01
Based on an appropriate Lyapunov function,this paper analyzes the design of a delay-dependent robust H∞ state feedback control,with a focus on a class of non linear uncertainty linear time-delay systems with input delay using linear matrix inequalities.Under the condition that the nonlinear uncertain functions are gain bounded,a sufficient condition dependent on the delays of the state and input is presented for the existence of H∞ controller.The proposed controller not only stabilized closed-loop uncertain systems but also guaranteed a prescribed H∞ norm bound of closed-loop transfer matrix from the disturbance to controlled output.By solving a linear matrix inequation,we can obtain the robust H∞ controller.An example is given to show the effectiveness of the proposed method.
Korayem, M H; Nekoo, S R
2015-07-01
This work studies an optimal control problem using the state-dependent Riccati equation (SDRE) in differential form to track for time-varying systems with state and control nonlinearities. The trajectory tracking structure provides two nonlinear differential equations: the state-dependent differential Riccati equation (SDDRE) and the feed-forward differential equation. The independence of the governing equations and stability of the controller are proven along the trajectory using the Lyapunov approach. Backward integration (BI) is capable of solving the equations as a numerical solution; however, the forward solution methods require the closed-form solution to fulfill the task. A closed-form solution is introduced for SDDRE, but the feed-forward differential equation has not yet been obtained. Different ways of solving the problem are expressed and analyzed. These include BI, closed-form solution with corrective assumption, approximate solution, and forward integration. Application of the tracking problem is investigated to control robotic manipulators possessing rigid or flexible joints. The intention is to release a general program for automatic implementation of an SDDRE controller for any manipulator that obeys the Denavit-Hartenberg (D-H) principle when only D-H parameters are received as input data.
Institute of Scientific and Technical Information of China (English)
Shuxin Huang; Chuanjing Lu; Ron Marshall
2005-01-01
A new simple thixotropy model was proposed in the present paper to characterize the thixotropy-loop experiments and the start-up experiment of an LDPE (PE-FSB23D022/Q200) melt. The thixotropy model is a combination of a viscoelastic-component and a postulated kinetics process of structure change, which is constituted in terms of the indirect microstructural approach usually adopted in the characterization of thixotropy. The descriptions of the thixotropy model on both the thixotropy-loop tests and the startup test show good agreement with the experimental values, indicating the good capability of the model in characterizing the time-dependent nonlinear viscoelastic. The stress overshoot phenomenon and the stress relaxation after cessation of the thixotropy loop test can be described well by the model, whereas both of the typical viscoelastic phenomena could not be described in our previous work with a variant Huang model.
Röken, Christian; Schöneberg, Sebastian; Schuppan, Florian
2016-01-01
A leptonic one-zone model accounting for the radiation emission of blazars is presented. This model describes multiple successive injections of mono-energetic, ultra-relativistic, interacting electron populations, which are subjected to synchrotron and synchrotron-self Compton radiative losses. The electron number density is computed analytically by solving a time-dependent, relativistic transport equation. Moreover, the synchrotron and synchrotron-self Compton intensities as well as the corresponding total fluences are explicitly calculated. The lightcurves and fluences are plotted for realistic parameter values, showing that the model can simultaneously explain both the specific short-time variability in the flaring of blazars and the characteristic broad-band fluence behavior.
Strubbe, David A.; Andrade, Xavier; Rubio, Angel; Louie, Steven G.
2010-03-01
Chloroform is often used as a solvent when measuring non-linear optical properties of organic molecules. We assess the influence of the solution environment on the molecular properties by calculating directly the non-linear susceptibilities of liquid chloroform at optical frequencies. We use the Sternheimer equation in time-dependent density-functional theory [J. Chem. Phys. 126, 184106 (2007)], on snapshots from ab initio molecular dynamics. We compare the results to those in the gas and solid phases, and to experimental values. We also calculate ab initio local-field factors, used to analyze electric-field-induced second-harmonic generation (EFISH) and hyper-Rayleigh scattering (HRS) experiments.
Li, Huiping; Shi, Yang
2012-10-01
This article focuses on the state-feedback ℋ∞ control problem for the stochastic nonlinear systems with state and disturbance-dependent noise and time-varying state delays. Based on the maxmin optimisation approach, both the delay-independent and the delay-dependent Hamilton-Jacobi-inequalities (HJIs) are developed for synthesising the state-feedback ℋ∞ controller for a general type of stochastic nonlinear systems. It is shown that the resulting control system achieves stochastic stability in probability and the prescribed disturbance attenuation level. For a class of stochastic affine nonlinear systems, the delay-independent as well as delay-dependent matrix-valued inequalities are proposed; the resulting control system satisfies global asymptotic stability in the mean-square sense and the required disturbance attenuation level. By modelling the nonlinearities as uncertainties in corresponding stochastic time-delay systems, the sufficient conditions in terms of a linear matrix inequality (LMI) and a bilinear matrix inequality (BMI) are derived to facilitate the design of the state-feedback ℋ∞ controller. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed methods.
Directory of Open Access Journals (Sweden)
Sirada Pinjai
2013-01-01
Full Text Available This paper is concerned with the problem of robust exponential stability for linear parameter-dependent (LPD neutral systems with mixed time-varying delays and nonlinear perturbations. Based on a new parameter-dependent Lyapunov-Krasovskii functional, Leibniz-Newton formula, decomposition technique of coefficient matrix, free-weighting matrices, Cauchy’s inequality, modified version of Jensen’s inequality, model transformation, and linear matrix inequality technique, new delay-dependent robust exponential stability criteria are established in terms of linear matrix inequalities (LMIs. Numerical examples are given to show the effectiveness and less conservativeness of the proposed methods.
Caplan, R M
2011-01-01
An easy to implement modulus-squared Dirichlet (MSD) boundary condition is formulated for numerical simulations of time-dependent complex partial differential equations in multidimensional settings. The MSD boundary condition approximates a constant modulus-square value of the solution at the boundaries. Application of the MSD boundary condition to the nonlinear Schr\\"odinger equation is shown, and numerical simulations are performed to demonstrate its usefulness and advantages over other simple boundary conditions.
Directory of Open Access Journals (Sweden)
Baoyan Zhu
2015-01-01
Full Text Available Delay-dependent finite-time H∞ controller design problems are investigated for a kind of nonlinear descriptor system via a T-S fuzzy model in this paper. The solvable conditions of finite-time H∞ controller are given to guarantee that the loop-closed system is impulse-free and finite-time bounded and holds the H∞ performance to a prescribed disturbance attenuation level γ. The method given is the ability to eliminate the impulsive behavior caused by descriptor systems in a finite-time interval, which confirms the existence and uniqueness of solutions in the interval. By constructing a nonsingular matrix, we overcome the difficulty that results in an infeasible linear matrix inequality (LMI. Using the FEASP solver and GEVP solver of the LMI toolbox, we perform simulations to validate the proposed methods for a nonlinear descriptor system via the T-S fuzzy model, which shows the application of the T-S fuzzy method in studying the finite-time control problem of a nonlinear system. Meanwhile the method was also applied to the biological economy system to eliminate impulsive behavior at the bifurcation value, stabilize the loop-closed system in a finite-time interval, and achieve a H∞ performance level.
Non-linear effects in time-dependent transonic flows: An analysis of analogue black hole stability
Michel, Florent
2015-01-01
We study solutions of the one dimensional Gross-Pitaevskii equation to better understand dynamical instabilities occurring in flowing atomic condensates. Whereas transonic stationary flows can be fully described in simple terms, time dependent flows exhibit a wide variety of behaviors. When the sound speed is crossed once, we observe that flows analogous to black holes obey a kind of "no-hair theorem" since their late time profile is stationary and uniquely fixed by parameters entering the Hamiltonian and conserved quantities. For flows analogous to white holes, at late time one finds a macroscopic undulation in the supersonic side which has either a fixed amplitude, or a widely varying one signaling a quasi periodic emission of solitons on the subsonic side. When considering flows which cross twice the sound speed, we observe various scenarii which can be understood from the above behaviors, and from the hierarchy of the growth rates of the dynamical instabilities characterizing such flows.
Liu, Pin-Lin
2015-07-01
This paper studies the problem of the stability analysis of interval time-varying delay systems with nonlinear perturbations. Based on the Lyapunov-Krasovskii functional (LKF), a sufficient delay-range-dependent criterion for asymptotic stability is derived in terms of linear matrix inequality (LMI) and integral inequality approach (IIA) and delayed decomposition approach (DDA). Further, the delay range is divided into two equal segments for stability analysis. Both theoretical and numerical comparisons have been provided to show the effectiveness and efficiency of the present method. Two well-known examples are given to show less conservatism of our obtained results and the effectiveness of the proposed method.
Energy Technology Data Exchange (ETDEWEB)
Merton, S. R.; Smedley-Stevenson, R. P. [Computational Physics Group, AWE Aldermaston, Reading, Berkshire RG7 4PR (United Kingdom); Pain, C. C. [Dept. of Earth Science and Engineering, Imperial College London, London SW7 2AZ (United Kingdom)
2012-07-01
This paper describes a Non-Linear Discontinuous Petrov-Galerkin method and its application to the one-speed Boltzmann Transport Equation (BTE) for space-time problems. The purpose of the method is to remove unwanted oscillations in the transport solution which occur in the vicinity of sharp flux gradients, while improving computational efficiency and numerical accuracy. This is achieved by applying artificial dissipation in the solution gradient direction, internal to an element using a novel finite element (FE) Riemann approach. The added dissipation is calculated at each node of the finite element mesh based on local behaviour of the transport solution on both the spatial and temporal axes of the problem. Thus a different dissipation is used in different elements. The magnitude of dissipation that is used is obtained from a gradient-informed scaling of the advection velocities in the stabilisation term. This makes the method in its most general form non-linear. The method is implemented within a very general finite element Riemann framework. This makes it completely independent of choice of angular basis function allowing one to use different descriptions of the angular variation. Results show the non-linear scheme performs consistently well in demanding time-dependent multi-dimensional neutron transport problems. (authors)
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
Directory of Open Access Journals (Sweden)
Pratibha Joshi
2014-12-01
Full Text Available In this paper, we have achieved high order solution of a three dimensional nonlinear diffusive-convective problem using modified variational iteration method. The efficiency of this approach has been shown by solving two examples. All computational work has been performed in MATHEMATICA.
A Solar Cycle Dependence of Nonlinearity in Magnetospheric Activity
Energy Technology Data Exchange (ETDEWEB)
Johnson, Jay R; Wing, Simon
2005-03-08
The nonlinear dependencies inherent to the historical K(sub)p data stream (1932-2003) are examined using mutual information and cumulant based cost as discriminating statistics. The discriminating statistics are compared with surrogate data streams that are constructed using the corrected amplitude adjustment Fourier transform (CAAFT) method and capture the linear properties of the original K(sub)p data. Differences are regularly seen in the discriminating statistics a few years prior to solar minima, while no differences are apparent at the time of solar maximum. These results suggest that the dynamics of the magnetosphere tend to be more linear at solar maximum than at solar minimum. The strong nonlinear dependencies tend to peak on a timescale around 40-50 hours and are statistically significant up to one week. Because the solar wind driver variables, VB(sub)s and dynamical pressure exhibit a much shorter decorrelation time for nonlinearities, the results seem to indicate that the nonlinearity is related to internal magnetospheric dynamics. Moreover, the timescales for the nonlinearity seem to be on the same order as that for storm/ring current relaxation. We suggest that the strong solar wind driving that occurs around solar maximum dominates the magnetospheric dynamics suppressing the internal magnetospheric nonlinearity. On the other hand, in the descending phase of the solar cycle just prior to solar minimum, when magnetospheric activity is weaker, the dynamics exhibit a significant nonlinear internal magnetospheric response that may be related to increased solar wind speed.
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
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.
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 ...
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.
Discrete-time nonlinear sliding mode controller
African Journals Online (AJOL)
user
: 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.
Energy Technology Data Exchange (ETDEWEB)
Camporeale, Enrico, E-mail: e.camporeale@cwi.nl [Center for Mathematics and Computer Science (CWI), 1098 XG Amsterdam (Netherlands); Zimbardo, Gaetano [Department of Physics, University of Calabria, Ponte P. Bucci, Cubo 31C, I-87036 Rende (Italy)
2015-09-15
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 Earth's 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 radiation belt studies. In particular, we show that pitch angle diffusion is enhanced during the linear growth phase, and it rapidly saturates well before a single bounce period. This calls into question the widely used bounce average performed in most radiation belt diffusion calculations. Furthermore, we discuss how the saturation is related to the fact that the domain in which the particles pitch angle diffuses is bounded, and to the well-known problem of 90° diffusion barrier.
Camporeale, Enrico
2014-01-01
We present self-consistent Particle-in-Cell simulations of the resonant interactions between anisotropic energetic electrons and a population of whistler waves, with parameters relevant to the Earth's radiation belt. By tracking PIC particles, and comparing with test-particles 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 radiation belt studies. In particular we show that pitch angle diffusion is enhanced during the linear growth phase, and it rapidly saturates. We discuss how the saturation is related to the fact that the domain in which the particles' pitch angle diffuse is bounded, and to the well-known problem of $90^\\circ$ diffusion barrier.
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.
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.
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).
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.
Kyoung, Ho Han; H. J., Shin
2010-12-01
We investigate the Painlevé integrability of nonautonomous nonlinear Schrödinger (NLS) equations with both space- and time-dependent dispersion, nonlinearity, and external potentials. The Painlevé analysis is carried out without using the Kruskal's simplification, which results in more generalized form of inhomogeneous equations. The obtained equations are shown to be reducible to the standard NLS equation by using a point transformation. We also construct the corresponding Lax pair and carry out its Kundu-type reduction to the standard Lax pair. Special cases of equations from choosing limited form of coefficients coincide with the equations from the previous Painlevé analyses and/or become unknown new equations.
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.
State dependent matrices and balanced energy functions for nonlinear systems
Scherpen, Jacquelien M.A.; Gray, W. Steven
2000-01-01
The nonlinear extension of the balancing procedure requires the case of state dependent quadratic forms for the energy functions, i.e., the nonlinear extensions of the linear Gramians are state dependent matrices. These extensions have some interesting ambiguities that do not occur in the linear cas
Non-linear dependences in finance
Chicheportiche, Rémy
2013-01-01
The thesis is composed of three parts. Part I introduces the mathematical and statistical tools that are relevant for the study of dependences, as well as statistical tests of Goodness-of-fit for empirical probability distributions. I propose two extensions of usual tests when dependence is present in the sample data and when observations have a fat-tailed distribution. The financial content of the thesis starts in Part II. I present there my studies regarding the "cross-sectional" dependences among the time series of daily stock returns, i.e. the instantaneous forces that link several stocks together and make them behave somewhat collectively rather than purely independently. A calibration of a new factor model is presented here, together with a comparison to measurements on real data. Finally, Part III investigates the temporal dependences of single time series, using the same tools and measures of correlation. I propose two contributions to the study of the origin and description of "volatility clustering"...
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.
Sato, Shunsuke A.; Taniguchi, Yasutaka; Shinohara, Yasushi; Yabana, Kazuhiro
2015-12-01
We develop methods to calculate electron dynamics in crystalline solids in real-time time-dependent density functional theory employing exchange-correlation potentials which reproduce band gap energies of dielectrics; a meta-generalized gradient approximation was proposed by Tran and Blaha [Phys. Rev. Lett. 102, 226401 (2009)] (TBm-BJ) and a hybrid functional was proposed by Heyd, Scuseria, and Ernzerhof [J. Chem. Phys. 118, 8207 (2003)] (HSE). In time evolution calculations employing the TB-mBJ potential, we have found it necessary to adopt the predictor-corrector step for a stable time evolution. We have developed a method to evaluate electronic excitation energy without referring to the energy functional which is unknown for the TB-mBJ potential. For the HSE functional, we have developed a method for the operation of the Fock-like term in Fourier space to facilitate efficient use of massive parallel computers equipped with graphic processing units. We compare electronic excitations in silicon and germanium induced by femtosecond laser pulses using the TB-mBJ, HSE, and a simple local density approximation (LDA). At low laser intensities, electronic excitations are found to be sensitive to the band gap energy: they are close to each other using TB-mBJ and HSE and are much smaller in LDA. At high laser intensities close to the damage threshold, electronic excitation energies do not differ much among the three cases.
Energy Technology Data Exchange (ETDEWEB)
Sato, Shunsuke A. [Graduate School of Pure and Applied Sciences, University of Tsukuba, Tsukuba 305-8571 (Japan); Taniguchi, Yasutaka [Center for Computational Science, University of Tsukuba, Tsukuba 305-8571 (Japan); Department of Medical and General Sciences, Nihon Institute of Medical Science, 1276 Shimogawara, Moroyama-Machi, Iruma-Gun, Saitama 350-0435 (Japan); Shinohara, Yasushi [Max Planck Institute of Microstructure Physics, 06120 Halle (Germany); Yabana, Kazuhiro [Graduate School of Pure and Applied Sciences, University of Tsukuba, Tsukuba 305-8571 (Japan); Center for Computational Science, University of Tsukuba, Tsukuba 305-8571 (Japan)
2015-12-14
We develop methods to calculate electron dynamics in crystalline solids in real-time time-dependent density functional theory employing exchange-correlation potentials which reproduce band gap energies of dielectrics; a meta-generalized gradient approximation was proposed by Tran and Blaha [Phys. Rev. Lett. 102, 226401 (2009)] (TBm-BJ) and a hybrid functional was proposed by Heyd, Scuseria, and Ernzerhof [J. Chem. Phys. 118, 8207 (2003)] (HSE). In time evolution calculations employing the TB-mBJ potential, we have found it necessary to adopt the predictor-corrector step for a stable time evolution. We have developed a method to evaluate electronic excitation energy without referring to the energy functional which is unknown for the TB-mBJ potential. For the HSE functional, we have developed a method for the operation of the Fock-like term in Fourier space to facilitate efficient use of massive parallel computers equipped with graphic processing units. We compare electronic excitations in silicon and germanium induced by femtosecond laser pulses using the TB-mBJ, HSE, and a simple local density approximation (LDA). At low laser intensities, electronic excitations are found to be sensitive to the band gap energy: they are close to each other using TB-mBJ and HSE and are much smaller in LDA. At high laser intensities close to the damage threshold, electronic excitation energies do not differ much among the three cases.
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.
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...
Crystalline structure and symmetry dependence of acoustic nonlinearity parameters
Cantrell, John H.
1994-01-01
A quantitative measure of elastic wave nonlinearity in crystals is provided by the acoustic nonlinearity parameters. The nonlinearity parameters are defined for arbitrary propagation modes for solids of arbitrary crystalline symmetry and are determined along the pure mode propagation directions for 33 crystals of cubic symmetry from data reported in the literature. The magnitudes of the nonlinearity parameters are found to exhibit a strong dependence on the crystalline structure and symmetries associated with the modal direction in the solid. Calculations based on the Born-Mayer potential for crystals having a dominant repulsive contribution to the elastic constants from the interatomic pair potential suggest that the origin of the structure dependence is associated with the shape rather than the strength of the potential. Considerations based on variations in crystal symmetry during loading along pure mode propagation directions of face-centered-cubic solids provide a qualitative explanation for the dependence of the acoustic nonlinearity parameters on modal direction.
Irregular Time Dependent Obstacles
Lindqvist, Peter
2010-01-01
We study the obstacle problem for the Evolutionary p-Laplace Equation when the obstacle is discontinuous and without regularity in the time variable. Two quite different procedures yield the same solution.
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.
Modelling Nonlinearities and Reference Dependence in General Practitioners' Income Preferences.
Holte, Jon Helgheim; Sivey, Peter; Abelsen, Birgit; Olsen, Jan Abel
2016-08-01
This paper tests for the existence of nonlinearity and reference dependence in income preferences for general practitioners. Confirming the theory of reference dependent utility within the context of a discrete choice experiment, we find that losses loom larger than gains in income for Norwegian general practitioners, i.e. they value losses from their current income level around three times higher than the equivalent gains. Our results are validated by comparison with equivalent contingent valuation values for marginal willingness to pay and marginal willingness to accept compensation for changes in job characteristics. Physicians' income preferences determine the effectiveness of 'pay for performance' and other incentive schemes. Our results may explain the relative ineffectiveness of financial incentive schemes that rely on increasing physicians' incomes. Copyright © 2015 John Wiley & Sons, Ltd.
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...
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.
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...
Ioannidou, Theodora
2016-01-01
An extended version of the BPS Skyrme model that admits time-dependent solutions is discussed. Initially, by introducing a power law at the original potential term of the BPS Skyrme model the existence, stability and structure of the corresponding solutions is investigated. Then, the frequencies and half-lifes of the radial oscillations of the constructed time-dependent solutions are determined.
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.
Nonlinear Structure Formation with the Environmentally Dependent Dilaton
Brax, Phil; Davis, Anne-C; Li, Baojiu; Shaw, Douglas J
2011-01-01
We have studied the nonlinear structure formation of the environmentally dependent dilaton model using $N$-body simulations. We find that the mechanism of suppressing the scalar fifth force in high-density regions works very well. Within the parameter space allowed by the solar system tests, the dilaton model predicts small deviations of the matter power spectrum and the mass function from their $\\Lambda$CDM counterparts. The importance of taking full account of the nonlinearity of the model is also emphasized.
1983-12-01
of appropriate time step lengths is complicated by the fact that two distinct processes are involved, i.e. water flow and soil plasticity . Thus a...1981. 9. DeNatale, 3.S., L.R. Herrmann, and Y.F. Dafalias, "User’s Manual for MODCAL-Bounding Surface Soil Plasticity Model Calibration and Prediction
Time-Dependent Lagrangian Biomechanics
Ivancevic, Tijana T
2009-01-01
In this paper we present the time-dependent generalization of an 'ordinary' autonomous human musculo-skeletal biomechanics. We start with the configuration manifold of human body, given as a set of its all active degrees of freedom (DOF). This is a Riemannian manifold with a material metric tensor given by the total mass-inertia matrix of the human body segments. This is the base manifold for standard autonomous biomechanics. To make its time-dependent generalization, we need to extend it with a real time axis. On this extended configuration space we develop time-dependent biomechanical Lagrangian dynamics, using derived jet spaces of velocities and accelerations, as well as the underlying geometric evolution of the mass-inertia matrix. Keywords: Human time-dependent biomechanics, configuration manifold, jet spaces, geometric evolution
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.
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.
On time dependent Ekman transports
National Research Council Canada - National Science Library
Roed, L.P
1973-01-01
One of the most cited papers in ocean current theories is the paper by Ekman (1905). Here we take his paper as a starting point for computing time dependent solutions for the integrated velocities or the transports.
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.
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.
Models for dependent time series
Tunnicliffe Wilson, Granville; Haywood, John
2015-01-01
Models for Dependent Time Series addresses the issues that arise and the methodology that can be applied when the dependence between time series is described and modeled. Whether you work in the economic, physical, or life sciences, the book shows you how to draw meaningful, applicable, and statistically valid conclusions from multivariate (or vector) time series data.The first four chapters discuss the two main pillars of the subject that have been developed over the last 60 years: vector autoregressive modeling and multivariate spectral analysis. These chapters provide the foundational mater
Dispersion and polarization dependence of mobile carrier optical nonlinearities
Rustagi, K. C.
1984-06-01
Based on the author's earlier work, it is shown that the proper inclusion of carrier scattering should strongly modify the frequency and polarization dependence of optical nonlinearities due to mobile carriers in semiconductors. When the momentum relaxation is much faster than the energy relaxation, the intensity dependent refractive index is enhanced, the induced birefringence becomes a sharp function of the difference frequency ωa-ωb, and a collision induced stimulated Raman effect becomes important.
Tiberkevich, V. S.; Slavin, A. N.; Kim, Joo-Von
2008-01-01
The temperature dependence of the generation linewidth for an auto-oscillator with a nonlinear frequency shift is calculated. It is shown that the frequency nonlinearity creates a finite correlation time, tau, for the phase fluctuations. In the low-temperature limit in which the spectral linewidth is smaller than 1/tau, the line shape is approximately Lorentzian and the linewidth is linear in temperature. In the opposite high-temperature limit in which the linewidth is larger than 1/tau, the ...
Time-Dependent Lagrangian Biomechanics
Ivancevic, Tijana T.
2009-01-01
In this paper we present the time-dependent generalization of an 'ordinary' autonomous human musculo-skeletal biomechanics. We start with the configuration manifold of human body, given as a set of its all active degrees of freedom (DOF). This is a Riemannian manifold with a material metric tensor given by the total mass-inertia matrix of the human body segments. This is the base manifold for standard autonomous biomechanics. To make its time-dependent generalization, we need to extend it wit...
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.
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.
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
An analysis of a new nonlinear estimation technique: The state-dependent Ricatti equation method
Ewing, Craig Michael
1999-10-01
Research into nonlinear estimation techniques for terminal homing missiles has been conducted for many decades. The terminal state estimator, also called the guidance filter, is responsible for providing accurate estimates of target motion for use in guiding the missile to a collision course with the target. Some form of the extended-Kalman filter (EKF) has become the standard estimation technique employed in most modern weapon guidance systems. EKF linearization of nonlinear dynamics and/or measurements can cause problems of divergence when confronted by highly nonlinear conditions. The objective of this dissertation is to analyze a new nonlinear estimation technique that is based on the parameterization of the nonlinearities. This parameterization converts the nonlinear estimation problem into the form of a steady-state continuous Kalman filtering problem with state-dependent coefficients. This new technique, called the state-dependent Ricatti equation filter (SDREF), allows the nonlinearities of the system to be fully incorporated into the filter design, before stochastic uncertainties are imposed, without the need for linearization. The SDREF was investigated in three problems: an exoatmospheric, terminal homing, ballistic-missile intercept problem; a highly nonlinear pendulum example; and an algorithmic loss of observability problem. The exoatmospheric guidance problem examined nonlinear measurements with linear dynamics. To investigate the SDREF when used with a combination of nonlinear dynamics and nonlinear measurements, a highly nonlinear, two-state pendulum problem was also examined. While these problems were useful in gaining insight into the performance characteristics of the SDREF, no formal proof of stability could be determined for the original formulation of the estimator. The original SDREF solved an algebraic SDRE that arose from an infinite-time horizon formulation of the nonlinear filtering problem. A modification to the SDREF formulation was
Time dependence of immersion freezing
Directory of Open Access Journals (Sweden)
A. Welti
2012-05-01
Full Text Available The time dependence of immersion freezing was studied for temperatures between 236 K and 243 K. Droplets with single immersed, size-selected 400 nm and 800 nm kaolinite particles were produced at 300 K, cooled down to supercooled temperatures typical for mixed-phase cloud conditions, and the fraction of frozen droplets with increasing residence time was detected. To simulate the conditions of immersion freezing in mixed-phase clouds we used the Zurich Ice Nucleation Chamber (ZINC and its vertical extension, the Immersion Mode Cooling chAmber (IMCA. We observed that the frozen fraction of droplets increased with increasing residence time in the chamber. This suggests that there is a time dependence of immersion freezing and supports the importance of a stochastic component in the ice nucleation process. The rate at which droplets freeze was observed to decrease towards higher temperatures and smaller particle sizes. Comparison of the laboratory data with four different ice nucleation models, three based on classical nucleation theory with different representations of the particle surface properties and one singular, suggest that the classical, stochastic approach combined with a distribution of contact angles is able to reproduce the ice nucleation observed in these experiments most accurately. Using the models to calculate the increase in frozen fraction at typical mixed-phase cloud temperatures over an extended period of time, yields an equivalent effect of −1 K temperature shift and an increase in time scale by a factor of ~10.
