Time-Dependent Mean-Field Games with Logarithmic Nonlinearities
Gomes, Diogo A.; Pimentel, Edgard
2015-01-01
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.
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.
Time-dependent nonlinear cosmic ray shocks confirming abstract
International Nuclear Information System (INIS)
Dorfi, E.A.
1985-01-01
Numerical studies of time dependent cosmic ray shock structures in planar geometry are interesting because analytical time-independent solutions are available which include the non-linear reactions on the plasma flow. A feature of these time asymptotic solutions is that for higher Mach numbers (M approximately 5) and for a low cosmic ray upstream pressure the solution is not uniquely determined by the usual conservation laws of mass, momentum and energy. These numerical solutions clearly indicate that much work needs to be done before we understand shock acceleration as a time dependent process. The slowness of the process is possibly due to the fact that there is a diffusive flux into the downstream region in addition to the usual advective losses. Analytic investigations of this phenomenon are required
Nonlinear time-dependent simulation of helix traveling wave tubes
International Nuclear Information System (INIS)
Peng Wei-Feng; Yang Zhong-Hai; Hu Yu-Lu; Li Jian-Qing; Lu Qi-Ru; Li Bin
2011-01-01
A one-dimensional nonlinear time-dependent theory for helix traveling wave tubes is studied. A generalized electromagnetic field is applied to the expression of the radio frequency field. To simulate the variations of the high frequency structure, such as the pitch taper and the effect of harmonics, the spatial average over a wavelength is substituted by a time average over a wave period in the equation of the radio frequency field. Under this assumption, the space charge field of the electron beam can be treated by a space charge wave model along with the space charge coefficient. The effects of the radio frequency and the space charge fields on the electrons are presented by the equations of the electron energy and the electron phase. The time-dependent simulation is compared with the frequency-domain simulation for a helix TWT, which validates the availability of this theory. (interdisciplinary physics and related areas of science and technology)
System Identification for Nonlinear FOPDT Model with Input-Dependent Dead-Time
DEFF Research Database (Denmark)
Sun, Zhen; Yang, Zhenyu
2011-01-01
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....
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.
Nonlinear diffusion in the presence of a time-dependent external electric field
International Nuclear Information System (INIS)
Lima e Silva, T. de; Galvao, R.M.O.
1987-09-01
The influence of a time-dependent external electric field on the nonlinear diffusion process of weakly ionized plasmas is investigated. A new solution of the diffusion equation is obtained for the case when electron-ion collisions can be neglected. (author) [pt
Reactivity-induced time-dependencies of EBR-II linear and non-linear feedbacks
International Nuclear Information System (INIS)
Grimm, K.N.; Meneghetti, D.
1988-01-01
Time-dependent linear feedback reactivities are calculated for stereotypical subassemblies in the EBR-II reactor. These quantities are calculated from nodal reactivities obtained from a kinetic code analysis of an experiment in which the change in power resulted from the dropping of a control rod. Shown with these linear reactivities are the reactivity associated with the control-rod shaft contraction and also time-dependent non-linear (mainly bowing) component deduced from the inverse kinetics of the experimentally measured fission power and the calculated linear reactivities. (author)
Existence of solutions to nonlinear parabolic unilateral problems with an obstacle depending on time
Directory of Open Access Journals (Sweden)
Nabila Bellal
2014-10-01
Full Text Available Using the penalty method, we prove the existence of solutions to nonlinear parabolic unilateral problems with an obstacle depending on time. To find a solution, the original inequality is transformed into an equality by adding a positive function on the right-hand side and a complementary condition. This result can be seen as a generalization of the results by Mokrane in [11] where the obstacle is zero.
Time-dependent nonlinear Jaynes-Cummings dynamics of a trapped ion
Krumm, F.; Vogel, W.
2018-04-01
In quantum interaction problems with explicitly time-dependent interaction Hamiltonians, the time ordering plays a crucial role for describing the quantum evolution of the system under consideration. In such complex scenarios, exact solutions of the dynamics are rarely available. Here we study the nonlinear vibronic dynamics of a trapped ion, driven in the resolved sideband regime with some small frequency mismatch. By describing the pump field in a quantized manner, we are able to derive exact solutions for the dynamics of the system. This eventually allows us to provide analytical solutions for various types of time-dependent quantities. In particular, we study in some detail the electronic and the motional quantum dynamics of the ion, as well as the time evolution of the nonclassicality of the motional quantum state.
International Nuclear Information System (INIS)
Barhen, J.; Bjerke, M.A.; Cacuci, D.G.; Mullins, C.B.; Wagschal, G.G.
1982-01-01
An advanced methodology for performing systematic uncertainty analysis of time-dependent nonlinear systems is presented. This methodology includes a capability for reducing uncertainties in system parameters and responses by using Bayesian inference techniques to consistently combine prior knowledge with additional experimental information. The determination of best estimates for the system parameters, for the responses, and for their respective covariances is treated as a time-dependent constrained minimization problem. Three alternative formalisms for solving this problem are developed. The two ''off-line'' formalisms, with and without ''foresight'' characteristics, require the generation of a complete sensitivity data base prior to performing the uncertainty analysis. The ''online'' formalism, in which uncertainty analysis is performed interactively with the system analysis code, is best suited for treatment of large-scale highly nonlinear time-dependent problems. This methodology is applied to the uncertainty analysis of a transient upflow of a high pressure water heat transfer experiment. For comparison, an uncertainty analysis using sensitivities computed by standard response surface techniques is also performed. The results of the analysis indicate the following. Major reduction of the discrepancies in the calculation/experiment ratios is achieved by using the new methodology. Incorporation of in-bundle measurements in the uncertainty analysis significantly reduces system uncertainties. Accuracy of sensitivities generated by response-surface techniques should be carefully assessed prior to using them as a basis for uncertainty analyses of transient reactor safety problems
International Nuclear Information System (INIS)
Cao Rui; Zhang Jian
2013-01-01
In this paper, the trial function method is extended to study the generalized nonlinear Schrödinger equation with time-dependent coefficients. On the basis of a generalized traveling wave transformation and a trial function, we investigate the exact envelope traveling wave solutions of the generalized nonlinear Schrödinger equation with time-dependent coefficients. Taking advantage of solutions to trial function, we successfully obtain exact solutions for the generalized nonlinear Schrödinger equation with time-dependent coefficients under constraint conditions. (general)
Goorjian, Peter M.; Silberberg, Yaron; Kwak, Dochan (Technical Monitor)
1995-01-01
This paper will present results in computational nonlinear optics. An algorithm will be described that solves the full vector nonlinear Maxwell's equations exactly without the approximations that we currently made. Present methods solve a reduced scalar wave equation, namely the nonlinear Schrodinger equation, and neglect the optical carrier. Also, results will be shown of calculations of 2-D electromagnetic nonlinear waves computed by directly integrating in time the nonlinear vector Maxwell's equations. The results will include simulations of 'light bullet' like pulses. Here diffraction and dispersion will be counteracted by nonlinear effects. The time integration efficiently implements linear and nonlinear convolutions for the electric polarization, and can take into account such quantum effects as Karr and Raman interactions. The present approach is robust and should permit modeling 2-D and 3-D optical soliton propagation, scattering, and switching directly from the full-vector Maxwell's equations.
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.
International Nuclear Information System (INIS)
Biswas, Anjan
2009-01-01
In this Letter, the 1-soliton solution of the Zakharov-Kuznetsov equation with power law nonlinearity and nonlinear dispersion along with time-dependent coefficients is obtained. There are two models for this kind of an equation that are studied. The constraint relation between these time-dependent coefficients is established for the solitons to exist. Subsequently, this equation is again analysed with generalized evolution. The solitary wave ansatz is used to carry out this investigation.
Energy Technology Data Exchange (ETDEWEB)
Richert, Ranko [School of Molecular Sciences, Arizona State University, Tempe, Arizona 85287-1604 (United States)
2016-03-21
A model of non-linear dielectric polarization is studied in which the field induced entropy change is the source of polarization dependent retardation time constants. Numerical solutions for the susceptibilities of the system are obtained for parameters that represent the dynamic and thermodynamic behavior of glycerol. The calculations for high amplitude sinusoidal fields show a significant enhancement of the steady state loss for frequencies below that of the low field loss peak. Also at relatively low frequencies, the third harmonic susceptibility spectrum shows a “hump,” i.e., a maximum, with an amplitude that increases with decreasing temperature. Both of these non-linear effects are consistent with experimental evidence. While such features have been used to conclude on a temperature dependent number of dynamically correlated particles, N{sub corr}, the present result demonstrates that the third harmonic susceptibility display a peak with an amplitude that tracks the variation of the activation energy in a model that does not involve dynamical correlations or spatial scales.
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.
Chang, Insu
The objective of the thesis is to introduce a relatively general nonlinear controller/estimator synthesis framework using a special type of the state-dependent Riccati equation technique. The continuous time state-dependent Riccati equation (SDRE) technique is extended to discrete-time under input and state constraints, yielding constrained (C) discrete-time (D) SDRE, referred to as CD-SDRE. For the latter, stability analysis and calculation of a region of attraction are carried out. The derivation of the D-SDRE under state-dependent weights is provided. Stability of the D-SDRE feedback system is established using Lyapunov stability approach. Receding horizon strategy is used to take into account the constraints on D-SDRE controller. Stability condition of the CD-SDRE controller is analyzed by using a switched system. The use of CD-SDRE scheme in the presence of constraints is then systematically demonstrated by applying this scheme to problems of spacecraft formation orbit reconfiguration under limited performance on thrusters. Simulation results demonstrate the efficacy and reliability of the proposed CD-SDRE. The CD-SDRE technique is further investigated in a case where there are uncertainties in nonlinear systems to be controlled. First, the system stability under each of the controllers in the robust CD-SDRE technique is separately established. The stability of the closed-loop system under the robust CD-SDRE controller is then proven based on the stability of each control system comprising switching configuration. A high fidelity dynamical model of spacecraft attitude motion in 3-dimensional space is derived with a partially filled fuel tank, assumed to have the first fuel slosh mode. The proposed robust CD-SDRE controller is then applied to the spacecraft attitude control system to stabilize its motion in the presence of uncertainties characterized by the first fuel slosh mode. The performance of the robust CD-SDRE technique is discussed. Subsequently
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
International Nuclear Information System (INIS)
Wilson, G.L.; Rydin, R.A.; Orivuori, S.
1988-01-01
Two highly efficient nonlinear time-dependent heat conduction methodologies, the nonlinear time-dependent nodal integral technique (NTDNT) and IVOHEAT are compared using one- and two-dimensional time-dependent benchmark problems. The NTDNT is completely based on newly developed time-dependent nodal integral methods, whereas IVOHEAT is based on finite elements in space and Crank-Nicholson finite differences in time. IVOHEAT contains the geometric flexibility of the finite element approach, whereas the nodal integral method is constrained at present to Cartesian geometry. For test problems where both methods are equally applicable, the nodal integral method is approximately six times more efficient per dimension than IVOHEAT when a comparable overall accuracy is chosen. This translates to a factor of 200 for a three-dimensional problem having relatively homogeneous regions, and to a smaller advantage as the degree of heterogeneity increases
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...
International Nuclear Information System (INIS)
Ghayesh, Mergen H.; Amabili, Marco; Farokhi, Hamed
2013-01-01
In the present study, the coupled nonlinear dynamics of an axially moving viscoelastic beam with time-dependent axial speed is investigated employing a numerical technique. The equations of motion for both the transverse and longitudinal motions are obtained using Newton’s second law of motion and the constitutive relations. A two-parameter rheological model of the Kelvin–Voigt energy dissipation mechanism is employed in the modelling of the viscoelastic beam material, in which the material time derivative is used in the viscoelastic constitutive relation. The Galerkin method is then applied to the coupled nonlinear equations, which are in the form of partial differential equations, resulting in a set of nonlinear ordinary differential equations (ODEs) with time-dependent coefficients due to the axial acceleration. A change of variables is then introduced to this set of ODEs to transform them into a set of first-order ordinary differential equations. A variable step-size modified Rosenbrock method is used to conduct direct time integration upon this new set of first-order nonlinear ODEs. The mean axial speed and the amplitude of the speed variations, which are taken as bifurcation parameters, are varied, resulting in the bifurcation diagrams of Poincaré maps of the system. The dynamical characteristics of the system are examined more precisely via plotting time histories, phase-plane portraits, Poincaré sections, and fast Fourier transforms (FFTs)
International Nuclear Information System (INIS)
Qin, Hong; Davidson, Ronald C.
2011-01-01
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.
Energy Technology Data Exchange (ETDEWEB)
Zahariev, Federico; Gordon, Mark S., E-mail: mark@si.msg.chem.iastate.edu [Department of Chemistry, Iowa State University, Ames, Iowa 50011 (United States)
2014-05-14
This work presents an extension of the linear response TDDFT/EFP method to the nonlinear-response regime together with the implementation of nonlinear-response TDDFT/EFP in the quantum-chemistry computer package GAMESS. Included in the new method is the ability to calculate the two-photon absorption cross section and to incorporate solvent effects via the EFP method. The nonlinear-response TDDFT/EFP method is able to make correct qualitative predictions for both gas phase values and aqueous solvent shifts of several important nonlinear properties.
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.
Prandtl-Ishlinskii hysteresis models for complex time dependent hysteresis nonlinearities
Czech Academy of Sciences Publication Activity Database
Al Janaideh, M.; Krejčí, Pavel
2012-01-01
Roč. 407, č. 9 (2012), s. 1365-1367 ISSN 0921-4526 R&D Projects: GA ČR GAP201/10/2315 Institutional research plan: CEZ:AV0Z10190503 Keywords : complex hysteresis * time dependent hysteresis * Prandtl-Ishlinskii model Subject RIV: BA - General Mathematics Impact factor: 1.327, year: 2012 http://www.sciencedirect.com/science/article/pii/S092145261100932X
Solution of large nonlinear time-dependent problems using reduced coordinates
International Nuclear Information System (INIS)
Mish, K.D.
1987-01-01
This research is concerned with the idea of reducing a large time-dependent problem, such as one obtained from a finite-element discretization, down to a more manageable size while preserving the most-important physical behavior of the solution. This reduction process is motivated by the concept of a projection operator on a Hilbert Space, and leads to the Lanczos Algorithm for generation of approximate eigenvectors of a large symmetric matrix. The Lanczos Algorithm is then used to develop a reduced form of the spatial component of a time-dependent problem. The solution of the remaining temporal part of the problem is considered from the standpoint of numerical-integration schemes in the time domain. All of these theoretical results are combined to motivate the proposed reduced coordinate algorithm. This algorithm is then developed, discussed, and compared to related methods from the mechanics literature. The proposed reduced coordinate method is then applied to the solution of some representative problems in mechanics. The results of these problems are discussed, conclusions are drawn, and suggestions are made for related future research
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.
Towards adjoint-based inversion of time-dependent mantle convection with nonlinear viscosity
Li, Dunzhu; Gurnis, Michael; Stadler, Georg
2017-04-01
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-dependent 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 pre-conditioned 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.
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.
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. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.
International Nuclear Information System (INIS)
Esrick, M.A.
1981-01-01
A time-dependent, nonlinear, Schrodinger-like equation for the superconductivity order parameter is derived from the Gor'kov equations. Three types of traveling wave solutions of the equation are discussed. The phases and amplitudes of these solutions propagate at different speeds. The first type of solution has an amplitude that propagates as a soliton and it is suggested that this solution might correspond to the recently observed propagating collective modes of the order parameter. The amplitude of the second type of solution propagates as a periodic disturbance in space and time. It is suggested that this type of solution might explain the recently observed multiple values of the superconductor energy gap as well as the spatially inhomogenous superconducting state. The third type of solution, which is of a more general character, might provide some insight into non-periodic, inhomogeneous states occuring in superconductors. It is also proposed that quasiparticle injection and microwave irradiation might generate soliton-like disturbances in superconductors
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.
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.
International Nuclear Information System (INIS)
Herring, G.; Kevrekidis, P.G.; Williams, F.; Christodoulakis, T.; Frantzeskakis, D.J.
2008-01-01
In this work we revisit the topic of two-dimensional Bose-Einstein condensates under the influence of time-dependent magnetic confinement and time-dependent scattering length. A moment approach reduces the examination of moments of the wavefunction (in particular, of its width) to an Ermakov-Pinney (EP) ordinary differential equation (ODE). We use the well-known structure of the solutions of this nonlinear ODE to 'engineer' trapping and interatomic interaction conditions that lead to condensates dispersing, breathing or even collapsing. The advantage of the approach is that it is fully tractable analytically, in excellent agreement with our numerical observations. As an aside, we also discuss how similar time-dependent EP equations may arise in the description of anisotropic scalar field cosmologies
International Nuclear Information System (INIS)
Herring, G.; Kevrekidis, P.G.; Williams, F.; Christodoulakis, T.; Frantzeskakis, D.J.
2007-01-01
In this work we revisit the topic of two-dimensional Bose-Einstein condensates under the influence of time-dependent magnetic confinement and time-dependent scattering length. A moment approach reduces the examination of moments of the wavefunction (in particular, of its width) to an Ermakov-Pinney (EP) ordinary differential equation (ODE). We use the well-known structure of the solutions of this nonlinear ODE to 'engineer' trapping and interatomic interaction conditions that lead to condensates dispersing, breathing or even collapsing. The advantage of the approach is that it is fully tractable analytically, in excellent agreement with our numerical observations. As an aside, we also discuss how similar time-dependent EP equations may arise in the description of anisotropic scalar field cosmologies
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.
Time series with tailored nonlinearities
Räth, C.; Laut, I.
2015-10-01
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 uncorrelated 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.
International Nuclear Information System (INIS)
1983-04-01
VISCOT is a non-linear, transient, thermal-stress finite-element code designed to determine the viscoelastic, fiscoplastic, or elastoplastic deformation of a rock mass due to mechanical and thermal loading. The numerical solution of the nonlinear incremental equilibrium equations within VISCOT is performed by using an explicit Euler time-stepping scheme. The rock mass may be modeled as a viscoplastic or viscoelastic material. The viscoplastic material model can be described by a Tresca, von Mises, Drucker-Prager or Mohr-Coulomb yield criteria (with or without strain hardening) with an associated flow rule which can be a power or an exponential law. The viscoelastic material model within VISCOT is a temperature- and stress-dependent law which has been developed specifically for salt rock masses by Pfeifle, Mellegard and Senseny in ONWI-314 topical report (1981). Site specific parameters for this creep law at the Richton, Permian, Paradox and Vacherie salt sites have been calculated and are given in ONWI-314 topical report (1981). A major application of VISCOT (in conjunction with a SCEPTER heat transfer code such as DOT) is the thermomechanical analysis of a rock mass such as salt in which significant time-dependent nonlinear deformations are expected to occur. Such problems include room- and canister-scale studies during the excavation, operation, and long-term post-closure stages in a salt repository. In Section 1.5 of this document the code custodianship and control is described along with the status of verification, validation and peer review of this report
Blow-Up Time for Nonlinear Heat Equations with Transcendental Nonlinearity
Directory of Open Access Journals (Sweden)
Hee Chul Pak
2012-01-01
Full Text Available A blow-up time for nonlinear heat equations with transcendental nonlinearity is investigated. An upper bound of the first blow-up time is presented. It is pointed out that the upper bound of the first blow-up time depends on the support of the initial datum.
Nonlinear system theory: another look at dependence.
Wu, Wei Biao
2005-10-04
Based on the nonlinear system theory, we introduce previously undescribed dependence measures for stationary causal processes. Our physical and predictive dependence measures quantify the degree of dependence of outputs on inputs in physical systems. The proposed dependence measures provide a natural framework for a limit theory for stationary processes. In particular, under conditions with quite simple forms, we present limit theorems for partial sums, empirical processes, and kernel density estimates. The conditions are mild and easily verifiable because they are directly related to the data-generating mechanisms.
Reconstructing time-dependent dynamics
Clemson, Philip; Lancaster, Gemma; Stefanovska, Aneta
2016-01-01
The usefulness of the information extracted from biomedical data relies heavily on the underlying theory of the methods used in its extraction. The assumptions of stationarity and autonomicity traditionally applied to dynamical systems break down when considering living systems, due to their inherent time-variability. Living systems are thermodynamically open, and thus constantly interacting with their environment. This results in highly nonlinear, time-dependent dynamics. The aim of signal a...
Establishment of regression dependences. Linear and nonlinear dependences
International Nuclear Information System (INIS)
Onishchenko, A.M.
1994-01-01
The main problems of determination of linear and 19 types of nonlinear regression dependences are completely discussed. It is taken into consideration that total dispersions are the sum of measurement dispersions and parameter variation dispersions themselves. Approaches to all dispersions determination are described. It is shown that the least square fit gives inconsistent estimation for industrial objects and processes. The correction methods by taking into account comparable measurement errors for both variable give an opportunity to obtain consistent estimation for the regression equation parameters. The condition of the correction technique application expediency is given. The technique for determination of nonlinear regression dependences taking into account the dependence form and comparable errors of both variables is described. 6 refs., 1 tab
International Nuclear Information System (INIS)
Belmonte-Beitia, Juan; Calvo, Gabriel F.
2009-01-01
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
Three-dimensional solutions in media with spatial dependence of nonlinear refractive index
International Nuclear Information System (INIS)
Kovachev, L.M.; Kaymakanova, N.I.; Dakova, D.Y.; Pavlov, L.I.; Donev, S.G.; Pavlov, R.L.