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.
Network-timing-dependent plasticity
Directory of Open Access Journals (Sweden)
Vincent eDelattre
2015-06-01
Full Text Available Bursts of activity in networks of neurons are thought to convey salient information and drive synaptic plasticity. Here we report that network bursts also exert a profound effect on Spike-Timing-Dependent Plasticity (STDP. In acute slices of juvenile rat somatosensory cortex we paired a network burst, which alone induced long-term depression (LTD, with STDP-induced long-term potentiation and depression (LTP and LTD. We observed that STDP-induced LTP was either unaffected, blocked or flipped into LTD by the network burst, and that STDP-induced LTD was either saturated or flipped into LTP, depending on the relative timing of the network burst with respect to spike coincidences of the STDP event. We hypothesized that network bursts flip STDP-induced LTP to LTD by depleting resources needed for LTP and therefore developed a resource-dependent STDP learning rule. In a model neural network under the influence of the proposed resource-dependent STDP rule, we found that excitatory synaptic coupling was homeostatically regulated to produce power law distributed burst amplitudes reflecting self-organized criticality, a state that ensures optimal information coding.
Network-timing-dependent plasticity.
Delattre, Vincent; Keller, Daniel; Perich, Matthew; Markram, Henry; Muller, Eilif B
2015-01-01
Bursts of activity in networks of neurons are thought to convey salient information and drive synaptic plasticity. Here we report that network bursts also exert a profound effect on Spike-Timing-Dependent Plasticity (STDP). In acute slices of juvenile rat somatosensory cortex we paired a network burst, which alone induced long-term depression (LTD), with STDP-induced long-term potentiation (LTP) and LTD. We observed that STDP-induced LTP was either unaffected, blocked or flipped into LTD by the network burst, and that STDP-induced LTD was either saturated or flipped into LTP, depending on the relative timing of the network burst with respect to spike coincidences of the STDP event. We hypothesized that network bursts flip STDP-induced LTP to LTD by depleting resources needed for LTP and therefore developed a resource-dependent STDP learning rule. In a model neural network under the influence of the proposed resource-dependent STDP rule, we found that excitatory synaptic coupling was homeostatically regulated to produce power law distributed burst amplitudes reflecting self-organized criticality, a state that ensures optimal information coding.
Time-dependent correlations in electricity markets
Energy Technology Data Exchange (ETDEWEB)
Alvarez-Ramirez, Jose; Escarela-Perez, Rafael [Departamento de Energia, Universidad Autonoma Metropolitana, Mexico DF, 09340 (Mexico)
2010-03-15
In the last years, many electricity markets were subjected to deregulated operation where prices are set by the action of market participants. In this form, producers and consumers rely on demand and price forecasts to decide their bidding strategies, allocate assets, negotiate bilateral contracts, hedge risks, and plan facility investments. A basic feature of efficient market hypothesis is the absence of correlations between price increments over any time scale leading to random walk-type behavior of prices, so arbitrage is not possible. However, recent studies have suggested that this is not the case and correlations are present in the behavior of diverse electricity markets. In this paper, a temporal quantification of electricity market correlations is made by means of detrended fluctuation and Allan analyses. The approach is applied to two Canadian electricity markets, Ontario and Alberta. The results show the existence of correlations in both demand and prices, exhibiting complex time-dependent behavior with lower correlations in winter while higher in summer. Relatively steady annual cycles in demand but unstable cycles in prices are detected. On the other hand, the more significant nonlinear effects (measured in terms of a multifractality index) are found for winter months, while the converse behavior is displayed during the summer period. In terms of forecasting models, our results suggest that nonlinear recursive models (e.g., feedback NNs) should be used for accurate day-ahead price estimation. In contrast, linear models can suffice for demand forecasting purposes. (author)
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...
A DELAY-DEPENDENT STABILITY CRITERION FOR NONLINEAR STOCHASTIC DELAY-INTEGRO-DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
Niu Yuanling; Zhang Chengjian; Duan Jinqiao
2011-01-01
A type of complex systems under both random influence and memory effects is considered.The systems are modeled by a class of nonlinear stochastic delay-integrodifferential equations.A delay-dependent stability criterion for such equations is derived under the condition that the time lags are small enough.Numerical simulations are presented to illustrate the theoretical result.
Nonlinear closed loop optimal control: a modified state-dependent Riccati equation.
Rafee Nekoo, S
2013-03-01
The state-dependent Riccati equation (SDRE), as a controller, has been introduced and implemented since the 90s. In this article, the other aspects of this controller are declared which shows the capability of this technique. First, a general case which has control nonlinearities and time varying weighting matrix Q is solved with three approaches: exact solution (ES), online control update (OCU) and power series approximation (PSA). The proposed PSA in this paper is able to deal with time varying or state-dependent Q in nonlinear systems. As a result of having the solution of nonlinear systems with complex Q containing constraints, using OCU and proposed PSA, a method is introduced to prevent the collision of an end-effector of a robot and an obstacle which shows the adaptability of the SDRE controller. Two examples to support the idea are presented and conferred. Supplementing constraints to the SDRE via matrix Q, this approach is named a modified SDRE.
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.
Delay-dependent passive control of linear systems with nonlinear perturbation
Institute of Scientific and Technical Information of China (English)
Li Caina; Cui Baotong
2008-01-01
The problem of delay-dependent passive control of a class of linear systems with nonlinear perturbation and time-varying delay in states is studied. The main idea aims at designing a state-feedback controller such that for a time-varying delay in states, the linear system with nonlinear perturbation remains robustly stable and passive.In the system, the delay is time-varying. And the derivation of delay has the maximum and minimum value. The time-varying nonlinear perturbation is allowed to be norm-bounded. Using the effective linear matrix inequality methodology, the sufficient condition is primarily obtained for the system to have robust stability and passivity.Subsequently the existent condition of a state feedback controller is given, and the explicit expression of the controller is obtained by means of the solution of linear matrix inequalities (LMIs). In the end, a numerical example is given to demonstrate the validity and applicability of the proposed approach.
Directional dependence of nonlinear surface acoustic waves in the (001) plane of cubic crystals.
Kumon, R E; Hamilton, M F
2002-05-01
Spectral evolution equations are used to perform analytical and numerical studies of nonlinear surface acoustic waves in the (001) plane of a variety of nonpiezoelectric cubic crystals. The basic theory underlying the model equations is outlined, and quasilinear solutions of the equations are presented. Expressions are also developed for a characteristic length scale for nonlinear distortion and a nonlinearity coefficient. A time-domain equation corresponding to the spectral equations is derived. Numerical calculations based on measured second- and third-order elastic constants taken from the literature are performed to predict the evolution of initially monofrequency surface waves. Nonlinearity matrix elements that indicate the coupling strength of harmonic interactions are shown to provide a useful tool for characterizing waveform distortion. The formation of compression or rarefaction shocks can be strongly dependent on the direction of propagation, and harmonic generation is suppressed or increased in certain directions.
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.
Amplitude-dependent contraction/elongation of nonlinear Lamb waves
Packo, Pawel; Staszewski, Wieslaw J.; Uhl, Tadeusz; Leamy, Michael J.
2016-04-01
Nonlinear elastic guided waves find application in various disciplines of science and engineering, such as non- destructive testing and structural health monitoring. Recent recognition and quantification of their amplitude- dependent changes in spectral properties has contributed to the development of new monitoring concepts for mechanical structures. The focus of this work is to investigate and predict amplitude-dependent shifts in Lamb wave dispersion curves. The theory for frequency/wavenumber shifts for plate waves, based on a Lindstedt-Poincaré perturbation approach, was presented by the authors in previous years. Equivalently, spectral properties changes can be seen as wavelength contraction/elongation. Within the proposed framework, the wavelength of a Lamb wave depends on several factors; e.g., wave amplitude and second-, third- and fourth-order elastic constants, and others. Various types of nonlinear effects are considered in presented studies. Sensitivity studies for model parameters, i.e. higher-order elastic constants, are performed to quantify their influence on Lamb wave frequency/wavenumber shifting, and to identify the key parameters governing wavelength tuning.
Time dependent mean-field games
Gomes, Diogo A.
2014-01-06
We consider time dependent mean-field games (MFG) with a local power-like dependence on the measure and Hamiltonians satisfying both sub and superquadratic growth conditions. We establish existence of smooth solutions under a certain set of conditions depending both on the growth of the Hamiltonian as well as on the dimension. In the subquadratic case this is done by combining a Gagliardo-Nirenberg type of argument with a new class of polynomial estimates for solutions of the Fokker-Planck equation in terms of LrLp- norms of DpH. These techniques do not apply to the superquadratic case. In this setting we recur to a delicate argument that combines the non-linear adjoint method with polynomial estimates for solutions of the Fokker-Planck equation in terms of L1L1-norms of DpH. Concerning the subquadratic case, we substantially improve and extend the results previously obtained. Furthermore, to the best of our knowledge, the superquadratic case has not been addressed in the literature yet. In fact, it is likely that our estimates may also add to the current understanding of Hamilton-Jacobi equations with superquadratic Hamiltonians.
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.
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.
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.
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.
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.
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.
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.
Stability on time-dependent domains: convective and dilution effects
Krechetnikov, R.; Knobloch, E.
2017-03-01
We explore near-critical behavior of spatially extended systems on time-dependent spatial domains with convective and dilution effects due to domain flow. As a paradigm, we use the Swift-Hohenberg equation, which is the simplest nonlinear model with a non-zero critical wavenumber, to study dynamic pattern formation on time-dependent domains. A universal amplitude equation governing weakly nonlinear evolution of patterns on time-dependent domains is derived and proves to be a generalization of the standard Ginzburg-Landau equation. Its key solutions identified here demonstrate a substantial variety-spatially periodic states with a time-dependent wavenumber, steady spatially non-periodic states, and pulse-train solutions-in contrast to extended systems on time-fixed domains. The effects of domain flow, such as bifurcation delay due to domain growth and destabilization due to oscillatory domain flow, on the Eckhaus instability responsible for phase slips in spatially periodic states are analyzed with the help of both local and global stability analyses. A nonlinear phase equation describing the approach to a phase-slip event is derived. Detailed analysis of a phase slip using multiple time scale methods demonstrates different mechanisms governing the wavelength changing process at different stages.
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.
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.
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 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.
Qing Wang, Yan; Zu, Jean W.
2017-10-01
This work investigates the porosity-dependent nonlinear forced vibrations of functionally graded piezoelectric material (FGPM) plates by using both analytical and numerical methods. The FGPM plates contain porosities owing to the technical issues during the preparation of FGPMs. Two types of porosity distribution, namely, even and uneven distribution, are considered. A modified power law model is adopted to describe the material properties of the porous FGPM plates. Using D’Alembert’s principle, the out-of-plane equation of motion is derived by taking into account the Kármán nonlinear geometrical relations. After that, the Galerkin method is used to discretize the equation of motion, resulting in a set of ordinary differential equations with respect to time. These ordinary differential equations are solved analytically by employing the harmonic balance method. The approximate analytical results are verified by using the adaptive step-size fourth-order Runge–Kutta method. By means of the perturbation technique, the stability of approximate analytical solutions is examined. An interesting nonlinear broadband vibration phenomenon is detected in the FGPM plates with porosities. Nonlinear frequency-response characteristics of the present smart structures are investigated for various system parameters including the porosity type, the porosity volume fraction, the electric potential, the external excitation, the damping and the constituent volume fraction. It is found that these parameters have significant effects on the nonlinear vibration characteristics of porous FGPM plates.
Copulas and time series with long-ranged dependences
Chicheportiche, Rémy
2013-01-01
We review ideas on temporal dependences and recurrences in discrete time series from several areas of natural and social sciences. We revisit existing studies and redefine the relevant observables in the language of copulas (joint laws of the ranks). We propose that copulas provide an appropriate mathematical framework to study non-linear time dependences and related concepts - like aftershocks, Omori law, recurrences, waiting times. We also critically argue using this global approach that previous phenomenological attempts involving only a long-ranged autocorrelation function lacked complexity in that they were essentially mono-scale.
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.
Model Penjadwalan Batch Multi Item dengan Dependent Processing Time
Directory of Open Access Journals (Sweden)
Sukoyo Sukoyo
2010-01-01
Full Text Available This paper investigates a development of single machine batch scheduling for multi items with dependent processing time. The batch scheduling problem is to determine simultaneously number of batch (N, which item and its size allocated for each batch, and processing sequences of resulting batches. We use total actual flow time as the objective of schedule performance. The multi item batch scheduling problem could be formulated into a biner-integer nonlinear programming model because the number of batch should be in integer value, the allocation of items to resulting batch need binary values, and also there are some non-linearity on objective function and constraint due to the dependent processing time. By applying relaxation on the decision variable of number of batch (N as parameter, a heuristic procedure could be applied to find solution of the single machine batch scheduling problem for multi items.
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.
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....
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.
Zhou, Kai-Ge; Zhao, Min; Chang, Meng-Jie; Wang, Qiang; Wu, Xin-Zhi; Song, Yinglin; Zhang, Hao-Li
2015-02-11
Size-dependent nonlinear optical properties of modification-free transition metal dichalcogenide (TMD) nanosheets are reported, including MoS2 , WS2 , and NbSe2 . Firstly, a gradient centrifugation method is demonstrated to separate the TMD nanosheets into different sizes. The successful size separation allows the study of size-dependent nonlinear optical properties of nanoscale TMD materials for the first time. Z-scan measurements indicate that the dispersion of MoS2 and WS2 nanosheets that are 50-60 nm thick leads to reverse saturable absorption (RSA), which is in contrast to the saturable absorption (SA) seen in the thicker samples. Moreover, the NbSe2 nanosheets show no size-dependent effects because of their metallic nature. The mechanism behind the size-dependent nonlinear optical properties of the semiconductive TMD nanosheets is revealed by transient transmission spectra measurements. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
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.
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.
A test of time-dependent theories of stellar convection
Gastine, T
2011-01-01
Context: In Cepheids close to the red edge of the classical instability strip, a coupling occurs between the acoustic oscillations and the convective motions close to the surface.The best topical models that account for this coupling rely on 1-D time-dependent convection (TDC) formulations. However, their intrinsic weakness comes from the large number of unconstrained free parameters entering in the description of turbulent convection. Aims: We compare two widely used TDC models with the first two-dimensional nonlinear direct numerical simulations (DNS) of the convection-pulsation coupling in which the acoustic oscillations are self-sustained by the kappa-mechanism. Methods: The free parameters appearing in the Stellingwerf and Kuhfuss TDC recipes are constrained using a chi2-test with the time-dependent convective flux that evolves in nonlinear simulations of highly-compressible convection with kappa-mechanism. Results: This work emphasises some inherent limits of TDC models, that is, the temporal variabilit...
Time-Dependent Seismic Tomography
Julian, B. R.
2008-12-01
Temporal changes in seismic wave speeds in the Earth's crust have been measured at several locations, notably The Geysers geothermal area in California, in studies that used three-dimensional seismic tomography. These studies have used conventional tomography methods to invert multiple seismic-wave arrival time data sets independently and assumed that any differences in the derived structures reflect real temporal variations. Such an assumption is dangerous because the results of repeated tomography experiments would differ even if the structure did not change, simply because of variation in the seismic ray distribution caused by the natural variation in earthquake locations. This problem can be severe when changes in the seismicity distribution are systematic, as, for example, at the onset of an aftershock sequence. The sudden change in the ray distribution can produce artifacts that mimic changes in the seismic wave speeds at the time of a large earthquake. Even if the source locations did not change (if only explosion data were used, for example), derived structures would inevitably differ because of observational errors. A better approach to determining what temporal changes are truly required by the data is to invert multiple data sets simultaneously, imposing constraints to minimize differences between the models for different epochs. This problem is similar to that of seeking models similar to some a priori initial assumption, and a method similar to "damped least squares" can solve it. The order of the system of normal equations for inverting data from two epochs is twice as large as that for a single epoch, and solving it by standard methods requires eight times the computational labor. We present an algorithm for reducing this factor to two, so that inverting multiple epochs simultaneously is comparable in difficulty to inverting them independently, and illustrate its performance using synthetic arrival times and observed data from several areas in
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.
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.
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.
Holographic Complexity for Time-Dependent Backgrounds
Momeni, Davood; Bahamonde, Sebastian; Myrzakulov, Ratbay
2016-01-01
In this paper, we will analyse the holographic complexity for time-dependent asymptotically $AdS$ geometries. We will first use a covariant zero mean curvature slicing of the time-dependent bulk geometries, and then use this co-dimension one spacelike slice of the bulk spacetime to define a co-dimension two minimal surface. The time-dependent holographic complexity will be defined using the volume enclosed by this minimal surface. This time-dependent holographic complexity will reduce to the usual holographic complexity for static geometries. We will analyse the time-dependence as a perturbation of the asymptotically $AdS$ geometries. Thus, we will obtain time-dependent asymptotically $AdS$ geometries, and we will calculate the holographic complexity for such a time-dependent geometries.
Spectral methods for time dependent partial differential equations
Gottlieb, D.; Turkel, E.
1983-01-01
The theory of spectral methods for time dependent partial differential equations is reviewed. When the domain is periodic Fourier methods are presented while for nonperiodic problems both Chebyshev and Legendre methods are discussed. The theory is presented for both hyperbolic and parabolic systems using both Galerkin and collocation procedures. While most of the review considers problems with constant coefficients the extension to nonlinear problems is also discussed. Some results for problems with shocks are presented.
Non-linear equation: energy conservation and impact parameter dependence
Kormilitzin, Andrey
2010-01-01
In this paper we address two questions: how energy conservation affects the solution to the non-linear equation, and how impact parameter dependence influences the inclusive production. Answering the first question we solve the modified BK equation which takes into account energy conservation. In spite of the fact that we used the simplified kernel, we believe that the main result of the paper: the small ($\\leq 40%$) suppression of the inclusive productiondue to energy conservation, reflects a general feature. This result leads us to believe that the small value of the nuclear modification factor is of a non-perturbative nature. In the solution a new scale appears $Q_{fr} = Q_s \\exp(-1/(2 \\bas))$ and the production of dipoles with the size larger than $2/Q_{fr}$ is suppressed. Therefore, we can expect that the typical temperature for hadron production is about $Q_{fr}$ ($ T \\approx Q_{fr}$). The simplified equation allows us to obtain a solution to Balitsky-Kovchegov equation taking into account the impact pa...
Time-dependent seismic tomography
Julian, B.R.; Foulger, G.R.
2010-01-01
Of methods for measuring temporal changes in seismic-wave speeds in the Earth, seismic tomography is among those that offer the highest spatial resolution. 3-D tomographic methods are commonly applied in this context by inverting seismic wave arrival time data sets from different epochs independently and assuming that differences in the derived structures represent real temporal variations. This assumption is dangerous because the results of independent inversions would differ even if the structure in the Earth did not change, due to observational errors and differences in the seismic ray distributions. The latter effect may be especially severe when data sets include earthquake swarms or aftershock sequences, and may produce the appearance of correlation between structural changes and seismicity when the wave speeds are actually temporally invariant. A better approach, which makes it possible to assess what changes are truly required by the data, is to invert multiple data sets simultaneously, minimizing the difference between models for different epochs as well as the rms arrival-time residuals. This problem leads, in the case of two epochs, to a system of normal equations whose order is twice as great as for a single epoch. The direct solution of this system would require twice as much memory and four times as much computational effort as would independent inversions. We present an algorithm, tomo4d, that takes advantage of the structure and sparseness of the system to obtain the solution with essentially no more effort than independent inversions require. No claim to original US government works Journal compilation ?? 2010 RAS.
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...
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.``
Sarkar, Tanmay
2015-06-01
In this paper, we demonstrate that previously reported traveling wave solutions for the fifth order KdV type equations with time dependent coefficients (Triki and Wazwaz, 2014) are incorrect. We present the corrected traveling wave solutions for fifth order KdV type equations using sine-cosine method. In addition, we provide traveling wave solutions for the Kawahara equation and Kaup-Kupershmidt equation as an application.
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.
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...
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...
Competing risks and time-dependent covariates
DEFF Research Database (Denmark)
Cortese, Giuliana; Andersen, Per K
2010-01-01
Time-dependent covariates are frequently encountered in regression analysis for event history data and competing risks. They are often essential predictors, which cannot be substituted by time-fixed covariates. This study briefly recalls the different types of time-dependent covariates...
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.
Real time process algebra with time-dependent conditions
Baeten, J.C.M.; Middelburg, C.A.
2000-01-01
We extend the main real time version of ACP presented in [6] with conditionals in which the condition depends on time. This extension facilitates flexible dependence of proccess behaviour on initialization time. We show that the conditions concerned generalize the conditions introduced earlier in a
Real time process algebra with time-dependent conditions
Baeten, J.C.M.; Middelburg, C.A.
2008-01-01
We extend the main real time version of ACP presented in [6] with conditionals in which the condition depends on time. This extension facilitates flexible dependence of proccess behaviour on initialization time. We show that the conditions concerned generalize the conditions introduced earlier in a
Real time process algebra with time-dependent conditions
Baeten, J.C.M.; Middelburg, C.A.
We extend the main real time version of ACP presented in [6] with conditionals in which the condition depends on time. This extension facilitates flexible dependence of proccess behaviour on initialization time. We show that the conditions concerned generalize the conditions introduced earlier
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.
Bohr Hamiltonian with time-dependent potential
Naderi, L.; Hassanabadi, H.; Sobhani, H.
2016-04-01
In this paper, Bohr Hamiltonian has been studied with the time-dependent potential. Using the Lewis-Riesenfeld dynamical invariant method appropriate dynamical invariant for this Hamiltonian has been constructed and the exact time-dependent wave functions of such a system have been derived due to this dynamical invariant.
Institute of Scientific and Technical Information of China (English)
GUO Qintao; ZHANG Lingmi; TAO Zheng
2008-01-01
Thin wall component is utilized to absorb impact energy of a structure. However, the dynamic behavior of such thin-walled structure is highly non-linear with material, geometry and boundary non-linearity. A model updating and validation procedure is proposed to build accurate finite element model of a frame structure with a non-linear thin-walled component for dynamic analysis. Design of experiments (DOE) and principal component decomposition (PCD) approach are applied to extract dynamic feature from nonlinear impact response for correlation of impact test result and FE model of the non-linear structure. A strain-rate-dependent non-linear model updating method is then developed to build accurate FE model of the structure. Computer simulation and a real frame structure with a highly non-linear thin-walled component are employed to demonstrate the feasibility and effectiveness of the proposed approach.
Zamani, Iman; Shafiee, Masoud; Ibeas, Asier
2014-05-01
The issue of exponential stability of a class of continuous-time switched nonlinear singular systems consisting of a family of stable and unstable subsystems with time-varying delay is considered in this paper. Based on the free-weighting matrix approach, the average dwell-time approach and by constructing a Lyapunov-like Krasovskii functional, delay-dependent sufficient conditions are derived and formulated to check the exponential stability of such systems in terms of linear matrix inequalities (LMIs). By checking the corresponding LMI conditions, the average dwell-time and switching signal conditions are obtained. This paper also highlights the relationship between the average dwell-time of the switched nonlinear singular time-delay system, its stability and the exponential convergence rate of differential and algebraic states. A numerical example shows the effectiveness of the proposed method.
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.
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.
Energy Technology Data Exchange (ETDEWEB)
Cloutier, J.R.; D`Souza, C.N.; Mracek, C.P. [Air Force Armament Directorate, Eglin, FL (United States)
1994-12-31
A little known technique for systematically designing nonlinear regulators is analyzed. The technique consists of first using direct parameterization to bring the nonlinear system to a linear structure having state-dependent coefficients (SDC). A state-dependent Riccati equation (SDRE) is then solved at each point x along the trajectory to obtain a nonlinear feedback controller of the form u = -R{sup -1}(x)B{sup T}(x)P(x)x, where P(x) is the solution of the SDRE. In the case of scalar x, it is shown that the SDRE approach yields a control solution which satisfies all of the necessary conditions for optimality even when the state and control weightings are functions of the state. It is also shown that the solution is globally asymptotically stable. In the multivariable case, the optimality, suboptimality and stability properties of the SDRE method are investigated. Under various mild assumptions of controllability and observability, the following is shown: (a) concerning the necessary conditions for optimality, where H is the Hamiltonian of the system, H{sub u} = 0 is always satisfied and, under stability, {lambda} = -H{sub x} is asymptotically satisfied at a quadratic rate as the states are driven toward the origin, (b) if it exists, a parameter-dependent SDC parameterization can be computed such that the multivariable SDRE closed loop solution satisfies all of the necessary conditions for optimality for a given initial condition, and (c) the method is locally asymptotically stable. A general nonlinear minimum-energy (nonlinear H{sub {infinity}}) problem is then posed. For this problem, the SDRF, method involves the solution of two coupled state-dependent Riccati equations at each point x along the trajectory. In the case of full state information, again under mild assumptions of controllability and observability, it is shown that the SDRE non-linear H{sub {infinity}} controller is internally locally asymptotically stable.
Riccati and Ermakov Equations in Time-Dependent and Time-Independent Quantum Systems
Directory of Open Access Journals (Sweden)
Dieter Schuch
2008-05-01
Full Text Available The time-evolution of the maximum and the width of exact analytic wave packet (WP solutions of the time-dependent Schrödinger equation (SE represents the particle and wave aspects, respectively, of the quantum system. The dynamics of the maximum, located at the mean value of position, is governed by the Newtonian equation of the corresponding classical problem. The width, which is directly proportional to the position uncertainty, obeys a complex nonlinear Riccati equation which can be transformed into a real nonlinear Ermakov equation. The coupled pair of these equations yields a dynamical invariant which plays a key role in our investigation. It can be expressed in terms of a complex variable that linearizes the Riccati equation. This variable also provides the time-dependent parameters that characterize the Green's function, or Feynman kernel, of the corresponding problem. From there, also the relation between the classical and quantum dynamics of the systems can be obtained. Furthermore, the close connection between the Ermakov invariant and the Wigner function will be shown. Factorization of the dynamical invariant allows for comparison with creation/annihilation operators and supersymmetry where the partner potentials fulfil (real Riccati equations. This provides the link to a nonlinear formulation of time-independent quantum mechanics in terms of an Ermakov equation for the amplitude of the stationary state wave functions combined with a conservation law. Comparison with SUSY and the time-dependent problems concludes our analysis.