2004-01-01
We investigate a nonparaxial vector generalization of the scalar 3D+1 Nonlinear Schrodinger Equation (NSE). Exact analytical 3D+1 soliton solutions are obtained for the first time in media of spatial dependence of the nonlinear refractive index
International Nuclear Information System (INIS)
Yun, Sung Hwan
2004-02-01
Radiative transfer is a complex phenomenon in which radiation field interacts with material. This thermal radiative transfer phenomenon is composed of two equations which are the balance equation of photons and the material energy balance equation. The two equations involve non-linearity due to the temperature and that makes the radiative transfer equation more difficult to solve. During the last several years, there have been many efforts to solve the non-linear radiative transfer problems by Monte Carlo method. Among them, it is known that Semi-Analog Monte Carlo (SMC) method developed by Ahrens and Larsen is accurate regard-less of the time step size in low temperature region. But their works are limited to one-dimensional, low temperature problems. In this thesis, we suggest some method to remove their limitations in the SMC method and apply to the more realistic problems. An initially cold problem was solved over entire temperature region by using piecewise linear interpolation of the heat capacity, while heat capacity is still fitted as a cubic curve within the lowest temperature region. If we assume the heat capacity to be linear in each temperature region, the non-linearity still remains in the radiative transfer equations. We then introduce the first-order Taylor expansion to linearize the non-linear radiative transfer equations. During the linearization procedure, absorption-reemission phenomena may be described by a conventional reemission time sampling scheme which is similar to the repetitive sampling scheme in particle transport Monte Carlo method. But this scheme causes significant stochastic errors, which necessitates many histories. Thus, we present a new reemission time sampling scheme which reduces stochastic errors by storing the information of absorption times. The results of the comparison of the two schemes show that the new scheme has less stochastic errors. Therefore, the improved SMC method is able to solve more realistic problems with
Time Variance of the Suspension Nonlinearity
DEFF Research Database (Denmark)
Agerkvist, Finn T.; Pedersen, Bo Rohde
2008-01-01
but recovers quickly. The the high power and long term measurements affect the non-linearity of the speaker, by incresing the compliance value for all values of displacement. This level dependency is validated with distortion measurements and it is demonstrated how improved accuracy of the non-linear model can...
Time Dependent Quantum Mechanics
Morrison, Peter G.
2012-01-01
We present a systematic method for dealing with time dependent quantum dynamics, based on the quantum brachistochrone and matrix mechanics. We derive the explicit time dependence of the Hamiltonian operator for a number of constrained finite systems from this formalism. Once this has been achieved we go on to calculate the wavevector as a function of time, in order to demonstrate the use of matrix methods with respect to several concrete examples. Interesting results are derived for elliptic ...
Inglesfield, J. E.
2007-01-01
A method of solving the time-dependent Schr\\"odinger equation is presented, in which a finite region of space is treated explicitly, with the boundary conditions for matching the wave-functions on to the rest of the system replaced by an embedding term added on to the Hamiltonian. This time-dependent embedding term is derived from the Fourier transform of the energy-dependent embedding potential, which embeds the time-independent Schr\\"odinger equation. Results are presented for a one-dimensi...
International Nuclear Information System (INIS)
Kobayashi, T.; Yoshikawa, K.; Takaoka, E.; Nakazawa, M.; Shikama, Y.
2002-01-01
A time history nonlinear earthquake response analysis method was proposed and applied to earthquake response prediction analysis for a Large Scale Seismic Test (LSST) Program in Hualien, Taiwan, in which a 1/4 scale model of a nuclear reactor containment structure was constructed on sandy gravel layer. In the analysis both of strain-dependent material nonlinearity, and geometrical nonlinearity by base mat uplift, were considered. The 'Lattice Model' for the soil-structure interaction model was employed. An earthquake record on soil surface at the site was used as control motion, and deconvoluted to the input motion of the analysis model at GL-52 m with 300 Gal of maximum acceleration. The following two analyses were considered: (A) time history nonlinear, (B) equivalent linear, and the advantage of time history nonlinear earthquake response analysis method is discussed
Discrete-time nonlinear sliding mode controller
African Journals Online (AJOL)
user
Keywords: Discrete-time delay system, Sliding mode control, nonlinear sliding ... of engineering systems such as chemical process control, delay in the actuator ...... instrumentation from Motilal Nehru National Institute of Technology (MNNIT),.
Kaza, Nikhil
2015-01-01
Many place based accessibility studies ignore the time component. Relying on theoretical frameworks that treat distance between two fixed points as constant, these methods ignore the diurnal and seasonal changes in accessibility. Network distances between two nodes are dependent on the network structure and weight distribution on the edges. These weights can change quite frequently and the network structure itself is subject to modification because of availability and unavailability of links ...
Space and time evolution of two nonlinearly coupled variables
International Nuclear Information System (INIS)
Obayashi, H.; Totsuji, H.; Wilhelmsson, H.
1976-12-01
The system of two coupled linear differential equations are studied assuming that the coupling terms are proportional to the product of the dependent variables, representing e.g. intensities or populations. It is furthermore assumed that these variables experience different linear dissipation or growth. The derivations account for space as well as time dependence of the variables. It is found that certain particular solutions can be obtained to this system, whereas a full solution in space and time as an initial value problem is outside the scope of the present paper. The system has a nonlinear equilibrium solution for which the nonlinear coupling terms balance the terms of linear dissipation. The case of space and time evolution of a small perturbation of the nonlinear equilibrium state, given the initial one-dimensional spatial distribution of the perturbation, is also considered in some detail. (auth.)
Selfsimilar time dependent shock structures
International Nuclear Information System (INIS)
Beck, R.; Drury, L.O.
1985-01-01
Diffusive shock acceleration as an astrophysical mechanism for accelerating charged particles has the advantage of being highly efficient. This means however that the theory is of necessity nonlinear; the reaction of the accelerated particles on the shock structure and the acceleration process must be self-consistently included in any attempt to develop a complete theory of diffusive shock acceleration. Considerable effort has been invested in attempting, at least partially, to do this and it has become clear that in general either the maximum particle energy must be restricted by introducing additional loss processes into the problem or the acceleration must be treated as a time dependent problem (Drury, 1984). It is concluded that stationary modified shock structures can only exist for strong shocks if additional loss processes limit the maximum energy a particle can attain. This is certainly possible and if it occurs the energy loss from the shock will lead to much greater shock compressions. It is however equally possible that no such processes exist and we must then ask what sort of nonstationary shock structure develops. The same argument which excludes stationary structures also rules out periodic solutions and indeed any solution where the width of the shock remains bounded. It follows that the width of the shock must increase secularly with time and it is natural to examine the possibility of selfsimilar time dependent solutions
Selfsimilar time dependent shock structures
Beck, R.; Drury, L. O.
1985-01-01
Diffusive shock acceleration as an astrophysical mechanism for accelerating charged particles has the advantage of being highly efficient. This means however that the theory is of necessity nonlinear; the reaction of the accelerated particles on the shock structure and the acceleration process must be self-consistently included in any attempt to develop a complete theory of diffusive shock acceleration. Considerable effort has been invested in attempting, at least partially, to do this and it has become clear that in general either the maximum particle energy must be restricted by introducing additional loss processes into the problem or the acceleration must be treated as a time dependent problem (Drury, 1984). It is concluded that stationary modified shock structures can only exist for strong shocks if additional loss processes limit the maximum energy a particle can attain. This is certainly possible and if it occurs the energy loss from the shock will lead to much greater shock compressions. It is however equally possible that no such processes exist and we must then ask what sort of nonstationary shock structure develops. The ame argument which excludes stationary structures also rules out periodic solutions and indeed any solution where the width of the shock remains bounded. It follows that the width of the shock must increase secularly with time and it is natural to examine the possibility of selfsimilar time dependent solutions.
Forecasting with nonlinear time series models
DEFF Research Database (Denmark)
Kock, Anders Bredahl; Teräsvirta, Timo
In this paper, nonlinear models are restricted to mean nonlinear parametric models. Several such models popular in time series econo- metrics are presented and some of their properties discussed. This in- cludes two models based on universal approximators: the Kolmogorov- Gabor polynomial model...... 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...... 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...
Time dependent drift Hamiltonian
International Nuclear Information System (INIS)
Boozer, A.H.
1982-04-01
The motion of individual charged particles in a given magnetic and an electric fields is discussed. An idea of a guiding center distribution function f is introduced. The guiding center distribution function is connected to the asymptotic Hamiltonian through the drift kinetic equation. The general non-stochastic magnetic field can be written in a contravariant and a covariant forms. The drift Hamiltonian is proposed, and the canonical gyroradius is presented. The proposed drift Hamiltonian agrees with Alfven's drift velocity to lowest non-vanishing order in the gyroradius. The relation between the exact, time dependent equations of motion and the guiding center equation is clarified by a Lagrangian analysis. The deduced Lagrangian represents the drift motion. (Kato, T.)
Soliton solutions of some nonlinear evolution equations with time ...
Indian Academy of Sciences (India)
Abstract. In this paper, we obtain exact soliton solutions of the modified KdV equation, inho- mogeneous nonlinear Schrödinger equation and G(m, n) equation with variable coefficients using solitary wave ansatz. The constraint conditions among the time-dependent coefficients turn out as necessary conditions for the ...
Modeling vector nonlinear time series using POLYMARS
de Gooijer, J.G.; Ray, B.K.
2003-01-01
A modified multivariate adaptive regression splines method for modeling vector nonlinear time series is investigated. The method results in models that can capture certain types of vector self-exciting threshold autoregressive behavior, as well as provide good predictions for more general vector
Some Nonlinear Dynamic Inequalities on Time Scales
Indian Academy of Sciences (India)
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 ...
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.
Detecting nonlinear structure in time series
International Nuclear Information System (INIS)
Theiler, J.
1991-01-01
We describe an approach for evaluating the statistical significance of evidence for nonlinearity in a time series. The formal application of our method requires the careful statement of a null hypothesis which characterizes a candidate linear process, the generation of an ensemble of ''surrogate'' data sets which are similar to the original time series but consistent with the null hypothesis, and the computation of a discriminating statistic for the original and for each of the surrogate data sets. The idea is to test the original time series against the null hypothesis by checking whether the discriminating statistic computed for the original time series differs significantly from the statistics computed for each of the surrogate sets. While some data sets very cleanly exhibit low-dimensional chaos, there are many cases where the evidence is sketchy and difficult to evaluate. We hope to provide a framework within which such claims of nonlinearity can be evaluated. 5 refs., 4 figs
On Nonlinear Prices in Timed Automata
Directory of Open Access Journals (Sweden)
Devendra Bhave
2016-12-01
Full Text Available Priced timed automata provide a natural model for quantitative analysis of real-time systems and have been successfully applied in various scheduling and planning problems. The optimal reachability problem for linearly-priced timed automata is known to be PSPACE-complete. In this paper we investigate priced timed automata with more general prices and show that in the most general setting the optimal reachability problem is undecidable. We adapt and implement the construction of Audemard, Cimatti, Kornilowicz, and Sebastiani for non-linear priced timed automata using state-of-the-art theorem prover Z3 and present some preliminary results.
Nonlinear analysis of river flow time sequences
Porporato, Amilcare; Ridolfi, Luca
1997-06-01
Within the field of chaos theory several methods for the analysis of complex dynamical systems have recently been proposed. In light of these ideas we study the dynamics which control the behavior over time of river flow, investigating the existence of a low-dimension deterministic component. The present article follows the research undertaken in the work of Porporato and Ridolfi [1996a] in which some clues as to the existence of chaos were collected. Particular emphasis is given here to the problem of noise and to nonlinear prediction. With regard to the latter, the benefits obtainable by means of the interpolation of the available time series are reported and the remarkable predictive results attained with this nonlinear method are shown.
Evaluation of nonlinearity and validity of nonlinear modeling for complex time series.
Suzuki, Tomoya; Ikeguchi, Tohru; Suzuki, Masuo
2007-10-01
Even if an original time series exhibits nonlinearity, it is not always effective to approximate the time series by a nonlinear model because such nonlinear models have high complexity from the viewpoint of information criteria. Therefore, we propose two measures to evaluate both the nonlinearity of a time series and validity of nonlinear modeling applied to it by nonlinear predictability and information criteria. Through numerical simulations, we confirm that the proposed measures effectively detect the nonlinearity of an observed time series and evaluate the validity of the nonlinear model. The measures are also robust against observational noises. We also analyze some real time series: the difference of the number of chickenpox and measles patients, the number of sunspots, five Japanese vowels, and the chaotic laser. We can confirm that the nonlinear model is effective for the Japanese vowel /a/, the difference of the number of measles patients, and the chaotic laser.
Amplitude-dependent topological edge states in nonlinear phononic lattices
Pal, Raj Kumar; Vila, Javier; Leamy, Michael; Ruzzene, Massimo
2018-03-01
This work investigates the effect of nonlinearities on topologically protected edge states in one- and two-dimensional phononic lattices. We first show that localized modes arise at the interface between two spring-mass chains that are inverted copies of each other. Explicit expressions derived for the frequencies of the localized modes guide the study of the effect of cubic nonlinearities on the resonant characteristics of the interface, which are shown to be described by a Duffing-like equation. Nonlinearities produce amplitude-dependent frequency shifts, which in the case of a softening nonlinearity cause the localized mode to migrate to the bulk spectrum. The case of a hexagonal lattice implementing a phononic analog of a crystal exhibiting the quantum spin Hall effect is also investigated in the presence of weakly nonlinear cubic springs. An asymptotic analysis provides estimates of the amplitude dependence of the localized modes, while numerical simulations illustrate how the lattice response transitions from bulk-to-edge mode-dominated by varying the excitation amplitude. In contrast with the interface mode of the first example studies, this occurs both for hardening and softening springs. The results of this study provide a theoretical framework for the investigation of nonlinear effects that induce and control topologically protected wave modes through nonlinear interactions and amplitude tuning.
Nonlinear time heteronymous damping in nonlinear parametric planetary systems
Czech Academy of Sciences Publication Activity Database
Hortel, Milan; Škuderová, Alena
2014-01-01
Roč. 225, č. 7 (2014), s. 2059-2073 ISSN 0001-5970 Institutional support: RVO:61388998 Keywords : nonlinear dynamics * planetary systems * heteronymous damping Subject RIV: JT - Propulsion, Motors ; Fuels Impact factor: 1.465, year: 2014
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...
Time-dependent Hartree approximation and time-dependent harmonic oscillator model
International Nuclear Information System (INIS)
Blaizot, J.P.
1982-01-01
We present an analytically soluble model for studying nuclear collective motion within the framework of the time-dependent Hartree (TDH) approximation. The model reduces the TDH equations to the Schroedinger equation of a time-dependent harmonic oscillator. Using canonical transformations and coherent states we derive a few properties of the time-dependent harmonic oscillator which are relevant for applications. We analyse the role of the normal modes in the time evolution of a system governed by TDH equations. We show how these modes couple together due to the anharmonic terms generated by the non-linearity of the theory. (orig.)
International Nuclear Information System (INIS)
Chen, S.-F.
2009-01-01
The asymptotic stability problem for discrete-time systems with time-varying delay subject to saturation nonlinearities is addressed in this paper. In terms of linear matrix inequalities (LMIs), a delay-dependent sufficient condition is derived to ensure the asymptotic stability. A numerical example is given to demonstrate the theoretical results.
Spinor Field Nonlinearity and Space-Time Geometry
Saha, Bijan
2018-03-01
Within the scope of Bianchi type VI,VI0,V, III, I, LRSBI and FRW cosmological models we have studied the role of nonlinear spinor field on the evolution of the Universe and the spinor field itself. It was found that due to the presence of non-trivial non-diagonal components of the energy-momentum tensor of the spinor field in the anisotropic space-time, there occur some severe restrictions both on the metric functions and on the components of the spinor field. In this report we have considered a polynomial nonlinearity which is a function of invariants constructed from the bilinear spinor forms. It is found that in case of a Bianchi type-VI space-time, depending of the sign of self-coupling constants, the model allows either late time acceleration or oscillatory mode of evolution. In case of a Bianchi VI 0 type space-time due to the specific behavior of the spinor field we have two different scenarios. In one case the invariants constructed from bilinear spinor forms become trivial, thus giving rise to a massless and linear spinor field Lagrangian. This case is equivalent to the vacuum solution of the Bianchi VI 0 type space-time. The second case allows non-vanishing massive and nonlinear terms and depending on the sign of coupling constants gives rise to accelerating mode of expansion or the one that after obtaining some maximum value contracts and ends in big crunch, consequently generating space-time singularity. In case of a Bianchi type-V model there occur two possibilities. In one case we found that the metric functions are similar to each other. In this case the Universe expands with acceleration if the self-coupling constant is taken to be a positive one, whereas a negative coupling constant gives rise to a cyclic or periodic solution. In the second case the spinor mass and the spinor field nonlinearity vanish and the Universe expands linearly in time. In case of a Bianchi type-III model the space-time remains locally rotationally symmetric all the time
Energy Technology Data Exchange (ETDEWEB)
Sarler, B; Alujevic, A [Univerza B. Kardelja, Institut ' Jozef Stefan' , Ljubljana (Yugoslavia)
1988-07-01
The basic principles of self-adaptive algorithm for treatment of transient nonlinear nonhomogeneous radial heat flow, based on direct Boundary Element method formulation, are presented. The indicators of discretization error are developed, together with binary-tree strategy for manipulation with time domain mesh, assuring automatic optimisation of calculation procedure with respect to predetermined error. The developed method is particularly suitable for use in a spectrum of extremely nonlinear cases, occurring in thermal analyses of reactor components.(author)
Nonlinear structure formation with the environmentally dependent dilaton
International Nuclear Information System (INIS)
Brax, Philippe; Bruck, Carsten van de; Davis, Anne-Christine; Shaw, Douglas J.; Li, Baojiu
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 ΛCDM counterparts. The importance of taking full account of the nonlinearity of the model is also emphasized.
Scheduling with time-dependent execution times
Woeginger, G.J.
1995-01-01
We consider systems of tasks where the task execution times are time-dependent and where all tasks have some common deadline. We describe how to compute in polynomial time a schedule that minimizes the number of late tasks. This answers a question raised in a recent paper by Ho, Leung and Wei.
International Nuclear Information System (INIS)
Shore, B.W.; Eberly, J.H.
1983-01-01
The definition of a time-dependent spectrum registered by an idealized spectrometer responding to a time-varying electromagnetic field as proposed by Eberly and Wodkiewicz and subsequently applied to the spectrum of laser-induced fluorescence by Eberly, Kunasz, and Wodkiewicz is here extended to allow a stochastically fluctuating (interruption model) environment: we provide an algorithm for numerical determination of the time-dependent fluorescence spectrum of an atom subject to excitation by an intense noisy laser and interruptive relaxation
International Nuclear Information System (INIS)
Graefe, E. M.; Korsch, H. J.; Witthaut, D.
2006-01-01
We investigate the dynamics of a Bose-Einstein condensate in a triple-well trap in a three-level approximation. The interatomic interactions are taken into account in a mean-field approximation (Gross-Pitaevskii equation), leading to a nonlinear three-level model. Additional eigenstates emerge due to the nonlinearity, depending on the system parameters. Adiabaticity breaks down if such a nonlinear eigenstate disappears when the parameters are varied. The dynamical implications of this loss of adiabaticity are analyzed for two important special cases: A three-level Landau-Zener model and the stimulated Raman adiabatic passage (STIRAP) scheme. We discuss the emergence of looped levels for an equal-slope Landau-Zener model. The Zener tunneling probability does not tend to zero in the adiabatic limit and shows pronounced oscillations as a function of the velocity of the parameter variation. Furthermore we generalize the STIRAP scheme for adiabatic coherent population transfer between atomic states to the nonlinear case. It is shown that STIRAP breaks down if the nonlinearity exceeds the detuning
1991-09-30
0196 or 413 545-0720 PI E-mail Address: krithi@nirvan.cs.umass.edu, stankovic(ocs.umass.edu Grant or Contract Title: Dependable Real - Time Systems Grant...Dependable Real - Time Systems " Grant or Contract Number: N00014-85-k-0398 L " Reporting Period: 1 Oct 87 - 30 Sep 91 , 2. Summary of Accomplishments ’ 2.1 Our...in developing a sound approach to scheduling tasks in complex real - time systems , (2) developed a real-time operating system kernel, a preliminary
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
Modeling of Volatility with Non-linear Time Series Model
Kim Song Yon; Kim Mun Chol
2013-01-01
In this paper, non-linear time series models are used to describe volatility in financial time series data. To describe volatility, two of the non-linear time series are combined into form TAR (Threshold Auto-Regressive Model) with AARCH (Asymmetric Auto-Regressive Conditional Heteroskedasticity) error term and its parameter estimation is studied.
Solitary wave dynamics in time-dependent potentials
International Nuclear Information System (INIS)
Abou Salem, Walid K.
2008-01-01
The long time dynamics of solitary wave solutions of the nonlinear Schroedinger equation in time-dependent external potentials is rigorously studied. To set the stage, the well-posedness of the Cauchy problem for a generalized nonautonomous nonlinear Schroedinger equation with time-dependent nonlinearities and potential is established. Afterward, the dynamics of NLS solitary waves in time-dependent potentials is studied. It is shown that in the space-adiabatic regime where the external potential varies slowly in space compared to the size of the soliton, the dynamics of the center of the soliton is described by Hamilton's equations, plus terms due to radiation damping. Finally, two physical applications are discussed: the first is adiabatic transportation of solitons and the second is the Mathieu instability of trapped solitons due to time-periodic perturbations
International Nuclear Information System (INIS)
Kara, Tolgay; Eker, Ilyas
2004-01-01
Modeling and identification of mechanical systems constitute an essential stage in practical control design and applications. Controllers commanding systems that operate at varying conditions or require high precision operation raise the need for a nonlinear approach in modeling and identification. Most mechanical systems used in industry are composed of masses moving under the action of position and velocity dependent forces. These forces exhibit nonlinear behavior in certain regions of operation. For a multi-mass rotational system, the nonlinearities, like Coulomb friction and dead zone, significantly influence the system operation when the rotation changes direction. The paper presents nonlinear modeling and identification of a DC motor rotating in two directions together with real time experiments. Linear and nonlinear models for the system are obtained for identification purposes, and the major nonlinearities in the system, such as Coulomb friction and dead zone, are investigated and integrated in the nonlinear model. The Hammerstein nonlinear system approach is used for identification of the nonlinear system model. Online identification of the linear and nonlinear system models is performed using the recursive least squares method. Results of the real time experiments are graphically and numerically presented, and the advantages of the nonlinear identification approach are revealed
Time dependent fracture and cohesive zones
Knauss, W. G.