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.
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.
Manimala, James M; Sun, C T
2016-06-01
The amplitude-dependent dynamic response in acoustic metamaterials having nonlinear local oscillator microstructures is studied using numerical simulations on representative discrete mass-spring models. Both cubically nonlinear hardening and softening local oscillator cases are considered. Single frequency, bi-frequency, and wave packet excitations at low and high amplitude levels were used to interrogate the models. The propagation and attenuation characteristics of harmonic waves in a tunable frequency range is found to correspond to the amplitude and nonlinearity-dependent shifts in the local resonance bandgap for such nonlinear acoustic metamaterials. A predominant shift in the propagated wave spectrum towards lower frequencies is observed. Moreover, the feasibility of amplitude and frequency-dependent selective filtering of composite signals consisting of individual frequency components which fall within propagating or attenuating regimes is demonstrated. Further enrichment of these wave manipulation mechanisms in acoustic metamaterials using different combinations of nonlinear microstructures presents device implications for acoustic filters and waveguides.
Yan, Xuehua
2014-01-01
This paper is the further investigation of work of Yan and Liu, 2011, and considers the global practical tracking problem by output feedback for a class of uncertain nonlinear systems with not only unmeasured states dependent growth but also time-varying time delay. Compared with the closely related works, the remarkableness of the paper is that the time-varying time delay and unmeasurable states are permitted in the system nonlinear growth. Motivated by the related tracking results and flexibly using the ideas and techniques of universal control and dead zone, an adaptive output-feedback tracking controller is explicitly designed with the help of a new Lyapunov-Krasovskii functional, to make the tracking error prescribed arbitrarily small after a finite time while keeping all the closed-loop signals bounded. A numerical example demonstrates the effectiveness of the results. PMID:25276859
Ansari, R.; Faraji Oskouie, M.; Gholami, R.
2016-01-01
In recent decades, mathematical modeling and engineering applications of fractional-order calculus have been extensively utilized to provide efficient simulation tools in the field of solid mechanics. In this paper, a nonlinear fractional nonlocal Euler-Bernoulli beam model is established using the concept of fractional derivative and nonlocal elasticity theory to investigate the size-dependent geometrically nonlinear free vibration of fractional viscoelastic nanobeams. The non-classical fractional integro-differential Euler-Bernoulli beam model contains the nonlocal parameter, viscoelasticity coefficient and order of the fractional derivative to interpret the size effect, viscoelastic material and fractional behavior in the nanoscale fractional viscoelastic structures, respectively. In the solution procedure, the Galerkin method is employed to reduce the fractional integro-partial differential governing equation to a fractional ordinary differential equation in the time domain. Afterwards, the predictor-corrector method is used to solve the nonlinear fractional time-dependent equation. Finally, the influences of nonlocal parameter, order of fractional derivative and viscoelasticity coefficient on the nonlinear time response of fractional viscoelastic nanobeams are discussed in detail. Moreover, comparisons are made between the time responses of linear and nonlinear models.
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
Directory of Open Access Journals (Sweden)
A. D. Pataraya
Full Text Available Non-linear α-ω; dynamo waves existing in an incompressible medium with the turbulence dissipative coefficients depending on temperature are studied in this paper. We investigate of α-ω solar non-linear dynamo waves when only the first harmonics of magnetic induction components are included. If we ignore the second harmonics in the non-linear equation, the turbulent magnetic diffusion coefficient increases together with the temperature, the coefficient of turbulent viscosity decreases, and for an interval of time the value of dynamo number is greater than 1. In these conditions a stationary solution of the non-linear equation for the dynamo wave's amplitude exists; meaning that the magnetic field is sufficiently excited. The amplitude of the dynamo waves oscillates and becomes stationary. Using these results we can explain the existence of Maunder's minimum.
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.
Scattering of time-harmonic elastic waves by an elastic inclusion with quadratic nonlinearity.
Tang, Guangxin; Jacobs, Laurence J; Qu, Jianmin
2012-04-01
This paper considers the scattering of a plane, time-harmonic wave by an inclusion with heterogeneous nonlinear elastic properties embedded in an otherwise homogeneous linear elastic solid. When the inclusion and the surrounding matrix are both isotropic, the scattered second harmonic fields are obtained in terms of the Green's function of the surrounding medium. It is found that the second harmonic fields depend on two independent acoustic nonlinearity parameters related to the third order elastic constants. Solutions are also obtained when these two acoustic nonlinearity parameters are given as spatially random functions. An inverse procedure is developed to obtain the statistics of these two random functions from the measured forward and backscattered second harmonic fields.
Directory of Open Access Journals (Sweden)
Kanit Mukdasai
2012-01-01
Full Text Available This paper investigates the problem of robust exponential stability for linear parameter-dependent (LPD systems with discrete and distributed time-varying delays and nonlinear perturbations. Parameter dependent Lyapunov-Krasovskii functional, Leibniz-Newton formula, and linear matrix inequality are proposed to analyze the stability. On the basis of the estimation and by utilizing free-weighting matrices, new delay-dependent exponential stability criteria are established in terms of linear matrix inequalities (LMIs. Numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.
Dyja, Robert; van der Zee, Kristoffer G
2016-01-01
We present an adaptive methodology for the solution of (linear and) non-linear time dependent problems that is especially tailored for massively parallel computations. The basic concept is to solve for large blocks of space-time unknowns instead of marching sequentially in time. The methodology is a combination of a computationally efficient implementation of a parallel-in-space-time finite element solver coupled with a posteriori space-time error estimates and a parallel mesh generator. This methodology enables, in principle, simultaneous adaptivity in both space and time (within the block) domains. We explore this basic concept in the context of a variety of time-steppers including $\\Theta$-schemes and Backward Differentiate Formulas. We specifically illustrate this framework with applications involving time dependent linear, quasi-linear and semi-linear diffusion equations. We focus on investigating how the coupled space-time refinement indicators for this class of problems affect spatial adaptivity. Final...
Some results of a nodal method for nonlinear space-time reactor dynamics
Energy Technology Data Exchange (ETDEWEB)
Le, T.T. (Westinghouse Savannah River Co., Aiken, SC (United States)); Grossman, L.M. (California Univ., Berkeley, CA (United States). Dept. of Nuclear Engineering)
1991-01-01
There are many reports about nodal methods for static and dynamic problems, but not many for the nonlinear feedback cases. In this paper, a class of nodal methods called mathematical nodal method'' (MNM) is studied with the temperature feedback problems. The spatially complex domain of the problem is represented as a collection of geometrically simple subdomains of the size of fuel assemblies called nodes. Over each node, the time dependent coefficients of the neutron flux, precursor concentrations, fuel and coolant temperatures are the surface and volume weighted average (moment) values of the unknown solutions; the space dependent basis functions are a combination of Legendre polynomials. If the material parameters are a linear function of fuel and coolant temperatures, the coupled equations can be put in a dimensionless form and a system of time dependent ordinary differential equations containing nonlinear feedback terms is obtained. These nonlinear feedback terms are updated at each time step during the time iteration process. Results of some benchmark problems are included in this report.
Some results of a nodal method for nonlinear space-time reactor dynamics
Energy Technology Data Exchange (ETDEWEB)
Le, T.T. [Westinghouse Savannah River Co., Aiken, SC (United States); Grossman, L.M. [California Univ., Berkeley, CA (United States). Dept. of Nuclear Engineering
1991-12-31
There are many reports about nodal methods for static and dynamic problems, but not many for the nonlinear feedback cases. In this paper, a class of nodal methods called ``mathematical nodal method`` (MNM) is studied with the temperature feedback problems. The spatially complex domain of the problem is represented as a collection of geometrically simple subdomains of the size of fuel assemblies called nodes. Over each node, the time dependent coefficients of the neutron flux, precursor concentrations, fuel and coolant temperatures are the surface and volume weighted average (moment) values of the unknown solutions; the space dependent basis functions are a combination of Legendre polynomials. If the material parameters are a linear function of fuel and coolant temperatures, the coupled equations can be put in a dimensionless form and a system of time dependent ordinary differential equations containing nonlinear feedback terms is obtained. These nonlinear feedback terms are updated at each time step during the time iteration process. Results of some benchmark problems are included in this report.
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.
Chen, Weisheng; Jiao, Licheng; Li, Jing; Li, Ruihong
2010-06-01
For the first time, this paper addresses the problem of adaptive output-feedback control for a class of uncertain stochastic nonlinear strict-feedback systems with time-varying delays using neural networks (NNs). The circle criterion is applied to designing a nonlinear observer, and no linear growth condition is imposed on nonlinear functions depending on system states. Under the assumption that time-varying delays exist in the system output, only an NN is employed to compensate for all unknown nonlinear terms depending on the delayed output, and thus, the proposed control algorithm is more simple even than the existing NN backstepping control schemes for uncertain systems described by ordinary differential equations. Three examples are given to demonstrate the effectiveness of the control scheme proposed in this paper.
Machine scheduling with resource dependent processing times
Grigoriev, A.; Sviridenko, M.; Uetz, Marc Jochen
We consider machine scheduling on unrelated parallel machines with the objective to minimize the schedule makespan. We assume that, in addition to its machine dependence, the processing time of any job is dependent on the usage of a discrete renewable resource, e.g. workers. A given amount of that
Time-Dependent Transport in Nanoscale Devices
Institute of Scientific and Technical Information of China (English)
CHEN Zhi-Dong; ZHANG Jin-Yu; YU Zhi-Ping
2009-01-01
A method for simulating ballistic time-dependent device transport,which solves the time-dependent SchrSdinger equation using the finite difference time domain (FDTD) method together with Poisson's equation,is described in detail The effective mass SchrSdinger equation is solved. The continuous energy spectrum of the system is discretized using adaptive mesh,resulting in energy levels that sample the density-of-states.By calculating time evolution of wavefunctions at sampled energies,time-dependent transport characteristics such as current and charge density distributions are obtained.Simulation results in a uanowire and a coaxially gated carbon nanotube field-effect transistor (CNTFET) are presented.Transient effects,e.g.,finite rising time,are investigated in these devices.
Institute of Scientific and Technical Information of China (English)
Weihai ZHANG; Xuezhen LIU; Shulan KONG; Qinghua LI
2006-01-01
This paper treats the feedback stabilization of nonlinear stochastic time-delay systems with state and control-dependent noise. Some locally (globally) robustly stabilizable conditions are given in terms of matrix inequalities that are independent of the delay size. When it is applied to linear stochastic time-delay systems, sufficient conditions for the state-feedback stabilization are presented via linear matrix inequalities. Several previous results are extended to more general systems with both state and control-dependent noise, and easy computation algorithms are also given.
Time-dependent viscoelastic behavior of an LDPE melt
Institute of Scientific and Technical Information of China (English)
Shuxin Huang; Chuanjing Lu; Yurun Fan
2006-01-01
Two differential constitutive equations,i.e.Giesekus model and Johnson-Segalman model were employed here to predict the time-dependent viscoelastic behavior of an LDPE melt in thixotropy-loop experiments and step shear rate experiment. Multiple relaxation modes were adopted, and the parameters used to describe the nonlinear viscoelasticity in the two models were obtained by fitting the shear-thinning viscosity. The predictions on those transient shear characteristics by the two models are found in qualitative agreement with our previous experiments. Johnson-Segalman model predicts oscillation behavior in the thixotropy-loop and step shear rate experiments, whereas Giesekus model does not. Both models predict higher shear stresses than the experimental data in the case of long time shearing, implying that both models are not able to completely characterize the time-dependent shear stress of the-melt at high shear rate.
ALCHEMIC: Advanced time-dependent chemical kinetics
Semenov, Dmitry A.
2017-08-01
ALCHEMIC solves chemical kinetics problems, including gas-grain interactions, surface reactions, deuterium fractionization, and transport phenomena and can model the time-dependent chemical evolution of molecular clouds, hot cores, corinos, and protoplanetary disks.
Size-dependent nonlinear absorption and refraction of Ag nanoparticles excited by femtosecond lasers
Institute of Scientific and Technical Information of China (English)
Fan Guang-Hua; Qu Shi-Liang; Guo Zhong-Yi; Wang Qiang; Li Zhong-Guo
2012-01-01
Silver (Ag) nanoparticles with different average sizes are prepared,and the nonlinear absorption and refraction of these nanoparticles are investigated with femtosecond laser pulses at 800 nm.The smallest Ag nanoparticles show insignificant nonlinear absorption,whereas the larger ones show saturable absorption.By considering the previously reported positive nonlinear absorption of 9 nm Ag nanoparticles,the nonlinear absorptions of Ag nanoparticles are found to be size-dependent.All these nonlinear absorptions can be compatibly explained from the viewpoints of electronic transitions,energy bands and electronic structures in the conduction band of Ag nanoparticles.The nonlinear refraction is attributed to the effect of hot electrons arising from the intraband transition in the s-p conduction band of Ag nanoparticles.
Time delay in thin slabs with self-focusing Kerr-type nonlinearity
Isić, G.; Milanović, V.; Radovanović, J.; Ikonić, Z.; Indjin, D.; Harrison, P.
2008-03-01
Time delays for an intense transverse electric (TE) wave propagating through a Kerr-type nonlinear slab are investigated. The relation between the bidirectional group delay and the dwell time is derived and it is shown that the difference between them can be separated into three terms. The first one is the familiar self-interference time, due to the dispersion of the medium surrounding the slab. The other two terms are caused by the nonlinearity and oblique incidence of the TE wave. It is shown that the electric field distribution along the slab may be expressed in terms of Jacobi elliptic functions while the phase difference introduced by the slab is given in terms of incomplete elliptic integrals. The expressions for the field-intensity-dependent complex reflection and transmission coefficients are derived and the multivalued oscillatory behavior of the delay times for the case of a thin slab is demonstrated.
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
Coasting cosmologies with time dependent cosmological constant
Pimentel, L O; Pimentel, Luis O.
1999-01-01
The effect of a time dependent cosmological constant is considered in a family of scalar tensor theories. Friedmann-Robertson-Walker cosmological models for vacumm and perfect fluid matter are found. They have a linear expansion factor, the so called coasting cosmology, the gravitational "constant" decreace inversely with time; this model satisfy the Dirac hipotesis. The cosmological "constant" decreace inversely with the square of time, therefore we can have a very small value for it at present time.
Time-dependent Integrated Predictive Modeling of ITER Plasmas
Institute of Scientific and Technical Information of China (English)
R.V. Budny
2007-01-01
@@ Introduction Modeling burning plasmas is important for speeding progress toward practical Tokamak energy production. Examples of issues that can be elucidated by modelinginclude requirements for heating, fueling, torque, and current drive systems, design of diagnostics, and estimates of the plasma performance (e.g., fusion power production) in various plasma scenarios. The modeling should be time-dependent to demonstrate that burning plasmas can be created, maintained (controlled), and terminated successfully. The modeling also should be integrated to treat self-consistently the nonlinearities and strong coupling between the plasma, heating, current drive, confinement, and control systems.
Wang, Chao; Yuan, Yizhong; Tian, Xiaohui; Sun, Jinyu; Shao, Hongjuan; Sun, Zhenrong
2013-09-01
The linear and third-order nonlinear optical properties of four polymethine cyanines (PC-1-PC-4) were investigated by UV-visible absorption spectroscopy and degenerate four-wave mixing (DFWM) technique. The second-order hyperpolarizabilities γ of the four chromophores achieve 10-31 esu. The dependence of their third-order optical nonlinearities on the molecular structure was discussed based on density functional theory (DFT) and time-dependent density functional theory (TDDFT) calculations. The calculated second-order hyperpolarizabilities γ well-reproduce the experimental trends. The results show that the third-order optical nonlinearities of the chromophores can be drastically enhanced by bulky heteroatom (such as selenium) with low electro-negativity, or extended π-conjugated terminal group.
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.
Sierra, Carlos; Müller, Markus
2016-04-01
SoilR is an R package for implementing diverse models representing soil organic matter dynamics. In previous releases of this package, we presented the implementation of linear first-order models with any number of pools as well as radiocarbon dynamics. We present here new improvements of the package regarding the possibility to implement models with nonlinear interactions among state variables and the possibility to calculate ages and transit times for nonlinear models with time dependencies. We show here examples on how to implement model structures with Michaelis-Menten terms for explicit microbial growth and resource use efficiency, and Langmuir isotherms for representing adsorption of organic matter to mineral surfaces. These nonlinear terms can be implemented for any number of organic matter pools, microbial functional groups, or mineralogy, depending on user's requirements. Through a simple example, we also show how transit times of organic matter in soils are controlled by the time-dependencies of the input terms.
Noncommutative quantum mechanics in a time-dependent background
Dey, Sanjib; Fring, Andreas
2014-10-01
We investigate a quantum mechanical system on a noncommutative space for which the structure constant is explicitly time dependent. Any autonomous Hamiltonian on such a space acquires a time-dependent form in terms of the conventional canonical variables. We employ the Lewis-Riesenfeld method of invariants to construct explicit analytical solutions for the corresponding time-dependent Schrödinger equation. The eigenfunctions are expressed in terms of the solutions of variants of the nonlinear Ermakov-Pinney equation and discussed in detail for various types of background fields. We utilize the solutions to verify a generalized version of Heisenberg's uncertainty relations for which the lower bound becomes a time-dependent function of the background fields. We study the variance for various states, including standard Glauber coherent states with their squeezed versions and Gaussian Klauder coherent states resembling a quasiclassical behavior. No type of coherent state appears to be optimal in general with regard to achieving minimal uncertainties, as this feature turns out to be background field dependent.
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.
Pulsar braking: Time dependent moment of inertia?
Urbanec, Martin
2017-08-01
Pulsars rotate with extremely stable rotational frequency enabling one to measure its first and second time derivatives. These observed values can be combined to the so-called braking index. However observed values of braking index differ from the theoretical value of 3 corresponding to braking by magnetic dipole radiation being the dominant theoretical model. Such a difference can be explained by contribution of other mechanism like pulsar wind or quadrupole radiation, or by time dependency of magnetic field or moment of inertia. In this presentation we focus on influence of time dependent moment of inertia on the braking index. We will also discuss possible physical models for time-dependence of moment of inertia.
Time-dependent species sensitivity distributions.
Fox, David R; Billoir, Elise
2013-02-01
Time is a central component of toxicity assessments. However, current ecotoxicological practice marginalizes time in concentration-response (C-R) modeling and species sensitivity distribution (SSD) analyses. For C-R models, time is invariably fixed, and toxicity measures are estimated from a function fitted to the data at that time. The estimated toxicity measures are used as inputs to the SSD modeling phase, which similarly avoids explicit recognition of the temporal component. The present study extends some commonly employed probability models for SSDs to derive theoretical results that characterize the time-dependent nature of hazardous concentration (HCx) values. The authors' results show that even from very simple assumptions, more complex patterns in the SSD time dependency can be revealed.
Institute of Scientific and Technical Information of China (English)
Xiao Li; Zhang Wei; Huang Yi-Dong; Peng Jiang-De
2008-01-01
High nonlinear microstructure fibre (HNMF) is preferred in nonlinear fibre optics, especially in the applications of optical parametric effects, due to its high optical nonlinear coefficient. However, polarization dependent dispersion will impact the nonlinear optical parametric process in HNMFs. In this paper, modulation instability (MI) method is used to measure the polarization dependent dispersion of a piece of commercial HNMF, including the group velocity dispersion, the dispersion slope, the fourth-order dispersion and group birefringence. It also experimentally demonstrates the impact of the polarization dependent dispersion on the continuous wave supercontinuum (SC) generation. On one axis MI sidebands with symmetric frequency dctunings are generated, while on the other axis with larger MI frequency detuning, SC is generated by soliton self-frequency shift.
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
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.
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.
The quantile spectral density and comparison based tests for nonlinear time series
Lee, Junbum
2011-01-01
In this paper we consider tests for nonlinear time series, which are motivated by the notion of serial dependence. The proposed tests are based on comparisons with the quantile spectral density, which can be considered as a quantile version of the usual spectral density function. The quantile spectral density 'measures' sequential dependence structure of a time series, and is well defined under relatively weak mixing conditions. We propose an estimator for the quantile spectral density and derive its asympototic sampling properties. We use the quantile spectral density to construct a goodness of fit test for time series and explain how this test can also be used for comparing the sequential dependence structure of two time series. The method is illustrated with simulations and some real data examples.
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.
Hamiltonian formulation of time-dependent plausible inference
Davis, Sergio
2014-01-01
Maximization of the path information entropy is a clear prescription for performing time-dependent plausible inference. Here it is shown that, following this prescription under the assumption of arbitrary instantaneous constraints on position and velocity, a Lagrangian emerges which determines the most probable trajectory. Deviations from the probability maximum can be consistently described as slices in time by a Hamiltonian, according to a nonlinear Langevin equation and its associated Fokker-Planck equation. The connections unveiled between the maximization of path entropy and the Langevin/Fokker-Planck equations imply that missing information about the phase space coordinate never decreases in time, a purely information-theoretical version of the Second Law of Thermodynamics. All of these results are independent of any physical assumptions, and thus valid for any generalized coordinate as a function of time, or any other parameter. This reinforces the view that the Second Law is a fundamental property of ...
Fredette, Luke; Dreyer, Jason T.; Rook, Todd E.; Singh, Rajendra
2016-06-01
The dynamic stiffness properties of automotive hydraulic bushings exhibit significant amplitude sensitivity which cannot be captured by linear time-invariant models. Quasi-linear and nonlinear models are therefore proposed with focus on the amplitude sensitivity in magnitude and loss angle spectra (up to 50 Hz). Since production bushing model parameters are unknown, dynamic stiffness tests and laboratory experiments are utilized to extract model parameters. Nonlinear compliance and resistance elements are incorporated, including their interactions in order to improve amplitude sensitive predictions. New solution approximations for the new nonlinear system equations refine the multi-term harmonic balance term method. Quasi-linear models yield excellent accuracy but cannot predict trends in amplitude sensitivity since they rely on available dynamic stiffness measurements. Nonlinear models containing both nonlinear resistance and compliance elements yield superior predictions to those of prior models (with a single nonlinearity) while also providing more physical insight. Suggestion for further work is briefly mentioned.
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
Investigations of Low Temperature Time Dependent Cracking
Energy Technology Data Exchange (ETDEWEB)
Van der Sluys, W A; Robitz, E S; Young, B A; Bloom, J
2002-09-30
The objective of this project was to investigate metallurgical and mechanical phenomena associated with time dependent cracking of cold bent carbon steel piping at temperatures between 327 C and 360 C. Boiler piping failures have demonstrated that understanding the fundamental metallurgical and mechanical parameters controlling these failures is insufficient to eliminate it from the field. The results of the project consisted of the development of a testing methodology to reproduce low temperature time dependent cracking in laboratory specimens. This methodology was used to evaluate the cracking resistance of candidate heats in order to identify the factors that enhance cracking sensitivity. The resultant data was integrated into current available life prediction tools.
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.
Differential Geometry of Time-Dependent Mechanics
Giachetta, G; Sardanashvily, G
1997-01-01
The usual formulations of time-dependent mechanics start from a given splitting $Y=R\\times M$ of the coordinate bundle $Y\\to R$. From physical viewpoint, this splitting means that a reference frame has been chosen. Obviously, such a splitting is broken under reference frame transformations and time-dependent canonical transformations. Our goal is to formulate time-dependent mechanics in gauge-invariant form, i.e., independently of any reference frame. The main ingredient in this formulation is a connection on the bundle $Y\\to R$ which describes an arbitrary reference frame. We emphasize the following peculiarities of this approach to time-dependent mechanics. A phase space does not admit any canonical contact or presymplectic structure which would be preserved under reference frame transformations, whereas the canonical Poisson structure is degenerate. A Hamiltonian fails to be a function on a phase space. In particular, it can not participate in a Poisson bracket so that the evolution equation is not reduced...
Indian Academy of Sciences (India)
Hari Prakash; Devendra K Singh
2010-03-01
It is shown that all optical polarization states of light except plane and circular polarization states undergo an intensity-dependent change in normal incidence of light in an isotropic nonlinear Kerr medium. This effect should be detectable and we propose an experiment for detecting nonlinear susceptibility involved in that part of nonlinear polarization, which depends on the polarization state of light also.
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...
Queues with waiting time dependent service
DEFF Research Database (Denmark)
Bekker, R.; Koole, G. M.; Nielsen, Bo Friis
2011-01-01
Motivated by service levels in terms of the waiting-time distribution seen, for instance, in call centers, we consider two models for systems with a service discipline that depends on the waiting time. The first model deals with a single server that continuously adapts its service rate based...... on the waiting time of the first customer in line. In the second model, one queue is served by a primary server which is supplemented by a secondary server when the waiting of the first customer in line exceeds a threshold. Using level crossings for the waiting-time process of the first customer in line, we...
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.
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
Time-dependent problems and difference methods
Gustafsson, Bertil; Oliger, Joseph
2013-01-01
Praise for the First Edition "". . . fills a considerable gap in the numerical analysis literature by providing a self-contained treatment . . . this is an important work written in a clear style . . . warmly recommended to any graduate student or researcher in the field of the numerical solution of partial differential equations."" -SIAM Review Time-Dependent Problems and Difference Methods, Second Edition continues to provide guidance for the analysis of difference methods for computing approximate solutions to partial differential equations for time-de
dependent time-delay: Stability and stabilizability
Directory of Open Access Journals (Sweden)
E. K. Boukas
2002-01-01
Full Text Available This paper considers stochastic stability and stochastic stabilizability of linear discrete-time systems with Markovian jumps and mode-dependent time-delays. Linear matrix inequality (LMI techniques are used to obtain sufficient conditions for the stochastic stability and stochastic stabilizability of this class of systems. A control design algorithm is also provided. A numerical example is given to demonstrate the effectiveness of the obtained theoretical results.
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...
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.
Directory of Open Access Journals (Sweden)
Espen R. Jakobsen
2002-05-01
Full Text Available Using the maximum principle for semicontinuous functions [3,4], we prove a general ``continuous dependence on the nonlinearities'' estimate for bounded Holder continuous viscosity solutions of fully nonlinear degenerate elliptic equations. Furthermore, we provide existence, uniqueness, and Holder continuity results for bounded viscosity solutions of such equations. Our results are general enough to encompass Hamilton-Jacobi-Bellman-Isaacs's equations of zero-sum, two-player stochastic differential games. An immediate consequence of the results obtained herein is a rate of convergence for the vanishing viscosity method for fully nonlinear degenerate elliptic equations.
Barut—Girardello Coherent States for Nonlinear Oscillator with Position-Dependent Mass
Amir, Naila; Iqbal, Shahid
2016-07-01
Using ladder operators for the non-linear oscillator with position-dependent effective mass, realization of the dynamic group SU(1,1) is presented. Keeping in view the algebraic structure of the non-linear oscillator, coherent states are constructed using Barut—Girardello formalism and their basic properties are discussed. Furthermore, the statistical properties of these states are investigated by means of Mandel parameter and second order correlation function. Moreover, it is shown that in the harmonic limit, all the results obtained for the non-linear oscillator with spatially varying mass reduce to corresponding results of the linear oscillator with constant mass.
Thankappan, Aparna; Nampoori, V. P. N.; Thomas, Sabu
2016-09-01
In this report, we report the intensity dependant nonlinear absorption properties of bio-inspired hybrid materials (betanin-ZnO) embedded in polymeric matrices through the Z-scan technique using an Nd: YAG laser (532 nm, 7 ns, 10 Hz). We observed a change over in the sign of nonlinearity due to the interplay of exciton bleaching and optical limiting mechanisms. Light confinement effect and ship-in-a bottle effect play crucial roles. Theoretical analysis has been performed using a model based on nonlinear absorption coefficient and saturation intensity. The result of present study gives an additional mechanism for the gain enhancement in dye doped ZnO matrix.
Exact solutions to the supply chain equations for arbitrary, time-dependent demands
DEFF Research Database (Denmark)
Warburton, Roger D.H.; Hodgson, J.P.E.; Nielsen, Erland Hejn
2014-01-01
We study the impact on inventory of an unexpected, non-linear, time-dependent demand and present the exact solutions over time to the supply chain equations without requiring any approximations. We begin by imposing a boundary condition of stability at infinity, from which we derive expressions...... for the estimated demand and the target work in progress when the demand is time-dependent. The resulting inventory equation is solved in terms of the Lambert modes with all of the demand non-linearities confined to the pre-shape function. The series solution is exact, and all terms are reasonably easy to calculate......, so users can determine the inventory behavior to any desired precision. To illustrate, we solve the equations for a non-linear, quadratic time-dependence in the demand. For practical use, only a few terms in the series are required, a proposition illustrated by the For All Practical Purposes (FAPP...
Exact solutions to the supply chain equations for arbitrary, time-dependent demands
DEFF Research Database (Denmark)
Warburton, Roger D.H.; Hodgson, J.P.E.; Nielsen, Erland Hejn
2014-01-01
, so users can determine the inventory behavior to any desired precision. To illustrate, we solve the equations for a non-linear, quadratic time-dependence in the demand. For practical use, only a few terms in the series are required, a proposition illustrated by the For All Practical Purposes (FAPP......We study the impact on inventory of an unexpected, non-linear, time-dependent demand and present the exact solutions over time to the supply chain equations without requiring any approximations. We begin by imposing a boundary condition of stability at infinity, from which we derive expressions...... for the estimated demand and the target work in progress when the demand is time-dependent. The resulting inventory equation is solved in terms of the Lambert modes with all of the demand non-linearities confined to the pre-shape function. The series solution is exact, and all terms are reasonably easy to calculate...
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.
Temperature dependent nonlinear Hall effect in macroscopic Si-MOS antidot array
Kuntsevich, A. Yu.; Shupltetsov, A. V.; Nunuparov, M. S.
2015-01-01
By measuring magnetoresistance and Hall effect in classically moderate perpendicular magnetic field in Si-MOSFET-type macroscopic antidot array we found a novel effect: nonlinear with field, temperature- and density-dependent Hall resistivity. We discuss qualitative explanation of the phenomenon and suggest that it might originate from strong temperature dependence of the resistivity and mobility in the shells of the antidots.
Quantum Size- Dependent Third- Order Nonlinear Optical Susceptibility in Semiconductor Quantum Dots
Institute of Scientific and Technical Information of China (English)
SUN Ting; XIONG Gui-guang
2005-01-01
The density matrix approach has been employed to investigate the optical nonlinear polarization in a single semiconductor quantum dot(QD). Electron states are considered to be confined within a quantum dot with infinite potential barriers. It is shown, by numerical calculation, that the third-order nonlinear optical susceptibilities for a typical Si quantum dot is dependent on the quantum size of the quantum dot and the frequency of incident light.
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.
Directory of Open Access Journals (Sweden)
Xia Zhou
2013-01-01
Full Text Available The problem of bounded-input bounded-output (BIBO stabilization in mean square for a class of discrete-time stochastic control systems with mixed time-varying delays and nonlinear perturbations is investigated. Some novel delay-dependent stability conditions for the previously mentioned system are established by constructing a novel Lyapunov-Krasovskii function. These conditions are expressed in the forms of linear matrix inequalities (LMIs, whose feasibility can be easily checked by using MATLAB LMI Toolbox. Finally, a numerical example is given to illustrate the validity of the obtained results.
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.
Computing Finite-Time Lyapunov Exponents with Optimally Time Dependent Reduction
Babaee, Hessam; Farazmand, Mohammad; Sapsis, Themis; Haller, George
2016-11-01
We present a method to compute Finite-Time Lyapunov Exponents (FTLE) of a dynamical system using Optimally Time-Dependent (OTD) reduction recently introduced by H. Babaee and T. P. Sapsis. The OTD modes are a set of finite-dimensional, time-dependent, orthonormal basis {ui (x , t) } |i=1N that capture the directions associated with transient instabilities. The evolution equation of the OTD modes is derived from a minimization principle that optimally approximates the most unstable directions over finite times. To compute the FTLE, we evolve a single OTD mode along with the nonlinear dynamics. We approximate the FTLE from the reduced system obtained from projecting the instantaneous linearized dynamics onto the OTD mode. This results in a significant reduction in the computational cost compared to conventional methods for computing FTLE. We demonstrate the efficiency of our method for double Gyre and ABC flows. ARO project 66710-EG-YIP.
Time-Dependent Erosion of Ion Optics
Wirz, Richard E.; Anderson, John R.; Katz, Ira; Goebel, Dan M.
2008-01-01
The accurate prediction of thruster life requires time-dependent erosion estimates for the ion optics assembly. Such information is critical to end-of-life mechanisms such as electron backstreaming. CEX2D was recently modified to handle time-dependent erosion, double ions, and multiple throttle conditions in a single run. The modified code is called "CEX2D-t". Comparisons of CEX2D-t results with LDT and ELT post-tests results show good agreement for both screen and accel grid erosion including important erosion features such as chamfering of the downstream end of the accel grid and reduced rate of accel grid aperture enlargement with time.
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.
Timing intervals using population synchrony and spike timing dependent plasticity
Directory of Open Access Journals (Sweden)
Wei Xu
2016-12-01
Full Text Available We present a computational model by which ensembles of regularly spiking neurons can encode different time intervals through synchronous firing. We show that a neuron responding to a large population of convergent inputs has the potential to learn to produce an appropriately-timed output via spike-time dependent plasticity. We explain why temporal variability of this population synchrony increases with increasing time intervals. We also show that the scalar property of timing and its violation at short intervals can be explained by the spike-wise accumulation of jitter in the inter-spike intervals of timing neurons. We explore how the challenge of encoding longer time intervals can be overcome and conclude that this may involve a switch to a different population of neurons with lower firing rate, with the added effect of producing an earlier bias in response. Experimental data on human timing performance show features in agreement with the model’s output.
Sahoo, Avimanyu; Xu, Hao; Jagannathan, Sarangapani
2017-03-01
This paper presents an approximate optimal control of nonlinear continuous-time systems in affine form by using the adaptive dynamic programming (ADP) with event-sampled state and input vectors. The knowledge of the system dynamics is relaxed by using a neural network (NN) identifier with event-sampled inputs. The value function, which becomes an approximate solution to the Hamilton-Jacobi-Bellman equation, is generated by using event-sampled NN approximator. Subsequently, the NN identifier and the approximated value function are utilized to obtain the optimal control policy. Both the identifier and value function approximator weights are tuned only at the event-sampled instants leading to an aperiodic update scheme. A novel adaptive event sampling condition is designed to determine the sampling instants, such that the approximation accuracy and the stability are maintained. A positive lower bound on the minimum inter-sample time is guaranteed to avoid accumulation point, and the dependence of inter-sample time upon the NN weight estimates is analyzed. A local ultimate boundedness of the resulting nonlinear impulsive dynamical closed-loop system is shown. Finally, a numerical example is utilized to evaluate the performance of the near-optimal design. The net result is the design of an event-sampled ADP-based controller for nonlinear continuous-time systems.
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.
Time Circular Birefringence in Time-Dependent Magnetoelectric Media
Zhang, Ruo-Yang; Lin, Shi-Rong; Zhao, Qing; Wen, Weijia; Ge, Mo-Lin
2015-01-01
Light traveling in time-dependent media has many extraordinary properties which can be utilized to convert frequency, achieve temporal cloaking, and simulate cosmological phenomena. In this paper, we focus on time-dependent axion-type magnetoelectric (ME) media, and prove that light in these media always has two degenerate modes with opposite circular polarizations corresponding to one wave vector $\\mathbf{k}$, and name this effect "time circular birefringence" (TCB). By interchanging the status of space and time, the pair of TCB modes can appear simultaneously via "time refraction" and "time reflection" of a linear polarized incident wave at a time interface of ME media. The superposition of the two TCB modes causes the "time Faraday effect", namely the globally unified polarization axes rotate with time. A circularly polarized Gaussian pulse traversing a time interface is also studied. If the wave-vector spectrum of a pulse mainly concentrates in the non-traveling-wave band, the pulse will be trapped with n...
Discrete time queues with phase dependent arrivals
Daigle, J. N.; Lee, Y.; Magalhaes, M. N.
1994-02-01
The queueing behavior of many communication systems is well modeled by a queueing system in which time is slotted, and the number of entities that arrive during a slot is dependent upon the state of a discrete time, discrete state Markov chain. Techniques for analyzing such systems have appeared in the literature from time to time, but distributions have been presented in only rare instances. In this paper, we present the probability generating function (PGF) for joint and marginal buffer occupancy distributions of statistical time division multiplexing systems in this class. We discuss inversion of the PGF using discrete Fourier transforms, and also discuss a simple technique for obtaining moments of the queue length distribution. Numerical results, including queue length distributions for some special cases, are presented.
Transformation of time dependence to linear algebra
Menšík, Miroslav
2005-10-01
Reduced density matrix and memory function in the Nakajima-Zwanzig equation are expanded in properly chosen basis of special functions. This trick completely transforms time dependence to linear algebra. Then, the master equation for memory function is constructed and expanded in the same basis functions. For the model of a simple harmonic oscillator it is shown that this trick introduces infinite partial summation of the memory function in the system-bath interaction.
Nonlinear Dependence of Global Warming Prediction on Ocean State
Liang, M.; Lin, L.; Tung, K. K.; Yung, Y. L.; Sun, S.
2010-12-01
Global temperature has increased by 0.8 C since the pre-industrial era, and is likely to increase further if greenhouse gas emission continues unchecked. Various mitigation efforts are being negotiated among nations to keep the increase under 2 C, beyond which the outcome is believed to be catastrophic. Such policy efforts are currently based on predictions by the state-of-the-art coupled atmosphere ocean models (AOGCM). Caution is advised for their use for the purpose of short-term (less than a century) climate prediction as the predicted warming and spatial patterns vary depending on the initial state of the ocean, even in an ensemble mean. The range of uncertainty in such predictions by Intergovernmental Panel on Climate Change (IPCC) models may be underreported when models were run with their oceans at various stages of adjustment with their atmospheres. By comparing a very long run (> 1000 years) of the coupled Goddard Institute for Space Studies (GISS) model with what was reported to IPCC Fourth Assessment Report (AR4), we show that the fully adjusted model transient climate sensitivity should be 30% higher for the same model, and the 2 C warming should occur sooner than previously predicted. Using model archives we further argue that this may be a common problem for the IPCC AR4 models, since few, if any, of the models has a fully adjusted ocean. For all models, multi-decadal climate predictions to 2050 are highly dependent on the initial ocean state (and so are unreliable). Such dependence cannot be removed simply by subtracting the climate drift from control runs.
Institute of Scientific and Technical Information of China (English)
ZHOU Feifan; MU Mu
2012-01-01
This study examines the time and regime dependencies of sensitive areas identified by the conditional nonlinear optimal perturbation (CNOP) method for forecasts of two typhoons.Typhoon Meari (2004) was weakly nonlinear and is herein referred to as the linear case,while Typhoon Matsa (2005) was strongly nonlinear and is herein referred to as the nonlinear case.In the linear case,the sensitive areas identified for special forecast times when the initial time was fixed resembled those identified for other forecast times.Targeted observations deployed to improve a special time forecast would thus also benefit forecasts at other times.In the nonlinear case,the similarities among the sensitive areas identified for different forecast times were more limited.The deployment of targeted observations in the nonlinear case would therefore need to be adapted to achieve large improvenents for different targeted forecasts.For both cases,the closer the forecast time,the higher the similarities of the sensitive areas.When the forecast time was fixed,the sensitive areas in the linear case diverged continuously from the verification area as the forecast period lengthened,while those in the nonlinear case were always located around the initial cyclones.The deployment of targeted observations to improve a special forecast depends strongly on the time of deployment.An examination of the efficiency gained by reducing initial errors within the identified sensitive areas confirmed these results.In general,the greatest improvement in a special time forecast was obtained by identifying the sensitive areas for the corresponding forecast time period.
The Time Dependent CP Violation in Charm
Inguglia, Gianluca
2012-01-01
A model which describes the time-dependent CP formalism in $D^0$ decays has recently been proposed. There it has been highlighted a possible measurement of the angle $\\beta_c$, in the charm unitarity triangle, using the decays $D^0\\to K^+ K^-$ and $D^0\\to \\pi^+ \\pi^-$, and a measurement of the mixing phase $\\phi_{MIX}$. The same method can be used to measure the value of the parameter $x$, one of the two parameters defining charm mixing. We numerically evaluate the impact of a time-dependent analysis in terms of the possible outcomes from present and future experiments. We consider the scenarios of correlated $D^0$ mesons production at the center of mass energy of the $\\Psi(3770)$ at Super$B$, uncorrelated production at the center of mass energy of the $\\Upsilon(4S)$ at Super$B$ and Belle II, and LHCb. Recently a hint of direct CP violation in charm decays was reported by the LHCb collaboration, we estimate the rate of time-dependent asymmetry that could be achieved using their available data, and we generali...
Dissipative time-dependent quantum transport theory.
Zhang, Yu; Yam, Chi Yung; Chen, GuanHua
2013-04-28
A dissipative time-dependent quantum transport theory is developed to treat the transient current through molecular or nanoscopic devices in presence of electron-phonon interaction. The dissipation via phonon is taken into account by introducing a self-energy for the electron-phonon coupling in addition to the self-energy caused by the electrodes. Based on this, a numerical method is proposed. For practical implementation, the lowest order expansion is employed for the weak electron-phonon coupling case and the wide-band limit approximation is adopted for device and electrodes coupling. The corresponding hierarchical equation of motion is derived, which leads to an efficient and accurate time-dependent treatment of inelastic effect on transport for the weak electron-phonon interaction. The resulting method is applied to a one-level model system and a gold wire described by tight-binding model to demonstrate its validity and the importance of electron-phonon interaction for the quantum transport. As it is based on the effective single-electron model, the method can be readily extended to time-dependent density functional theory.
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...
Substituent Dependence of Third-Order Optical Nonlinearity in Chalcone Derivatives
Kiran, Anthony John; Satheesh Rai, Nooji; Chandrasekharan, Keloth; Kalluraya, Balakrishna; Rotermund, Fabian
2008-08-01
The third-order nonlinear optical properties of derivatives of dibenzylideneacetone were investigated using the single beam z-scan technique at 532 nm. A strong dependence of third-order optical nonlinearity on electron donor and acceptor type of substituents was observed. An enhancement in χ(3)-value of one order of magnitude was achieved upon the substitution of strong electron donors compared to that of the molecule substituted with an electron acceptor. The magnitude of nonlinear refractive index of these chalcones is as high as of 10-11 esu. Their nonlinear optical coefficients are larger than those of widely used thiophene oligomers and trans-1-[p-(p-dimethylaminobenzyl-azo)-benzyl]-2-(N-methyl-4-pyridinium)-ethene iodide (DABA-PEI) organic compounds.
Time-dependent Dyson orbital theory.
Gritsenko, O V; Baerends, E J
2016-08-21
Although time-dependent density functional theory (TDDFT) has become the tool of choice for real-time propagation of the electron density ρ(N)(t) of N-electron systems, it also encounters problems in this application. The first problem is the neglect of memory effects stemming from the, in TDDFT virtually unavoidable, adiabatic approximation, the second problem is the reliable evaluation of the probabilities P(n)(t) of multiple photoinduced ionization, while the third problem (which TDDFT shares with other approaches) is the reliable description of continuum states of the electrons ejected in the process of ionization. In this paper time-dependent Dyson orbital theory (TDDOT) is proposed. Exact TDDOT equations of motion (EOMs) for time-dependent Dyson orbitals are derived, which are linear differential equations with just static, feasible potentials of the electron-electron interaction. No adiabatic approximation is used, which formally resolves the first TDDFT problem. TDDOT offers formally exact expressions for the complete evolution in time of the wavefunction of the outgoing electron. This leads to the correlated probability of single ionization P(1)(t) as well as the probabilities of no ionization (P(0)(t)) and multiple ionization of n electrons, P(n)(t), which formally solves the second problem of TDDFT. For two-electron systems a proper description of the required continuum states appears to be rather straightforward, and both P(1)(t) and P(2)(t) can be calculated. Because of the exact formulation, TDDOT is expected to reproduce a notorious memory effect, the "knee structure" of the non-sequential double ionization of the He atom.
Adaptive output feedback control for nonlinear time-delay systems using neural network
Institute of Scientific and Technical Information of China (English)
Weisheng CHEN; Junmin LI
2006-01-01
This paper extends the adaptive neural network (NN) control approaches to a class of unknown output feedback nonlinear time-delay systems. An adaptive output feedback NN tracking controller is designed by backstepping technique. NNs are used to approximate unknown functions dependent on time delay. Delay-dependent filters are introduced for state estimation. The domination method is used to deal with the smooth time-delay basis functions. The adaptive bounding technique is employed to estimate the upper bound of the NN approximation errors. Based on LyapunovKrasovskii functional, the semi-global uniform ultimate boundedness of all the signals in the closed-loop system is proved.The feasibility is investigated by two illustrative simulation examples.
Fan, Xiaopeng; Zheng, Weihao; Liu, Hongjun; Zhuang, Xiujuan; Fan, Peng; Gong, Yanfang; Li, Honglai; Wu, Xueping; Jiang, Ying; Zhu, Xiaoli; Zhang, Qinglin; Zhou, Hong; Hu, Wei; Wang, Xiao; Duan, Xiangfeng; Pan, Anlian
2017-06-01
Recombination dynamics during photoluminescence (PL) in two-dimensional (2D) semiconducting transition metal dichalcogenides (TMDs) are complicated and can be easily affected by the surroundings because of their atomically thin structures. Herein, we studied the excitation power and temperature dependence of the recombination dynamics on the chemical vapor deposition-grown monolayer WS2via a combination of Raman, PL, and time-resolved PL spectroscopies. We found a red shift and parabolic intensity increase in the PL emission of the monolayer WS2 with the increasing excitation power and the decay time constants corresponding to the recombination of trions and excitons from transient PL dynamics. We attributed the abovementioned nonlinear changes in the PL peak positions and intensities to the combination of increasing carrier interaction and band structure renormalization rather than to the thermal effect from a laser. Furthermore, the excitation power-dependent Raman measurements support our conclusion. These findings and understanding will provide important information for the development of TMD-based optoelectronics and photonics.
Simulation of transverse beam splitting using time-dependent dipolar or quadrupolar kicks
Capoani, Federico
2017-01-01
Two simple systems with high relevance for accelerator physics have been studied in detail in the context of this Summer Student Project. These systems describe the motion under the influence of detuning with amplitude due to non-linear magnets and an external, time-dependent force of dipolar or quadrupolar nature.Two simple systems with high relevance for accelerator physics have been studied in detail in the context of this Summer Student Project. These systems describe the motion under the influence of detuning with amplitude due to non-linear magnets and an external, time-dependent force of dipolar or quadrupolar nature.
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.
Decoupled Scheme for Time-Dependent Natural Convection Problem II: Time Semidiscreteness
Directory of Open Access Journals (Sweden)
Tong Zhang
2014-01-01
stability and the corresponding optimal error estimates are presented. Furthermore, a decoupled numerical scheme is proposed by decoupling the nonlinear terms via temporal extrapolation; optimal error estimates are established. Finally, some numerical results are provided to verify the performances of the developed algorithms. Compared with the coupled numerical scheme, the decoupled algorithm not only keeps good accuracy but also saves a lot of computational cost. Both theoretical analysis and numerical experiments show the efficiency and effectiveness of the decoupled method for time-dependent natural convection problem.
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.
Müller, Markus; Meztler, Holger; Glatt, Anna; Sierra, Carlos
2016-04-01
We present theoretical methods to compute dynamic residence and transit time distributions for non-autonomous systems of pools governed by coupled nonlinear differential equations. Although transit time and age distributions have been used to describe reservoir models for a long time, a closer look to their assumptions reveals two major restrictions of generality in previous studies. First, the systems are assumed to be in equilibrium; and second, the equations under consideration are assumed to be linear. While both these assumptions greatly ease the computation and interpretation of transit time and age distributions they are not applicable to a wide range of problems. Moreover, the transfer of previous results learned from linear systems in steady state to the more complex nonlinear non-autonomous systems that do not even need to have equilibria, can be dangerously misleading. Fortunately the topic of time dependent age and transit time distributions has received some attention recently in hydrology, we aim to compute these distributions for systems of multiple reservoirs. We will discuss how storage selection functions can augment the information represented in an ODE system describing a system of reservoirs. We will present analytical and numerical algorithms and a Monte Carlo simulator to compute solutions for system transit time and age distributions for system-wide storage selection functions including the most simple, but important case of well mixed pools.
An SIR Epidemic Model with Time Delay and General Nonlinear Incidence Rate
Directory of Open Access Journals (Sweden)
Mingming Li
2014-01-01
Full Text Available An SIR epidemic model with nonlinear incidence rate and time delay is investigated. The disease transmission function and the rate that infected individuals recovered from the infected compartment are assumed to be governed by general functions F(S,I and G(I, respectively. By constructing Lyapunov functionals and using the Lyapunov-LaSalle invariance principle, the global asymptotic stability of the disease-free equilibrium and the endemic equilibrium is obtained. It is shown that the global properties of the system depend on both the properties of these general functions and the basic reproductive number R0.
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.
Uncovering Discrete Non-Linear Dependence with Information Theory
Directory of Open Access Journals (Sweden)
Anton Golub
2015-04-01
Full Text Available In this paper, we model discrete time series as discrete Markov processes of arbitrary order and derive the approximate distribution of the Kullback-Leibler divergence between a known transition probability matrix and its sample estimate. We introduce two new information-theoretic measurements: information memory loss and information codependence structure. The former measures the memory content within a Markov process and determines its optimal order. The latter assesses the codependence among Markov processes. Both measurements are evaluated on toy examples and applied on high frequency foreign exchange data, focusing on 2008 financial crisis and 2010/2011 Euro crisis.
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.
Frequency, pressure, and strain dependence of nonlinear elasticity in Berea Sandstone
Rivière, Jacques; Pimienta, Lucas; Scuderi, Marco; Candela, Thibault; Shokouhi, Parisa; Fortin, Jérôme; Schubnel, Alexandre; Marone, Chris; Johnson, Paul A.
2016-04-01
Acoustoelasticity measurements in a sample of room dry Berea sandstone are conducted at various loading frequencies to explore the transition between the quasi-static (f→0) and dynamic (few kilohertz) nonlinear elastic response. We carry out these measurements at multiple confining pressures and perform a multivariate regression analysis to quantify the dependence of the harmonic content on strain amplitude, frequency, and pressure. The modulus softening (equivalent to the harmonic at 0f) increases by a factor 2-3 over 3 orders of magnitude increase in frequency. Harmonics at 2f, 4f, and 6f exhibit similar behaviors. In contrast, the harmonic at 1f appears frequency independent. This result corroborates previous studies showing that the nonlinear elasticity of rocks can be described with a minimum of two physical mechanisms. This study provides quantitative data that describes the rate dependency of nonlinear elasticity. These findings can be used to improve theories relating the macroscopic elastic response to microstructural features.
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 ...
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.
SYMTRAN - A Time-dependent Symmetric Tandem Mirror Transport Code
Energy Technology Data Exchange (ETDEWEB)
Hua, D; Fowler, T
2004-06-15
A time-dependent version of the steady-state radial transport model in symmetric tandem mirrors in Ref. [1] has been coded up and first tests performed. Our code, named SYMTRAN, is an adaptation of the earlier SPHERE code for spheromaks, now modified for tandem mirror physics. Motivated by Post's new concept of kinetic stabilization of symmetric mirrors, it is an extension of the earlier TAMRAC rate-equation code omitting radial transport [2], which successfully accounted for experimental results in TMX. The SYMTRAN code differs from the earlier tandem mirror radial transport code TMT in that our code is focused on axisymmetric tandem mirrors and classical diffusion, whereas TMT emphasized non-ambipolar transport in TMX and MFTF-B due to yin-yang plugs and non-symmetric transitions between the plugs and axisymmetric center cell. Both codes exhibit interesting but different non-linear behavior.
A new differential equations-based model for nonlinear history-dependent magnetic behaviour
Aktaa, J
2000-01-01
The paper presents a new kind of numerical model describing nonlinear magnetic behaviour. The model is formulated as a set of differential equations taking into account history dependence phenomena like the magnetisation hysteresis as well as saturation effects. The capability of the model is demonstrated carrying out comparisons between measurements and calculations.
Input-output finite-time stabilisation of nonlinear stochastic system with missing measurements
Song, Jun; Niu, Yugang; Jia, Tinggang
2016-09-01
This paper considers the problem of the input-output finite-time stabilisation for a class of nonlinear stochastic system with state-dependent noise. The phenomenon of the missing measurements may occur when state signals are transmitted via communication networks. An estimating method is proposed to compensate the lost state information. And then, a compensator-based controller is designed to ensure the input-output finite-time stochastic stability (IO-FTSS) of the closed-loop system. Some parameters-dependent sufficient conditions are derived and the corresponding solving approach is given. Finally, numerical simulations are provided to demonstrate the feasibility and effectiveness of the developed IO-FTSS scheme.