1993-01-01
This presentation is concerned with the fracture response of materials which develop cohesive or bridging zones at crack tips. Of special interest are concerns regarding crack stability as a function of the law which governs the interrelation between the displacement(s) or strain across these zones and the corresponding holding tractions. It is found that for some materials unstable crack growth can occur, even before the crack tip has experienced a critical COD or strain across the crack, while for others a critical COD will guarantee the onset of fracture. Also shown are results for a rate dependent nonlinear material model for the region inside of a craze for exploring time dependent crack propagation of rate sensitive materials.
Simulation of the Nonlinear Dose Dependence of Stabilized Point Defects
International Nuclear Information System (INIS)
Chen, R; Pagonis, V; Lawless, J L
2010-01-01
The dose dependence of the concentration of point defects in alkali-halides as well as other crystals, as exhibited by the dependence of the thermoluminescence (TL), optical absorption and ESR on the dose of non-ionizing UV excitation is studied using numerical simulation. The relevant set of coupled rate equations are first written and plausible sets of trapping parameters are chosen. Instead of using simplifying assumptions previously used for reaching conclusions concerning this dose behavior, exact numerical solutions have now been reached. Depending on the parameters chosen, different dose dependencies are seen. In some cases, linear dose dependence is reached in a broad range. Sublinear dose dependence, close to a D 1/2 dependence when D is the dose of excitation can be reached when retrapping is stronger than trapping in other traps stabilizing the defects. When strong competition between stabilizing traps takes place, an initial linear range is observed followed by strong superlinearity and an approach to saturation. All these behaviors have been observed experimentally in TL measurements as well as ESR and optical absorption in different materials. Similarities and dissimilarities to linear and non-linear dose dependencies obtained experimentally and by simulations when ionizing irradiation is used for excitation are discussed.
Calvi, Marta
2011-01-01
This review reports preliminary results of time-dependent measurements of decays of $B^0$ mesons and $B^0_s$ mesons coming from the analysis of about 36 pb$^{-1}$ of data collected by the LHCb experiment during the 2010 run of the Large Hadron Collider at $\\sqrt{s}$ = 7 TeV.
Calvi, Marta; Collaboration, for the LHCb
2011-01-01
This review reports preliminary results of time-dependent measurements of decays of B^0 mesons and B^0_s mesons coming from the analysis of about 36 pb^-1 of data collected by the LHCb experiment during the 2010 run of the Large Hadron Collider at sqrt(s)=7 TeV.
Time dependent view factor methods
International Nuclear Information System (INIS)
Kirkpatrick, R.C.
1998-03-01
View factors have been used for treating radiation transport between opaque surfaces bounding a transparent medium for several decades. However, in recent years they have been applied to problems involving intense bursts of radiation in enclosed volumes such as in the laser fusion hohlraums. In these problems, several aspects require treatment of time dependence
Nonlinear analysis of shock absorbers with amplitude-dependent damping
Łuczko, Jan; Ferdek, Urszula; Łatas, Waldemar
2018-01-01
This paper contains an analysis of a quarter-car model representing a vehicle equipped with a hydraulic damper whose characteristics are dependent on the piston stroke. The damper, compared to a classical mono-tube damper, has additional internal chambers. Oil flow in those chambers is controlled by relative piston displacement. The proposed nonlinear model of the system is aimed to test the effect of key design parameters of the damper on the quality indices representing ride comfort and driving safety. Numerical methods were used to determine the characteristic curves of the damper and responses of the system to harmonic excitations with their amplitude decreasing as the values of frequency increase.
Time-dependent correlations in electricity markets
International Nuclear Information System (INIS)
Alvarez-Ramirez, Jose; Escarela-Perez, Rafael
2010-01-01
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)
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
Volume fraction dependence of transient absorption signal and nonlinearities in metal nanocolloids
International Nuclear Information System (INIS)
Jayabalan, J; Singh, Asha; Khan, Salahuddin; Chari, Rama
2013-01-01
Electron–lattice thermalization dynamics in metal nanoparticles or in bulk metal is usually estimated by measuring the decay time of the change in transmission following an optical excitation. Such measurements can be performed in transient absorption geometry using a femtosecond laser. We find that for silver nanoplatelet/water colloids, the decay time of the transient absorption depends on the volume fraction of silver in water. By estimating the volume fraction dependence of nonlinearities in the same samples, we show that the variation in the measured decay time is due to pump-depletion effects present in the sample. The correct correction factor for taking into account pump-depletion effects in fifth- and higher-order nonlinearities is also presented. (paper)
forecasting with nonlinear time series model: a monte-carlo
African Journals Online (AJOL)
PUBLICATIONS1
Carlo method of forecasting using a special nonlinear time series model, called logistic smooth transition ... We illustrate this new method using some simulation ..... in MATLAB 7.5.0. ... process (DGP) using the logistic smooth transi-.
Betweenness in time dependent networks
International Nuclear Information System (INIS)
Alsayed, Ahmad; Higham, Desmond J.
2015-01-01
The concept of betweenness has given rise to a very useful class of network centrality measures. Loosely, betweenness quantifies the level of importance of a node in terms of its propensity to act as an intermediary when messages are passed around the network. In this work we generalize a walk-based betweenness measure to the case of time-dependent networks, such as those arising in telecommunications and on-line social media. We also introduce a new kind of betweenness measure, temporal betweenness, which quantifies the importance of a time-point. We illustrate the effectiveness of these new measures on synthetic examples, and also give results on real data sets involving voice call, email and Twitter
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.
Time-dependent quantum fluid density functional theory of hydrogen ...
Indian Academy of Sciences (India)
A time-dependent generalized non-linear Schrödinger equation (GNLSE) of motion was earlier derived in our laboratory by combining density functional theory and quantum fluid dynamics in threedimensional space. In continuation of the work reported previously, the GNLSE is applied to provide additional knowledge on ...
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.
Long-time predictions in nonlinear dynamics
Szebehely, V.
1980-01-01
It is known that nonintegrable dynamical systems do not allow precise predictions concerning their behavior for arbitrary long times. The available series solutions are not uniformly convergent according to Poincare's theorem and numerical integrations lose their meaningfulness after the elapse of arbitrary long times. Two approaches are the use of existing global integrals and statistical methods. This paper presents a generalized method along the first approach. As examples long-time predictions in the classical gravitational satellite and planetary problems are treated.
Physics constrained nonlinear regression models for time series
International Nuclear Information System (INIS)
Majda, Andrew J; Harlim, John
2013-01-01
A central issue in contemporary science is the development of data driven statistical nonlinear dynamical models for time series of partial observations of nature or a complex physical model. It has been established recently that ad hoc quadratic multi-level regression (MLR) models can have finite-time blow up of statistical solutions and/or pathological behaviour of their invariant measure. Here a new class of physics constrained multi-level quadratic regression models are introduced, analysed and applied to build reduced stochastic models from data of nonlinear systems. These models have the advantages of incorporating memory effects in time as well as the nonlinear noise from energy conserving nonlinear interactions. The mathematical guidelines for the performance and behaviour of these physics constrained MLR models as well as filtering algorithms for their implementation are developed here. Data driven applications of these new multi-level nonlinear regression models are developed for test models involving a nonlinear oscillator with memory effects and the difficult test case of the truncated Burgers–Hopf model. These new physics constrained quadratic MLR models are proposed here as process models for Bayesian estimation through Markov chain Monte Carlo algorithms of low frequency behaviour in complex physical data. (paper)
Some nonlinear dynamic inequalities on time scales
Indian Academy of Sciences (India)
In 1988, Stefan Hilger [10] introduced the calculus on time scales which unifies continuous and discrete analysis. Since then many authors have expounded on various aspects of the theory of dynamic equations on time scales. Recently, there has been much research activity concerning the new theory. For example, we ...
Nonlinear Time Series Analysis via Neural Networks
Volná, Eva; Janošek, Michal; Kocian, Václav; Kotyrba, Martin
This article deals with a time series analysis based on neural networks in order to make an effective forex market [Moore and Roche, J. Int. Econ. 58, 387-411 (2002)] pattern recognition. Our goal is to find and recognize important patterns which repeatedly appear in the market history to adapt our trading system behaviour based on them.
Nonlinear time series analysis with R
Huffaker, Ray; Rosa, Rodolfo
2017-01-01
In the process of data analysis, the investigator is often facing highly-volatile and random-appearing observed data. A vast body of literature shows that the assumption of underlying stochastic processes was not necessarily representing the nature of the processes under investigation and, when other tools were used, deterministic features emerged. Non Linear Time Series Analysis (NLTS) allows researchers to test whether observed volatility conceals systematic non linear behavior, and to rigorously characterize governing dynamics. Behavioral patterns detected by non linear time series analysis, along with scientific principles and other expert information, guide the specification of mechanistic models that serve to explain real-world behavior rather than merely reproducing it. Often there is a misconception regarding the complexity of the level of mathematics needed to understand and utilize the tools of NLTS (for instance Chaos theory). However, mathematics used in NLTS is much simpler than many other subjec...
forecasting with nonlinear time series model: a monte-carlo
African Journals Online (AJOL)
PUBLICATIONS1
erated recursively up to any step greater than one. For nonlinear time series model, point forecast for step one can be done easily like in the linear case but forecast for a step greater than or equal to ..... London. Franses, P. H. (1998). Time series models for business and Economic forecasting, Cam- bridge University press.
The Photoplethismographic Signal Processed with Nonlinear Time Series Analysis Tools
International Nuclear Information System (INIS)
Hernandez Caceres, Jose Luis; Hong, Rolando; Garcia Lanz, Abel; Garcia Dominguez, Luis; Cabannas, Karelia
2001-01-01
Finger photoplethismography (PPG) signals were submitted to nonlinear time series analysis. The applied analytical techniques were: (i) High degree polynomial fitting for baseline estimation; (ii) FFT analysis for estimating power spectra; (iii) fractal dimension estimation via the Higuchi's time-domain method, and (iv) kernel nonparametric estimation for reconstructing noise free-attractors and also for estimating signal's stochastic components
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 the present paper a conservative time integration algorithm is developed in a format using only the internal forces and the associated tangent stiffness at the specific time integration points. Thus, the procedure is computationally very similar to a collocation method, consisting of a series of nonlinear...... 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...
Nonlinear time series analysis of the human electrocardiogram
International Nuclear Information System (INIS)
Perc, Matjaz
2005-01-01
We analyse the human electrocardiogram with simple nonlinear time series analysis methods that are appropriate for graduate as well as undergraduate courses. In particular, attention is devoted to the notions of determinism and stationarity in physiological data. We emphasize that methods of nonlinear time series analysis can be successfully applied only if the studied data set originates from a deterministic stationary system. After positively establishing the presence of determinism and stationarity in the studied electrocardiogram, we calculate the maximal Lyapunov exponent, thus providing interesting insights into the dynamics of the human heart. Moreover, to facilitate interest and enable the integration of nonlinear time series analysis methods into the curriculum at an early stage of the educational process, we also provide user-friendly programs for each implemented method
Exponential integrators in time-dependent density-functional calculations
Kidd, Daniel; Covington, Cody; Varga, Kálmán
2017-12-01
The integrating factor and exponential time differencing methods are implemented and tested for solving the time-dependent Kohn-Sham equations. Popular time propagation methods used in physics, as well as other robust numerical approaches, are compared to these exponential integrator methods in order to judge the relative merit of the computational schemes. We determine an improvement in accuracy of multiple orders of magnitude when describing dynamics driven primarily by a nonlinear potential. For cases of dynamics driven by a time-dependent external potential, the accuracy of the exponential integrator methods are less enhanced but still match or outperform the best of the conventional methods tested.
Time reversal invariance for a nonlinear scatterer exhibiting contact acoustic nonlinearity
Blanloeuil, Philippe; Rose, L. R. Francis; Veidt, Martin; Wang, Chun H.
2018-03-01
The time reversal invariance of an ultrasonic plane wave interacting with a contact interface characterized by a unilateral contact law is investigated analytically and numerically. It is shown analytically that despite the contact nonlinearity, the re-emission of a time reversed version of the reflected and transmitted waves can perfectly recover the original pulse shape, thereby demonstrating time reversal invariance for this type of contact acoustic nonlinearity. With the aid of finite element modelling, the time-reversal analysis is extended to finite-size nonlinear scatterers such as closed cracks. The results show that time reversal invariance holds provided that all the additional frequencies generated during the forward propagation, such as higher harmonics, sub-harmonics and zero-frequency component, are fully included in the retro-propagation. If the scattered waves are frequency filtered during receiving or transmitting, such as through the use of narrowband transducers, the recombination of the time-reversed waves will not exactly recover the original incident wave. This discrepancy due to incomplete time invariance can be exploited as a new method for characterizing damage by defining damage indices that quantify the departure from time reversal invariance. The sensitivity of these damage indices for various crack lengths and contact stress levels is investigated computationally, indicating some advantages of this narrowband approach relative to the more conventional measurement of higher harmonic amplitude, which requires broadband transducers.
Linear time heteronymous damping in nonlinear parametric systems
Czech Academy of Sciences Publication Activity Database
Hortel, Milan; Škuderová, Alena; Houfek, Martin
2016-01-01
Roč. 40, 23-24 (2016), s. 10038-10051 ISSN 0307-904X Institutional support: RVO:61388998 Keywords : nonlinear dynamics of systems * parametric systems * time heteronymous damping * gears Subject RIV: JT - Propulsion, Motors ; Fuels Impact factor: 2.350, year: 2016
Hybrid time/frequency domain modeling of nonlinear components
DEFF Research Database (Denmark)
Wiechowski, Wojciech Tomasz; Lykkegaard, Jan; Bak, Claus Leth
2007-01-01
This paper presents a novel, three-phase hybrid time/frequency methodology for modelling of nonlinear components. The algorithm has been implemented in the DIgSILENT PowerFactory software using the DIgSILENT Programming Language (DPL), as a part of the work described in [1]. Modified HVDC benchmark...
Nonlinear Time Series Prediction Using Chaotic Neural Networks
Li, Ke-Ping; Chen, Tian-Lun
2001-06-01
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. The project supported by National Basic Research Project "Nonlinear Science" and National Natural Science Foundation of China under Grant No. 60074020
Mixed-integer nonlinear approach for the optimal scheduling of a head-dependent hydro chain
Energy Technology Data Exchange (ETDEWEB)
Catalao, J.P.S.; Pousinho, H.M.I. [Department of Electromechanical Engineering, University of Beira Interior, R. Fonte do Lameiro, 6201-001 Covilha (Portugal); Mendes, V.M.F. [Department of Electrical Engineering and Automation, Instituto Superior de Engenharia de Lisboa, R. Conselheiro Emidio Navarro, 1950-062 Lisbon (Portugal)
2010-08-15
This paper is on the problem of short-term hydro scheduling (STHS), particularly concerning a head-dependent hydro chain. We propose a novel mixed-integer nonlinear programming (MINLP) approach, considering hydroelectric power generation as a nonlinear function of water discharge and of the head. As a new contribution to earlier studies, we model the on-off behavior of the hydro plants using integer variables, in order to avoid water discharges at forbidden areas. Thus, an enhanced STHS is provided due to the more realistic modeling presented in this paper. Our approach has been applied successfully to solve a test case based on one of the Portuguese cascaded hydro systems with a negligible computational time requirement. (author)
Elements of nonlinear time series analysis and forecasting
De Gooijer, Jan G
2017-01-01
This book provides an overview of the current state-of-the-art of nonlinear time series analysis, richly illustrated with examples, pseudocode algorithms and real-world applications. Avoiding a “theorem-proof” format, it shows concrete applications on a variety of empirical time series. The book can be used in graduate courses in nonlinear time series and at the same time also includes interesting material for more advanced readers. Though it is largely self-contained, readers require an understanding of basic linear time series concepts, Markov chains and Monte Carlo simulation methods. The book covers time-domain and frequency-domain methods for the analysis of both univariate and multivariate (vector) time series. It makes a clear distinction between parametric models on the one hand, and semi- and nonparametric models/methods on the other. This offers the reader the option of concentrating exclusively on one of these nonlinear time series analysis methods. To make the book as user friendly as possible...
Nonlinear time-domain cochlear model for transient stimulation and human otoacoustic emission
DEFF Research Database (Denmark)
Verhulst, Sarah; Dau, Torsten; Shera, Christopher A.
2012-01-01
This paper describes the implementation and performance of a nonlinear time-domain model of the cochlea for transient stimulation and human otoacoustic emission generation. The nonlinearity simulates compressive growth of measured basilar-membrane impulse responses. The model accounts...... for reflection and distortion-source otoacoustic emissions (OAEs) and simulates spontaneous OAEs through manipulation of the middle-ear reflectance. The model was calibrated using human psychoacoustical and otoacoustic tuning parameters. It can be used to investigate time-dependent properties of cochlear...
Time-dependent Autler-Townes spectroscopy
International Nuclear Information System (INIS)
Qamar, Sajid; Zhu, S.-Y.; Zubairy, M Suhail
2003-01-01
Autler-Townes spontaneous emission spectroscopy is revisited for a time-dependent case. We report the results of spontaneous emission spectra for nonstationary scattered light signals using the definition of the time-dependent physical spectrum. This is a rare example of problems where time-dependent spectra can be calculated exactly
Time-dependent Autler-Townes spectroscopy
Energy Technology Data Exchange (ETDEWEB)
Qamar, Sajid [Institute for Quantum Studies, Department of Physics, Texas A and M University, College Station, TX 77843-4242 (United States); Zhu, S.-Y. [Institute for Quantum Studies, Department of Physics, Texas A and M University, College Station, TX 77843-4242 (United States); Zubairy, M Suhail [Institute for Quantum Studies, Department of Physics, Texas A and M University, College Station, TX 77843-4242 (United States)
2003-04-01
Autler-Townes spontaneous emission spectroscopy is revisited for a time-dependent case. We report the results of spontaneous emission spectra for nonstationary scattered light signals using the definition of the time-dependent physical spectrum. This is a rare example of problems where time-dependent spectra can be calculated exactly.
Energy dependence of the Cronin effect from nonlinear QCD evolution
International Nuclear Information System (INIS)
Albacete, Javier L.; Armesto, Nestor; Salgado, Carlos A.; Wiedemann, Urs Achim; Kovner, Alex
2004-01-01
The nonlinear evolution of dense partonic systems has been suggested as a novel physics mechanism relevant for the dynamics of p-A and A-A collisions at collider energies. Here we study to what extent the description of Cronin enhancement in the framework of this nonlinear evolution is consistent with the recent observation in √(s)=200 GeV d-Au collisions at the Relativistic Heavy Ion Collider. We solve the Balitsky-Kovchegov evolution equation numerically for several initial conditions encoding Cronin enhancement. We find that the properly normalized nuclear gluon distribution is suppressed at all momenta relative to that of a single nucleon. For the resulting spectrum of produced gluons in p-A and A-A collisions, the nonlinear QCD evolution is unable to generate a Cronin-type enhancement, and it quickly erases any such enhancement which may be present at lower energies
Wide localized solutions of the parity-time-symmetric nonautonomous nonlinear Schrödinger equation
Meza, L. E. Arroyo; Dutra, A. de Souza; Hott, M. B.; Roy, P.
2015-01-01
By using canonical transformations we obtain localized (in space) exact solutions of the nonlinear Schrödinger equation (NLSE) with cubic and quintic space and time modulated nonlinearities and in the presence of time-dependent and inhomogeneous external potentials and amplification or absorption (source or drain) coefficients. We obtain a class of wide localized exact solutions of NLSE in the presence of a number of non-Hermitian parity-time (PT )-symmetric external potentials, which are constituted by a mixing of external potentials and source or drain terms. The exact solutions found here can be applied to theoretical studies of ultrashort pulse propagation in optical fibers with focusing and defocusing nonlinearities. We show that, even in the presence of gain or loss terms, stable solutions can be found and that the PT symmetry is an important feature to guarantee the conservation of the average energy of the system.
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.
Time- and place dependent tariffs
International Nuclear Information System (INIS)
Wangensteen, I.; Feilberg, N.; Hornnes, K.S.
1996-11-01
To study the variation of the marginal losses in the Norwegian regional and distribution networks, a stylized radial network and an existing network example were analyzed as described in this report. The main conclusion is that the marginal-cost (the marginal losses) varies with time and place in a way that is little reflected in the energy components of the transfer- and distribution tariffs. The difference between the actual marginal-cost at a given time at a given place and the transport price that confronts an actor through the tariffs is so large that one must ask if there is any point in basing a price on marginal-cost as long as today's calculation methods are used. The problem varies somewhat between the network levels. In the distribution network the range of variation is large within the same voltage level/tariff level. If the situation improves, a time differentiation is still required. A further improvement can be obtained by a place differentiation, for example by differentiation between densely and sparsely populated areas. However, this is difficult to realize. In the central network the problem is the same, but it is easier technically and administratively to arrive at a more correct arrangement. In practice there are no great problems in differentiating the price down to individual bus bars. This would relate input and output tariffs more correctly and logically. If time differentiation is intended to capture load variations, it seems that certain improvements are possible in the present classification. It appears that spring and autumn should stand apart as one period. Furthermore, the marginal loss tariff should be based on the water supply situation at the beginning of the tariff period. 10 refs., 13 figs., 17 tabs
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.