Constitutive model with time-dependent deformations
DEFF Research Database (Denmark)
Krogsbøll, Anette
1998-01-01
are common in time as well as size. This problem is adressed by means of a new constitutive model for soils. It is able to describe the behavior of soils at different deformation rates. The model defines time-dependent and stress-related deformations separately. They are related to each other and they occur......In many geological and Engineering problems it is necessary to transform information from one scale to another. Data collected at laboratory scale are often used to evaluate field problems on a much larger scale. This is certainly true for geological problems where extreme scale differences...... simultanelously. The model is based on concepts from elasticity and viscoplasticity theories. In addition to Hooke's law for the elastic behavior, the framework for the viscoplastic behavior consists, in the general case (two-dimensional or three-dimensional), of a yield surface, an associated flow rule...
Time-dependent Cooling in Photoionized Plasma
Gnat, Orly
2017-02-01
I explore the thermal evolution and ionization states in gas cooling from an initially hot state in the presence of external photoionizing radiation. I compute the equilibrium and nonequilibrium cooling efficiencies, heating rates, and ion fractions for low-density gas cooling while exposed to the ionizing metagalactic background radiation at various redshifts (z = 0 ‑ 3), for a range of temperatures (108–104 K), densities (10‑7–103 cm‑3), and metallicities (10‑3–2 times solar). The results indicate the existence of a threshold ionization parameter, above which the cooling efficiencies are very close to those in photoionization equilibrium (so that departures from equilibrium may be neglected), and below which the cooling efficiencies resemble those in collisional time-dependent gas cooling with no external radiation (and are thus independent of density).
Nonlinear frequency-dependent synchronization in the developing hippocampus.
Prida, L M; Sanchez-Andres, J V
1999-07-01
Synchronous population activity is present both in normal and pathological conditions such as epilepsy. In the immature hippocampus, synchronous bursting is an electrophysiological conspicuous event. These bursts, known as giant depolarizing potentials (GDPs), are generated by the synchronized activation of interneurons and pyramidal cells via GABAA, N-methyl-D-aspartate, and AMPA receptors. Nevertheless the mechanism leading to this synchronization is still controversial. We have investigated the conditions under which synchronization arises in developing hippocampal networks. By means of simultaneous intracellular recordings, we show that GDPs result from local cooperation of active cells within an integration period prior to their onset. During this time interval, an increase in the number of excitatory postsynaptic potentials (EPSPs) takes place building up full synchronization between cells. These EPSPs are correlated with individual action potentials simultaneously occurring in neighboring cells. We have used EPSP frequency as an indicator of the neuronal activity underlying GDP generation. By comparing EPSP frequency with the occurrence of synchronized GDPs between CA3 and the fascia dentata (FD), we found that GDPs are fired in an all-or-none manner, which is characterized by a specific threshold of EPSP frequency from which synchronous GDPs emerge. In FD, the EPSP frequency-threshold for GDP onset is 17 Hz. GDPs are triggered similarly in CA3 by appropriate periodic stimulation of mossy fibers. The frequency threshold for CA3 GDP onset is 12 Hz. These findings clarify the local mechanism of synchronization underlying bursting in the developing hippocampus, indicating that GDPs are fired when background levels of EPSPs or action potentials have built up full synchronization by firing at specific frequencies (>12 Hz). Our results also demonstrate that spontaneous EPSPs and action potentials are important for the initiation of synchronous bursts in the
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...
The time-dependent Gutzwiller approximation
Fabrizio, Michele
2015-03-01
The time-dependent Gutzwiller Approximation (t-GA) is shown to be capable of tracking the off-equilibrium evolution both of coherent quasiparticles and of incoherent Hubbard bands. The method is used to demonstrate that the sharp dynamical crossover observed by time-dependent DMFT in the quench-dynamics of a half-filled Hubbard model can be identified within the t-GA as a genuine dynamical transition separating two distinct physical phases. This result, strictly variational for lattices of infinite coordination number, is intriguing as it actually questions the occurrence of thermalization. Next, we shall present how t-GA works in a multi-band model for V2O3 that displays a first-order Mott transition. We shall show that a physically accessible excitation pathway is able to collapse the Mott gap down and drive off-equilibrium the insulator into a metastable metal phase. Work supported by the European Union, Seventh Framework Programme, under the project GO FAST, Grant Agreement No. 280555.
Shagoshtasbi, Hooman; Deng, Peigang; Lee, Yi-Kuen
2015-08-01
Electroporation (EP) is a process of applying a pulsed intense electric field on the cell membrane to temporarily induce nanoscale electropores on the plasma membrane of biological cells. A nonlinear size-dependent equivalent circuit model of a single-cell electroporation system is proposed to investigate dynamic electromechanical behavior of cells on microfluidic chips during EP. This model consists of size-dependent electromechanical components of a cell, electrical components of poration media, and a microfluidic chip. A single-cell microfluidic EP chip with 3D microelectrode arrays along a microchannel is designed and fabricated to experimentally analyze the permeabilization of a cell. Predicted electrical current responses of the model are in good agreement (average error of 6%) with that of single-cell EP. The proposed model can successfully predict the time responses of transmembrane voltage, pore diameter, and pore density at four different stages of permeabilization. These stages are categorized based on electromechanical changes of the lipid membrane. The current-voltage characteristic curve of the cell membrane during EP is also investigated at different EP stages in detail. The model can precisely predict the electric breakdown of different cell lines at a specific critical cell membrane voltage of the target cell lines.
Synchronization transitions in coupled time-delay electronic circuits with a threshold nonlinearity.
Srinivasan, K; Senthilkumar, D V; Murali, K; Lakshmanan, M; Kurths, J
2011-06-01
Experimental observations of typical kinds of synchronization transitions are reported in unidirectionally coupled time-delay electronic circuits with a threshold nonlinearity and two time delays, namely feedback delay τ(1) and coupling delay τ(2). We have observed transitions from anticipatory to lag via complete synchronization and their inverse counterparts with excitatory and inhibitory couplings, respectively, as a function of the coupling delay τ(2). The anticipating and lag times depend on the difference between the feedback and the coupling delays. A single stability condition for all the different types of synchronization is found to be valid as the stability condition is independent of both the delays. Further, the existence of different kinds of synchronizations observed experimentally is corroborated by numerical simulations and from the changes in the Lyapunov exponents of the coupled time-delay systems.
Time Dependence of Hawking Radiation Entropy
Page, Don N
2013-01-01
If a black hole starts in a pure quantum state and evaporates completely by a unitary process, the von Neumann entropy of the Hawking radiation initially increases and then decreases back to zero when the black hole has disappeared. Here numerical results are given for an approximation to the time dependence of the radiation entropy under an assumption of fast scrambling, for large nonrotating black holes that emit essentially only photons and gravitons. The maximum of the von Neumann entropy then occurs after about 53.81% of the evaporation time, when the black hole has lost about 40.25% of its original Bekenstein-Hawking (BH) entropy (an upper bound for its von Neumann entropy) and then has a BH entropy that equals the entropy in the radiation, which is about 59.75% of the original BH entropy 4 pi M_0^2, or about 7.509 M_0^2 \\approx 6.268\\times 10^{76}(M_0/M_\\odot)^2, using my 1976 calculations that the photon and graviton emission process into empty space gives about 1.4847 times the BH entropy loss of the...
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.
Time-dependent tunneling of spin-polarized electrons in coupled quantum wells
Energy Technology Data Exchange (ETDEWEB)
Cruz, H; Luis, D [Departamento de Fisica Basica, Universidad de La Laguna, 38204 La Laguna, Tenerife (Spain)], E-mail: hcruz@ull.es
2008-02-15
We have solved the in-plane momentum-dependent effective-mass nonlinear Schroedinger equation for a spin-polarized electron wave packet in a InAs double quantum well system with an interlayer voltage. Considering a time-dependent Hartree potential, we have calculated the spin-polarized nonlinear electron dynamics between both quantum wells at different in-plane momentum values and applied bias. The spin-splitting caused by the Rashba effect is combined with the level matching between the spin dependent resonant tunneling levels making possible the observed local spin density oscillations which depend on the applied bias value. The filtering efficiency has been studied using time-dependent calculations.
Time dependent friction in a free gas
Fanelli, Cristiano; Sisti, Francesco; Stagno, Gabriele V.
2016-03-01
We consider a body moving in a perfect gas, described by the mean-field approximation and interacting elastically with the body, we study the friction exerted by the gas on the body fixed at constant velocities. The time evolution of the body in this setting was studied in Caprino et al. [Math. Phys. 264, 167-189 (2006)], Caprino et al. [Math. Models Methods Appl. Sci. 17, 1369-1403 (2007)], and Cavallaro [Rend. Mat. Appl. 27, 123-145 (2007)] for object with simple shape; the first study where a simple kind of concavity was considered was in Sisti and Ricciuti [SIAM J. Math. Anal. 46, 3759-3611 (2014)], showing new features in the dynamic but not in the friction term. The case of more general shape of the body was left out for further difficulties, and we believe indeed that there are actually non-trivial issues to be faced for these more general cases. To show this and in the spirit of getting a more realistic perspective in the study of friction problems, in this paper, we focused our attention on the friction term itself, studying its behavior on a body with a more general kind of concavity and fixed at constant velocities. We derive the expression of the friction term for constant velocities, we show how it is time dependent, and we give its exact estimate in time. Finally, we use this result to show the absence of a constant velocity in the actual dynamic of such a body.
Institute of Scientific and Technical Information of China (English)
ZHAO Shuang; WU Chong-Qing; WANG Yong-Jun
2009-01-01
Linewidth enhancement factors (LEFs) of the transverse electric mode and the transverse magnetic mode in bulk semiconductor optical amplifiers are measured using the nonlinear optical loop mirror method and the principal state of polarization vector method.The polarization dependence of LEFs plays an important role in the nonlinear polarization rotation.The relationship between the polarization-dependence of LEFs and nonlinear polarization rotation in the Stokes space is demonstrated.
Time-dependent Backgrounds Of String Theory
Maloney, A D
2003-01-01
This thesis is devoted to the study of time-dependent backgrounds in string theory. The first chapter contains a brief, non-technical introduction to the subject. In the second chapter quantum field theory in d-dimensional de Sitter space is studied, with an emphasis on the dS/CFT correspondence. We study a one-parameter family of dS-invariant vacua; this bulk vacuum dependence is dual to a deformation of the boundary CFT by a marginal operator. In odd spacetime dimensions the state with no particles on I- has no particles on I+ , implying the absence of particle production. In Kerr-dS, a thermal density matrix is found by tracing over causally inaccessible modes. Assuming Cardy's formula, the microscopic entropy of such a thermal state in the boundary CFT precisely equals the Bekenstein-Hawking value. Next, we construct de Sitter vacua of supercritical string theories in D > 10 dimensions. Compactifying D − 4 of these dimensions on a carefully constructed asymmetric orientifold projects out t...
Doping dependent nonlinear Hall effect in SmFeAsO(1-x)F(x).
Riggs, Scott C; McDonald, R D; Kemper, J B; Stegen, Z; Boebinger, G S; Balakirev, F F; Kohama, Y; Migliori, A; Chen, H; Liu, R H; Chen, X H
2009-10-14
We report the Hall resistivity, ρ(xy), of polycrystalline SmFeAsO(1-x)F(x) for four different fluorine concentrations from the onset of superconductivity through the collapse of the structural phase transition. For the two more highly doped samples, ρ(xy) is linear in magnetic field up to 50 T with only weak temperature dependence, reminiscent of a simple Fermi liquid. For the lightly doped samples with x<0.15, we find a low temperature regime characterized as ρ(xy)(H) being both nonlinear in magnetic field and strongly temperature-dependent even though the Hall angle is small. The onset temperature for this nonlinear regime is in the vicinity of the structural phase (SPT)/magnetic ordering (MO) transitions. The temperature dependence of the Hall resistivity is consistent with a thermal activation of carriers across an energy gap. The evolution of the energy gap with doping is reported.
Directory of Open Access Journals (Sweden)
Anju K. Augustine
2014-01-01
Full Text Available We present third-order optical nonlinear absorption in CdSe quantum dots (QDs with particle sizes in the range of 4.16–5.25 nm which has been evaluated by the Z-scan technique. At an excitation irradiance of 0.54 GW/cm2 the CdSe QDs exhibit reverse saturation indicating a clear nonlinear behavior. Nonlinearity increases with particle size in CdSe QDs within the range of our investigations which in turn depends on the optical band gap. The optical limiting threshold of the QDs varies from 0.35 GW/cm2 to 0.57 GW/cm2 which makes CdSe QDs a promising candidate for reverse-saturable absorption based devices at high laser intensities such as optical limiters.
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
Non-Linear Dynamic Analysis of Inter-Word Time Intervals in Psychotic Speech.
Todder, Doron; Avissar, Sofia; Schreiber, Gabriel
2013-01-01
"Language is a form and not a substance" - Ferdinand de Saussure Objective: Analyses of speech processes in schizophrenia are invariably focused on words as vocal signals. The results of such analyses are, however, strongly related to content, and may be language- and culture-dependent. Little attention has been paid to a pure measure of the form of speech, unrelated to its content: inter-words time intervals. 15 patients with schizophrenia and 15 healthy volunteers are recorded spontaneously speaking for 10-15 min. Recordings are analyzed for inter-words time intervals using the following non-linear dynamical methods: unstable periodic orbits, correlation dimension, bi-spectral analysis, and symbolic dynamics. The series of inter-word time intervals in normal speech have the characteristics of a low-dimensional chaotic attractor with a correlation dimension of [Formula: see text]. Deconstruction of the attractor appears in psychosis with re-establishment after anti-psychotic treatment. Shannon entropy, a measure of the complexity in the time series, calculated from symbolic dynamics, is higher for psychotic speech, which is also characterized by higher levels of phase coupling: higher bicoherence, obtained using bi-spectral analysis. Non-linear dynamical methods applied to ITIs thus enable a content-independent, pure measure of the form of normal thought, its distortion in psychosis, and its restoration under treatment.
Moradi, Hojjatullah; Majd, Vahid Johari
2016-05-01
In this paper, the problem of robust stability of nonlinear genetic regulatory networks (GRNs) is investigated. The developed method is an integral sliding mode control based redesign for a class of perturbed dissipative switched GRNs with time delays. The control law is redesigned by modifying the dissipativity-based control law that was designed for the unperturbed GRNs with time delays. The switched GRNs are switched from one mode to another based on time, state, etc. Although, the active subsystem is known in any instance, but the switching law and the transition probabilities are not known. The model for each mode is considered affine with matched and unmatched perturbations. The redesigned control law forces the GRN to always remain on the sliding surface and the dissipativity is maintained from the initial time in the presence of the norm-bounded perturbations. The global stability of the perturbed GRNs is maintained if the unperturbed model is globally dissipative. The designed control law for the perturbed GRNs guarantees robust exponential or asymptotic stability of the closed-loop network depending on the type of stability of the unperturbed model. The results are applied to a nonlinear switched GRN, and its convergence to the origin is verified by simulation.
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...
Forecasting the future: is it possible for adiabatically time-varying nonlinear dynamical systems?
Yang, Rui; Lai, Ying-Cheng; Grebogi, Celso
2012-09-01
Nonlinear dynamical systems in reality are often under environmental influences that are time-dependent. To assess whether such a system can perform as desired or as designed and is sustainable requires forecasting its future states and attractors based solely on time series. We propose a viable solution to this challenging problem by resorting to the compressive-sensing paradigm. In particular, we demonstrate that, for a dynamical system whose equations are unknown, a series expansion in both dynamical and time variables allows the forecasting problem to be formulated and solved in the framework of compressive sensing using only a few measurements. We expect our method to be useful in addressing issues of significant current concern such as the sustainability of various natural and man-made systems.
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....
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
Nonlinear decline-rate dependence and intrinsic variation of typeIa supernova luminosities
Energy Technology Data Exchange (ETDEWEB)
Wang, Lifan; Strovink, Mark; Conley, Alexander; Goldhaber,Gerson; Kowalski, Marek; Perlmutter, Saul; Siegrist, James
2005-12-14
Published B and V fluxes from nearby Type Ia supernova are fitted to light-curve templates with 4-6 adjustable parameters. Separately, B magnitudes from the same sample are fitted to a linear dependence on B-V color within a post-maximum time window prescribed by the CMAGIC method. These fits yield two independent SN magnitude estimates B{sub max} and B{sub BV}. Their difference varies systematically with decline rate {Delta}m{sub 15} in a form that is compatible with a bilinear but not a linear dependence; a nonlinear form likely describes the decline-rate dependence of B{sub max} itself. A Hubble fit to the average of B{sub max} and B{sub BV} requires a systematic correction for observed B-V color that can be described by a linear coefficient R = 2.59 {+-} 0.24, well below the coefficient R{sub B} {approx} 4.1 commonly used to characterize the effects of Milky Way dust. At 99.9% confidence the data reject a simple model in which no color correction is required for SNe that are clustered at the blue end of their observed color distribution. After systematic corrections are performed, B{sub max} and B{sub BV} exhibit mutual rms intrinsic variation equal to 0.074 {+-} 0.019 mag, of which at least an equal share likely belongs to B{sub BV}. SN magnitudes measured using maximum-luminosity or cmagic methods show comparable rms deviations of order {approx}0.14 mag from the Hubble line. The same fit also establishes a 95% confidence upper limit of 486 km s{sup -1} on the rms peculiar velocity of nearby SNe relative to the Hubble flow.
He, Fei; Wei, Hua-Liang; Billings, Stephen A.
2015-08-01
This paper introduces a new approach for nonlinear and non-stationary (time-varying) system identification based on time-varying nonlinear autoregressive moving average with exogenous variable (TV-NARMAX) models. The challenging model structure selection and parameter tracking problems are solved by combining a multiwavelet basis function expansion of the time-varying parameters with an orthogonal least squares algorithm. Numerical examples demonstrate that the proposed approach can track rapid time-varying effects in nonlinear systems more accurately than the standard recursive algorithms. Based on the identified time domain model, a new frequency domain analysis approach is introduced based on a time-varying generalised frequency response function (TV-GFRF) concept, which enables the analysis of nonlinear, non-stationary systems in the frequency domain. Features in the TV-GFRFs which depend on the TV-NARMAX model structure and time-varying parameters are investigated. It is shown that the high-dimensional frequency features can be visualised in a low-dimensional time-frequency space.
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.
Time dependence of Hawking radiation entropy
Page, Don N.
2013-09-01
If a black hole starts in a pure quantum state and evaporates completely by a unitary process, the von Neumann entropy of the Hawking radiation initially increases and then decreases back to zero when the black hole has disappeared. Here numerical results are given for an approximation to the time dependence of the radiation entropy under an assumption of fast scrambling, for large nonrotating black holes that emit essentially only photons and gravitons. The maximum of the von Neumann entropy then occurs after about 53.81% of the evaporation time, when the black hole has lost about 40.25% of its original Bekenstein-Hawking (BH) entropy (an upper bound for its von Neumann entropy) and then has a BH entropy that equals the entropy in the radiation, which is about 59.75% of the original BH entropy 4πM02, or about 7.509M02 ≈ 6.268 × 1076(M0/Msolar)2, using my 1976 calculations that the photon and graviton emission process into empty space gives about 1.4847 times the BH entropy loss of the black hole. Results are also given for black holes in initially impure states. If the black hole starts in a maximally mixed state, the von Neumann entropy of the Hawking radiation increases from zero up to a maximum of about 119.51% of the original BH entropy, or about 15.018M02 ≈ 1.254 × 1077(M0/Msolar)2, and then decreases back down to 4πM02 = 1.049 × 1077(M0/Msolar)2.
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...
Maraghechi, Borna; Hasani, Mojtaba H; Kolios, Michael C; Tavakkoli, Jahan
2016-05-01
Ultrasound-based thermometry requires a temperature-sensitive acoustic parameter that can be used to estimate the temperature by tracking changes in that parameter during heating. The objective of this study is to investigate the temperature dependence of acoustic harmonics generated by nonlinear ultrasound wave propagation in water at various pulse transmit frequencies from 1 to 20 MHz. Simulations were conducted using an expanded form of the Khokhlov-Zabolotskaya-Kuznetsov nonlinear acoustic wave propagation model in which temperature dependence of the medium parameters was included. Measurements were performed using single-element transducers at two different transmit frequencies of 3.3 and 13 MHz which are within the range of frequencies simulated. The acoustic pressure signals were measured by a calibrated needle hydrophone along the axes of the transducers. The water temperature was uniformly increased from 26 °C to 46 °C in increments of 5 °C. The results show that the temperature dependence of the harmonic generation is different at various frequencies which is due to the interplay between the mechanisms of absorption, nonlinearity, and focusing gain. At the transmit frequencies of 1 and 3.3 MHz, the harmonic amplitudes decrease with increasing the temperature, while the opposite temperature dependence is observed at 13 and 20 MHz.
Controlling chaos in a nonlinear pendulum using an extended time-delayed feedback control method
Energy Technology Data Exchange (ETDEWEB)
Souza de Paula, Aline [COPPE - Department of Mechanical Engineering, Universidade Federal do Rio de Janeiro, P.O. Box 68503, 21.941-972 Rio de Janeiro, RJ (Brazil)], E-mail: alinesp@ufrj.br; Savi, Marcelo Amorim [COPPE - Department of Mechanical Engineering, Universidade Federal do Rio de Janeiro, P.O. Box 68503, 21.941-972 Rio de Janeiro, RJ (Brazil)], E-mail: savi@mecanica.ufrj.br
2009-12-15
Chaos control is employed for the stabilization of unstable periodic orbits (UPOs) embedded in chaotic attractors. The extended time-delayed feedback control uses a continuous feedback loop incorporating information from previous states of the system in order to stabilize unstable orbits. This article deals with the chaos control of a nonlinear pendulum employing the extended time-delayed feedback control method. The control law leads to delay-differential equations (DDEs) that contain derivatives that depend on the solution of previous time instants. A fourth-order Runge-Kutta method with linear interpolation on the delayed variables is employed for numerical simulations of the DDEs and its initial function is estimated by a Taylor series expansion. During the learning stage, the UPOs are identified by the close-return method and control parameters are chosen for each desired UPO by defining situations where the largest Lyapunov exponent becomes negative. Analyses of a nonlinear pendulum are carried out by considering signals that are generated by numerical integration of the mathematical model using experimentally identified parameters. Results show the capability of the control procedure to stabilize UPOs of the dynamical system, highlighting some difficulties to achieve the stabilization of the desired orbit.
Andrzejak, Ralph G.; Schindler, Kaspar; Rummel, Christian
2012-10-01
To derive tests for randomness, nonlinear-independence, and stationarity, we combine surrogates with a nonlinear prediction error, a nonlinear interdependence measure, and linear variability measures, respectively. We apply these tests to intracranial electroencephalographic recordings (EEG) from patients suffering from pharmacoresistant focal-onset epilepsy. These recordings had been performed prior to and independent from our study as part of the epilepsy diagnostics. The clinical purpose of these recordings was to delineate the brain areas to be surgically removed in each individual patient in order to achieve seizure control. This allowed us to define two distinct sets of signals: One set of signals recorded from brain areas where the first ictal EEG signal changes were detected as judged by expert visual inspection (“focal signals”) and one set of signals recorded from brain areas that were not involved at seizure onset (“nonfocal signals”). We find more rejections for both the randomness and the nonlinear-independence test for focal versus nonfocal signals. In contrast more rejections of the stationarity test are found for nonfocal signals. Furthermore, while for nonfocal signals the rejection of the stationarity test increases the rejection probability of the randomness and nonlinear-independence test substantially, we find a much weaker influence for the focal signals. In consequence, the contrast between the focal and nonfocal signals obtained from the randomness and nonlinear-independence test is further enhanced when we exclude signals for which the stationarity test is rejected. To study the dependence between the randomness and nonlinear-independence test we include only focal signals for which the stationarity test is not rejected. We show that the rejection of these two tests correlates across signals. The rejection of either test is, however, neither necessary nor sufficient for the rejection of the other test. Thus, our results suggest that
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...
What makes polymer crystallization depend on time
Piccarolo, Stefano
2015-12-01
Here we report a series of objections to the mechanism of polymer crystallization by secondary nucleation plausible for very mild cooling conditions, i.e. when solidification time is long enough or when the molecular weight, M, is not too large, conditions not preventing segregation at the growth front to take place. With a manichean approach, if otherwise time is controlling, e.g. in polymer processing, or M is large, segregation is precluded and accumulation of topological defects takes place in the amorphous phase preventing sequential growth of crystalline domains. A non crystalline phase forms very much departed from equilibrium, constrained by the crystalline domains and frozen to an extent dependent on the morphology developed. Consequences are discussed, themselves a proof that segregation simplifies topology when crystallization conditions are mild. A situation responsible for the often reported memory effects as well as for mechanical and rheological properties. Results collected from our own experimental evidence by the originally developed Continuous Cooling Transformation are discussed within this framework and related to the broad, albeit often overlooked, literature on subjects intimately connected to crystallization and therefore spanning different fields of polymer science. We focus our attention on two recent results opening the way to this new perspective on polymer crystallization: the onset of the nodular morphology in iPP also in the presence of the stable a-monoclinic phase and the extended crystallization behaviour of polyester blends once local mobility is enhanced. Observing that demixing at the growth front controls crystallization under processing conditions we speculate that the high cooling rate solidification experiment is but a peculiar transient rheological measurement. Implications of this view are far reaching as the crucial role of the melt before solidification is evident.
Shen, B. W.