Closed form solutions of two time fractional nonlinear wave equations
Directory of Open Access Journals (Sweden)
M. Ali Akbar
2018-06-01
Full Text Available In this article, we investigate the exact traveling wave solutions of two nonlinear time fractional wave equations. The fractional derivatives are described in the sense of conformable fractional derivatives. In addition, the traveling wave solutions are accomplished in the form of hyperbolic, trigonometric, and rational functions involving free parameters. To investigate such types of solutions, we implement the new generalized (G′/G-expansion method. The extracted solutions are reliable, useful and suitable to comprehend the optimal control problems, chaotic vibrations, global and local bifurcations and resonances, furthermore, fission and fusion phenomena occur in solitons, the relativistic energy-momentum relation, scalar electrodynamics, quantum relativistic one-particle theory, electromagnetic interactions etc. The results reveal that the method is very fruitful and convenient for exploring nonlinear differential equations of fractional order treated in theoretical physics. Keywords: Traveling wave solution, Soliton, Generalized (G′/G-expansion method, Time fractional Duffing equation, Time fractional Riccati equation
Holographic complexity for time-dependent backgrounds
Energy Technology Data Exchange (ETDEWEB)
Momeni, Davood, E-mail: davoodmomeni78@gmail.com [Eurasian International Center for Theoretical Physics and Department of General Theoretical Physics, Eurasian National University, Astana 010008 (Kazakhstan); Faizal, Mir, E-mail: mirfaizalmir@googlemail.com [Irving K. Barber School of Arts and Sciences, University of British Columbia, Okanagan, 3333 University Way, Kelowna, British Columbia V1V 1V7 (Canada); Department of Physics and Astronomy, University of Lethbridge, Lethbridge, Alberta, T1K 3M4 (Canada); Bahamonde, Sebastian, E-mail: sebastian.beltran.14@ucl.ac.uk [Department of Mathematics, University College London, Gower Street, London, WC1E 6BT (United Kingdom); Myrzakulov, Ratbay [Eurasian International Center for Theoretical Physics and Department of General Theoretical Physics, Eurasian National University, Astana 010008 (Kazakhstan)
2016-11-10
In this paper, we will analyze 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 analyze 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 time-dependent geometries.
Directory of Open Access Journals (Sweden)
S. Djebali
2011-02-01
Full Text Available This paper is concerned with a second-order nonlinear boundary value problem with a derivative depending nonlinearity and posed on the positive half-line. The derivative operator is time dependent. Upon a priori estimates and under a Nagumo growth condition, the Schauder's fixed point theorem combined with the method of upper and lower solutions on unbounded domains are used to prove existence of solutions. A uniqueness theorem is also obtained and some examples of application illustrate the obtained results.
Non-linear time reversal ultrasonic pseudo-tomography
Czech Academy of Sciences Publication Activity Database
Převorovský, Zdeněk; Vejvodová, Šárka; Krofta, Josef; Převorovský, David
2011-01-01
Roč. 6, 3/4 (2011), s. 206-213 ISSN 1741-8410. [NDT in Progress. Praha, 05.11.2007-07.11.2007] R&D Projects: GA MPO(CZ) FR-TI1/274 Institutional research plan: CEZ:AV0Z20760514 Keywords : NDT * nonlinear elastic wave spectroscopy * time reversal mirrors * ultrasonic pseudo-tomography Subject RIV: BI - Acoustics http://www.inderscience.com/offer.php?id=43216
Directory of Open Access Journals (Sweden)
A. D. Pataraya
1997-01-01
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.
Parameterisation effect on the behaviour of a head-dependent hydro chain using a nonlinear model
International Nuclear Information System (INIS)
Catalao, J.P.S.; Mariano, S.J.P.S.; Mendes, V.M.F.; Ferreira, L.A.F.M.
2006-01-01
This paper is on the problem of short-term hydro scheduling (STHS), particularly concerning a head-dependent hydro chain. We use a method based on nonlinear programming (NLP), namely quadratic programming, to consider hydroelectric power generation a function of water discharge and of the head. The method has been applied successfully to solve a test case based on a realistic cascaded hydro system with a negligible computational time requirement and is also applied to show that the role played by reservoirs in the hydro chain do not depend only on their relative position. As a new contribution to earlier studies, which presented reservoir operation rules mainly for medium and long-term planning procedures, we show that the physical data defining hydro chain parameters used in the nonlinear model have an effect on the STHS, implying different optimal storage trajectories for the reservoirs accordingly not only with their position in the hydro chain but also with the new parameterisation defining the data for the hydro system. Moreover, considering head dependency in the hydroelectric power generation, usually neglected for hydro plants with a large storage capacity, provides a better short-term management of the conversion of the potential energy available in the reservoirs into electric energy, which represents a major advantage for the hydroelectric utilities in a competitive electricity market. (author)
Shah, A A; Xing, W W; Triantafyllidis, V
2017-04-01
In this paper, we develop reduced-order models for dynamic, parameter-dependent, linear and nonlinear partial differential equations using proper orthogonal decomposition (POD). The main challenges are to accurately and efficiently approximate the POD bases for new parameter values and, in the case of nonlinear problems, to efficiently handle the nonlinear terms. We use a Bayesian nonlinear regression approach to learn the snapshots of the solutions and the nonlinearities for new parameter values. Computational efficiency is ensured by using manifold learning to perform the emulation in a low-dimensional space. The accuracy of the method is demonstrated on a linear and a nonlinear example, with comparisons with a global basis approach.
Time-dependent behavior of concrete
International Nuclear Information System (INIS)
Pfeiffer, P.A.; Tanabe, Tada-aki
1992-01-01
This paper is a condensed version of the material presented at the International Workshop on Finite Element Analysis of Reinforced Concrete, Session 4 -- Time Dependent Behavior, held at Columbia University, New York on June 3--6, 1991. Dr. P.A. Pfeiffer presented recent developments in time-dependent behavior of concrete and Professor T. Tanabe presented a review of research in Japan on time-dependent behavior of concrete. The paper discusses the recent research of time-dependent behavior of concrete in the past few years. 6 refs
Closed form solutions of two time fractional nonlinear wave equations
Akbar, M. Ali; Ali, Norhashidah Hj. Mohd.; Roy, Ripan
2018-06-01
In this article, we investigate the exact traveling wave solutions of two nonlinear time fractional wave equations. The fractional derivatives are described in the sense of conformable fractional derivatives. In addition, the traveling wave solutions are accomplished in the form of hyperbolic, trigonometric, and rational functions involving free parameters. To investigate such types of solutions, we implement the new generalized (G‧ / G) -expansion method. The extracted solutions are reliable, useful and suitable to comprehend the optimal control problems, chaotic vibrations, global and local bifurcations and resonances, furthermore, fission and fusion phenomena occur in solitons, the relativistic energy-momentum relation, scalar electrodynamics, quantum relativistic one-particle theory, electromagnetic interactions etc. The results reveal that the method is very fruitful and convenient for exploring nonlinear differential equations of fractional order treated in theoretical physics.
International Nuclear Information System (INIS)
Frank, T D; Mongkolsakulvong, S
2015-01-01
In a previous study strongly nonlinear autoregressive (SNAR) models have been introduced as a generalization of the widely-used time-discrete autoregressive models that are known to apply both to Markov and non-Markovian systems. In contrast to conventional autoregressive models, SNAR models depend on process mean values. So far, only linear dependences have been studied. We consider the case in which process mean values can have a nonlinear impact on the processes under consideration. It is shown that such models describe Markov and non-Markovian many-body systems with mean field forces that exhibit a nonlinear impact on single subsystems. We exemplify that such nonlinear dependences can describe order-disorder phase transitions of time-discrete Markovian and non-Markovian many-body systems. The relevant order parameter equations are derived and issues of stability and stationarity are studied. (paper)
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
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......, as classified by Kalbfleisch and Prentice [The Statistical Analysis of Failure Time Data, Wiley, New York, 2002] with the intent of clarifying their role and emphasizing the limitations in standard survival models and in the competing risks setting. If random (internal) time-dependent covariates...
International Nuclear Information System (INIS)
Xiao Li; Zhang Wei; Huang Yidong; Peng Jiangde
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 detunings are generated, while on the other axis with larger MI frequency detuning, SC is generated by soliton self-frequency shift
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
Tewatia, D K; Tolakanahalli, R P; Paliwal, B R; Tomé, W A
2011-04-07
The underlying requirements for successful implementation of any efficient tumour motion management strategy are regularity and reproducibility of a patient's breathing pattern. The physiological act of breathing is controlled by multiple nonlinear feedback and feed-forward couplings. It would therefore be appropriate to analyse the breathing pattern of lung cancer patients in the light of nonlinear dynamical system theory. The purpose of this paper is to analyse the one-dimensional respiratory time series of lung cancer patients based on nonlinear dynamics and delay coordinate state space embedding. It is very important to select a suitable pair of embedding dimension 'm' and time delay 'τ' when performing a state space reconstruction. Appropriate time delay and embedding dimension were obtained using well-established methods, namely mutual information and the false nearest neighbour method, respectively. Establishing stationarity and determinism in a given scalar time series is a prerequisite to demonstrating that the nonlinear dynamical system that gave rise to the scalar time series exhibits a sensitive dependence on initial conditions, i.e. is chaotic. Hence, once an appropriate state space embedding of the dynamical system has been reconstructed, we show that the time series of the nonlinear dynamical systems under study are both stationary and deterministic in nature. Once both criteria are established, we proceed to calculate the largest Lyapunov exponent (LLE), which is an invariant quantity under time delay embedding. The LLE for all 16 patients is positive, which along with stationarity and determinism establishes the fact that the time series of a lung cancer patient's breathing pattern is not random or irregular, but rather it is deterministic in nature albeit chaotic. These results indicate that chaotic characteristics exist in the respiratory waveform and techniques based on state space dynamics should be employed for tumour motion management.
Energy Technology Data Exchange (ETDEWEB)
Tewatia, D K; Tolakanahalli, R P; Paliwal, B R; Tome, W A, E-mail: tewatia@wisc.edu [Department of Human Oncology, University of Wisconsin, Madison, WI (United States)
2011-04-07
The underlying requirements for successful implementation of any efficient tumour motion management strategy are regularity and reproducibility of a patient's breathing pattern. The physiological act of breathing is controlled by multiple nonlinear feedback and feed-forward couplings. It would therefore be appropriate to analyse the breathing pattern of lung cancer patients in the light of nonlinear dynamical system theory. The purpose of this paper is to analyse the one-dimensional respiratory time series of lung cancer patients based on nonlinear dynamics and delay coordinate state space embedding. It is very important to select a suitable pair of embedding dimension 'm' and time delay '{tau}' when performing a state space reconstruction. Appropriate time delay and embedding dimension were obtained using well-established methods, namely mutual information and the false nearest neighbour method, respectively. Establishing stationarity and determinism in a given scalar time series is a prerequisite to demonstrating that the nonlinear dynamical system that gave rise to the scalar time series exhibits a sensitive dependence on initial conditions, i.e. is chaotic. Hence, once an appropriate state space embedding of the dynamical system has been reconstructed, we show that the time series of the nonlinear dynamical systems under study are both stationary and deterministic in nature. Once both criteria are established, we proceed to calculate the largest Lyapunov exponent (LLE), which is an invariant quantity under time delay embedding. The LLE for all 16 patients is positive, which along with stationarity and determinism establishes the fact that the time series of a lung cancer patient's breathing pattern is not random or irregular, but rather it is deterministic in nature albeit chaotic. These results indicate that chaotic characteristics exist in the respiratory waveform and techniques based on state space dynamics should be employed
International Nuclear Information System (INIS)
Tewatia, D K; Tolakanahalli, R P; Paliwal, B R; Tome, W A
2011-01-01
The underlying requirements for successful implementation of any efficient tumour motion management strategy are regularity and reproducibility of a patient's breathing pattern. The physiological act of breathing is controlled by multiple nonlinear feedback and feed-forward couplings. It would therefore be appropriate to analyse the breathing pattern of lung cancer patients in the light of nonlinear dynamical system theory. The purpose of this paper is to analyse the one-dimensional respiratory time series of lung cancer patients based on nonlinear dynamics and delay coordinate state space embedding. It is very important to select a suitable pair of embedding dimension 'm' and time delay 'τ' when performing a state space reconstruction. Appropriate time delay and embedding dimension were obtained using well-established methods, namely mutual information and the false nearest neighbour method, respectively. Establishing stationarity and determinism in a given scalar time series is a prerequisite to demonstrating that the nonlinear dynamical system that gave rise to the scalar time series exhibits a sensitive dependence on initial conditions, i.e. is chaotic. Hence, once an appropriate state space embedding of the dynamical system has been reconstructed, we show that the time series of the nonlinear dynamical systems under study are both stationary and deterministic in nature. Once both criteria are established, we proceed to calculate the largest Lyapunov exponent (LLE), which is an invariant quantity under time delay embedding. The LLE for all 16 patients is positive, which along with stationarity and determinism establishes the fact that the time series of a lung cancer patient's breathing pattern is not random or irregular, but rather it is deterministic in nature albeit chaotic. These results indicate that chaotic characteristics exist in the respiratory waveform and techniques based on state space dynamics should be employed for tumour motion management.
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.
Nonlinear Time-Reversal in a Wave Chaotic System
Frazier, Matthew; Taddese, Biniyam; Ott, Edward; Antonsen, Thomas; Anlage, Steven
2012-02-01
Time reversal mirrors are particularly simple to implement in wave chaotic systems and form the basis for a new class of sensors [1-3]. These sensors work by applying the quantum mechanical concepts of Loschmidt echo and fidelity decay to classical waves. The sensors make explicit use of time-reversal invariance and spatial reciprocity in a wave chaotic system to remotely measure the presence of small perturbations to the system. The underlying ray chaos increases the sensitivity to small perturbations throughout the volume explored by the waves. We extend our time-reversal mirror to include a discrete element with a nonlinear dynamical response. The initially injected pulse interacts with the nonlinear element, generating new frequency components originating at the element. By selectively filtering for and applying the time-reversal mirror to the new frequency components, we focus a pulse only onto the element, without knowledge of its location. Furthermore, we demonstrate transmission of arbitrary patterns of pulses to the element, creating a targeted communication channel to the exclusion of 'eavesdroppers' at other locations in the system. [1] Appl. Phys. Lett. 95, 114103 (2009) [2] J. Appl. Phys. 108, 1 (2010) [3] Acta Physica Polonica A 112, 569 (2007)
Time dependent non-extinction probability for prompt critical systems
International Nuclear Information System (INIS)
Gregson, M. W.; Prinja, A. K.
2009-01-01
The time dependent non-extinction probability equation is presented for slab geometry. Numerical solutions are provided for a nested inner/outer iteration routine where the fission terms (both linear and non-linear) are updated and then held fixed over the inner scattering iteration. Time dependent results are presented highlighting the importance of the injection position and angle. The iteration behavior is also described as the steady state probability of initiation is approached for both small and large time steps. Theoretical analysis of the nested iteration scheme is shown and highlights poor numerical convergence for marginally prompt critical systems. An acceleration scheme for the outer iterations is presented to improve convergence of such systems. Theoretical analysis of the acceleration scheme is also provided and the associated decrease in computational run time addressed. (authors)
International Nuclear Information System (INIS)
Wang Haobin; Thoss, Michael
2008-01-01
A quantum dynamical method is presented to accurately simulate time-resolved nonlinear spectra for complex molecular systems. The method combines the nonpertubative approach to describe nonlinear optical signals with the multilayer multiconfiguration time-dependent Hartree theory to calculate the laser-induced polarization for the overall field-matter system. A specific nonlinear optical signal is obtained by Fourier decomposition of the overall polarization. The performance of the method is demonstrated by applications to photoinduced ultrafast electron transfer reactions in mixed-valence compounds and at dye-semiconductor interfaces
Santos, Serge Dos; Farova, Zuzana; Kus, Vaclav; Prevorovsky, Zdenek
2012-05-01
This paper examines possibilities of using Nonlinear Elastic Wave Spectroscopy (NEWS) methods in dental investigations. Themain task consisted in imaging cracks or other degradation signatures located in dentin close to the Enamel-Dentine Junction (EDJ). NEWS approach was investigated experimentally with a new bi-modal acousto-optic set-up based on the chirp-coded nonlinear ultrasonic time reversal (TR) concepts. Complex internal structure of the tooth is analyzed by the TR-NEWS procedure adapted to tomography-like imaging of the tooth damages. Ultrasonic instrumentation with 10 MHz bandwidth has been set together including laser vibrometer used to detect responses of the tooth on its excitation carried out by a contact piezoelectric transducer. Bi-modal TR-NEWS images of the tooth were created before and after focusing, which resulted from the time compression. The polar B-scan of the tooth realized with TR-NEWS procedure is suggested to be applied as a new echodentography imaging.
Residual distribution for general time-dependent conservation laws
International Nuclear Information System (INIS)
Ricchiuto, Mario; Csik, Arpad; Deconinck, Herman
2005-01-01
We consider the second-order accurate numerical solution of general time-dependent hyperbolic conservation laws over unstructured grids in the framework of the Residual Distribution method. In order to achieve full conservation of the linear, monotone and first-order space-time schemes of (Csik et al., 2003) and (Abgrall et al., 2000), we extend the conservative residual distribution (CRD) formulation of (Csik et al., 2002) to prismatic space-time elements. We then study the design of second-order accurate and monotone schemes via the nonlinear mapping of the local residuals of linear monotone schemes. We derive sufficient and necessary conditions for the well-posedness of the mapping. We prove that the schemes obtained with the CRD formulation satisfy these conditions by construction. Thus the nonlinear schemes proposed in this paper are always well defined. The performance of the linear and nonlinear schemes are evaluated on a series of test problems involving the solution of the Euler equations and of a two-phase flow model. We consider the resolution of strong shocks and complex interacting flow structures. The results demonstrate the robustness, accuracy and non-oscillatory character of the proposed schemes. d schemes
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.
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.
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.
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.
Time-dependent, Bianchi II, rotating universe
International Nuclear Information System (INIS)
Reboucas, M.J.
1981-01-01
An exact cosmological solution of Einstein's equations which has time-dependent rotation is presented. The t-constant sections are of Bianchi type II. The source of this geometry is a fluid which has not been thermalized. (Author) [pt
Topic 5: Time-Dependent Behavior
International Nuclear Information System (INIS)
Pfeiffer, P.A.; Tanabe, Tada-aki
1991-01-01
This chapter is a report of the material presented at the International Workshop on Finite Element Analysis of Reinforced Concrete, Session 4 -- Time Dependent Behavior, held at Columbia University, New York on June 3--6, 1991. Dr. P.A. Pfeiffer presented recent developments in time-dependent behavior of concrete and Professor T. Tanabe presented a review of research in Japan on time-dependent behavior of concrete. The chapter discusses the recent research of time-dependent behavior of concrete in the past few years in both the USA-European and Japanese communities. The author appreciates the valuable information provided by Zdenek P. Bazant in preparing the USA-European Research section
Time-dependent friction and solvation time correlation function
International Nuclear Information System (INIS)
Samanta, Alok; Ali, Sk Musharaf; Ghosh, Swapan K
2005-01-01
We have derived a new relation between the time-dependent friction and solvation time correlation function (STCF) for non-polar fluids. The friction values calculated using this relation and simulation results on STCF for a Lennard-Jones fluid are shown to have excellent agreement with the same obtained through mode-coupling theory. Also derived is a relation between the time-dependent dielectric friction and STCF for polar fluids. Routes are thus provided to obtain the time-dependent friction (non-polar as well as dielectric) from an experimentally measured quantity like STCF, even if the interparticle interaction potential is not known
Finite-time stabilisation of a class of switched nonlinear systems with state constraints
Huang, Shipei; Xiang, Zhengrong
2018-06-01
This paper investigates the finite-time stabilisation for a class of switched nonlinear systems with state constraints. Some power orders of the system are allowed to be ratios of positive even integers over odd integers. A Barrier Lyapunov function is introduced to guarantee that the state constraint is not violated at any time. Using the convex combination method and a recursive design approach, a state-dependent switching law and state feedback controllers of individual subsystems are constructed such that the closed-loop system is finite-time stable without violation of the state constraint. Two examples are provided to show the effectiveness of the proposed method.
One-Time Pad as a nonlinear dynamical system
Nagaraj, Nithin
2012-11-01
The One-Time Pad (OTP) is the only known unbreakable cipher, proved mathematically by Shannon in 1949. In spite of several practical drawbacks of using the OTP, it continues to be used in quantum cryptography, DNA cryptography and even in classical cryptography when the highest form of security is desired (other popular algorithms like RSA, ECC, AES are not even proven to be computationally secure). In this work, we prove that the OTP encryption and decryption is equivalent to finding the initial condition on a pair of binary maps (Bernoulli shift). The binary map belongs to a family of 1D nonlinear chaotic and ergodic dynamical systems known as Generalized Luröth Series (GLS). Having established these interesting connections, we construct other perfect secrecy systems on the GLS that are equivalent to the One-Time Pad, generalizing for larger alphabets. We further show that OTP encryption is related to Randomized Arithmetic Coding - a scheme for joint compression and encryption.
Nonlinear MHD dynamics of tokamak plasmas on multiple time scales
International Nuclear Information System (INIS)
Kruger, S.E.; Schnack, D.D.; Brennan, D.P.; Gianakon, T.A.; Sovinec, C.R.
2003-01-01
Two types of numerical, nonlinear simulations using the NIMROD code are presented. In the first simulation, we model the disruption occurring in DIII-D discharge 87009 as an ideal MHD instability driven unstable by neutral-beam heating. The mode grows faster than exponential, but on a time scale that is a hybrid of the heating rate and the ideal MHD growth rate as predicted by analytic theory. The second type of simulations, which occur on a much longer time scale, focus on the seeding of tearing modes by sawteeth. Pressure effects play a role both in the exterior region solutions and in the neoclassical drive terms. The results of both simulations are reviewed and their implications for experimental analysis is discussed. (author)
Recurrence Density Enhanced Complex Networks for Nonlinear Time Series Analysis
Costa, Diego G. De B.; Reis, Barbara M. Da F.; Zou, Yong; Quiles, Marcos G.; Macau, Elbert E. N.
We introduce a new method, which is entitled Recurrence Density Enhanced Complex Network (RDE-CN), to properly analyze nonlinear time series. Our method first transforms a recurrence plot into a figure of a reduced number of points yet preserving the main and fundamental recurrence properties of the original plot. This resulting figure is then reinterpreted as a complex network, which is further characterized by network statistical measures. We illustrate the computational power of RDE-CN approach by time series by both the logistic map and experimental fluid flows, which show that our method distinguishes different dynamics sufficiently well as the traditional recurrence analysis. Therefore, the proposed methodology characterizes the recurrence matrix adequately, while using a reduced set of points from the original recurrence plots.
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. Copyright © 2013 ISA. Published by Elsevier Ltd. All rights reserved.
Time dependent policy-based access control
DEFF Research Database (Denmark)
Vasilikos, Panagiotis; Nielson, Flemming; Nielson, Hanne Riis
2017-01-01
also on other attributes of the environment such as the time. In this paper, we use systems of Timed Automata to model distributed systems and we present a logic in which one can express time-dependent policies for access control. We show how a fragment of our logic can be reduced to a logic......Access control policies are essential to determine who is allowed to access data in a system without compromising the data's security. However, applications inside a distributed environment may require those policies to be dependent on the actual content of the data, the flow of information, while...... that current model checkers for Timed Automata such as UPPAAL can handle and we present a translator that performs this reduction. We then use our translator and UPPAAL to enforce time-dependent policy-based access control on an example application from the aerospace industry....
Chatterjee, Roshmi; Basu, Mousumi
2018-02-01
The well known time transformation method is used here to derive the temporal and spectral electric field distribution at the output end of a multilayer waveguide which consists of different layers of Kerr nonlinear media. A highly nonlinear CS 3-68 glass is considered as one of the materials of the waveguide which mainly comprises of different chalcogenide glass layers. The results indicate that there is sufficient time delay as well as frequency shift between the input and output pulses which is associated with the phenomenon of adiabatic wavelength conversion (AWC). Depending on different arrangements of materials, the time delay and frequency shift can be changed. As a result an input pulse in visible green region can be blue-shifted or red-shifted according to the choices of refractive index of the non-dispersive Kerr nonlinear media. The results show that under certain conditions the input pulse is broadened or compressed for different combinations of materials. This process of AWC also includes the variation of temporal and spectral phase, time delay, temporal peak power etc. For different input pulse shapes the change in time delay is also presented. The study may be useful to find applications of AWC in optical resonators or optical signal processing to be applicable to different photonic devices.
Nonlinear Aerodynamics-Structure Time Simulation for HALE Aircraft Design/Analysis, Phase I
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...
Sahmani, S.; Aghdam, M. M.
2018-03-01
A wide range of biological applications such as drug delivery, biosensors and hemodialysis can be provided by nanoporous biomaterials due to their uniform pore size as well as considerable pore density. In the current study, the size dependency in the nonlinear primary resonance of micro/nano-beams made of nanoporous biomaterials is anticipated. To accomplish this end, a refined truncated cube is introduced to model the lattice structure of nanoporous biomaterial. Accordingly, analytical expressions for the mechanical properties of material are derived as functions of pore size. After that, based upon a nonlocal strain gradient beam model, the size-dependent nonlinear Duffing type equation of motion is constructed. The Galerkin technique together with the multiple time-scales method is employed to obtain the nonlocal strain gradient frequency-response and amplitude-response related to the nonlinear primary resonance of a micro/nano-beam made of the nanoporous biomaterial with different pore sizes. It is indicated that the nonlocality causes to decrease the response amplitudes associated with the both bifurcation points of the jump phenomenon, while the strain gradient size dependency causes to increase them. Also, it is found that increasing the pore size leads to enhance the nonlinearity, so the maximum deflection of response occurs at higher excitation frequency.
Non-Gaussian lineshapes and dynamics of time-resolved linear and nonlinear (correlation) spectra.
Dinpajooh, Mohammadhasan; Matyushov, Dmitry V
2014-07-17
Signatures of nonlinear and non-Gaussian dynamics in time-resolved linear and nonlinear (correlation) 2D spectra are analyzed in a model considering a linear plus quadratic dependence of the spectroscopic transition frequency on a Gaussian nuclear coordinate of the thermal bath (quadratic coupling). This new model is contrasted to the commonly assumed linear dependence of the transition frequency on the medium nuclear coordinates (linear coupling). The linear coupling model predicts equality between the Stokes shift and equilibrium correlation functions of the transition frequency and time-independent spectral width. Both predictions are often violated, and we are asking here the question of whether a nonlinear solvent response and/or non-Gaussian dynamics are required to explain these observations. We find that correlation functions of spectroscopic observables calculated in the quadratic coupling model depend on the chromophore's electronic state and the spectral width gains time dependence, all in violation of the predictions of the linear coupling models. Lineshape functions of 2D spectra are derived assuming Ornstein-Uhlenbeck dynamics of the bath nuclear modes. The model predicts asymmetry of 2D correlation plots and bending of the center line. The latter is often used to extract two-point correlation functions from 2D spectra. The dynamics of the transition frequency are non-Gaussian. However, the effect of non-Gaussian dynamics is limited to the third-order (skewness) time correlation function, without affecting the time correlation functions of higher order. The theory is tested against molecular dynamics simulations of a model polar-polarizable chromophore dissolved in a force field water.
Time-dependent Dyson orbital theory
Gritsenko, O.V.; Baerends, E.J.
2016-01-01
Although time-dependent density functional theory (TDDFT) has become the tool of choice for real-time propagation of the electron density ρN(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
Fermions in interaction with time dependent fields
International Nuclear Information System (INIS)
Falkensteiner, P.; Grosse, H.
1988-01-01
We solve a two dimensional model describing the interaction of fermions with time dependent external fields. We work out the second quantized formulation and obtain conditions for equivalence of representations at different times. This implies the existence of sectors which describe charged states. We obtain the time dependence of charges and observe that charge differences become integer for unitary equivalent states. For scattering we require the equivalence of in- and out-representations; nevertheless charged sectors may be reached by suitable interactions and ionization is possible. 20 refs. (Author)
Unit-time scheduling problems with time dependent resources
Tautenhahn, T.; Woeginger, G.
1997-01-01
We investigate the computational complexity of scheduling problems, where the operations consume certain amounts of renewable resources which are available in time-dependent quantities. In particular, we consider unit-time open shop problems and unit-time scheduling problems with identical parallel
Theoretical investigation of intensity-dependent optical nonlinearity in graphene-aided D-microfiber
Shah, Manoj Kumar; Lu, Rongguo; Zhang, Yali; Ye, Shengwei; Zhang, Shangjian; Liu, Yong
2018-01-01
We theoretically investigate the intensity-dependent optical nonlinearity in graphene-aided D-microfiber, by tuning the chemical potential of graphene and varying radial distance and radii of the D-microfiber. Utilizing an interplay between graphene and the enhanced evanescent field of a guided mode in the waveguide of interest, the net utility of nonlinear coefficient is harnessed up to a very high value of 106 W-1m-1. Importantly, which is ∼ two orders of magnitude larger than in PMMA-graphene-PMMA waveguide. The highly dispersive nature of the waveguide, D ∼ 103 ps/nm-km, and large nonlinear figure-of-merit, FOMNL ∼ 1.29, have raised the possibilities of utilizing slow light structures to operate devices at few watts power level with microscale length. These studies have opened one window towards the next-generation all fiber-optic graphene nonlinear optical devices.
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.
Wave function for time-dependent harmonically confined electrons in a time-dependent electric field.
Li, Yu-Qi; Pan, Xiao-Yin; Sahni, Viraht
2013-09-21
The many-body wave function of a system of interacting particles confined by a time-dependent harmonic potential and perturbed by a time-dependent spatially homogeneous electric field is derived via the Feynman path-integral method. The wave function is comprised of a phase factor times the solution to the unperturbed time-dependent Schrödinger equation with the latter being translated by a time-dependent value that satisfies the classical driven equation of motion. The wave function reduces to that of the Harmonic Potential Theorem wave function for the case of the time-independent harmonic confining potential.
Constitutive modeling for uniaxial time-dependent ratcheting of SS304 stainless steel
International Nuclear Information System (INIS)
Kan Qianhua; Kang Guozheng; Zhang Juan
2007-01-01
Based on the experimental results of uniaxial time-dependent ratcheting behavior of SS304 stainless steel at room temperature and 973K, a new time-dependent constitutive model was proposed. The model describes the time-dependent ratcheting by adding a static/thermal recovery into the Abdel-Karim-Ohno non-linear kinematic hardening rule. The capability of the model to describe the time-dependent ratcheting was discussed by comparing the simulations with the corresponding experimental results. It is shown that the revised unified viscoplastic model can simulate the time-dependent ratcheting reasonably both at room and high temperatures. (authors)
A time-domain finite element model reduction method for viscoelastic linear and nonlinear systems
Directory of Open Access Journals (Sweden)
Antônio Marcos Gonçalves de Lima
Full Text Available AbstractMany authors have shown that the effective design of viscoelastic systems can be conveniently carried out by using modern mathematical models to represent the frequency- and temperature-dependent behavior of viscoelastic materials. However, in the quest for design procedures of real-word engineering structures, the large number of exact evaluations of the dynamic responses during iterative procedures, combined with the typically high dimensions of large finite element models, makes the numerical analysis very costly, sometimes unfeasible. It is especially true when the viscoelastic materials are used to reduce vibrations of nonlinear systems. As a matter of fact, which the resolution of the resulting nonlinear equations of motion with frequency- and temperature-dependent viscoelastic damping forces is an interesting, but hard-to-solve problem. Those difficulties motivate the present study, in which a time-domain condensation strategy of viscoelastic systems is addressed, where the viscoelastic behavior is modeled by using a four parameter fractional derivative model. After the discussion of various theoretical aspects, the exact and reduced time responses are calculated for a three-layer sandwich plate by considering nonlinear boundary conditions.
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.
Distributed synchronization of networked drive-response systems: A nonlinear fixed-time protocol.
Zhao, Wen; Liu, Gang; Ma, Xi; He, Bing; Dong, Yunfeng
2017-11-01
The distributed synchronization of networked drive-response systems is investigated in this paper. A novel nonlinear protocol is proposed to ensure that the tracking errors converge to zeros in a fixed-time. By comparison with previous synchronization methods, the present method considers more practical conditions and the synchronization time is not dependent of arbitrary initial conditions but can be offline pre-assign according to the task assignment. Finally, the feasibility and validity of the presented protocol have been illustrated by a numerical simulation. Copyright © 2017. Published by Elsevier Ltd.
Time-dependent scattering in resonance lines
International Nuclear Information System (INIS)
Kunasz, P.B.
1983-01-01
A numerical finite-difference method is presented for the problem of time-dependent line transfer in a finite slab in which material density is sufficiently low that the time of flight between scatterings greatly exceeds the relaxation time of the upper state of the scattering transition. The medium is assumed to scatter photons isotropically, with complete frequency redistribution. Numerical solutions are presented for a homogeneous, time-independent slab illuminated by an externally imposed radiation field which enters the slab at t = 0. Graphical results illustrate relaxation to steady state of trapped internal radiation, emergent energy, and emergent profiles. A review of the literature is also given in which the time-dependent line transfer problem is discussed in the context of recent analytical work
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.
Evaluation of time integration methods for transient response analysis of nonlinear structures
International Nuclear Information System (INIS)
Park, K.C.
1975-01-01
Recent developments in the evaluation of direct time integration methods for the transient response analysis of nonlinear structures are presented. These developments, which are based on local stability considerations of an integrator, show that the interaction between temporal step size and nonlinearities of structural systems has a pronounced effect on both accuracy and stability of a given time integration method. The resulting evaluation technique is applied to a model nonlinear problem, in order to: 1) demonstrate that it eliminates the present costly process of evaluating time integrator for nonlinear structural systems via extensive numerical experiments; 2) identify the desirable characteristics of time integration methods for nonlinear structural problems; 3) develop improved stiffly-stable methods for application to nonlinear structures. Extension of the methodology for examination of the interaction between a time integrator and the approximate treatment of nonlinearities (such as due to pseudo-force or incremental solution procedures) is also discussed. (Auth.)
Integrable Time-Dependent Quantum Hamiltonians
Sinitsyn, Nikolai A.; Yuzbashyan, Emil A.; Chernyak, Vladimir Y.; Patra, Aniket; Sun, Chen
2018-05-01
We formulate a set of conditions under which the nonstationary Schrödinger equation with a time-dependent Hamiltonian is exactly solvable analytically. The main requirement is the existence of a non-Abelian gauge field with zero curvature in the space of system parameters. Known solvable multistate Landau-Zener models satisfy these conditions. Our method provides a strategy to incorporate time dependence into various quantum integrable models while maintaining their integrability. We also validate some prior conjectures, including the solution of the driven generalized Tavis-Cummings model.
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.
Compression-rate-dependent nonlinear mechanics of normal and impaired porcine knee joints.
Rodriguez, Marcel Leonardo; Li, LePing
2017-11-14
The knee joint performs mechanical functions with various loading and unloading processes. Past studies have focused on the kinematics and elastic response of the joint with less understanding of the rate-dependent load response associated with viscoelastic and poromechanical behaviors. Forty-five fresh porcine knee joints were used in the present study to determine the loading-rate-dependent force-compression relationship, creep and relaxation of normal, dehydrated and meniscectomized joints. The mechanical tests of all normal intact joints showed similar strong compression-rate-dependent behavior: for a given compression-magnitude up to 1.2 mm, the reaction force varied 6 times over compression rates. While the static response was essentially linear, the nonlinear behavior was boosted with the increased compression rate to approach the asymptote or limit at approximately 2 mm/s. On the other hand, the joint stiffness varied approximately 3 times over different joints, when accounting for the maturity and breed of the animals. Both a loss of joint hydration and a total meniscectomy greatly compromised the load support in the joint, resulting in a reduction of load support as much as 60% from the corresponding intact joint. However, the former only weakened the transient load support, but the latter also greatly weakened the equilibrium load support. A total meniscectomy did not diminish the compression-rate-dependence of the joint though. These findings are consistent with the fluid-pressurization loading mechanism, which may have a significant implication in the joint mechanical function and cartilage mechanobiology.
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...... was the difference in time scale between the geological process of deposition (millions of years) and the laboratory measurements of mechanical properties (minutes or hours). In addition, the time scale relevant to the production history of the oil field was interesting (days or years)....
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...
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
Time dependent resonating Hartree-Bogoliubov theory
International Nuclear Information System (INIS)
Nishiyama, Seiya; Fukutome, Hideo.
1989-01-01
Very recently, we have developed a theory of excitations in superconducting Fermion systems with large quantum fluctuations that can be described by resonance of time dependent non-orthogonal Hartree-Bogoliubov (HB) wave functions with different correlation structures. We have derived a new kind of variation equation called the time dependent Resonating HB equation, in order to determine both the time dependent Resonating HB wave functions and coefficients of a superposition of the HB wave functions. Further we have got a new approximation for excitations from time dependent small fluctuations of the Resonating HB ground state, i.e., the Resonating HB RPA. The Res HB RPA equation is represented in a given single particle basis. It, however, has drawbacks that the constraints for the Res HB RPA amplitudes are not taken into account and the equation contains equations which are not independent. We shall derive another form of the Res HB RPA equation eliminating these drawbacks. The Res HB RPA gives a unified description of the vibrons and resonons and their interactions. (author)
Biological repair with time-dependent irradiation
International Nuclear Information System (INIS)
Broyles, A.A.; Shapiro, C.S.
1985-01-01
Recent experiments have provided new data that explore the effectiveness of biological repair in assessing damage due to exposures from ionizing radiation. These data are mainly from experiments conducted at constant dose rates, to study the effectiveness per unit dose of different dose rates. Here, we develop new formulae to estimate the effectiveness of an arbitrary time-dependent dose rate exposure
Hartree--Fock time-dependent problem
Energy Technology Data Exchange (ETDEWEB)
Bove, A; Fano, G [Bologna Univ. (Italy). Istituto di Fisica; Istituto Nazionale di Fisica Nucleare, Bologna (Italy)); Da Prato, G [Rome Univ. (Italy). Istituto di Matematica
1976-06-01
A previous result is generalized. An existence and uniqueness theorem is proved for the Hartree--Fock time-dependent problem in the case of a finite Fermi system interacting via a two body potential which is supposed to be dominated by the kinetic energy part of the one-particle Hamiltonian.
Maritime Load Dependent Lead Times - An Analysis
DEFF Research Database (Denmark)
Pahl, Julia; Voss, Stefan
2017-01-01
in production. Inspired by supply chain planning systems, we analyze the current state of (collaborative) planning in the maritime transport chain with focus on containers. Regarding the problem of congestion, we particularly emphasize on load dependent lead times (LDLT) which are well studied in production....
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...
Directory of Open Access Journals (Sweden)
Wentao Wang
2012-01-01
Full Text Available This paper presents a new generalized Nicholson’s blowflies system with patch structure and nonlinear density-dependent mortality terms. Under appropriate conditions, we establish some criteria to guarantee the exponential extinction of this system. Moreover, we give two examples and numerical simulations to demonstrate our main results.
A new differential equations-based model for nonlinear history-dependent magnetic behaviour
International Nuclear Information System (INIS)
Aktaa, J.; Weth, A. von der
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
Efficient Discovery of Nonlinear Dependencies in a Combinatorial Catalyst Data Set
Czech Academy of Sciences Publication Activity Database
Cawse, J.N.; Baerns, M.; Holeňa, Martin
2004-01-01
Roč. 44, č. 3 (2004), s. 143-146 ISSN 0095-2338 Source of funding: V - iné verejné zdroje Keywords : combinatorial catalysis * genetic algorithms * nonlinear dependency * data analysis * high-order interactions Subject RIV: IN - Informatics, Computer Science Impact factor: 2.810, year: 2004
Extracting Leading Nonlinear Modes of Changing Climate From Global SST Time Series
Mukhin, D.; Gavrilov, A.; Loskutov, E. M.; Feigin, A. M.; Kurths, J.
2017-12-01
Data-driven modeling of climate requires adequate principal variables extracted from observed high-dimensional data. For constructing such variables it is needed to find spatial-temporal patterns explaining a substantial part of the variability and comprising all dynamically related time series from the data. The difficulties of this task rise from the nonlinearity and non-stationarity of the climate dynamical system. The nonlinearity leads to insufficiency of linear methods of data decomposition for separating different processes entangled in the observed time series. On the other hand, various forcings, both anthropogenic and natural, make the dynamics non-stationary, and we should be able to describe the response of the system to such forcings in order to separate the modes explaining the internal variability. The method we present is aimed to overcome both these problems. The method is based on the Nonlinear Dynamical Mode (NDM) decomposition [1,2], but takes into account external forcing signals. An each mode depends on hidden, unknown a priori, time series which, together with external forcing time series, are mapped onto data space. Finding both the hidden signals and the mapping allows us to study the evolution of the modes' structure in changing external conditions and to compare the roles of the internal variability and forcing in the observed behavior. The method is used for extracting of the principal modes of SST variability on inter-annual and multidecadal time scales accounting the external forcings such as CO2, variations of the solar activity and volcanic activity. The structure of the revealed teleconnection patterns as well as their forecast under different CO2 emission scenarios are discussed.[1] Mukhin, D., Gavrilov, A., Feigin, A., Loskutov, E., & Kurths, J. (2015). Principal nonlinear dynamical modes of climate variability. Scientific Reports, 5, 15510. [2] Gavrilov, A., Mukhin, D., Loskutov, E., Volodin, E., Feigin, A., & Kurths, J. (2016
Development of constitutive model for composites exhibiting time dependent properties
International Nuclear Information System (INIS)
Pupure, L; Joffe, R; Varna, J; Nyström, B
2013-01-01
Regenerated cellulose fibres and their composites exhibit highly nonlinear behaviour. The mechanical response of these materials can be successfully described by the model developed by Schapery for time-dependent materials. However, this model requires input parameters that are experimentally determined via large number of time-consuming tests on the studied composite material. If, for example, the volume fraction of fibres is changed we have a different material and new series of experiments on this new material are required. Therefore the ultimate objective of our studies is to develop model which determines the composite behaviour based on behaviour of constituents of the composite. This paper gives an overview of problems and difficulties, associated with development, implementation and verification of such model
Monolayer phosphorene under time-dependent magnetic field
Nascimento, J. P. G.; Aguiar, V.; Guedes, I.
2018-02-01
We obtain the exact wave function of a monolayer phosphorene under a low-intensity time-dependent magnetic field using the dynamical invariant method. We calculate the quantum-mechanical energy expectation value and the transition probability for a constant and an oscillatory magnetic field. For the former we observe that the Landau level energy varies linearly with the quantum numbers n and m and the magnetic field intensity B0. No transition takes place. For the latter, we observe that the energy oscillates in time, increasing linearly with the Landau level n and m and nonlinearly with the magnetic field. The (k , l) →(n , m) transitions take place only for l = m. We investigate the (0,0) →(n , 0) and (1 , l) and (2 , l) probability transitions.
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...... derive steady-state waiting-time distributions for both models. The results are illustrated with numerical examples....... 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...
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.
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.
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 ...