2016-12-01
In this study, we construct a seven-dimensional Lorenz model (7DLM) to discuss the impact of an extended nonlinear feedback loop on solutions' stability and illustrate the hierarchical scale dependence of chaotic solutions. Compared to the 5DLM, the 7DLM includes two additional high wavenumber modes that are selected based on an analysis of the nonlinear temperature advection term. Fourier modes that represent temperature in the 7DLM can be categorized into three major scales as the primary (the largest scale), secondary, and tertiary (the smallest scale) modes. Further extension of the nonlinear feedback loop within the 7DLM can provide negative nonlinear feedback to stabilize solutions, thus leading to a much larger critical value for the Rayleigh parameter (rc ˜ 116.9) for the onset of chaos, as compared to an rc of 42.9 for the 5DLM as well as an rc of 24.74 for the 3DLM. The rc is determined by an analysis of ensemble Lyapunov exponents (eLEs) with a Prandtl number (σ) of 10. To examine the dependence of rc on the value of the Prandtl number, a linear stability analysis is performed by solving for the analytical solutions of the critical points and by calculating the eigenvalues of the linearized system. Within the range of (5 ≤ σ ≤ 25), the 7DLM requires a larger rc for the onset of chaos than the 5DLM. In addition to the negative nonlinear feedback illustrated and emulated by the quasi-equilibrium state solutions for high wavenumber modes, the 7DLM reveals the hierarchical scale dependence of chaotic solutions. For solutions with r = 120, the Pearson correlation coefficients (PCCs) between the primary and secondary modes (i.e., Z and Z1) and between the secondary and tertiary modes (i.e., Z1 and Z2) are 0.988 and 0.998, respectively. Here, Z, Z1, and Z2 represent the time-varying amplitudes of the primary, secondary, and tertiary modes, respectively. High PCCs indicate a strong linear relationship among the modes at various scales and a hierarchy of
Polarization dependence of nonlinear wave mixing of spinor polaritons in semiconductor microcavities
Lewandowski, Przemyslaw; Baudin, Emmanuel; Chan, Chris K P; Leung, P T; Luk, Samuel M H; Galopin, Elisabeth; Lemaitre, Aristide; Bloch, Jacqueline; Tignon, Jerome; Roussignol, Philippe; Kwong, N H; Binder, Rolf; Schumacher, Stefan
2015-01-01
The pseudo-spin dynamics of propagating exciton-polaritons in semiconductor microcavities are known to be strongly influenced by TE-TM splitting. As a vivid consequence, in the Rayleigh scattering regime, the TE-TM splitting gives rise to the optical spin Hall effect (OSHE). Much less is known about its role in the nonlinear optical regime in which four-wave mixing for example allows the formation of spatial patterns in the polariton density, such that hexagons and two-spot patterns are observable in the far field. Here we present a detailed analysis of spin-dependent four-wave mixing processes, by combining the (linear) physics of TE-TM splitting with spin-dependent nonlinear processes, i.e., exciton-exciton interaction and fermionic phase-space filling. Our combined theoretical and experimental study elucidates the complex physics of the four-wave mixing processes that govern polarization and orientation of off-axis modes.
Ranjbaran, Mina; Galiana, Henrietta L
2013-11-01
Studies of the vestibulo-ocular reflex (VOR) have revealed that this type of involuntary eye movement is influenced by viewing distance. This paper presents a bilateral model for the horizontal angular VOR in the dark based on realistic physiological mechanisms. It is shown that by assigning proper nonlinear neural computations at the premotor level, the model is capable of replicating target-distance-dependent VOR responses that are in agreement with geometrical requirements. Central premotor responses in the model are also shown to be consistent with experimental observations. Moreover, the model performance after simulated unilateral canal plugging also reproduces experimental observations, an emerging property. Such local nonlinear computations could similarly generate context-dependent behaviors in other more complex motor systems.
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.
Studies of Spuriously Time-dependent Resonances in Time-dependent Density Functional Theory
Luo, Kai; Maitra, Neepa T
2016-01-01
Adiabatic approximations in time-dependent density functional theory (TDDFT) will in general yield unphysical time-dependent shifts in the resonance positions of a system driven far from its ground-state. This spurious time-dependence is rationalized in [J. I. Fuks, K. Luo, E. D. Sandoval and N. T. Maitra, Phys. Rev. Lett. {\\bf 114}, 183002 (2015)] in terms of the violation of an exact condition by the non-equilibrium exchange-correlation kernel of TDDFT. Here we give details on the derivation and discuss reformulations of the exact condition that apply in special cases. In its most general form, the condition states that when a system is left in an arbitrary state, in the absence of time-dependent external fields nor ionic motion, the TDDFT resonance position for a given transition is independent of the state. Special cases include the invariance of TDDFT resonances computed with respect to any reference interacting stationary state of a fixed potential, and with respect to any choice of appropriate stationa...
Large time behavior for solutions of nonlinear parabolic problems with sign-changing measure data
Directory of Open Access Journals (Sweden)
Francesco Petitta
2008-09-01
Full Text Available Let $Omegasubseteq mathbb{R}^N$ a bounded open set, $Ngeq 2$, and let $p>1$; in this paper we study the asymptotic behavior with respect to the time variable $t$ of the entropy solution of nonlinear parabolic problems whose model is $$displaylines{ u_{t}(x,t-Delta_{p} u(x,t=mu quad hbox{in } Omegaimes(0,infty,cr u(x,0=u_{0}(x quad hbox{in } Omega, }$$ where $u_0 in L^{1}(Omega$, and $muin mathcal{M}_{0}(Q$ is a measure with bounded variation over $Q=Omegaimes(0,infty$ which does not charge the sets of zero $p$-capacity; moreover we consider $mu$ that does not depend on time. In particular, we prove that solutions of such problems converge to stationary solutions.
New results on stability analysis for time-varying delay systems with non-linear perturbations.
Liu, Pin-Lin
2013-05-01
The problem of stability for linear time-varying delay systems under nonlinear perturbation is discussed, with delay assumed as time-varying. Delay decomposition approach allows information of the delayed plant states to be fully considered. A less conservative delay-dependent robust stability condition is derived, using integral inequality approach to express the relationship of Leibniz-Newton formula terms in the within the framework of linear matrix inequalities (LMIs). Merits of the proposed results lie in lesser conservatism, which are realized by choosing different Lyapunov matrices in the decomposed integral intervals and estimating the upper bound of some cross term more exactly. Numerical examples are given to illustrate the effectiveness and lesser conservatism of the proposed method.
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...
Correction of Frequency-Dependent Nonlinear Errors in Direct-Conversion Transceivers
2016-03-31
University of Oklahoma Norman , Oklahoma, USA, 73019 pyraminxrox@ou.edu, fulton@ou.edu Abstract: Correction of nonlinear and frequency dependent...behavior of low -cost integrated transceivers, especially in the area of phased arrays, where many transceivers will be used to comprise the system as...analog RF portion of the receive chain of the low -cost, direct-conversion radar system initially presented in [2]. The spectral distortion seen here
Size dependent nonlinear optical properties of YCrO{sub 3} nanosystems
Energy Technology Data Exchange (ETDEWEB)
Krishnan, Shiji, E-mail: shijikrish@gmail.com [School of Pure and Applied Physics, Mahatma Gandhi University, Kottayam-686 560, Kerala (India); Shafakath, K.; Philip, Reji [Light and Matter Physics Group, Raman Research Institute, Bangalore- 560 080, Karnataka (India); Kalarikkal, Nandakumar, E-mail: nkkalarikkal@mgu.ac.in [School of Pure and Applied Physics, Mahatma Gandhi University, Kottayam-686 560, Kerala and Center for Nanoscience and Nanotechnology, Mahatma Gandhi University, Kottayam-686 560, Kerala (India)
2014-01-28
We report size-dependent optical limiting response of YCrO{sub 3} nanosystems upon illumination by nanosecond laser pulses at 532 nm. The limiting properties were investigated using the open aperture z-scan technique. Three-photon absorption coefficient is found to increase with particle size within the range of our investigations. We propose that the obtained nonlinearity is caused by two photon absorption, followed by excited state absorption.
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
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.
On shallow water waves in a medium with time-dependent
Directory of Open Access Journals (Sweden)
Hamdy I. Abdel-Gawad
2015-07-01
Full Text Available In this paper, we studied the progression of shallow water waves relevant to the variable coefficient Korteweg–de Vries (vcKdV equation. We investigated two kinds of cases: when the dispersion and nonlinearity coefficients are proportional, and when they are not linearly dependent. In the first case, it was shown that the progressive waves have some geometric structures as in the case of KdV equation with constant coefficients but the waves travel with time dependent speed. In the second case, the wave structure is maintained when the nonlinearity balances the dispersion. Otherwise, water waves collapse. The objectives of the study are to find a wide class of exact solutions by using the extended unified method and to present a new algorithm for treating the coupled nonlinear PDE’s.
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.
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.
On the supercritical KdV equation with time-oscillating nonlinearity
Panthee, M
2011-01-01
For the initial value problem (IVP) associated the generalized Korteweg-de Vries (gKdV) equation with supercritical nonlinearity, u_{t}+\\partial_x^3u+\\partial_x(u^{k+1}) =0,\\qquad k\\geq 5, numerical evidence \\cite{BDKM1, BSS1} shows that there are initial data $\\phi\\in H^1(\\mathbb{R})$ such that the corresponding solution may blow-up in finite time. Also, with the evidence from numerical simulation \\cite{ACKM, KP}, the physicists claim that a periodic time dependent term in factor of the nonlinearity would disturb the blow-up solution, either accelerating or delaying it. In this work, we investigate the IVP associated to the gKdV equation u_{t}+\\partial_x^3u+g(\\omega t)\\partial_x(u^{k+1}) =0, where $g$ is a periodic function and $k\\geq 5$ is an integer. We prove that, for given initial data $\\phi \\in H^1(\\R)$, as $|\\omega|\\to \\infty$, the solution $u_{\\omega}$ converges to the solution $U$ of the initial value problem associated to U_{t}+\\partial_x^3U+m(g)\\partial_x(U^{k+1}) =0, with the same initial data, wh...
Time-dependent cortical activation in voluntary muscle contraction.
Yang, Qi; Wang, Xiaofeng; Fang, Yin; Siemionow, Vlodek; Yao, Wanxiang; Yue, Guang H
2011-01-01
This study was to characterize dynamic source strength changes estimated from high-density scalp electroencephalogram (EEG) at different phases of a submaximal voluntary muscle contraction. Eight healthy volunteers performed isometric handgrip contractions of the right arm at 20% maximal intensity. Signals of the handgrip force, electromyography (EMG) from the finger flexor and extensor muscles and 64-channel EEG were acquired simultaneously. Sources of the EEG were analyzed at 19 time points across preparation, execution and sustaining phases of the handgrip. A 3-layer boundary element model (BEM) based on the MNI (Montréal Neurological Institute) brain MRI was used to overlay the sources. A distributed current density model, LORETA L1 norm method was applied to the data that had been processed by independent component analysis (ICA). Statistical analysis based on a mixed-effects polynomial regression model showed a significant and consistent time-dependent non-linear source strength change pattern in different phases of the handgrip. The source strength increased at the preparation phase, peaked at the force onset time and decreased in the sustaining phase. There was no significant difference in the changing pattern of the source strength among Brodmann's areas 1, 2, 3, 4, and 6. These results show, for the first time, a high time resolution increasing-and-decreasing pattern of activation among the sensorimotor regions with the highest activity occurs at the muscle activity onset. The similarity in the source strength time courses among the cortical centers examined suggests a synchronized parallel function in controlling the motor activity.
Time-dependence in mixture toxicity prediction.
Dawson, Douglas A; Allen, Erin M G; Allen, Joshua L; Baumann, Hannah J; Bensinger, Heather M; Genco, Nicole; Guinn, Daphne; Hull, Michael W; Il'Giovine, Zachary J; Kaminski, Chelsea M; Peyton, Jennifer R; Schultz, T Wayne; Pöch, Gerald
2014-12-04
The value of time-dependent toxicity (TDT) data in predicting mixture toxicity was examined. Single chemical (A and B) and mixture (A+B) toxicity tests using Microtox(®) were conducted with inhibition of bioluminescence (Vibrio fischeri) being quantified after 15, 30 and 45-min of exposure. Single chemical and mixture tests for 25 sham (A1:A2) and 125 true (A:B) combinations had a minimum of seven duplicated concentrations with a duplicated control treatment for each test. Concentration/response (x/y) data were fitted to sigmoid curves using the five-parameter logistic minus one parameter (5PL-1P) function, from which slope, EC25, EC50, EC75, asymmetry, maximum effect, and r(2) values were obtained for each chemical and mixture at each exposure duration. Toxicity data were used to calculate percentage-based TDT values for each individual chemical and mixture of each combination. Predicted TDT values for each mixture were calculated by averaging the TDT values of the individual components and regressed against the observed TDT values obtained in testing, resulting in strong correlations for both sham (r(2)=0.989, n=25) and true mixtures (r(2)=0.944, n=125). Additionally, regression analyses confirmed that observed mixture TDT values calculated for the 50% effect level were somewhat better correlated with predicted mixture TDT values than at the 25 and 75% effect levels. Single chemical and mixture TDT values were classified into five levels in order to discern trends. The results suggested that the ability to predict mixture TDT by averaging the TDT of the single agents was modestly reduced when one agent of the combination had a positive TDT value and the other had a minimal or negative TDT value. Copyright © 2014 Elsevier Ireland Ltd. All rights reserved.
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.
Time-dependent constrained Hamiltonian systems and Dirac brackets
Energy Technology Data Exchange (ETDEWEB)
Leon, Manuel de [Instituto de Matematicas y Fisica Fundamental, Consejo Superior de Investigaciones Cientificas, Madrid (Spain); Marrero, Juan C. [Departamento de Matematica Fundamental, Facultad de Matematicas, Universidad de La Laguna, La Laguna, Tenerife, Canary Islands (Spain); Martin de Diego, David [Departamento de Economia Aplicada Cuantitativa, Facultad de Ciencias Economicas y Empresariales, UNED, Madrid (Spain)
1996-11-07
In this paper the canonical Dirac formalism for time-dependent constrained Hamiltonian systems is globalized. A time-dependent Dirac bracket which reduces to the usual one for time-independent systems is introduced. (author)
Incompatibility of Time-Dependent Bogoliubov-de-Gennes and Ginzburg-Landau Equations
Frank, Rupert L.; Hainzl, Christian; Schlein, Benjamin; Seiringer, Robert
2016-07-01
We study the time-dependent Bogoliubov-de-Gennes equations for generic translation-invariant fermionic many-body systems. For initial states that are close to thermal equilibrium states at temperatures near the critical temperature, we show that the magnitude of the order parameter stays approximately constant in time and, in particular, does not follow a time-dependent Ginzburg-Landau equation, which is often employed as a phenomenological description and predicts a decay of the order parameter in time. The full non-linear structure of the equations is necessary to understand this behavior.
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
Temperature dependence of the magnetization M(T) of two-band superconductors is studied in the vicinity of upper critical field Hc2 by using a two-band Ginzburg-Landau (GL) theory. It is shown that magnetization M(T) has a nonlinear character due to positive curvature of upper critical field Hc2(T) and temperature dependence of effective Ginzburg-Landau parameter (n)eff(T). The results are shown to be in qualitative agreement with experimental data for the superconducting magnesium diboride, MgB2.
Nonlinear pressure dependence of TN in almost multiferroic EuTiO3
Guguchia, Z.; Caslin, K.; Kremer, R. K.; Keller, H.; Shengelaya, A.; Maisuradze, A.; Bettis, J. L., Jr.; Köhler, J.; Bussmann-Holder, A.; Whangbo, M.-H.
2013-09-01
The antiferromagnetic (AFM) phase transition temperature TN of EuTiO3 has been studied as a function of pressure p. The data reveal a nonlinear dependence of TN on p with TN increasing with increasing pressure. The exchange interactions exhibit an analogous dependence on p as TN (if the absolute value of the nearest neighbor interaction is considered) and there is evidence that the AFM transition is robust with increasing pressure. The corresponding Weiss temperature ΘW remains anomalous since it always exhibits positive values. The data are analyzed within the Bloch power law model and provide excellent agreement with experiment.
Amir, Naila; Iqbal, Shahid
2017-08-01
We develop generalized coherent states for a class of nonlinear oscillators with position-dependent effective mass in the context of the Gazeau-Klauder formalism and discuss some of their properties. In order to investigate the temporal evolution we first explore the statistical properties by means of weighting distribution and the Mandel parameter. It is found that the temporal evolution of the coherent states may exhibit the phenomena of quantum revivals and fractional revivals for a particular choice of position-dependent mass oscillator.
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.
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.
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.
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.
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.
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.
Intelligent modeling and control for nonlinear systems with rate-dependent hysteresis
Institute of Scientific and Technical Information of China (English)
MAO JianQin; DING HaiShan
2009-01-01
A new modeling approach for nonlinear systems with rate-dependent hysteresis is proposed. The ap-proach is used for the modeling of the giant magnetostrictive actuator, which has the rate-dependent nonlinear property. The models built are simpler than the existed approaches. Compared with the exper-intent result, the model built can well describe the hysteresis nonlinear of the actuator for Input signals with complex frequency. An adaptive direct inverse control approach is proposed based on the fuzzy tree model and Inverse learning and special learning that are used in neural network broadly. In this approach, the inverse model of the plant is identified to be the initial controller firstly. Then, the inverse model Is connected with the plant in series and the linear parameters of the controller are adjusted using the least mean square algorithm by on-line manner. The direct Inverse control approach based on the fuzzy tree model is applied on the tracing control of the actuator by simulation. The simulation results show the correctness of the approach.
Goldberg, Robert K.
2000-01-01
There has been no accurate procedure for modeling the high-speed impact of composite materials, but such an analytical capability will be required in designing reliable lightweight engine-containment systems. The majority of the models in use assume a linear elastic material response that does not vary with strain rate. However, for containment systems, polymer matrix composites incorporating ductile polymers are likely to be used. For such a material, the deformation response is likely to be nonlinear and to vary with strain rate. An analytical model has been developed at the NASA Glenn Research Center at Lewis Field that incorporates both of these features. A set of constitutive equations that was originally developed to analyze the viscoplastic deformation of metals (Ramaswamy-Stouffer equations) was modified to simulate the nonlinear, rate-dependent deformation of polymers. Specifically, the effects of hydrostatic stresses on the inelastic response, which can be significant in polymers, were accounted for by a modification of the definition of the effective stress. The constitutive equations were then incorporated into a composite micromechanics model based on the mechanics of materials theory. This theory predicts the deformation response of a composite material from the properties and behavior of the individual constituents. In this manner, the nonlinear, rate-dependent deformation response of a polymer matrix composite can be predicted.
Time-dependent delta-interactions for 1D Schr\\"odinger Hamiltonians
Hmidi, Taoufik; Nier, Francis
2009-01-01
The non autonomous Cauchy problem for time dependent 1D point interactions is considered. The regularity assumptions for the coupling parameter are accurately analyzed and show that the general results for non autonomous linear evolution equations in Banach spaces are far from being optimal. In the mean time, this article shows an unexpected application of paraproduct techniques, initiated by J.M. Bony for nonlinear partial differential equations, to a classical linear problem.
Mahmood, T.; Shahzad, A.; Iqbal, Z.; Ahmed, J.; Khan, M.
A study is presented for the flow and heat transfer of Sisko fluid model over an unsteady stretching sheet in the presence of uniform magnetic field. While taking newly developed similarity transformations, the governing time dependent partial differential equations are reduced to nonlinear ordinary differential equations. Numerical solutions of the reduced nonlinear differential equations are found by employing Shooting method. The influence of physical parameters of interest on the velocity and temperature profiles are highlighted graphically and examined in detail. Moreover, the skin friction coefficient and Nusselt number are tabulated against influential parameters. Skin friction coefficient increases with unsteadiness parameter, magnetic field and suction parameter.
Intensity dependences of the nonlinear optical excitation of plasmons in graphene.
Constant, T J; Hornett, S M; Chang, D E; Hendry, E
2017-03-28
Recently, we demonstrated an all-optical coupling scheme for plasmons, which takes advantage of the intrinsic nonlinear optical response of graphene. Frequency mixing using free-space, visible light pulses generates surface plasmons in a planar graphene sample, where the phase matching condition can define both the wavevector and energy of surface waves and intraband transitions. Here, we also show that the plasmon generation process is strongly intensity-dependent, with resonance features washed out for absorbed pulse fluences greater than 0.1 J m(-2) This implies a subtle interplay between the nonlinear generation process and sample heating. We discuss these effects in terms of a non-equilibrium charge distribution using a two-temperature model.This article is part of the themed issue 'New horizons for nanophotonics'.
Surfactant and gravity dependent instability of two-layer Couette flows and its nonlinear saturation
Frenkel, Alexander L
2016-01-01
A horizontal flow of two immiscible fluid layers with different densities, viscosities and thicknesses, subject to vertical gravitational forces and with an insoluble surfactant present at the interface, is investigated. The base Couette flow is driven by the horizontal motion of the channel walls. Linear and nonlinear stages of the (inertialess) surfactant and gravity dependent long-wave instability are studied using the lubrication approximation, which leads to a system of coupled nonlinear evolution equations for the interface and surfactant disturbances. The linear stability is determined by an eigenvalue problem for the normal modes. The growth rates and the amplitudes of disturbances of the interface, surfactant, velocities, and pressures are found analytically. For each wavenumber, there are two active normal modes. For each mode, the instability threshold conditions in terms of the system parameters are determined. In particular, it transpires that for certain parametric ranges, even arbitrarily stron...
Huang, Y X
2014-01-01
In the marine environment, many fields have fluctuations over a large range of different spatial and temporal scales. These quantities can be nonlinear \\red{and} non-stationary, and often interact with each other. A good method to study the multiple scale dynamics of such time series, and their correlations, is needed. In this paper an application of an empirical mode decomposition based time dependent intrinsic correlation, \\red{of} two coastal oceanic time series, temperature and dissolved oxygen (saturation percentage) is presented. The two time series are recorded every 20 minutes \\red{for} 7 years, from 2004 to 2011. The application of the Empirical Mode Decomposition on such time series is illustrated, and the power spectra of the time series are estimated using the Hilbert transform (Hilbert spectral analysis). Power-law regimes are found with slopes of 1.33 for dissolved oxygen and 1.68 for temperature at high frequencies (between 1.2 and 12 hours) \\red{with} both close to 1.9 for lower frequencies (t...
Korayem, M H; Nekoo, S R
2015-01-01
This article investigates finite-time optimal and suboptimal controls for time-varying systems with state and control nonlinearities. The state-dependent Riccati equation (SDRE) controller was the main framework. A finite-time constraint imposed on the equation changes it to a differential equation, known as the state-dependent differential Riccati equation (SDDRE) and this equation was applied to the problem reported in this study that provides general formulation and stability analysis. The following four solution methods were developed for solving the SDDRE; backward integration, state transition matrix (STM) and the Lyapunov based method. In the Lyapunov approach, both positive and negative definite solutions to related SDRE were used to provide suboptimal gain for the SDDRE. Finite-time suboptimal control is applied for robotic manipulator, as finite-time constraint strongly decreases state error and operation time. General state-dependent coefficient (SDC) parameterizations for rigid and flexible joint arms (prismatic or revolute joints) are introduced. By including nonlinear control inputs in the formulation, the actuator׳s limits can be inserted directly to the state-space equation of a manipulator. A finite-time SDRE was implemented on a 6R manipulator both in theory and experimentally. And a reduced 3R arm was modeled and tested as a flexible joint robot (FJR). Evaluations of load carrying capacity and operation time were investigated to assess the capability of this approach, both of which showed significant improvement.
Nonlinear modal interactions in parity-time (${\\cal PT}$) symmetric lasers
Ge, Li
2016-01-01
Parity-time ($\\cal PT$) symmetric lasers have attracted considerable attention lately due to their promising applications and intriguing properties, such as free spectral range doubling and single-mode lasing. In this work we discuss nonlinear modal interactions in these laser systems under steady state conditions, and we demonstrate that several gain clamping scenarios can occur for lasing operation in the $\\cal PT$-symmetric and $\\cal PT$-broken phases. In particular, we show that, depending on the system's design and the external pump profile, its operation in the nonlinear regime falls into two different categories: in one the system is frozen in the $\\cal PT$ phase space as the applied gain increases, while in the other the system is pulled towards its exceptional point. These features are first illustrated by a coupled mode formalism and later verified by employing the Steady-state Ab-initio Laser Theory (SALT). Our findings shine light on the robustness of single-mode operation in these lasers against ...
Red'kov, V
2011-01-01
Non-linear electrodynamics arising in the frames of field theories in non-commutative space-time is examined on the base of the Riemann-Silberstein-Majorana-Oppenheimer formalism. The problem of form-invariance of the non-linear constitutive relations governed by six non-commutative parameters \\theta_{kl} \\sim {\\bf K} = {\\bf n} + i {\\bf m} is explored in detail on the base of the complex orthogonal group theory SO(3.C). Two Abelian 2-parametric small groups, isomorphic to each other in abstract sense, and leaving unchangeable the extended constitutive relations at arbitrary six parameters \\theta_{kl} of effective media have been found, their realization depends explicitly on invariant length {\\bf K}^{2}. In the case of non-vanishing length a special reference frame in which the small group has the structure SO(2) \\otimes SO(1,1) has been found. In isotropic case no such reference frame exists. The way to interpret both Abelian small groups in physical terms consists in factorizing corresponding Lorentz transf...
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.
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.
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.
Production Planning with Load Dependent Lead Times
DEFF Research Database (Denmark)
Pahl, Julia
2005-01-01
Lead times impact the performance of the supply chain significantly. Although there is a large literature concerning queuing models for the analysis of the relationship between capacity utilization and lead times, and there is a substantial literature concerning control and order release policies...... that take lead times into consideration, there have been only few papers describing models at the aggregate planning level that recognize the relationship between the planned utilization of capacity and lead times. In this paper we provide an in-depth discussion of the state-of-the art in this literature...
Load Dependent Lead Times and Sustainability
DEFF Research Database (Denmark)
Pahl, Julia; Voss, Stefan
2016-01-01
to prevent decreased quality or waste of production parts and products. This gains importance because waiting times imply longer lead times charging the production system with work in process inventories. Longer lead times can lead to quality losses due to depreciation, so that parts need to be reworked...... if possible or discarded. But return flows of products for rework or remanufacturing actions significantly complicate the production planning process. We analyze sustainability options with respect to lead time management by formulating a comprehensive mathematical model. We consider a deterministic, mixed...
Continuous-Time Modeling with Spatial Dependence
Oud, J.H.L.; Folmer, H.; Patuelli, R.; Nijkamp, P.
2012-01-01
(Spatial) panel data are routinely modeled in discrete time (DT). However, compelling arguments exist for continuous-time (CT) modeling of (spatial) panel data. Particularly, most social processes evolve in CT, so that statistical analysis in DT is an oversimplification, gives an incomplete
Continuous-Time Modeling with Spatial Dependence
Oud, J.; Folmer, H.; Patuelli, R.; Nijkamp, P.
(Spatial) panel data are routinely modeled in discrete time (DT). However, compelling arguments exist for continuous-time (CT) modeling of (spatial) panel data. Particularly, most social processes evolve in CT, so that statistical analysis in DT is an oversimplification, gives an incomplete
Composite control of a class of nonlinear singularly perturbed discrete-time systems via D-SDRE
Zhang, Yan; Subbaram Naidu, D.; Cai, Chenxiao; Zou, Yun
2016-08-01
In this paper, the regulation problem of a class of nonlinear singularly perturbed discrete-time systems is investigated. Using the theory of singular perturbations and time scales, the nonlinear system is decoupled into reduced-order slow and fast (boundary layer) subsystems. Then, a composite controller consisting of two sub-controllers for the slow and fast subsystems is developed using the discrete-time state-dependent Riccati equation (D-SDRE). It is proved that the equilibrium point of the original closed-loop system with a composite controller is locally asymptotically stable. Moreover, the region of attraction of the closed-loop system is estimated by using linear matrix inequality. One example is given to illustrate the effectiveness of the results obtained.