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-dependent 2-stream particle transport
International Nuclear Information System (INIS)
Corngold, Noel
2015-01-01
Highlights: • We consider time-dependent transport in the 2-stream or “rod” model via an attractive matrix formalism. • After reviewing some classical problems in homogeneous media we discuss transport in materials with whose density may vary. • There we achieve a significant contraction of the underlying Telegrapher’s equation. • We conclude with a discussion of stochastics, treated by the “first-order smoothing approximation.” - Abstract: We consider time-dependent transport in the 2-stream or “rod” model via an attractive matrix formalism. After reviewing some classical problems in homogeneous media we discuss transport in materials whose density may vary. There we achieve a significant contraction of the underlying Telegrapher’s equation. We conclude with a discussion of stochastics, treated by the “first-order smoothing approximation.”
Doping dependent nonlinear Hall effect in SmFeAsO1-xFx
International Nuclear Information System (INIS)
Riggs, Scott C; Kemper, J B; Stegen, Z; Boebinger, G S; McDonald, R D; Balakirev, F F; Kohama, Y; Migliori, A; Chen, H; Liu, R H; Chen, X H
2009-01-01
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 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. (fast track communication)
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.
Time-dependent angularly averaged inverse transport
International Nuclear Information System (INIS)
Bal, Guillaume; Jollivet, Alexandre
2009-01-01
This paper concerns the reconstruction of the absorption and scattering parameters in a time-dependent linear transport equation from knowledge of angularly averaged measurements performed at the boundary of a domain of interest. Such measurement settings find applications in medical and geophysical imaging. We show that the absorption coefficient and the spatial component of the scattering coefficient are uniquely determined by such measurements. We obtain stability results on the reconstruction of the absorption and scattering parameters with respect to the measured albedo operator. The stability results are obtained by a precise decomposition of the measurements into components with different singular behavior in the time domain
Time-dependent onshore tsunami response
Apotsos, Alex; Gelfenbaum, Guy R.; Jaffe, Bruce E.
2012-01-01
While bulk measures of the onshore impact of a tsunami, including the maximum run-up elevation and inundation distance, are important for hazard planning, the temporal evolution of the onshore flow dynamics likely controls the extent of the onshore destruction and the erosion and deposition of sediment that occurs. However, the time-varying dynamics of actual tsunamis are even more difficult to measure in situ than the bulk parameters. Here, a numerical model based on the non-linear shallow water equations is used to examine the effects variations in the wave characteristics, bed slope, and bottom roughness have on the temporal evolution of the onshore flow. Model results indicate that the onshore flow dynamics vary significantly over the parameter space examined. For example, the flow dynamics over steep, smooth morphologies tend to be temporally symmetric, with similar magnitude velocities generated during the run-up and run-down phases of inundation. Conversely, on shallow, rough onshore topographies the flow dynamics tend to be temporally skewed toward the run-down phase of inundation, with the magnitude of the flow velocities during run-up and run-down being significantly different. Furthermore, for near-breaking tsunami waves inundating over steep topography, the flow velocity tends to accelerate almost instantaneously to a maximum and then decrease monotonically. Conversely, when very long waves inundate over shallow topography, the flow accelerates more slowly and can remain steady for a period of time before beginning to decelerate. These results indicate that a single set of assumptions concerning the onshore flow dynamics cannot be applied to all tsunamis, and site specific analyses may be required.
Time- & Load-Dependence of Triboelectric Effect.
Pan, Shuaihang; Yin, Nian; Zhang, Zhinan
2018-02-06
Time- and load-dependent friction behavior is considered as important for a long time, due to its time-evolution and force-driving characteristics. However, its electronic behavior, mainly considered in triboelectric effect, has almost never been given the full attention and analyses from the above point of view. In this paper, by experimenting with fcc-latticed aluminum and copper friction pairs, the mechanical and electronic behaviors of friction contacts are correlated by time and load analyses, and the behind physical understanding is provided. Most importantly, the difference of "response lag" in force and electricity is discussed, the extreme points of coefficient of friction with the increasing normal loads are observed and explained with the surface properties and dynamical behaviors (i.e. wear), and the micro and macro theories linking tribo-electricity to normal load and wear (i.e. the physical explanation between coupled electrical and mechanical phenomena) are successfully developed and tested.
Vehicle routing with stochastic time-dependent travel times
Lecluyse, C.; Woensel, van T.; Peremans, H.
2009-01-01
Assigning and scheduling vehicle routes in a stochastic time-dependent environment is a crucial management problem. The assumption that in a real-life environment everything goes according to an a priori determined static schedule is unrealistic. Our methodology builds on earlier work in which the
Vehicle routing with stochastic time-dependent travel times
Lecluyse, C.; Woensel, van T.; Peremans, H.
2007-01-01
Assigning and scheduling vehicle routes in a stochastic time-dependent environment is a crucial management problem. The assumption that in a real-life environment everything goes according to an a priori determined static schedule is unrealistic. Our methodology builds on earlier work in which 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...
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.
Time-dependent EQPET analysis of TSC
International Nuclear Information System (INIS)
Takahashi, Akito
2006-01-01
Time-dependent fusion rates for 2D and 4D reactions are calculated for squeezing of tetrahedral symmetric condensate (TSC) from about 100 pm size to its minimum size (about 10 fm), within about 75 fs squeezing motion. Life time of the minimum TSC state is yet to be studied. Time-averaged fusion rates are given by assuming the life time of minimum TSC state is negligible. Time-averaged 2D fusion rate was given as 2.9x10 -25 f/s/pair, and time-averaged 4D fusion rate was 5.5x10 -8 f/s/cl. These values are compared with 1.0x10 -20 f/s/pair for 2D and 1.0x10 -9 f/s/cl for 4D, respectively, of previously estimated values by electronic quasi-particle expansion theory/TSC models. Effective fusion time by the TSC squeezing motion was estimated as 0.014 fs: namely fusions may happen in very short time interval. (author)
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.
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.
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.
Conservation laws for certain time fractional nonlinear systems of partial differential equations
Singla, Komal; Gupta, R. K.
2017-12-01
In this study, an extension of the concept of nonlinear self-adjointness and Noether operators is proposed for calculating conserved vectors of the time fractional nonlinear systems of partial differential equations. In our recent work (J Math Phys 2016; 57: 101504), by proposing the symmetry approach for time fractional systems, the Lie symmetries for some fractional nonlinear systems have been derived. In this paper, the obtained infinitesimal generators are used to find conservation laws for the corresponding fractional systems.
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
Cosmologies with a time dependent vacuum
International Nuclear Information System (INIS)
Sola, Joan
2011-01-01
The idea that the cosmological term Λ should be a time dependent quantity in cosmology is a most natural one. It is difficult to conceive an expanding universe with a strictly constant vacuum energy density, ρ Λ = Λ/(8π G), namely one that has remained immutable since the origin of time. A smoothly evolving vacuum energy density ρ Λ = ρ Λ (ξ(t)) that inherits its time-dependence from cosmological functions ξ = ξ(t), such as the Hubble rate H(t) or the scale factor a(t), is not only a qualitatively more plausible and intuitive idea, but is also suggested by fundamental physics, in particular by quantum field theory (QFT) in curved space-time. To implement this notion, is not strictly necessary to resort to ad hoc scalar fields, as usually done in the literature (e.g. in quintessence formulations and the like). A 'running' Λ term can be expected on very similar grounds as one expects (and observes) the running of couplings and masses with a physical energy scale in QFT. Furthermore, the experimental evidence that the equation of state (EOS) of the dark energy (DE) could be evolving with time/redshift (including the possibility that it might currently behave phantom-like) suggests that a time-variable Λ = Λ(t) term (possibly accompanied by a variable Newton's gravitational coupling too, G = G(t)) could account in a natural way for all these features. Remarkably enough, a class of these models (the 'new cosmon') could even be the clue for solving the old cosmological constant problem, including the coincidence problem.
Interacting particle systems in time-dependent geometries
Ali, A.; Ball, R. C.; Grosskinsky, S.; Somfai, E.
2013-09-01
Many complex structures and stochastic patterns emerge from simple kinetic rules and local interactions, and are governed by scale invariance properties in combination with effects of the global geometry. We consider systems that can be described effectively by space-time trajectories of interacting particles, such as domain boundaries in two-dimensional growth or river networks. We study trajectories embedded in time-dependent geometries, and the main focus is on uniformly expanding or decreasing domains for which we obtain an exact mapping to simple fixed domain systems while preserving the local scale invariance properties. This approach was recently introduced in Ali et al (2013 Phys. Rev. E 87 020102(R)) and here we provide a detailed discussion on its applicability for self-affine Markovian models, and how it can be adapted to self-affine models with memory or explicit time dependence. The mapping corresponds to a nonlinear time transformation which converges to a finite value for a large class of trajectories, enabling an exact analysis of asymptotic properties in expanding domains. We further provide a detailed discussion of different particle interactions and generalized geometries. All our findings are based on exact computations and are illustrated numerically for various examples, including Lévy processes and fractional Brownian motion.
Time-dependent, multimode interaction analysis of the gyroklystron amplifier
Energy Technology Data Exchange (ETDEWEB)
Swati, M. V., E-mail: swati.mv.ece10@iitbhu.ac.in; Chauhan, M. S.; Jain, P. K. [Department of Electronics Engineering, Indian Institute of Technology, Banaras Hindu University, Varanasi 221005 (India)
2016-08-15
In this paper, a time-dependent multimode nonlinear analysis for the gyroklystron amplifier has been developed by extending the analysis of gyrotron oscillators by employing the self-consistent approach. The nonlinear analysis developed here has been validated by taking into account the reported experimental results for a 32.3 GHz, three cavity, second harmonic gyroklystron operating in the TE{sub 02} mode. The analysis has been used to estimate the temporal RF growth in the operating mode as well as the nearby competing modes. Device gain and bandwidth have been computed for different drive powers and frequencies. The effect of various beam parameters, such as beam voltage, beam current, and pitch factor, has also been studied. The computational results have estimated the gyroklystron saturated RF power ∼319 kW at 32.3 GHz with efficiency ∼23% and gain ∼26.3 dB with device bandwidth ∼0.027% (8 MHz) for a 70 kV, 20 A electron beam. The computed results are found to be in agreement with the experimental values within 10%.
Time dependent variational method in quantum mechanics
International Nuclear Information System (INIS)
Torres del Castillo, G.F.
1987-01-01
Using the fact that the solutions to the time-dependent Schodinger equation can be obtained from a variational principle, by restricting the evolution of the state vector to some surface in the corresponding Hilbert space, approximations to the exact solutions can be obtained, which are determined by equations similar to Hamilton's equations. It is shown that, in order for the approximate evolution to be well defined on a given surface, the imaginary part of the inner product restricted to the surface must be non-singular. (author)
Time dependent black holes and thermal equilibration
International Nuclear Information System (INIS)
Bak, Dongsu; Gutperle, Michael; Karch, Andreas
2007-01-01
We study aspects of a recently proposed exact time dependent black hole solution of IIB string theory using the AdS/CFT correspondence. The dual field theory is a thermal system in which initially a vacuum density for a non-conserved operator is turned on. We can see that in agreement with general thermal field theory expectation the system equilibrates: the expectation value of the non-conserved operator goes to zero exponentially and the entropy increases. In the field theory the process can be described quantitatively in terms of a thermofield state and exact agreement with the gravity answers is found
Electromagnetic wave propagation in time-dependent media with antisymmetric magnetoelectric coupling
International Nuclear Information System (INIS)
Lin, Shi-Rong; Zhang, Ruo-Yang; Ma, Yi-Rong; Jia, Wei; Zhao, Qing
2016-01-01
Highlights: • Time-dependent permittivity combined with antisymmetric magnetoelectric coupling will yield a novel linear birefringence. • Distinct dynamical behaviors of these two birefringent modes are analyzed. • As a new nonlinear optical effect, a scheme utilizing optical Kerr effect in moving media is proposed. - Abstract: This paper deals with electromagnetic wave propagation in time-dependent media with an antisymmetric magnetoelectric coupling and an isotropic time-dependent permittivity. We identify a new mechanism of linear birefringence, originated from the combined action of the time-dependent permittivity and the antisymmetric magnetoelectric coupling. Permittivity with linear and exponential temporal variations exemplifies the creation and control of these two distinct types of linear birefringent modes. As a novel nonlinear optical effect, a scheme utilizing optical Kerr effect in moving media is proposed for the realization of the predicted birefringence.
Electromagnetic wave propagation in time-dependent media with antisymmetric magnetoelectric coupling
Energy Technology Data Exchange (ETDEWEB)
Lin, Shi-Rong [School of Physics, Beijing Institute of Technology, Beijing 100081 (China); Zhang, Ruo-Yang [Theoretical Physics Division, Chern Institute of Mathematics, Nankai University, Tianjin 300071 (China); Ma, Yi-Rong; Jia, Wei [School of Physics, Beijing Institute of Technology, Beijing 100081 (China); Zhao, Qing, E-mail: qzhaoyuping@bit.edu.cn [School of Physics, Beijing Institute of Technology, Beijing 100081 (China)
2016-07-29
Highlights: • Time-dependent permittivity combined with antisymmetric magnetoelectric coupling will yield a novel linear birefringence. • Distinct dynamical behaviors of these two birefringent modes are analyzed. • As a new nonlinear optical effect, a scheme utilizing optical Kerr effect in moving media is proposed. - Abstract: This paper deals with electromagnetic wave propagation in time-dependent media with an antisymmetric magnetoelectric coupling and an isotropic time-dependent permittivity. We identify a new mechanism of linear birefringence, originated from the combined action of the time-dependent permittivity and the antisymmetric magnetoelectric coupling. Permittivity with linear and exponential temporal variations exemplifies the creation and control of these two distinct types of linear birefringent modes. As a novel nonlinear optical effect, a scheme utilizing optical Kerr effect in moving media is proposed for the realization of the predicted birefringence.
CVA identification of nonlinear systems with LPV state-space models of affine dependence
Larimore, W.E.; Cox, P.B.; Toth, R.
2015-01-01
This paper discusses an improvement on the extension of linear subspace methods (originally developed in the Linear Time-Invariant (LTI) context) to the identification of Linear Parameter-Varying (LPV) and state-affine nonlinear system models. This includes the fitting of a special polynomial
Time evolution of absorption process in nonlinear metallic photonic crystals
Energy Technology Data Exchange (ETDEWEB)
Singh, Mahi R.; Hatef, Ali [Department of Physics and Astronomy, University of Western Ontario, London (Canada)
2009-05-15
The time evolution of the absorption coefficient in metallic photonic crystals has been studied numerically. These crystals are made from metallic spheres which are arranged periodically in air. The refractive index of the metallic spheres depends on the plasma frequency. Probe and pump fields are applied to monitor the absorption process. Ensembles of three-level particles are embedded in the crystal. Nanoparticles are interacting with the metallic crystals via the electron-photon interaction. It is found that when the resonance states lie away from the band edges system goes to transparent state. (copyright 2009 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)
Time-dependent Cooling in Photoionized Plasma
Energy Technology Data Exchange (ETDEWEB)
Gnat, Orly, E-mail: orlyg@phys.huji.ac.il [Racah Institute of Physics, The Hebrew University, Jerusalem 91904 (Israel)
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 (10{sup 8}–10{sup 4} K), densities (10{sup −7}–10{sup 3} cm{sup −3}), and metallicities (10{sup −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).
Quantum-Enhanced Sensing Based on Time Reversal of Nonlinear Dynamics.
Linnemann, D; Strobel, H; Muessel, W; Schulz, J; Lewis-Swan, R J; Kheruntsyan, K V; Oberthaler, M K
2016-07-01
We experimentally demonstrate a nonlinear detection scheme exploiting time-reversal dynamics that disentangles continuous variable entangled states for feasible readout. Spin-exchange dynamics of Bose-Einstein condensates is used as the nonlinear mechanism which not only generates entangled states but can also be time reversed by controlled phase imprinting. For demonstration of a quantum-enhanced measurement we construct an active atom SU(1,1) interferometer, where entangled state preparation and nonlinear readout both consist of parametric amplification. This scheme is capable of exhausting the quantum resource by detecting solely mean atom numbers. Controlled nonlinear transformations widen the spectrum of useful entangled states for applied quantum technologies.
Hoyer, Dirk; Leder, Uwe; Hoyer, Heike; Pompe, Bernd; Sommer, Michael; Zwiener, Ulrich
2002-01-01
The heart rate variability (HRV) is related to several mechanisms of the complex autonomic functioning such as respiratory heart rate modulation and phase dependencies between heart beat cycles and breathing cycles. The underlying processes are basically nonlinear. In order to understand and quantitatively assess those physiological interactions an adequate coupling analysis is necessary. We hypothesized that nonlinear measures of HRV and cardiorespiratory interdependencies are superior to the standard HRV measures in classifying patients after acute myocardial infarction. We introduced mutual information measures which provide access to nonlinear interdependencies as counterpart to the classically linear correlation analysis. The nonlinear statistical autodependencies of HRV were quantified by auto mutual information, the respiratory heart rate modulation by cardiorespiratory cross mutual information, respectively. The phase interdependencies between heart beat cycles and breathing cycles were assessed basing on the histograms of the frequency ratios of the instantaneous heart beat and respiratory cycles. Furthermore, the relative duration of phase synchronized intervals was acquired. We investigated 39 patients after acute myocardial infarction versus 24 controls. The discrimination of these groups was improved by cardiorespiratory cross mutual information measures and phase interdependencies measures in comparison to the linear standard HRV measures. This result was statistically confirmed by means of logistic regression models of particular variable subsets and their receiver operating characteristics.
The large discretization step method for time-dependent partial differential equations
Haras, Zigo; Taasan, Shlomo
1995-01-01
A new method for the acceleration of linear and nonlinear time dependent calculations is presented. It is based on the Large Discretization Step (LDS) approximation, defined in this work, which employs an extended system of low accuracy schemes to approximate a high accuracy discrete approximation to a time dependent differential operator. Error bounds on such approximations are derived. These approximations are efficiently implemented in the LDS methods for linear and nonlinear hyperbolic equations, presented here. In these algorithms the high and low accuracy schemes are interpreted as the same discretization of a time dependent operator on fine and coarse grids, respectively. Thus, a system of correction terms and corresponding equations are derived and solved on the coarse grid to yield the fine grid accuracy. These terms are initialized by visiting the fine grid once in many coarse grid time steps. The resulting methods are very general, simple to implement and may be used to accelerate many existing time marching schemes.
International Nuclear Information System (INIS)
Yao Ruo-Xia; Wang Wei; Chen Ting-Hua
2014-01-01
Motivated by the widely used ansätz method and starting from the modified Riemann—Liouville derivative together with a fractional complex transformation that can be utilized to transform nonlinear fractional partial differential equations to nonlinear ordinary differential equations, new types of exact traveling wave solutions to three important nonlinear space- and time-fractional partial differential equations are obtained simultaneously in terms of solutions of a Riccati equation. The results are new and first reported in this paper. (general)
Cracking chaos-based encryption systems ruled by nonlinear time delay differential equations
International Nuclear Information System (INIS)
Udaltsov, Vladimir S.; Goedgebuer, Jean-Pierre; Larger, Laurent; Cuenot, Jean-Baptiste; Levy, Pascal; Rhodes, William T.
2003-01-01
We report that signal encoding with high-dimensional chaos produced by delayed feedback systems with a strong nonlinearity can be broken. We describe the procedure and illustrate the method with chaotic waveforms obtained from a strongly nonlinear optical system that we used previously to demonstrate signal encryption/decryption with chaos in wavelength. The method can be extended to any systems ruled by nonlinear time-delayed differential equations
Influence of wavelength-dependent-loss on dispersive wave in nonlinear optical fibers.
Herrera, Rodrigo Acuna
2012-11-01
In this work, we study numerically the influence of wavelength-dependent loss on the generation of dispersive waves (DWs) in nonlinear fiber. This kind of loss can be obtained, for instance, by the acousto-optic effect in fiber optics. We show that this loss lowers DW frequency in an opposite way that the Raman effect does. Also, we see that the Raman effect does not change the DW frequency too much when wavelength-dependent loss is included. Finally, we show that the DW frequency is not practically affected by fiber length.
Controlling chaos in a nonlinear pendulum using an extended time-delayed feedback control method
International Nuclear Information System (INIS)
Souza de Paula, Aline; Savi, Marcelo Amorim
2009-01-01
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.
System reliability time-dependent models
International Nuclear Information System (INIS)
Debernardo, H.D.
1991-06-01
A probabilistic methodology for safety system technical specification evaluation was developed. The method for Surveillance Test Interval (S.T.I.) evaluation basically means an optimization of S.T.I. of most important system's periodically tested components. For Allowed Outage Time (A.O.T.) calculations, the method uses system reliability time-dependent models (A computer code called FRANTIC III). A new approximation, which was called Independent Minimal Cut Sets (A.C.I.), to compute system unavailability was also developed. This approximation is better than Rare Event Approximation (A.E.R.) and the extra computing cost is neglectible. A.C.I. was joined to FRANTIC III to replace A.E.R. on future applications. The case study evaluations verified that this methodology provides a useful probabilistic assessment of surveillance test intervals and allowed outage times for many plant components. The studied system is a typical configuration of nuclear power plant safety systems (two of three logic). Because of the good results, these procedures will be used by the Argentine nuclear regulatory authorities in evaluation of technical specification of Atucha I and Embalse nuclear power plant safety systems. (Author) [es
First passage time problems in time-dependent fields
International Nuclear Information System (INIS)
Fletcher, J.E.; Havlin, S.; Weiss, G.H.
1988-01-01
This paper discusses the simplest first passage time problems for random walks and diffusion processes on a line segment. When a diffusing particle moves in a time-varying field, use of the adjoint equation does not lead to any simplification in the calculation of moments of the first passage time as is the case for diffusion in a time-invariant field. We show that for a discrete random walk in the presence of a sinusoidally varying field there is a resonant frequency omega* for which the mean residence time on the line segment in a minimum. It is shown that for a random walk on a line segment of length L the mean residence time goes like L 2 for large L when omega omega*, but when omega = omega* the dependence is proportional to L. The results of our simulation are numerical, but can be regarded as exact. Qualitatively similar results are shown to hold for diffusion processes by a perturbation expansion in powers of a dimensionless velocity. These results are extended to higher values of this parameter by a numerical solution of the forward equation
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.
Time-dependent dilatancy for brittle rocks
Directory of Open Access Journals (Sweden)
Jie Li
2017-12-01
Full Text Available This paper presents a theoretical study on time-dependent dilatancy behaviors for brittle rocks. The theory employs a well-accepted postulation that macroscopically observed dilatancy originates from the expansion of microcracks. The mechanism and dynamic process that microcracks initiate from local stress concentration and grow due to localized tensile stress are analyzed. Then, by generalizing the results from the analysis of single cracks, a parameter and associated equations for its evolution are developed to describe the behaviors of the microcracks. In this circumstance, the relationship between microcracking and dilatancy can be established, and the theoretical equations for characterizing the process of rock dilatancy behaviors are derived. Triaxial compression and creep tests are conducted to validate the developed theory. With properly chosen model parameters, the theory yields a satisfactory accuracy in comparison with the experimental results.
Nonlinear Time Reversal Acoustic Method of Friction Stir Weld Assessment, Phase I
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...
Time-dependent radioactivity distribution in MAFF
International Nuclear Information System (INIS)
Nebel, F.; Zech, E.; Faestermann, T.; Kruecken, R.; Maier-Komor, P.; Assmann, W.; Szerypo, J.; Gross, M.; Kester, O.; Thirolf, P.G.; Groetzschel, R.
2006-01-01
The Munich Accelerator for Fission Fragments is planned to be installed at the FRM II in Garching. It will operate a uranium-carbide-loaded graphite matrix as a target for neutron-induced fission. The radioactive reaction fragments leave the ion source as both, atoms and ions. For radiation safety it is imperative to have a basic understanding of the fragment distribution within the beam line. Atoms leaving the graphite matrix will spread like a gas and stick to surfaces depending on their species. A probabilistic Monte-Carlo approach is used to predict the surface coating of internal surfaces of the beam line for all fission nuclides. To decrease calculation time, the problem is reduced to two dimensions with the surface areas being a measure for the probability, that they are hit by a particle. The program is completely time dependent to implement radioactive decay. Ions leaving the fission ion source are transported by electrostatic means towards the mass pre-separator, a low-resolution dipole magnet with a complex slit system in the focal plane. All unwanted ions are stopped at the slits, resulting in a high level of radioactive contamination. While it is advantageous for shielding purposes to have the majority of the contamination in one point, precautions must be taken to ensure that it stays that way. Material corrosion caused by sputtering will release previously implanted radionuclides. To reduce this effect, different methods are under investigation, one of which is changing the slit geometry. The considered designs will be described and experimental results will be shown
Nonlinear discrete-time multirate adaptive control of non-linear vibrations of smart beams
Georgiou, Georgios; Foutsitzi, Georgia A.; Stavroulakis, Georgios E.
2018-06-01
The nonlinear adaptive digital control of a smart piezoelectric beam is considered. It is shown that in the case of a sampled-data context, a multirate control strategy provides an appropriate framework in order to achieve vibration regulation, ensuring the stability of the whole control system. Under parametric uncertainties in the model parameters (damping ratios, frequencies, levels of non linearities and cross coupling, control input parameters), the scheme is completed with an adaptation law deduced from hyperstability concepts. This results in the asymptotic satisfaction of the control objectives at the sampling instants. Simulation results are presented.
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
Time-Dependent Variations of Accretion Disk
Directory of Open Access Journals (Sweden)
Hye-Weon Na
1987-06-01
Full Text Available In dward nova we assume the primary star as a white dwarf and the secondary as the late type star which filled Roche lobe. Mass flow from the secondary star leads to the formation of thin accretion disk around the white dwarf. We use the α parameter as viscosity to maintain the disk form and propose that the outburst in dwarf nova cause the steep increase of source term. With these assumptions we solve the basic equations of stellar structure using Newton-Raphson method. We show the physical parameters like temperature, density, pressure, opacity, surface density, height and flux to the radius of disk. Changing the value of α, we compare several parameters when mass flow rate is constant with those of when luminosity of disk is brightest. At the same time, we obtain time-dependent variations of luminosity and mass of disk. We propose the suitable range of α is 0.15-0.18 to the difference of luminosity. We compare several parameters of disk with those of the normal late type stars which have the same molecular weight of disk is lower. Maybe the outburst in dwarf nova is due to the variation of the α value instead of increment of mass flow from the secondary star.
Deformation aspects of time dependent fracture
International Nuclear Information System (INIS)
Li, C.Y.; Turner, A.P.L.; Diercks, D.R.; Laird, C.; Langdon, T.G.; Nix, W.D.; Swindeman, R.; Wolfer, W.G.; Woodford, D.A.
1979-01-01
For all metallic materials, particularly at elevated temperatures, deformation plays an important role in fracture. On the macro-continuum level, the inelastic deformation behavior of the material determines how stress is distributed in the body and thus determines the driving force for fracture. At the micro-continuum level, inelastic deformation alters the elastic stress singularity at the crack tip and so determines the local environment in which crack advance takes place. At the microscopic and mechanistic level, there are many possibilities for the mechanisms of deformation to be related to those for crack initiation and growth. At elevated temperatures, inelastic deformation in metallic systems is time dependent so that the distribution of stress in a body will vary with time, affecting conditions for crack initiation and propagation. Creep deformation can reduce the tendency for fracture by relaxing the stresses at geometric stress concentrations. It can also, under suitable constraints, cause a concentration of stresses at specific loading points as a result of relaxation elsewhere in the body. A combination of deformation and unequal heating, as in welding, can generate large residual stress which cannot be predicted from the external loads on the body. Acceleration of deformation by raising the temperature can be an effective way to relieve such residual stresses
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....
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.
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.
Implicit time-dependent finite different algorithm for quench simulation
International Nuclear Information System (INIS)
Koizumi, Norikiyo; Takahashi, Yoshikazu; Tsuji, Hiroshi
1994-12-01
A magnet in a fusion machine has many difficulties in its application because of requirement of a large operating current, high operating field and high breakdown voltage. A cable-in-conduit (CIC) conductor is the best candidate to overcome these difficulties. However, there remained uncertainty in a quench event in the cable-in-conduit conductor because of a difficulty to analyze a fluid dynamics equation. Several scientists, then, developed the numerical code for the quench simulation. However, most of them were based on an explicit time-dependent finite difference scheme. In this scheme, a discrete time increment is strictly restricted by CFL (Courant-Friedrichs-Lewy) condition. Therefore, long CPU time was consumed for the quench simulation. Authors, then, developed a new quench simulation code, POCHI1, which is based on an implicit time dependent scheme. In POCHI1, the fluid dynamics equation is linearlized according to a procedure applied by Beam and Warming and then, a tridiagonal system can be offered. Therefore, no iteration is necessary to solve the fluid dynamics equation. This leads great reduction of the CPU time. Also, POCHI1 can cope with non-linear boundary condition. In this study, comparison with experimental results was carried out. The normal zone propagation behavior was investigated in two samples of CIC conductors which had different hydraulic diameters. The measured and simulated normal zone propagation length showed relatively good agreement. However, the behavior of the normal voltage shows a little disagreement. These results indicate necessity to improve the treatment of the heat transfer coefficient in the turbulent flow region and the electric resistivity of the copper stabilizer in high temperature and high field region. (author)
Time dependent mean-field games
Gomes, Diogo A.; Pimentel, Edgard; Sá nchez-Morgado, Hé ctor
2014-01-01
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.
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.
Real-Time Implementation of Nonlinear Optical Processing Functions.
1986-09-30
information capacity) with the nonlinear error correction properties of associative neural nets such as the Hopfield model. Analogies between holography...symnolic ma.Ip’:ation Th.e error correcting -apart" :ty of non" ;n-ar associative merTtnies is necessary for s’uch structu-res Experimerta. results... 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
Non-linear ultrasonic time-reversal mirrors in NDT
Czech Academy of Sciences Publication Activity Database
Převorovský, Zdeněk
-, č. 4 (2012), s. 4-4 [World Conference on Nondestructive Testing /18./. 16.4.2012-20.4.2012, Durban] R&D Projects: GA MPO(CZ) FR-TI1/274; GA MPO(CZ) FR-T1/198; GA ČR(CZ) GAP104/10/1430 Institutional research plan: CEZ:AV0Z2076919 Keywords : non-linear ime reversal mirror * ultrasonic techniques * ESAM Subject RIV: BI - Acoustics http://www.academia-ndt.org/Downloads/AcademiaNews4.pdf
Core design and operation optimization methods based on time-dependent perturbation theory
International Nuclear Information System (INIS)
Greenspan, E.
1983-08-01
A general approach for the optimization of nuclear reactor core design and operation is outlined; it is based on two cornerstones: a newly developed time-dependent (or burnup-dependent) perturbation theory for nonlinear problems and a succesive iteration technique. The resulting approach is capable of handling realistic reactor models using computational methods of any degree of sophistication desired, while accounting for all the constraints imposed. Three general optimization strategies, different in the way for handling the constraints, are formulated. (author)
Spectral dependence of nonlinear optical absorption of silica glass with copper nanoparticles
International Nuclear Information System (INIS)
Golubev, A N; Nikitin, S I; Smirnov, M A; Stepanov, A L
2011-01-01
The nonlinear optical properties of silica glass with copper nanoparticles synthesized by ion implantation were investigated by z-scan method in nanosecond time scale. The reverse saturation absorption (RSA) at the wavelength range of 450–540 nm and saturation absorption (SA) at 550–585 nm were observed. It was supposed that the two-photon electron absorption from bound of d-states determined the RSA effect and the SA is due to saturation of plasmon excitation.
Time-dependent crashworthiness of polyurethane foam
Basit, Munshi Mahbubul; Cheon, Seong Sik
2018-05-01
Time-dependent stress-strain relationship as well as crashworthiness of polyurethane foam was investigated under constant impact energy with different velocities, considering inertia and strain-rate effects simultaneously during the impact testing. Even though the impact energies were same, the percentage in increase in densification strain due to higher impact velocities was found, which yielded the wider plateau region, i.e. growth in crashworthiness. This phenomenon is analyzed by the microstructure of polyurethane foam obtained from scanning electron microscopy. The equations, coupled with the Sherwood-Frost model and the impulse-momentum theory, were employed to build the constitutive equation of the polyurethane foam and calculate energy absorption capacity of the foam. The nominal stress-strain curves obtained from the constitutive equation were compared with results from impact tests and were found to be in good agreement. This study is dedicated to guiding designer use polyurethane foam in crashworthiness structures such as an automotive bumper system by providing crashworthiness data, determining the crush mode, and addressing a mathematical model of the crashworthiness.
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.
Effect of state-dependent delay on a weakly damped nonlinear oscillator.
Mitchell, Jonathan L; Carr, Thomas W
2011-04-01
We consider a weakly damped nonlinear oscillator with state-dependent delay, which has applications in models for lasers, epidemics, and microparasites. More generally, the delay-differential equations considered are a predator-prey system where the delayed term is linear and represents the proliferation of the predator. We determine the critical value of the delay that causes the steady state to become unstable to periodic oscillations via a Hopf bifurcation. Using asymptotic averaging, we determine how the system's behavior is influenced by the functional form of the state-dependent delay. Specifically, we determine whether the branch of periodic solutions will be either sub- or supercritical as well as an accurate estimation of the amplitude. Finally, we choose a few examples of state-dependent delay to test our analytical results by comparing them to numerical continuation.
Determinants of Rotavirus Transmission: A Lag Nonlinear Time Series Analysis.
van Gaalen, Rolina D; van de Kassteele, Jan; Hahné, Susan J M; Bruijning-Verhagen, Patricia; Wallinga, Jacco
2017-07-01
Rotavirus is a common viral infection among young children. As in many countries, the infection dynamics of rotavirus in the Netherlands are characterized by an annual winter peak, which was notably low in 2014. Previous study suggested an association between weather factors and both rotavirus transmission and incidence. From epidemic theory, we know that the proportion of susceptible individuals can affect disease transmission. We investigated how these factors are associated with rotavirus transmission in the Netherlands, and their impact on rotavirus transmission in 2014. We used available data on birth rates and rotavirus laboratory reports to estimate rotavirus transmission and the proportion of individuals susceptible to primary infection. Weather data were directly available from a central meteorological station. We developed an approach for detecting determinants of seasonal rotavirus transmission by assessing nonlinear, delayed associations between each factor and rotavirus transmission. We explored relationships by applying a distributed lag nonlinear regression model with seasonal terms. We corrected for residual serial correlation using autoregressive moving average errors. We inferred the relationship between different factors and the effective reproduction number from the most parsimonious model with low residual autocorrelation. Higher proportions of susceptible individuals and lower temperatures were associated with increases in rotavirus transmission. For 2014, our findings suggest that relatively mild temperatures combined with the low proportion of susceptible individuals contributed to lower rotavirus transmission in the Netherlands. However, our model, which overestimated the magnitude of the peak, suggested that other factors were likely instrumental in reducing the incidence that year.
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.
Dosage-dependent non-linear effect of L-dopa on human motor cortex plasticity.
Monte-Silva, Katia; Liebetanz, David; Grundey, Jessica; Paulus, Walter; Nitsche, Michael A
2010-09-15
The neuromodulator dopamine affects learning and memory formation and their likely physiological correlates, long-term depression and potentiation, in animals and humans. It is known from animal experiments that dopamine exerts a dosage-dependent, inverted U-shaped effect on these functions. However, this has not been explored in humans so far. In order to reveal a non-linear dose-dependent effect of dopamine on cortical plasticity in humans, we explored the impact of 25, 100 and 200 mg of L-dopa on transcranial direct current (tDCS)-induced plasticity in twelve healthy human subjects. The primary motor cortex served as a model system, and plasticity was monitored by motor evoked potential amplitudes elicited by transcranial magnetic stimulation. As compared to placebo medication, low and high dosages of L-dopa abolished facilitatory as well as inhibitory plasticity, whereas the medium dosage prolonged inhibitory plasticity, and turned facilitatory plasticity into inhibition. Thus the results show clear non-linear, dosage-dependent effects of dopamine on both facilitatory and inhibitory plasticity, and support the assumption of the importance of a specific dosage of dopamine optimally suited to improve plasticity. This might be important for the therapeutic application of dopaminergic agents, especially for rehabilitative purposes, and explain some opposing results in former studies.
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.
Non-linear behaviour of power density and exposure time of argon laser on ocular tissues
Energy Technology Data Exchange (ETDEWEB)
El-Sayed, E M; Talaat, M S; Salem, E F [Physics Department, Faculty of Science, Ain Shams University, Cairo (Egypt)
1997-12-31
In ophthalmology, the thermal effect of argon laser is the most widely used category of laser- tissue interaction. The rise in tissue temperature has to exceed a threshold value for photo coagulation of retinal blood vessels. This value mainly depends on the laser. The most suitable argon laser power P and exposure time (t) which would be more effective for thermal and electrical behaviour of chicken eye was studied. This was achieved by measuring the variations in ocular temperature in electroretinogram (ERG) records under the effect of argon experiment, while power density (P) and exposure time (t) were varied in four different ways for each dose (pt). Results indicated that for the same laser dose, the temperature distribution of the eye, using low power density and high exposure time was higher than that high power density and low exposure time, indicating non-linearity of the laser dose. This finding was confirmed by ERG records which showed similar variations in b-wave latency, amplitude and duration, for the laser exposure conditions. This indicates variations in retinal function due to laser-dependent temperature variations. 5 figs., 3 tabs.
Transformation of nonlinear discrete-time system into the extended observer form
Kaparin, V.; Kotta, Ü.
2018-04-01
The paper addresses the problem of transforming discrete-time single-input single-output nonlinear state equations into the extended observer form, which, besides the input and output, also depends on a finite number of their past values. Necessary and sufficient conditions for the existence of both the extended coordinate and output transformations, solving the problem, are formulated in terms of differential one-forms, associated with the input-output equation, corresponding to the state equations. An algorithm for transformation of state equations into the extended observer form is proposed and illustrated by an example. Moreover, the considered approach is compared with the method of dynamic observer error linearisation, which likewise is intended to enlarge the class of systems transformable into an observer form.
Non-linear time variant model intended for polypyrrole-based actuators
Farajollahi, Meisam; Madden, John D. W.; Sassani, Farrokh
2014-03-01
Polypyrrole-based actuators are of interest due to their biocompatibility, low operation voltage and relatively high strain and force. Modeling and simulation are very important to predict the behaviour of each actuator. To develop an accurate model, we need to know the electro-chemo-mechanical specifications of the Polypyrrole. In this paper, the non-linear time-variant model of Polypyrrole film is derived and proposed using a combination of an RC transmission line model and a state space representation. The model incorporates the potential dependent ionic conductivity. A function of ionic conductivity of Polypyrrole vs. local charge is proposed and implemented in the non-linear model. Matching of the measured and simulated electrical response suggests that ionic conductivity of Polypyrrole decreases significantly at negative potential vs. silver/silver chloride and leads to reduced current in the cyclic voltammetry (CV) tests. The next stage is to relate the distributed charging of the polymer to actuation via the strain to charge ratio. Further work is also needed to identify ionic and electronic conductivities as well as capacitance as a function of oxidation state so that a fully predictive model can be created.
A Nonlinear Least Squares Approach to Time of Death Estimation Via Body Cooling.
Rodrigo, Marianito R
2016-01-01
The problem of time of death (TOD) estimation by body cooling is revisited by proposing a nonlinear least squares approach that takes as input a series of temperature readings only. Using a reformulation of the Marshall-Hoare double exponential formula and a technique for reducing the dimension of the state space, an error function that depends on the two cooling rates is constructed, with the aim of minimizing this function. Standard nonlinear optimization methods that are used to minimize the bivariate error function require an initial guess for these unknown rates. Hence, a systematic procedure based on the given temperature data is also proposed to determine an initial estimate for the rates. Then, an explicit formula for the TOD is given. Results of numerical simulations using both theoretical and experimental data are presented, both yielding reasonable estimates. The proposed procedure does not require knowledge of the temperature at death nor the body mass. In fact, the method allows the estimation of the temperature at death once the cooling rates and the TOD have been calculated. The procedure requires at least three temperature readings, although more measured readings could improve the estimates. With the aid of computerized recording and thermocouple detectors, temperature readings spaced 10-15 min apart, for example, can be taken. The formulas can be straightforwardly programmed and installed on a hand-held device for field use. © 2015 American Academy of Forensic Sciences.
Nonlinear Spinor Field in Non-Diagonal Bianchi Type Space-Time
Directory of Open Access Journals (Sweden)
Saha Bijan
2018-01-01
Full Text Available Within the scope of the non-diagonal Bianchi cosmological models we have studied the role of the spinor field in the evolution of the Universe. In the non-diagonal Bianchi models the spinor field distribution along the main axis is anisotropic and does not vanish in the absence of the spinor field nonlinearity. Hence within these models perfect fluid, dark energy etc. cannot be simulated by the spinor field nonlinearity. The equation for volume scale V in the case of non-diagonal Bianchi models contains a term with first derivative of V explicitly and does not allow exact solution by quadratures. Like the diagonal models the non-diagonal Bianchi space-time becomes locally rotationally symmetric even in the presence of a spinor field. It was found that depending on the sign of the coupling constant the model allows either an open Universe that rapidly grows up or a close Universe that ends in a Big Crunch singularity.
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
Ulku, Huseyin Arda; Sayed, Sadeed Bin; Bagci, Hakan
2014-01-01
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
Robust model predictive control for constrained continuous-time nonlinear systems
Sun, Tairen; Pan, Yongping; Zhang, Jun; Yu, Haoyong
2018-02-01
In this paper, a robust model predictive control (MPC) is designed for a class of constrained continuous-time nonlinear systems with bounded additive disturbances. The robust MPC consists of a nonlinear feedback control and a continuous-time model-based dual-mode MPC. The nonlinear feedback control guarantees the actual trajectory being contained in a tube centred at the nominal trajectory. The dual-mode MPC is designed to ensure asymptotic convergence of the nominal trajectory to zero. This paper extends current results on discrete-time model-based tube MPC and linear system model-based tube MPC to continuous-time nonlinear model-based tube MPC. The feasibility and robustness of the proposed robust MPC have been demonstrated by theoretical analysis and applications to a cart-damper springer system and a one-link robot manipulator.
Awrejcewicz, J.; Krysko, V. A.; Yakovleva, T. V.; Pavlov, S. P.; Krysko, V. A.
2018-05-01
A mathematical model of complex vibrations exhibited by contact dynamics of size-dependent beam-plate constructions was derived by taking the account of constraints between these structural members. The governing equations were yielded by variational principles based on the moment theory of elasticity. The centre of the investigated plate was supported by a beam. The plate and the beam satisfied the Kirchhoff/Euler-Bernoulli hypotheses. The derived partial differential equations (PDEs) were reduced to the Cauchy problems by the Faedo-Galerkin method in higher approximations, whereas the Cauchy problem was solved using a few Runge-Kutta methods. Reliability of results was validated by comparing the solutions obtained by qualitatively different methods. Complex vibrations were investigated with the help of methods of nonlinear dynamics such as vibration signals, phase portraits, Fourier power spectra, wavelet analysis, and estimation of the largest Lyapunov exponents based on the Rosenstein, Kantz, and Wolf methods. The effect of size-dependent parameters of the beam and plate on their contact interaction was investigated. It was detected and illustrated that the first contact between the size-dependent structural members implies chaotic vibrations. In addition, problems of chaotic synchronization between a nanoplate and a nanobeam were addressed.
Time-resolved analysis of nonlinear optical limiting for laser synthesized carbon nanoparticles
Chen, G. X.; Hong, M. H.