Directory of Open Access Journals (Sweden)
Christopher Heine
2014-08-01
Full Text Available A detailed description of the rubber parts’ properties is gaining in importance in the current simulation models of multi-body simulation. One application example is a multi-body simulation of the washing machine movement. Inside the washing machine, there are different force transmission elements, which consist completely or partly of rubber. Rubber parts or, generally, elastomers usually have amplitude-dependant and frequency-dependent force transmission properties. Rheological models are used to describe these properties. A method for characterization of the amplitude and frequency dependence of such a rheological model is presented within this paper. Within this method, the used rheological model can be reduced or expanded in order to illustrate various non-linear effects. An original result is given with the automated parameter identification. It is fully implemented in Matlab. Such identified rheological models are intended for subsequent implementation in a multi-body model. This allows a significant enhancement of the overall model quality.
Time dependent deformation of Kilauea Volcano, Hawaii
Montgomery-Brown, Emily Kvietka Desmarais
to a decollement structure 8 km under the south flank, and the locations of the microearthquakes suggest that both occur on the same structure. In 2007, Episode 56 of the Pu'u 'O'o-Kupianaha eruption occurred. This episode was exciting both because it was the largest intrusion in the last decade, and because it occurred concurrently with a flank slow-slip event. The intrusion started on Father's day (June 17th), 2007 with increased seismicity and abrupt tilts at the summit and rift zones. Quasi-static models of the total deformation determined from GPS, tilt, and InSAR indicate that the intrusion occurred on two en echelon dike segments in the upper East Rift Zone along with deformation consistent with slow-slip in the same areas of previous events. The ˜ 2 m maximum opening occurred on the eastern segment near Makaopui crater. Unlike previous intrusions in 1997, 1999, and 2000, the dike model was not sufficient to explain deformation on the western flank. Additionally, a coastal tiltmeter installed in anticipation of a slow-slip event recorded tilts consistent with those observed during the 2005 slow-slip event. These observations led to the conclusion that a concurrent slow-slip event occurred. Geodetic models indicate a similar amount of decollement slip occurred as in previous slow-slip events. Sub-daily GPS positions were used to study the spatio-temporal distribution of the dike intrusion. The time-dependent intrusion model shows that the intrusion began on the western en echelon segment before jumping to the eastern segment, which accumulated the majority of the 2 m of opening. Sub-daily GPS positions limit the number of stations available since there are very few continuous stations north of the East Rift Zone, where coverage is critical for separating the intrusion from the slow-slip. However, an ENVISAT interferogram at 08:22 on June 18, 2007 provides additional spatial coverage of deformation up to that point. Combining this image with the GPS and tilt
Time dependences of atmospheric Carbon dioxide fluxes
DeSalvo, Riccardo
2014-01-01
Understanding the lifetime of CO2 in the atmosphere is critical for predictions regarding future climate changes. A simple mass conservation analysis presented here generates tight estimations for the atmosphere's retention time constant. The analysis uses a leaky integrator model that combines the observed deficit (only less than 40% of CO2 produced from combustion of fossil fuels is actually retained in the atmosphere, while more than 60% is continuously shed) with the exponential growth of fossil fuel burning. It reveals a maximum characteristic time of less than 23 year for the transfer of atmospheric CO2 to a segregation sink. This time constant is further constrained by the rapid disappearance of 14C after the ban of atmospheric atomic bomb tests, which provides a lower limit of 18 years for this transfer. The study also generates evaluations of other CO2 fluxes, exchange time constants and volumes exchanged. Analysis of large harmonic oscillations of atmospheric CO2 concentration, often neglected in th...
Lee, Ho-Jun; Saravanos, Dimitris A.
1997-01-01
Previously developed analytical formulations for piezoelectric composite plates are extended to account for the nonlinear effects of temperature on material properties. The temperature dependence of the composite and piezoelectric properties are represented at the material level through the thermopiezoelectric constitutive equations. In addition to capturing thermal effects from temperature dependent material properties, this formulation also accounts for thermal effects arising from: (1) coefficient of thermal expansion mismatch between the various composite and piezoelectric plies and (2) pyroelectric effects on the piezoelectric material. The constitutive equations are incorporated into a layerwise laminate theory to provide a unified representation of the coupled mechanical, electrical, and thermal behavior of smart structures. Corresponding finite element equations are derived and implemented for a bilinear plate element with the inherent capability to model both the active and sensory response of piezoelectric composite laminates. Numerical studies are conducted on a simply supported composite plate with attached piezoceramic patches under thermal gradients to investigate the nonlinear effects of material property temperature dependence on the displacements, sensory voltages, active voltages required to minimize thermal deflections, and the resultant stress states.
Westergaard, Philip G; Tieri, David; Matin, Rastin; Cooper, John; Holland, Murray; Ye, Jun; Thomsen, Jan W
2014-01-01
As an alternative to state-of-the-art laser frequency stabilisation using ultra-stable cavities, it has been proposed to exploit the non-linear effects from coupling of atoms with a narrow atomic transition to an optical cavity. Here we have constructed such a system and observed non-linear phase shifts of a narrow optical line by strong coupling of a sample of strontium-88 atoms to an optical cavity. The sample temperature of a few mK provides a domain where the Doppler energy scale is several orders of magnitude larger than the narrow linewidth of the optical transition. This makes the system sensitive to velocity dependent multi-photon scattering events (Dopplerons) that affect the cavity transmission significantly while leaving the phase signature relatively unaffected. By varying the number of atoms and the intra-cavity power we systematically study this non-linear phase signature which displays roughly the same features as for much lower temperature samples. This demonstration in a relatively simple sys...
He, Ling-Yun; Chen, Shu-Peng
2011-01-01
Nonlinear dependency between characteristic financial and commodity market quantities (variables) is crucially important, especially between trading volume and market price. Studies on nonlinear dependency between price and volume can provide practical insights into market trading characteristics, as well as the theoretical understanding of market dynamics. Actually, nonlinear dependency and its underlying dynamical mechanisms between price and volume can help researchers and technical analysts in understanding the market dynamics by integrating the market variables, instead of investigating them in the current literature. Therefore, for investigating nonlinear dependency of price-volume relationships in agricultural commodity futures markets in China and the US, we perform a new statistical test to detect cross-correlations and apply a new methodology called Multifractal Detrended Cross-Correlation Analysis (MF-DCCA), which is an efficient algorithm to analyze two spatially or temporally correlated time series. We discuss theoretically the relationship between the bivariate cross-correlation exponent and the generalized Hurst exponents for time series of respective variables. We also perform an empirical study and find that there exists a power-law cross-correlation between them, and that multifractal features are significant in all the analyzed agricultural commodity futures markets.
Quantum Drude friction for time-dependent density functional theory
Neuhauser, Daniel; Lopata, Kenneth
2008-10-01
Friction is a desired property in quantum dynamics as it allows for localization, prevents backscattering, and is essential in the description of multistage transfer. Practical approaches for friction generally involve memory functionals or interactions with system baths. Here, we start by requiring that a friction term will always reduce the energy of the system; we show that this is automatically true once the Hamiltonian is augmented by a term of the form ∫a(q ;n0)[∂j(q,t)/∂t]ṡJ(q)dq, which includes the current operator times the derivative of its expectation value with respect to time, times a local coefficient; the local coefficient will be fitted to experiment, to more sophisticated theories of electron-electron interaction and interaction with nuclear vibrations and the nuclear background, or alternately, will be artificially constructed to prevent backscattering of energy. We relate this term to previous results and to optimal control studies, and generalize it to further operators, i.e., any operator of the form ∫a(q ;n0)[∂c(q,t)/∂t]ṡC(q)dq (or a discrete sum) will yield friction. Simulations of a small jellium cluster, both in the linear and highly nonlinear excitation regime, demonstrate that the friction always reduces energy. The energy damping is essentially double exponential; the long-time decay is almost an order of magnitude slower than the rapid short-time decay. The friction term stabilizes the propagation (split-operator propagator here), therefore increasing the time-step needed for convergence, i.e., reducing the overall computational cost. The local friction also allows the simulation of a metal cluster in a uniform jellium as the energy loss in the excitation due to the underlying corrugation is accounted for by the friction. We also relate the friction to models of coupling to damped harmonic oscillators, which can be used for a more sophisticated description of the coupling, and to memory functionals. Our results open the
Coordinate time dependence in Quantum Gravity
Bojowald, M; Skirzewski, A; Bojowald, Martin; Singh, Parampreet; Skirzewski, Aureliano
2004-01-01
The intuitive classical space-time picture breaks down in quantum gravity, which makes a comparison and the development of semiclassical techniques quite complicated. Using ingredients of the group averaging method to solve constraints one can nevertheless introduce a classical coordinate time into the quantum theory, and use it to investigate the way a semiclassical continuous description emerges from discrete quantum evolution. Applying this technique to test effective classical equations of loop cosmology and their implications for inflation and bounces, we show that the effective semiclassical theory is in good agreement with the quantum description even at short scales.
Directory of Open Access Journals (Sweden)
Kilic Bulent
2016-01-01
Full Text Available This paper integrates dispersive optical solitons in special optical metamaterials with a time dependent coefficient. We obtained some optical solitons of the aforementioned equation. It is shown that the examined dependent coefficients are affected by the velocity of the wave. The first integral method (FIM and ansatz method are applied to reach the optical soliton solutions of the one-dimensional nonlinear Schrödinger’s equation (NLSE with time dependent coefficients.
Joglekar, D. M.; Mitra, Mira
2017-02-01
The nonlinear interaction of a dual frequency flexural wave with a breathing crack generates a peculiar frequency mixing phenomena, which is manifested in form of the side bands or peaks at combinations frequencies in frequency spectrum of the response. Although these peaks have been proven useful in ascertaining the presence of crack, they barely carry any information about the crack location. In this regards, the present article analyzes the time domain representation of the response obtained by employing a wavelet spectral finite element method. The study reveals that the combination tones generated at the crack location travel with dissimilar speeds along the waveguide, owing to its dispersive nature. The separation between the lobes corresponding to these combination tones therefore, depends on the distance that they have travelled. This observation is then used to formulate a method to predict the crack location with respect to the sensor. A brief parametric study shows marginal errors in predicting the crack location, which ascertains the validity of the method. This article also studies the frequency spectrum of the response. The peaks at combination tones are quantified in terms of a modulate parameter which depends on the severity of the crack. The inferences drawn from the time and the frequency domain study can be instrumental in designing a robust strategy for detecting location and severity of the crack.
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.
Energy Technology Data Exchange (ETDEWEB)
Brantley, P S
2006-09-27
We describe an asymptotic analysis of the coupled nonlinear system of equations describing time-dependent three-dimensional monoenergetic neutron transport and isotopic depletion and radioactive decay. The classic asymptotic diffusion scaling of Larsen and Keller [1], along with a consistent small scaling of the terms describing the radioactive decay of isotopes, is applied to this coupled nonlinear system of equations in a medium of specified initial isotopic composition. The analysis demonstrates that to leading order the neutron transport equation limits to the standard time-dependent neutron diffusion equation with macroscopic cross sections whose number densities are determined by the standard system of ordinary differential equations, the so-called Bateman equations, describing the temporal evolution of the nuclide number densities.
Accurate high-harmonic spectra from time-dependent two-particle reduced density matrix theory
Lackner, Fabian; Sato, Takeshi; Ishikawa, Kenichi L; Burgdörfer, Joachim
2016-01-01
The accurate description of the non-linear response of many-electron systems to strong-laser fields remains a major challenge. Methods that bypass the unfavorable exponential scaling with particle number are required to address larger systems. In this paper we present a fully three-dimensional implementation of the time-dependent two-particle reduced density matrix (TD-2RDM) method for many-electron atoms. We benchmark this approach by a comparison with multi-configurational time-dependent Hartree-Fock (MCTDHF) results for the harmonic spectra of beryllium and neon. We show that the TD-2RDM is very well-suited to describe the non-linear atomic response and to reveal the influence of electron-correlation effects.
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.
STUDY OF THE TIME DEPENDENCE OF RADIOACTIVITY
Directory of Open Access Journals (Sweden)
E Bellotti
2013-12-01
Full Text Available The activity of a 137Cs source was measured using a germanium detector installed deep underground in the Gran Sasso Laboratory. In total about 5100 energy spectra, one hour measuring time each, were collected and used to search for time variations of the decay constant with periods from a few hours to 1 year. No signal with amplitude larger than 9.6 × 10−5 at 95% C.L. was detected. These limits are more than one order of magnitude lower than the values on the oscillation amplitude reported in the literature. The same data give a value of 29.96±0.08 years for the 137Cs half life, which is in good agreement with the world mean value of 30.05 ± 0.08 years.
Delay-dependent criteria for the robust stability of systems with time-varying delay
Institute of Scientific and Technical Information of China (English)
Min WU; Yong HE; Jinhua SHE
2003-01-01
The problem of delay-dependent robust stability for systems with titne-varying delay has been considered. By using the S-procedure and the Park' s inequality in the recent issue, a delay-dependent robust stability criterion which is less conservative than the previous results has been derived for time-delay systems with time-varying structured uncertainties. The same idea has also been easily extended to the systems with nonlinear perturbations. Numerical examples illustrated the effectiveness and the improvement of the proposed approach.
Simulating Time-Dependent Energy Transfer Between Crossed Laser Beams in an Expanding Plasma
Energy Technology Data Exchange (ETDEWEB)
Hittinger, J F; Dorr, M R; Berger, R L; Williams, E A
2004-10-11
A coupled mode system is derived to investigate a three-wave parametric instability leading to energy transfer between co-propagating laser beams crossing in a plasma flow. The model includes beams of finite width refracting in a prescribed transverse plasma flow with spatial and temporal gradients in velocity and density. The resulting paraxial light equations are discretized spatially with a Crank-Nicholson-type scheme, and these algebraic constraints are nonlinearly coupled with ordinary differential equations in time that describe the ion acoustic response. The entire nonlinear differential-algebraic system is solved using an adaptive, backward-differencing method coupled with Newton's method. A numerical study is conducted in two dimensions that compares the intensity gain of the fully time-dependent coupled mode system with the gain computed under the further assumption of a strongly-damped ion acoustic response. The results demonstrate a time-dependent gain suppression when the beam diameter is commensurate with the velocity gradient scale length. The gain suppression is shown to depend on time-dependent beam refraction and is interpreted as a time-dependent frequency shift.
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.
Exact Analytical Solutions in Bose-Einstein Condensates with Time-Dependent Atomic Scattering Length
Institute of Scientific and Technical Information of China (English)
CHEN Yong; LI Biao; ZHENG Yu
2007-01-01
In the paper, the generalized Riccati equation rational expansion method is presented. Making use of the method and symbolic computation, we present three families of exact analytical solutions of Bose-Einstein condensates with the time-dependent interatomic interaction in an expulsive parabolic potential. Then the dynamics of two anlytical solutions are demonstrated by computer simulations under some selectable parameters including the Feshbach-managed nonlinear coefficient and the hyperbolic secant function coefficient.
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.
Pang, Yang; Prasad, Paras N.
1990-08-01
We have investigated the dynamics of resonant third-order optical nonlinearity of chemically prepared poly(3-dodecylthiophene) by the degenerate four wave mixing technique using 60 fs pulses at 620 nm. The measured effective value of χ(3) is 5.5×10-11 esu, sixfold smaller than that obtained with 400 fs pulses, emphasizing the pulse width dependence of effective χ(3) when the relaxation time of the photogenerated excitation responsible for the optical nonlinearity is comparable to the pulse width. Within the resolution of the optical pulse, the rise time of the nonlinear response is instantaneous and the dominant decay occurs within 200 fs, revealing that the short time, nonlinear response is derived from the initially photogenerated excitons. A detailed analysis of the total decay behavior is consistent with the polaron dynamics of the conformational deformation model proposed by Su, Schrieffer, and Heeger for a conjugated linear polymer with bond alternation.
Time Dependent Data Mining in RAVEN
Energy Technology Data Exchange (ETDEWEB)
Cogliati, Joshua Joseph [Idaho National Lab. (INL), Idaho Falls, ID (United States); Chen, Jun [Idaho National Lab. (INL), Idaho Falls, ID (United States); Patel, Japan Ketan [Idaho National Lab. (INL), Idaho Falls, ID (United States); Mandelli, Diego [Idaho National Lab. (INL), Idaho Falls, ID (United States); Maljovec, Daniel Patrick [Idaho National Lab. (INL), Idaho Falls, ID (United States); Alfonsi, Andrea [Idaho National Lab. (INL), Idaho Falls, ID (United States); Talbot, Paul William [Idaho National Lab. (INL), Idaho Falls, ID (United States); Rabiti, Cristian [Idaho National Lab. (INL), Idaho Falls, ID (United States)
2016-09-01
RAVEN is a generic software framework to perform parametric and probabilistic analysis based on the response of complex system codes. The goal of this type of analyses is to understand the response of such systems in particular with respect their probabilistic behavior, to understand their predictability and drivers or lack of thereof. Data mining capabilities are the cornerstones to perform such deep learning of system responses. For this reason static data mining capabilities were added last fiscal year (FY 15). In real applications, when dealing with complex multi-scale, multi-physics systems it seems natural that, during transients, the relevance of the different scales, and physics, would evolve over time. For these reasons the data mining capabilities have been extended allowing their application over time. In this writing it is reported a description of the new RAVEN capabilities implemented with several simple analytical tests to explain their application and highlight the proper implementation. The report concludes with the application of those newly implemented capabilities to the analysis of a simulation performed with the Bison code.
Temperature-Dependent Sellmeier Equations of IR Nonlinear Optical Crystal BaGa4Se7
Directory of Open Access Journals (Sweden)
Naixia Zhai
2017-02-01
Full Text Available The thermal dependent principal refractive indices of a new promising IR nonlinear optical crystal BaGa4Se7 at wavelengths of 0.546, 0.5806, 0.644, 0.7065, 1.530, 1.970, and 2.325μm were measured by using the vertical incidence method within the temperature range from 25 to 150 °C. We derived equations of thermal refractive index coefficients as a function of wavelength that could be used to calculate the principal thermal refractive indices at different wavelengths. The temperature-dependent Sellmeier equations were also obtained and used to calculate the phase matching angles for the optical parametric process of BaGa4Se7 crystal at different temperatures.
Saturation and time dependence of geodynamo models
Schrinner, M; Cameron, R; Hoyng, P
2009-01-01
In this study we address the question under which conditions a saturated velocity field stemming from geodynamo simulations leads to an exponential growth of the magnetic field in a corresponding kinematic calculation. We perform global self-consistent geodynamo simulations and calculate the evolution of a kinematically advanced tracer field. The self-consistent velocity field enters the induction equation in each time step, but the tracer field does not contribute to the Lorentz force. This experiment has been performed by Cattaneo & Tobias (2009) and is closely related to the test field method by Schrinner et al. (2005, 2007). We find two dynamo regimes in which the tracer field either grows exponentially or approaches a state aligned with the actual self-consistent magnetic field after an initial transition period. Both regimes can be distinguished by the Rossby number and coincide with the dipolar and multipolar dynamo regimes identified by Christensen & Aubert (2006). Dipolar dynamos with low Ros...
Improvement of the Exp-function method for solving the BBM equation with time-dependent coefficients
Jahani, Maghsoud; Manafian, Jalil
2016-03-01
In this article, we establish the exact solutions for the BBM equation with time-dependent coefficients. The Exp-function method (EFM) and improvement of the Exp-function method (IEFM) are used to construct solitary and soliton solutions of nonlinear evolution equations. These methods are developed for searching exact travelling wave solutions of nonlinear partial differential equations. The exact particular solutions are of four types: the hyperbolic function solution, trigonometric function solution, exponential solution and rational solution. It is shown that the EFM and IEFM, with the help of symbolic computation, provide a straightforward and powerful mathematical tool for solving nonlinear evolution equations in mathematical physics.
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.
Computing Resolution-Path Dependencies in Linear Time
Slivovsky, Friedrich
2012-01-01
The alternation of existential and universal quantifiers in a quantified boolean formula (QBF) generates dependencies among variables that must be respected when evaluating the formula. Dependency schemes provide a general framework for representing such dependencies. Since it is generally intractable to determine dependencies exactly, a set of potential dependencies is computed instead, which may include false positives. Among the schemes proposed so far, resolution-path dependencies introduce the fewest spurious dependencies. In this work, we describe an algorithm that detects resolution-path dependencies in linear time, resolving a problem posed by Van Gelder (CP 2011)
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).
Painleve V and time-dependent Jacobi polynomials
Energy Technology Data Exchange (ETDEWEB)
Basor, Estelle [American Institute of Mathematics, Palo Alto, CA 94306 (United States); Chen Yang [Department of Mathematics, Imperial College London, 180 Queen' s Gates, London SW7 2BZ (United Kingdom); Ehrhardt, Torsten [Department of Mathematics, University of California, Santa Cruz, CA 95064 (United States)], E-mail: ebasor@aimath.org, E-mail: ychen@imperial.ac.uk, E-mail: ehrhardt@math.ucsc.edu
2010-01-08
In this paper we study the simplest deformation on a sequence of orthogonal polynomials. This in turn induces a deformation on the moment matrix of the polynomials and associated Hankel determinant. We replace the original (or reference) weight w{sub 0}(x) (supported on R or subsets of R) by w{sub 0}(x) e{sup -tx}. It is a well-known fact that under such a deformation the recurrence coefficients denoted as {alpha}{sub n} and {beta}{sub n} evolve in t according to the Toda equations, giving rise to the time-dependent orthogonal polynomials and time-dependent determinants, using Sogo's terminology. If w{sub 0} is the normal density e{sup -x{sup 2}}, x element of R, or the gamma density x{sup {alpha}} e{sup -x}, x element of R{sub +}, {alpha} > -1, then the initial value problem of the Toda equations can be trivially solved. This is because under elementary scaling and translation the orthogonality relations reduce to the original ones. However, if w{sub 0} is the beta density (1 - x){sup {alpha}}(1 + x){sup {beta}}, x in [ - 1, 1], {alpha}, {beta} > -1, the resulting 'time-dependent' Jacobi polynomials will again satisfy a linear second-order ode, but no longer in the Sturm-Liouville form, which is to be expected. This deformation induces an irregular singular point at infinity in addition to three regular singular points of the hypergeometric equation satisfied by the Jacobi polynomials. We will show that the coefficients of this ode, as well as the Hankel determinant, are intimately related to a particular Painleve V. In particular we show that p{sub 1}(n,t), where p{sub 1}(n,t) is the coefficient of z{sup n-1} of the monic orthogonal polynomials associated with the 'time-dependent' Jacobi weight, satisfies, up to a translation in t, the Jimbo-Miwa {sigma}-form of the same P{sub V}; while a recurrence coefficient {alpha}{sub n}(t) is up to a translation in t and a linear fractional transformation P{sub V}({alpha}{sup 2}/2, - {beta}{sup 2
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.
Williams, G. Jackson; Lee, Sooheyong; Walko, Donald A.; Watson, Michael A.; Jo, Wonhuyk; Lee, Dong Ryeol; Landahl, Eric C.
2016-12-01
Nonlinear optical phenomena in semiconductors present several fundamental problems in modern optics that are of great importance for the development of optoelectronic devices. In particular, the details of photo-induced lattice dynamics at early time-scales prior to carrier recombination remain poorly understood. We demonstrate the first integrated measurements of both optical and structural, material-dependent quantities while also inferring the bulk impulsive strain profile by using high spatial-resolution time-resolved x-ray scattering (TRXS) on bulk crystalline gallium arsenide. Our findings reveal distinctive laser-fluence dependent crystal lattice responses, which are not described by previous TRXS experiments or models. The initial linear expansion of the crystal upon laser excitation stagnates at a laser fluence corresponding to the saturation of the free carrier density before resuming expansion in a third regime at higher fluences where two-photon absorption becomes dominant. Our interpretations of the lattice dynamics as nonlinear optical effects are confirmed by numerical simulations and by additional measurements in an n-type semiconductor that allows higher-order nonlinear optical processes to be directly observed as modulations of x-ray diffraction lineshapes.
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.
Institute of Scientific and Technical Information of China (English)
Axel Schulze-Halberg
2005-01-01
We study space-time transformations of the time-dependent Schr(o)dinger equation (TDSE) with time- and position-dependent (effective) mass. We obtain the most general space-time transformation that maps such a TDSE onto another one of its kind. The transformed potential is given in explicit form.
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.
Time-dependent theoretical treatments of the dynamics of electrons and nuclei in molecular systems
Deumens, E.; Diz, A.; Longo, R.; Öhrn, Y.
1994-07-01
An overview is presented of methods for time-dependent treatments of molecules as systems of electrons and nuclei. The theoretical details of these methods are reviewed and contrasted in the light of a recently developed time-dependent method called electron-nuclear dynamics. Electron-nuclear dynamics (END) is a formulation of the complete dynamics of electrons and nuclei of a molecular system that eliminates the necessity of constructing potential-energy surfaces. Because of its general formulation, it encompasses many aspects found in other formulations and can serve as a didactic device for clarifying many of the principles and approximations relevant in time-dependent treatments of molecular systems. The END equations are derived from the time-dependent variational principle applied to a chosen family of efficiently parametrized approximate state vectors. A detailed analysis of the END equations is given for the case of a single-determinantal state for the electrons and a classical treatment of the nuclei. The approach leads to a simple formulation of the fully nonlinear time-dependent Hartree-Fock theory including nuclear dynamics. The nonlinear END equations with the ab initio Coulomb Hamiltonian have been implemented at this level of theory in a computer program, ENDyne, and have been shown feasible for the study of small molecular systems. Implementation of the Austin Model 1 semiempirical Hamiltonian is discussed as a route to large molecular systems. The linearized END equations at this level of theory are shown to lead to the random-phase approximation for the coupled system of electrons and nuclei. The qualitative features of the general nonlinear solution are analyzed using the results of the linearized equations as a first approximation. Some specific applications of END are presented, and the comparison with experiment and other theoretical approaches is discussed.
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
K shortest paths in stochastic time-dependent networks
DEFF Research Database (Denmark)
Nielsen, Lars Relund; Pretolani, Daniele; Andersen, Kim Allan
2004-01-01
A substantial amount of research has been devoted to the shortest path problem in networks where travel times are stochastic or (deterministic and) time-dependent. More recently, a growing interest has been attracted by networks that are both stochastic and time-dependent. In these networks...
Real time propagation of the exact two component time-dependent density functional theory
Goings, Joshua J.; Kasper, Joseph M.; Egidi, Franco; Sun, Shichao; Li, Xiaosong
2016-09-01
We report the development of a real time propagation method for solving the time-dependent relativistic exact two-component density functional theory equations (RT-X2C-TDDFT). The method is fundamentally non-perturbative and may be employed to study nonlinear responses for heavy elements which require a relativistic Hamiltonian. We apply the method to several group 12 atoms as well as heavy-element hydrides, comparing with the extensive theoretical and experimental studies on this system, which demonstrates the correctness of our approach. Because the exact two-component Hamiltonian contains spin-orbit operators, the method is able to describe the non-zero transition moment of otherwise spin-forbidden processes in non-relativistic theory. Furthermore, the two-component approach is more cost effective than the full four-component approach, with similar accuracy. The RT-X2C-TDDFT will be useful in future studies of systems containing heavy elements interacting with strong external fields.
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
Band-structure-dependent nonlinear giant magnetoresistance in Ni1-xFex dual spin valves
Banerjee, N.; Robinson, J. W. A.; Aziz, A.; Ali, M.; Hickey, B. J.; Blamire, M. G.
2012-10-01
Conventional giant magnetoresistance (GMR) in spin valves is current-independent, so the resistance of a device depends only on the relative orientation of the magnetic layers. In dual spin valves consisting of three ferromagnetic (FM) layers separated by nonmagnetic (NM) spacers (i.e., a FM1/NM/FM2/NM/FM1), GMR can be current-dependent if spin can accumulate in FM2 when outer FM1 layers are aligned antiparallel. Currently the underlying physics is poorly understood, although spin accumulation in FM2 is likely to depend on the gradient in the density of states at the Fermi energy of the ferromagnet. To investigate this hypothesis, we have measured a series of dual spin valves with Ni1-xFex as FM2 layers of varying composition. We show that both the magnitude and sign of the nonlinear GMR depend strongly on the Fe content and thus on the band structure of the ferromagnet FM2.
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
Energy Technology Data Exchange (ETDEWEB)
Belendez, A; Gimeno, E; Mendez, D I; Alvarez, M L [Departamento de Fisica, IngenierIa de Sistemas y TeorIa de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Fernandez, E [Departamento de Optica, FarmacologIa y AnatomIa, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)], E-mail: a.belendez@ua.es
2008-06-15
A modified generalized, rational harmonic balance method is used to construct approximate frequency-amplitude relations for a conservative nonlinear singular oscillator in which the restoring force is inversely proportional to the dependent variable. The procedure is used to solve the nonlinear differential equation approximately. The approximate frequency obtained using this procedure is more accurate than those obtained using other approximate methods and the discrepancy between the approximate frequency and the exact one is lower than 0.40%.
Bhowmick, Aklant K.; Abarzhi, Snezhana
2016-11-01
Rayleigh Taylor instability in a power-law time dependent acceleration field is investigated theoretically for a flow with the symmetry group p6mm (hexagon) in the plane normal to acceleration. In the nonlinear regime, regular asymptotic solutions form a one-parameter family. The physically significant solution is identified with the one having the fastest growth and being stable (bubble tip velocity). Two distinct regimes are identified depending on the acceleration exponent. Particularly, the RM-type regime, where the dynamics is identical to conventional RM instability and is dominated by initial conditions, and the RT-type regime where the dynamics is dominated by the acceleration term. For the latter, the time dependence has profound effects on the dynamics. In the RT non-linear regime, the time dependence has no consequence on the morphology of the bubbles; the growth rate (bubble tip velocity) evolves as power law with the exponent set by the acceleration. The solutions for a one-parameter family, and are convergent with exponential decay of Fourier amplitudes. The solutions are stable at maximum tip velocity, whereas flat bubbles are unstable, and the growth/decay of perturbations is no longer purely exponential and depends on the acceleration exponent. The work is supported by the US National Science Foundation.
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.
Introduction to numerical methods for time dependent differential equations
Kreiss, Heinz-Otto
2014-01-01
Introduces both the fundamentals of time dependent differential equations and their numerical solutions Introduction to Numerical Methods for Time Dependent Differential Equations delves into the underlying mathematical theory needed to solve time dependent differential equations numerically. Written as a self-contained introduction, the book is divided into two parts to emphasize both ordinary differential equations (ODEs) and partial differential equations (PDEs). Beginning with ODEs and their approximations, the authors provide a crucial presentation of fundamental notions, such as the t
Directory of Open Access Journals (Sweden)
Merboldt Klaus-Dietmar
2010-07-01
Full Text Available Abstract Background Functional assessments of the heart by dynamic cardiovascular magnetic resonance (CMR commonly rely on (i electrocardiographic (ECG gating yielding pseudo real-time cine representations, (ii balanced gradient-echo sequences referred to as steady-state free precession (SSFP, and (iii breath holding or respiratory gating. Problems may therefore be due to the need for a robust ECG signal, the occurrence of arrhythmia and beat to beat variations, technical instabilities (e.g., SSFP "banding" artefacts, and limited patient compliance and comfort. Here we describe a new approach providing true real-time CMR with image acquisition times as short as 20 to 30 ms or rates of 30 to 50 frames per second. Methods The approach relies on a previously developed real-time MR method, which combines a strongly undersampled radial FLASH CMR sequence with image reconstruction by regularized nonlinear inversion. While iterative reconstructions are currently performed offline due to limited computer speed, online monitoring during scanning is accomplished using gridding reconstructions with a sliding window at the same frame rate but with lower image quality. Results Scans of healthy young subjects were performed at 3 T without ECG gating and during free breathing. The resulting images yield T1 contrast (depending on flip angle with an opposed-phase or in-phase condition for water and fat signals (depending on echo time. They completely avoid (i susceptibility-induced artefacts due to the very short echo times, (ii radiofrequency power limitations due to excitations with flip angles of 10° or less, and (iii the risk of peripheral nerve stimulation due to the use of normal gradient switching modes. For a section thickness of 8 mm, real-time images offer a spatial resolution and total acquisition time of 1.5 mm at 30 ms and 2.0 mm at 22 ms, respectively. Conclusions Though awaiting thorough clinical evaluation, this work describes a robust and
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
Random Time Dependent Resistance Analysis on Reinforced Concrete Structures
Institute of Scientific and Technical Information of China (English)
GUAN Chang-sheng; WU Ling
2002-01-01
The analysis method on random time dependence of reinforced concrete material is introduced,the effect mechanism on reinforced concrete are discussed, and the random time dependence resistance of reinforced concrete is studied. Furthermore, the corrosion of steel bar in reinforced concrete structures is analyzed. A practical statistical method of evaluating the random time dependent resistance, which includes material, structural size and calculation influence, is also established. In addition, an example of predicting random time dependent resistance of reinforced concrete structural element is given.
Topology optimization of nonlinear optical devices
DEFF Research Database (Denmark)
Jensen, Jakob Søndergaard
2011-01-01
This paper considers the design of nonlinear photonic devices. The nonlinearity stems from a nonlinear material model with a permittivity that depends on the local time-averaged intensity of the electric field. A finite element model is developed for time-harmonic wave propagation and an incremen......This paper considers the design of nonlinear photonic devices. The nonlinearity stems from a nonlinear material model with a permittivity that depends on the local time-averaged intensity of the electric field. A finite element model is developed for time-harmonic wave propagation...
Nonlinear Time-Domain Strip Theory Formulation for Low-Speed Manoeuvering and Station-Keeping
Directory of Open Access Journals (Sweden)
Thor I. Fossen
2004-10-01
Full Text Available This paper presents a computer effective nonlinear time-domain strip theory formulation for dynamic positioning (DP and low-speed manoeuvring. Strip theory or 2D potential theory, where the ship is divided in 20 to 30 cross sections, can be used to compute the potential coefficients (added mass and potential damping and the exciting wave loads (Froude-Krylov and diffraction forces. Commercially available programs are ShipX (VERES by Marintek (Fathi, 2004 and SEAWAY by Amarcon (Journée & Adegeest, 2003, for instance. The proposed method can easily be extended to utilize other strip theory formulations or 3-D potential programs like WAMIT (2004. The frequency dependent potential damping, which in classic theory results in a convolution integral not suited for real-time simulation, is compactly represented by using the state-space formulation of Kristiansen & Egeland (2003. The separation of the vessel model into a low-frequency model (represented by zerofrequency added mass and damping and a wave-frequency model (represented by motion transfer functions or RAOs, which is commonly used for simulation, is hence made superfluous. Transformations of motions and coefficients between different coordinate systems and origins, i.e. data frame, hydrodynamic frame, body frame, inertial frame etc., are put into the rigid framework of Fossen (1994, 2002. The kinematic equations of motion are formulated in a compact nonlinear vector representation and the classical kinematic assumption that the Euler angles are small is removed. This is important for computation of accurate control forces at higher roll and pitch angles. The hydrodynamic forces in the steadily translating hydrodynamic reference frame (equilibrium axes are, however, assumed tobe linear. Recipes for computation of retardation functions are presented and frequency dependent viscous damping is included. Emphasis is placed on numerical computations and representation of the data from VERES and
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
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.
Yuan, Jinlong; Zhang, Xu; Liu, Chongyang; Chang, Liang; Xie, Jun; Feng, Enmin; Yin, Hongchao; Xiu, Zhilong
2016-09-01
Time-delay dynamical systems, which depend on both the current state of the system and the state at delayed times, have been an active area of research in many real-world applications. In this paper, we consider a nonlinear time-delay dynamical system of dha-regulonwith unknown time-delays in batch culture of glycerol bioconversion to 1,3-propanediol induced by Klebsiella pneumonia. Some important properties and strong positive invariance are discussed. Because of the difficulty in accurately measuring the concentrations of intracellular substances and the absence of equilibrium points for the time-delay system, a quantitative biological robustness for the concentrations of intracellular substances is defined by penalizing a weighted sum of the expectation and variance of the relative deviation between system outputs before and after the time-delays are perturbed. Our goal is to determine optimal values of the time-delays. To this end, we formulate an optimization problem in which the time delays are decision variables and the cost function is to minimize the biological robustness. This optimization problem is subject to the time-delay system, parameter constraints, continuous state inequality constraints for ensuring that the concentrations of extracellular and intracellular substances lie within specified limits, a quality constraint to reflect operational requirements and a cost sensitivity constraint for ensuring that an acceptable level of the system performance is achieved. It is approximated as a sequence of nonlinear programming sub-problems through the application of constraint transcription and local smoothing approximation techniques. Due to the highly complex nature of this optimization problem, the computational cost is high. Thus, a parallel algorithm is proposed to solve these nonlinear programming sub-problems based on the filled function method. Finally, it is observed that the obtained optimal estimates for the time-delays are highly satisfactory
Thunis, P.; Clappier, A.; Pisoni, E.; Degraeuwe, B.
2015-02-01
Air quality models which are nowadays used for a wide range of scopes (i.e. assessment, forecast, planning) see their intrinsic complexity progressively increasing as better knowledge of the atmospheric chemistry processes is gained. As a result of this increased complexity potential non-linearities are implicitly and/or explicitly incorporated in the system. These non-linearities represent a key and challenging aspect of air quality modeling, especially to assess the robustness of the model responses. In this work the importance of non-linear effects in air quality modeling is quantified, especially as a function of time averaging. A methodology is proposed to decompose the concentration change resulting from an emission reduction over a given domain into its linear and non-linear contributions for each precursor as well as in the contribution resulting from the interactions among precursors. Simulations with the LOTOS-EUROS model have been performed by TNO over three regional geographical areas in Europe for this analysis. In all three regions the non-linear effects for PM10 and PM2.5 are shown to be relatively minor for yearly and monthly averages whereas they become significant for daily average values. For Ozone non-linearities become important already for monthly averages in some regions. An approach which explicitly deals with monthly variations seems therefore more appropriate for O3. In general non-linearities are more important at locations where concentrations are the lowest, i.e. at urban locations for O3 and at rural locations for PM10 and PM2.5. Finally the impact of spatial resolution (tested by comparing coarse and fine resolution simulations) on the degree of non-linearity has been shown to be minor as well. The conclusions developed here are model dependent and runs should be repeated with the particular model of interest but the proposed methodology allows with a limited number of runs to identify where efforts should be focused in order to
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,...
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.
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.
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.
Periodicity in a Nonlinear Predator-prey System with State Dependent Delays
Institute of Scientific and Technical Information of China (English)
Feng-de Chen; Jin-lin Shi
2005-01-01
With the help of a continuation theorem based on Gainesand Mawhin's coincidence degree, easily verifiable criteria are established for the global existence of positive periodic solutions of the following nonlinear state dependent delays predator-prey system{dN1(t)/dt=N1(t)[b1(t)-n∑i=1 ai(t)(N1(t-Ti(t,N1(t), N2(t))))ai-m∑cj(t)(N2(t-σj(t,Ni(t),N2(t))))βj],dN2(t)/dt=N2(t)[b2(t)-n∑i=1 di(t)(N1(t-Pi(t,N1(t), N2(t))))γi],where ai (t), cj (t), di(t) are continuous positive periodic functions with periodic ω＞ 0, b1 (t), b2 (t) are continuousare positive constants.
Institute of Scientific and Technical Information of China (English)
SUN Ren
2006-01-01
A slow thermocapillary migration of a droplet at vanishingly small Reynolds and Marangoni numbers was theoretically investigated. A force on the droplet released in another liquid subjected to arbitrary configuration of the gravitational field and an imposed thermal gradient for the case of constant liquid properties was derived using the general solutions given by Lamb. A solution to the migration was thereby obtained, which corresponds to the well-known YGB result as t →∞. In the case of variable physical properties with temperature, a nonlinear migration of the droplet was described by the dynamical equation of motion, and the numerical results were compared with available experimental data. The comparison exhibits a reasonable agreement between the theoretical prediction and the experimental results, which shows the dependence of physical properties on temperature is a primary cause of the continuous velocity variation in the thermocapillary droplet migration.
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.
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.
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.
Using missing ordinal patterns to detect nonlinearity in time series data
Kulp, Christopher W.; Zunino, Luciano; Osborne, Thomas; Zawadzki, Brianna
2017-08-01
The number of missing ordinal patterns (NMP) is the number of ordinal patterns that do not appear in a series after it has been symbolized using the Bandt and Pompe methodology. In this paper, the NMP is demonstrated as a test for nonlinearity using a surrogate framework in order to see if the NMP for a series is statistically different from the NMP of iterative amplitude adjusted Fourier transform (IAAFT) surrogates. It is found that the NMP works well as a test statistic for nonlinearity, even in the cases of very short time series. Both model and experimental time series are used to demonstrate the efficacy of the NMP as a test for nonlinearity.
Real-Time Monitoring of Non-linear Suicidal Dynamics: Methodology and a Demonstrative Case Report.
Fartacek, Clemens; Schiepek, Günter; Kunrath, Sabine; Fartacek, Reinhold; Plöderl, Martin
2016-01-01
In recent years, a number of different authors have stressed the usefulness of non-linear dynamic systems approach in suicide research and suicide prevention. This approach applies specific methods of time series analysis and, consequently, it requires a continuous and fine-meshed assessment of the processes under consideration. The technical means for this kind of process assessment and process analysis are now available. This paper outlines how suicidal dynamics can be monitored in high-risk patients by an Internet-based application for continuous self-assessment with integrated tools of non-linear time series analysis: the Synergetic Navigation System. This procedure is illustrated by data from a patient who attempted suicide at the end of a 90-day monitoring period. Additionally, future research topics and clinical applications of a non-linear dynamic systems approach in suicidology are discussed.
Evaluation of Time-Dependent Behavior of Soils
DEFF Research Database (Denmark)
Augustesen, Anders; Liingaard, Morten; Lade, Poul V.
2004-01-01
The time-dependent behavior of soils has been investigated extensively through one-dimensional and triaxial test conditions. Most of the observations in literature have focused on the determination of the time-dependent behavior of clayey soils, whereas the reported experimental studies of granul...
A novel class of highly efficient and accurate time-integrators in nonlinear computational mechanics
Wang, Xuechuan; Atluri, Satya N.
2017-05-01
A new class of time-integrators is presented for strongly nonlinear dynamical systems. These algorithms are far superior to the currently common time integrators in computational efficiency and accuracy. These three algorithms are based on a local variational iteration method applied over a finite interval of time. By using Chebyshev polynomials as trial functions and Dirac-Delta functions as the test functions over the finite time interval, the three algorithms are developed into three different discrete time-integrators through the collocation method. These time integrators are labeled as Chebyshev local iterative collocation methods. Through examples of the forced Duffing oscillator, the Lorenz system, and the multiple coupled Duffing equations (which arise as semi-discrete equations for beams, plates and shells undergoing large deformations), it is shown that the new algorithms are far superior to the 4th order Runge-Kutta and ODE45 of MATLAB, in predicting the chaotic responses of strongly nonlinear dynamical systems.
A novel class of highly efficient and accurate time-integrators in nonlinear computational mechanics
Wang, Xuechuan; Atluri, Satya N.
2017-01-01
A new class of time-integrators is presented for strongly nonlinear dynamical systems. These algorithms are far superior to the currently common time integrators in computational efficiency and accuracy. These three algorithms are based on a local variational iteration method applied over a finite interval of time. By using Chebyshev polynomials as trial functions and Dirac-Delta functions as the test functions over the finite time interval, the three algorithms are developed into three different discrete time-integrators through the collocation method. These time integrators are labeled as Chebyshev local iterative collocation methods. Through examples of the forced Duffing oscillator, the Lorenz system, and the multiple coupled Duffing equations (which arise as semi-discrete equations for beams, plates and shells undergoing large deformations), it is shown that the new algorithms are far superior to the 4th order Runge-Kutta and ODE45 of MATLAB, in predicting the chaotic responses of strongly nonlinear dynamical systems.
One Dimensional Time-Dependent Tunnelling of Excitons
Kilcullen, Patrick; Salayka-Ladouceur, Logan; Malmgren, Kevin; Reid, Matthew; Shegelski, Mark R. A.
2017-03-01
We study the time-dependent tunnelling of excitons in one dimension using numerical integration based on the Crank-Nicholson method. A complete development of the time-dependent simulator is provided. External barriers studied include single and double delta barriers. We find that the appearance of transmission resonances depends strongly on the dielectric constant, relative effective masses, and initial spatial spread of the wavefunction. A discussion regarding applications to realistic systems is provided.
Luo, Tao; Xin, Zhouping; Zeng, Huihui
2016-11-01
The nonlinear asymptotic stability of Lane-Emden solutions is proved in this paper for spherically symmetric motions of viscous gaseous stars with the density dependent shear and bulk viscosities which vanish at the vacuum, when the adiabatic exponent {γ} lies in the stability regime {(4/3, 2)}, by establishing the global-in-time regularity uniformly up to the vacuum boundary for the vacuum free boundary problem of the compressible Navier-Stokes-Poisson systems with spherical symmetry, which ensures the global existence of strong solutions capturing the precise physical behavior that the sound speed is {C^{{1}/{2}}}-Hölder continuous across the vacuum boundary, the large time asymptotic uniform convergence of the evolving vacuum boundary, density and velocity to those of Lane-Emden solutions with detailed convergence rates, and the detailed large time behavior of solutions near the vacuum boundary. Those uniform convergence are of fundamental importance in the study of vacuum free boundary problems which are missing in the previous results for global weak solutions. Moreover, the results obtained in this paper apply to much broader cases of viscosities than those in Fang and Zhang (Arch Ration Mech Anal 191:195-243, 2009) for the theory of weak solutions when the adiabatic exponent {γ} lies in the most physically relevant range. Finally, this paper extends the previous local-in-time theory for strong solutions to a global-in-time one.
Time-varying interaction leads to amplitude death in coupled nonlinear oscillators
Indian Academy of Sciences (India)
Awadhesh Prasad
2013-09-01
A new form of time-varying interaction in coupled oscillators is introduced. In this interaction, each individual oscillator has always time-independent self-feedback while its interaction with other oscillators are modulated with time-varying function. This interaction gives rise to a phenomenon called amplitude death even in diffusively coupled identical oscillators. The nonlinear variation of the locus of bifurcation point is shown. Results are illustrated with Landau–Stuart (LS) and Rössler oscillators.
The (G'/G)-expansion method for the nonlinear time fractional differential equations
Unsal, Omer; Guner, Ozkan; Bekir, Ahmet; Cevikel, Adem C.
2017-01-01
In this paper, we obtain exact solutions of two time fractional differential equations using Jumarie's modified Riemann-Liouville derivative which is encountered in mathematical physics and applied mathematics; namely (3 + 1)-dimensional time fractional KdV-ZK equation and time fractional ADR equation by using fractional complex transform and (G/'G )-expansion method. It is shown that the considered transform and method are very useful in solving nonlinear fractional differential equations.
Nonlinear Maps for Design of Discrete-Time Models of Neuronal Network Dynamics
2016-03-31
responsive tiring patterns . We propose to use modern DSP ideas to develop new efficient approaches to the design of such discrete-time models for...2016 Performance/Technic~ 03-01-2016- 03-31-2016 4. TITLE AND SUBTITLE Sa. CONTRACT NUMBER Nonlinear Maps for Design of Discrete-Time Models of...simulations is to design a neuronal model in the form of difference equations that generates neuronal states in discrete moments of time. In this
Wei, H. L.; Balikhin, M.; S. A. Billings
2003-01-01
Identification techniques for nonlinear time-varying systems are investigated based on the NARMAX model and multiresolution wavelet expansions. It is shown that a NARMAX model with time-varying coefficients can be reduced to a time-invariant linear-in-the-parameters analysis problem by then adapted to estimate the parameters. An application data relating to magnetic storms is used to illustrate the realistic application of the new identification technique.
Directory of Open Access Journals (Sweden)
Raseelo J. Moitsheki
2008-01-01
Full Text Available Lie point symmetry analysis is performed for an unsteady nonlinear heat diffusion problem modeling thermal energy storage in a medium with a temperature-dependent power law thermal conductivity and subjected to a convective heat transfer to the surrounding environment at the boundary through a variable heat transfer coefficient. Large symmetry groups are admitted even for special choices of the constants appearing in the governing equation. We construct one-dimensional optimal systems for the admitted Lie algebras. Following symmetry reductions, we construct invariant solutions.
Metzler, Holger; Müller, Markus; Sierra, Carlos A.
2017-04-01
Carbon fluxes in the ocean-atmosphere-biosphere system are governed by nonlinear processes, which are usually modeled by a system of ordinary differential equations. It is very difficult to analyze such nonlinear models and to predict their future behavior, particularly their internal age structure: How old is the carbon in different pools (ages) and how old is the carbon that leaves the system (transit times)? How is this age structure modified by the addition of fossil fuel emissions? To answer these questions, we developed a new mathematical approach that allows us to compute and visualize the age structure of models of well mixed pools even if they are nonlinear and nonautonomous. We do not only consider mean ages and mean transit times, but entire distributions. Consequently, we can consider important statistics such as the median, quantiles, or the variance. We applied this mathematical approach to a nonlinear global carbon model consisting of three pools (atmosphere, surface ocean, and terrestrial biosphere) and driven by four emission scenarios (RCP3-PD, RCP4.5, RCP6, RCP8.5). Results showed that the addition of fossil fuels modifies the age structure of C in the atmosphere by drastically increasing its proportion of young carbon. We found little differences among predicted mean ages for the four emission scenarios, but changes in the overall distributions were large with effects on median, quantiles and variance. In the short-term, fossil-fuel emissions have an important effect on the amount of carbon that is exchanged among Earth's main C reservoirs. In the long-term, most added C will eventually end up in the deep ocean, but the time required to return to pre-industrial C age distributions is largely dependent on emission scenarios.
Time-dependent injection as a model for rapid blazar flares
Zacharias, Michael
2016-01-01
Time-dependent injection can cause non-linear cooling effects, which lead to a faster energy loss of the electrons in jets. The most obvious result is the appearance of unique breaks in the SED, which would normally be attributed to a complicated electron distribution. The knowledge of the observation time and duration is important to interpret the observed spectra, because of the non-trivial evolution of the SED. Intrinsic gamma-gamma absorption processes in the emission region are only of minor importance.
Time-dependent density functional theory for open quantum systems with unitary propagation.
Yuen-Zhou, Joel; Tempel, David G; Rodríguez-Rosario, César A; Aspuru-Guzik, Alán
2010-01-29
We extend the Runge-Gross theorem for a very general class of open quantum systems under weak assumptions about the nature of the bath and its coupling to the system. We show that for Kohn-Sham (KS) time-dependent density functional theory, it is possible to rigorously include the effects of the environment within a bath functional in the KS potential. A Markovian bath functional inspired by the theory of nonlinear Schrödinger equations is suggested, which can be readily implemented in currently existing real-time codes. Finally, calculations on a helium model system are presented.
Estimating marginal properties of quantitative real-time PCR data using nonlinear mixed models
DEFF Research Database (Denmark)
Gerhard, Daniel; Bremer, Melanie; Ritz, Christian
2014-01-01
A unified modeling framework based on a set of nonlinear mixed models is proposed for flexible modeling of gene expression in real-time PCR experiments. Focus is on estimating the marginal or population-based derived parameters: cycle thresholds and ΔΔc(t), but retaining the conditional mixed mod...
ON THE PARTIAL EQUIASYMPTOTIC STABILITY OF NONLINEAR TIME-VARYING DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
JianJigui; JiangMinghui; ShenYanjun
2005-01-01
In this paper, the problem of partial equiasymptotic stability for nonlinear time-varying differential equations are analyzed. A sufficient condition of partial stability and a set of sufficient conditions of partial equiasymptotic stability are given. Some of these conditions allow the derivative of Lyapunov function to be positive. Finally, several numerical examples are also given to illustrate the main results.
Stability of quantized time-delay nonlinear systems : a Lyapunov–Krasowskii-functional approach
Persis, Claudio De; Mazenc, Frédéric
2010-01-01
Lyapunov–Krasowskii functionals are used to design quantized control laws for nonlinear continuous-time systems in the presence of constant delays in the input. The quantized control law is implemented via hysteresis to avoid chattering. Under appropriate conditions, our analysis applies to stabiliz
MINIMAL INVERSION AND ITS ALGORITHMS OF DISCRETE-TIME NONLINEAR SYSTEMS
Institute of Scientific and Technical Information of China (English)
ZHENG Yufan
2005-01-01
The left-inverse system with minimal order and its algorithms of discrete-time nonlinear systems are studied in a linear algebraic framework. The general structure of left-inverse system is described and computed in symbolic algorithm. Two algorithms are given for constructing left-inverse systems with minimal order.
Institute of Scientific and Technical Information of China (English)
Yepeng Xing; Qiong Wang; Valery G. Romanovski
2009-01-01
We prove several new comparison results and develop the monotone iterative tech-nique to show the existence of extremal solutions to a kind of periodic boundary value problem (PBVP) for nonlinear integro-differential equation of mixed type on time scales.
Variational space-time (dis)continuous Galerkin method for nonlinear free surface waves
Gagarina, E.; Vegt, van der J.J.W.; Ambati, V.R.; Bokhove, O.
2013-01-01
A new variational finite element method is developed for nonlinear free surface gravity water waves. This method also handles waves generated by a wave maker. Its formulation stems from Miles' variational principle for water waves together with a space-time finite element discretization that is cont