2010-11-01
Nonlinear optical limiting materials have attracted much research interest in recent years. Carbon nanoparticles suspended in liquids show a strong nonlinear optical limiting function. It is important to investigate the nonlinear optical limiting process of carbon nanoparticles for further improving their nonlinear optical limiting performance. In this study, carbon nanoparticles were prepared by laser ablation of a carbon target in tetrahydrofuran (THF). Optical limiting properties of the samples were studied with 532-nm laser light, which is in the most sensitive wavelength band for human eyes. The shape of the laser pulse plays an important role for initializing the nonlinear optical limiting effect. Time-resolved analysis of laser pulses discovered 3 fluence stages of optical limiting. Theoretical simulation indicates that the optical limiting is initialized by a near-field optical enhancement effect.
Energy Technology Data Exchange (ETDEWEB)
Ganguly, Jayanta [Department of Chemistry, Brahmankhanda Basapara High School, Basapara, Birbhum 731215, West Bengal (India); Ghosh, Manas, E-mail: pcmg77@rediffmail.com [Department of Chemistry, Physical Chemistry Section, Visva Bharati University, Santiniketan, Birbhum 731 235, West Bengal (India)
2014-05-07
We investigate the profiles of diagonal components of frequency-dependent first nonlinear (β{sub xxx} and β{sub yyy}) optical response of repulsive impurity doped quantum dots. We have assumed a Gaussian function to represent the dopant impurity potential. This study primarily addresses the role of noise on the polarizability components. We have invoked Gaussian white noise consisting of additive and multiplicative characteristics (in Stratonovich sense). The doped system has been subjected to an oscillating electric field of given intensity, and the frequency-dependent first nonlinear polarizabilities are computed. The noise characteristics are manifested in an interesting way in the nonlinear polarizability components. In case of additive noise, the noise strength remains practically ineffective in influencing the optical responses. The situation completely changes with the replacement of additive noise by its multiplicative analog. The replacement enhances the nonlinear optical response dramatically and also causes their maximization at some typical value of noise strength that depends on oscillation frequency.
Time-dependent transitions with time–space noncommutativity and its implications in quantum optics
International Nuclear Information System (INIS)
Chandra, Nitin
2012-01-01
We study the time-dependent transitions of a quantum-forced harmonic oscillator in noncommutative R 1,1 perturbatively to linear order in the noncommutativity θ. We show that the Poisson distribution gets modified, and that the vacuum state evolves into a ‘squeezed’ state rather than a coherent state. The time evolutions of uncertainties in position and momentum in vacuum are also studied and imply interesting consequences for modeling nonlinear phenomena in quantum optics. (paper)
Liu, Yan-Jun; Gao, Ying; Tong, Shaocheng; Chen, C L Philip
2016-01-01
In this paper, an effective adaptive control approach is constructed to stabilize a class of nonlinear discrete-time systems, which contain unknown functions, unknown dead-zone input, and unknown control direction. Different from linear dead zone, the dead zone, in this paper, is a kind of nonlinear dead zone. To overcome the noncausal problem, which leads to the control scheme infeasible, the systems can be transformed into a m -step-ahead predictor. Due to nonlinear dead-zone appearance, the transformed predictor still contains the nonaffine function. In addition, it is assumed that the gain function of dead-zone input and the control direction are unknown. These conditions bring about the difficulties and the complicacy in the controller design. Thus, the implicit function theorem is applied to deal with nonaffine dead-zone appearance, the problem caused by the unknown control direction can be resolved through applying the discrete Nussbaum gain, and the neural networks are used to approximate the unknown function. Based on the Lyapunov theory, all the signals of the resulting closed-loop system are proved to be semiglobal uniformly ultimately bounded. Moreover, the tracking error is proved to be regulated to a small neighborhood around zero. The feasibility of the proposed approach is demonstrated by a simulation example.
Dose- and time-dependent pharmacokinetics of apigenin trimethyl ether.
Elhennawy, Mai Gamal; Lin, Hai-Shu
2018-06-15
Apigenin trimethyl ether (5,7,4'-trimethoxyflavone, ATE), one of the key polymethoxyflavones present in black ginger (rhizome of Kaempferia parviflora) possesses various health-promoting activities. To optimize its medicinal application, the pharmacokinetics of ATE was assessed in Sprague-Dawley rats with emphases to identify the impacts from dose and repeated dosing on its major pharmacokinetic parameters. Plasma ATE levels were monitored by liquid chromatography-tandem mass spectrometry (LC-MS/MS) method. Upon single intravenous administration (2 mg/kg), plasma levels of ATE declined through an apparent first-order process while dose-escalation to 4 and 8 mg/kg led to its non-linear disposition, which could be described by the Michaelis-Menten model. Similarly, dose-dependent oral pharmacokinetics was confirmed and when the dose was escalated from 5 to 15 and 45 mg/kg, much longer mean residence time (MRT 0→last ), higher dose-normalized maximal plasma concentration (C max /Dose) and exposure (AUC/Dose) were observed at 15 and/or 45 mg/kg. One-week daily oral administration of ATE at 15 mg/kg caused its accelerated elimination and the plasma exposure (AUC) after intravenous (2 mg/kg) and oral administration (15 mg/kg) dropped ~40 and 60%, respectively. As ATE displayed both dose- and time-dependent pharmacokinetics, caution is needed in the medicinal applications of ATE and/or black ginger. Copyright © 2018 Elsevier B.V. All rights reserved.
Thickness-dependent nonlinear optical properties of CsPbBr3 perovskite nanosheets.
Zhang, Jun; Jiang, Tian; Zheng, Xin; Shen, Chao; Cheng, Xiang'ai
2017-09-01
Halide perovskite has attracted significant attention because of excellent optical properties. Here, we study the optical properties of CsPbBr 3 perovskite nanosheets and observe that the nonlinear optical properties can be tuned by the thickness. The photoluminescence (PL) properties and nonlinear absorption effects induced by saturation absorption (SA) and two-photon absorption (TPA) in CsPbBr 3 nanosheets with different thicknesses (from 104.6 to 195.4 nm) have been studied. The PL intensity increases nearly three times with changing from the thinnest one to the thinnest under the same excitation condition. Moreover, the same phenomenon takes place no matter when SA or TPA effects happen. The PL lifetime (τ) varies inversely with the thickness. When SA happens, τ decreases from 11.54 to 9.43 ns while when TPA happens new decay channels emerge with the increase of the thickness. Besides, both saturation intensity (I sat ) and the modulation depth are proportional to the thickness (I sat rises from 3.12 to 4.79 GW/cm 2 , the modulation depth increases from 18.6% to 32.3%), while the TPA coefficient (β) is inversely proportional with the thickness (decreases from 10.94 to 4.73 cm/GW). In addition, quantum yields and thicknesses are in the direct ratio. This Letter advocates great promise for nonlinear optical property related photonics devices.
Nonlinear Prediction Model for Hydrologic Time Series Based on Wavelet Decomposition
Kwon, H.; Khalil, A.; Brown, C.; Lall, U.; Ahn, H.; Moon, Y.
2005-12-01
Traditionally forecasting and characterizations of hydrologic systems is performed utilizing many techniques. Stochastic linear methods such as AR and ARIMA and nonlinear ones such as statistical learning theory based tools have been extensively used. The common difficulty to all methods is the determination of sufficient and necessary information and predictors for a successful prediction. Relationships between hydrologic variables are often highly nonlinear and interrelated across the temporal scale. A new hybrid approach is proposed for the simulation of hydrologic time series combining both the wavelet transform and the nonlinear model. The present model employs some merits of wavelet transform and nonlinear time series model. The Wavelet Transform is adopted to decompose a hydrologic nonlinear process into a set of mono-component signals, which are simulated by nonlinear model. The hybrid methodology is formulated in a manner to improve the accuracy of a long term forecasting. The proposed hybrid model yields much better results in terms of capturing and reproducing the time-frequency properties of the system at hand. Prediction results are promising when compared to traditional univariate time series models. An application of the plausibility of the proposed methodology is provided and the results conclude that wavelet based time series model can be utilized for simulating and forecasting of hydrologic variable reasonably well. This will ultimately serve the purpose of integrated water resources planning and management.
Xiao, Lin; Liao, Bolin; Li, Shuai; Chen, Ke
2018-02-01
In order to solve general time-varying linear matrix equations (LMEs) more efficiently, this paper proposes two nonlinear recurrent neural networks based on two nonlinear activation functions. According to Lyapunov theory, such two nonlinear recurrent neural networks are proved to be convergent within finite-time. Besides, by solving differential equation, the upper bounds of the finite convergence time are determined analytically. Compared with existing recurrent neural networks, the proposed two nonlinear recurrent neural networks have a better convergence property (i.e., the upper bound is lower), and thus the accurate solutions of general time-varying LMEs can be obtained with less time. At last, various different situations have been considered by setting different coefficient matrices of general time-varying LMEs and a great variety of computer simulations (including the application to robot manipulators) have been conducted to validate the better finite-time convergence of the proposed two nonlinear recurrent neural networks. Copyright © 2017 Elsevier Ltd. All rights reserved.
Defect solitons in saturable nonlinearity media with parity-time symmetric optical lattices
Energy Technology Data Exchange (ETDEWEB)
Hu, Sumei [Department of Physics, Guangdong University of Petrochemical Technology, Maoming 525000 (China); Laboratory of Nanophotonic Functional Materials and Devices, South China Normal University, Guangzhou 510631 (China); Hu, Wei, E-mail: huwei@scnu.edu.cn [Laboratory of Nanophotonic Functional Materials and Devices, South China Normal University, Guangzhou 510631 (China)
2013-11-15
We reported the existence and stability of defect solitons in saturable nonlinearity media with parity-time (PT) symmetric optical lattices. Families of fundamental and dipole solitons are found in the semi-infinite gap and the first gap. The power of solitons increases with the increasing of the propagation constant and saturation parameter. The existence areas of fundamental and dipole solitons shrink with the growth of saturation parameter. The instability of dipole solitons for positive and no defect induced by the imaginary part of PT symmetric potentials can be suppressed by the saturation nonlinearity, but for negative defect it cannot be suppressed by the saturation nonlinearity.
Time dependence of vacuum arc parameters
International Nuclear Information System (INIS)
Anders, A.; Anders, S.; Brown, I.G.
1993-01-01
Time-resolved investigations of the expanded plasma of vacuum arc cathode spots are described, including the study of the ion charge state distribution, the random cathode spot motion, and the crater formation. It was found that the ion charge state distribution changes over a time scale on the order of hundreds of microseconds. For the random spot motion two time scales were observed: a very short spot residence time of tens of nanoseconds which gives, combined with the step width, the diffusion parameter of the random motion, and a longer time scale on the order of 100 μs during which the diffusion parameter changes. Crater formation studies by scanning electron microscopy indicate the occurrence of larger craters at the end of crater chains. The existence of a time scale, much longer than the elementary times for crater formation and spot residence, can be explained by local heat accumulation
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...
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......, with particular attention to those models that are appropriate at the aggregate planning level....
Time-dependent transport in interacting and noninteracting resonant-tunneling systems
DEFF Research Database (Denmark)
Jauho, Antti-Pekka; Wingreen, Ned S.; Meir, Yigal
1994-01-01
noninteracting resonant-tunneling system are presented. Due to the coherence between the leads and the resonant site, the current does not follow the driving signal adiabatically: a ''ringing'' current is found as a response to a voltage pulse, and a complex time dependence results in the case of harmonic......We consider a mesoscopic region coupled to two leads under the influence of external time-dependent voltages. The time dependence is coupled to source and drain contacts, the gates controlling the tunnel-barrier heights, or to the gates that define the mesoscopic region. We derive, with the Keldysh...... nonequilibrium-Green-function technique, a formal expression for the fully nonlinear, time-dependent current through the system. The analysis admits arbitrary interactions in the mesoscopic region, but the leads are treated as noninteracting. For proportionate coupling to the leads, the time-averaged current...
The influence of noise on nonlinear time series detection based on Volterra-Wiener-Korenberg model
Energy Technology Data Exchange (ETDEWEB)
Lei Min [State Key Laboratory of Vibration, Shock and Noise, Shanghai Jiao Tong University, Shanghai 200030 (China)], E-mail: leimin@sjtu.edu.cn; Meng Guang [State Key Laboratory of Vibration, Shock and Noise, Shanghai Jiao Tong University, Shanghai 200030 (China)
2008-04-15
This paper studies the influence of noises on Volterra-Wiener-Korenberg (VWK) nonlinear test model. Our numerical results reveal that different types of noises lead to different behavior of VWK model detection. For dynamic noise, it is difficult to distinguish chaos from nonchaotic but nonlinear determinism. For time series, measure noise has no impact on chaos determinism detection. This paper also discusses various behavior of VWK model detection with surrogate data for different noises.
Acoustic wave focusing in complex media using Nonlinear Time Reversal coded signal processing
Czech Academy of Sciences Publication Activity Database
Dos Santos, S.; Dvořáková, Zuzana; Lints, M.; Kůs, V.; Salupere, A.; Převorovský, Zdeněk
2014-01-01
Roč. 19, č. 12 (2014) ISSN 1435-4934. [European Conference on Non-Destructive Testing (ECNDT 2014) /11./. Praha, 06.10.2014-10.10.2014] Institutional support: RVO:61388998 Keywords : ultrasonic testing (UT) * signal processing * TR- NEWS * nonlinear time reversal * NDT * nonlinear acoustics Subject RIV: BI - Acoustics http://www.ndt.net/events/ECNDT2014/app/content/Slides/590_DosSantos_Rev1.pdf
Sadovnikov, A. V.; Odintsov, S. A.; Beginin, E. N.; Sheshukova, S. E.; Sharaevskii, Yu. P.; Nikitov, S. A.
2017-10-01
We demonstrate that the nonlinear spin-wave transport in two laterally parallel magnetic stripes exhibit the intensity-dependent power exchange between the adjacent spin-wave channels. By the means of Brillouin light scattering technique, we investigate collective nonlinear spin-wave dynamics in the presence of magnetodipolar coupling. The nonlinear intensity-dependent effect reveals itself in the spin-wave mode transformation and differential nonlinear spin-wave phase shift in each adjacent magnetic stripe. The proposed analytical theory, based on the coupled Ginzburg-Landau equations, predicts the geometry design involving the reduction of power requirement to the all-magnonic switching. A very good agreement between calculation and experiment was found. In addition, a micromagnetic and finite-element approach has been independently used to study the nonlinear behavior of spin waves in adjacent stripes and the nonlinear transformation of spatial profiles of spin-wave modes. Our results show that the proposed spin-wave coupling mechanism provides the basis for nonlinear magnonic circuits and opens the perspectives for all-magnonic computing architecture.
On the synchronization of neural networks containing time-varying delays and sector nonlinearity
International Nuclear Information System (INIS)
Yan, J.-J.; Lin, J.-S.; Hung, M.-L.; Liao, T.-L.
2007-01-01
We present a systematic design procedure for synchronization of neural networks subject to time-varying delays and sector nonlinearity in the control input. Based on the drive-response concept and the Lyapunov stability theorem, a memoryless decentralized control law is proposed which guarantees exponential synchronization even when input nonlinearity is present. The supplementary requirement that the time-derivative of time-varying delays must be smaller than one is released for the proposed control scheme. A four-dimensional Hopfield neural network with time-varying delays is presented as the illustrative example to demonstrate the effectiveness of the proposed synchronization scheme
The Electromagnetic Field of Elementary Time-Dependent Toroidal Sources
International Nuclear Information System (INIS)
Afanas'ev, G.N.; Stepanovskij, Yu.P.
1994-01-01
The radiation field of toroidal-like time-dependent current configurations is investigated. Time-dependent charge-current sources are found outside which the electromagnetic strengths disappear but the potentials survive. This can be used to carry out time-dependent Aharonov-Bohm-like experiments and the information transfer. Using the Neumann-Helmholtz parametrization of the current density we present the time-dependent electromagnetic field in a form convenient for applications. 17 refs
International Nuclear Information System (INIS)
Zhang, Wenchao; Tan, Sichao; Gao, Puzhen; Wang, Zhanwei; Zhang, Liansheng; Zhang, Hong
2014-01-01
Highlights: • Natural circulation flow instabilities in rolling motion are studied. • The method of non-linear time series analysis is used. • Non-linear evolution characteristic of flow instability is analyzed. • Irregular complex flow oscillations are chaotic oscillations. • The effect of rolling parameter on the threshold of chaotic oscillation is studied. - Abstract: Non-linear characteristics of natural circulation flow instabilities under rolling motion conditions were studied by the method of non-linear time series analysis. Experimental flow time series of different dimensionless power and rolling parameters were analyzed based on phase space reconstruction theory. Attractors which were reconstructed in phase space and the geometric invariants, including correlation dimension, Kolmogorov entropy and largest Lyapunov exponent, were determined. Non-linear characteristics of natural circulation flow instabilities under rolling motion conditions was studied based on the results of the geometric invariant analysis. The results indicated that the values of the geometric invariants first increase and then decrease as dimensionless power increases which indicated the non-linear characteristics of the system first enhance and then weaken. The irregular complex flow oscillation is typical chaotic oscillation because the value of geometric invariants is at maximum. The threshold of chaotic oscillation becomes larger as the rolling frequency or rolling amplitude becomes big. The main influencing factors that influence the non-linear characteristics of the natural circulation system under rolling motion are thermal driving force, flow resistance and the additional forces caused by rolling motion. The non-linear characteristics of the natural circulation system under rolling motion changes caused by the change of the feedback and coupling degree among these influencing factors when the dimensionless power or rolling parameters changes
Initial state dependence of nonlinear kinetic equations: The classical electron gas
International Nuclear Information System (INIS)
Marchetti, M.C.; Cohen, E.G.D.; Dorfman, J.R.; Kirkpatrick, T.R.
1985-01-01
The method of nonequilibrium cluster expansion is used to study the decay to equilibrium of a weakly coupled inhomogeneous electron gas prepared in a local equilibrium state at the initial time, t=0. A nonlinear kinetic equation describing the long time behavior of the one-particle distribution function is obtained. For consistency, initial correlations have to be taken into account. The resulting kinetic equation-differs from that obtained when the initial state of the system is assumed to be factorized in a product of one-particle functions. The question of to what extent correlations in the initial state play an essential role in determining the form of the kinetic equation at long times is discussed. To that end, the present calculations are compared wih results obtained before for hard sphere gases and in general with strong short-range forces. A partial answer is proposed and some open questions are indicated
Time-dependent problems in quantum-mechanical state reconstruction
International Nuclear Information System (INIS)
Leonhardt, U.; Bardroff, P. J.
1997-01-01
We study the state reconstruction of wave packets that travel in time-dependent potentials. We solve the problem for explicitly time-dependent potentials. We solve the problem for explicitly time-dependent harmonic oscillators and sketch a general adaptive technique for finding the wave function that matches and observed evolution. (authors)
International Nuclear Information System (INIS)
Kravets, E.A.; Berezhnaya, V.V.; Sakada, V.I.; Rashidov, N.M.; Grodzinskij, D.M.; Kravets, E.A.; Berezhnaya, V.V.; Sakada, V.I.; Rashidov, N.M.; Grodzinskij, D.M.
2012-01-01
The dose dependences of the aberrant anaphases in the root meristem in 48 hours after the irradiation have non-linear character and a plateau in the region about 6-8 Gy. The plateau indicates the activation of recovery processes. In the plateau range, the level of damages for this genotype is 33% for aberrant anaphases (FAA), 2.3 aberrations per aberrant anaphase (A/AC), and 0.74 aberrations for the total number of anaphases. At 10 Gy, the dose curve forms the exponential region caused by the involvement of the large number of new cells with unrepaired damages in the mutation process. The increase of A/AC to 1.1 indicate the ''criticality'' of the meristem radiation damage.
Xu, Tianhua; Shevchenko, Nikita A; Lavery, Domaniç; Semrau, Daniel; Liga, Gabriele; Alvarado, Alex; Killey, Robert I; Bayvel, Polina
2017-02-20
The relationship between modulation format and the performance of multi-channel digital back-propagation (MC-DBP) in ideal Nyquist-spaced optical communication systems is investigated. It is found that the nonlinear distortions behave independent of modulation format in the case of full-field DBP, in contrast to the cases of electronic dispersion compensation and partial-bandwidth DBP. It is shown that the minimum number of steps per span required for MC-DBP depends on the chosen modulation format. For any given target information rate, there exists a possible trade-off between modulation format and back-propagated bandwidth, which could be used to reduce the computational complexity requirement of MC-DBP.
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.
Nonlinear effects on Turing patterns: Time oscillations and chaos
Aragó n, J. L.; Barrio, R. A.; Woolley, T. E.; Baker, R. E.; Maini, P. K.
2012-01-01
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
Real-Time Trajectory Generation for Autonomous Nonlinear Flight Systems
National Research Council Canada - National Science Library
Larsen, Michael; Beard, Randal W; McLain, Timothy W
2006-01-01
... to mobile threats such as radar, jammers, and unfriendly aircraft. In Phase 1 of this STTR project, real-time path planning and trajectory generation techniques for two dimensional flight were developed and demonstrated in software simulation...
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
Time-Dependent Dust Formation in Novae
Directory of Open Access Journals (Sweden)
Kyung-Won Suh
1991-06-01
Full Text Available The dust formation processes in novae are investigated with close attention to recent infrared observations. Using mainly the classical nucleation theory, we have calculated the time scales of dust formation and growth in the environments of novae. Those time scales roughly resemble the typical observations. We have classified the dust-forming novae into three classes according to their explosion properties and the thermodynamic properties of dust grains. Oxygen grains from much later than carbon grains because of their thermodynamic properties. The effect of grain formation to the efficiency of stellar winds to drive the material outward is tested with newly obtained Planck mean values of dust grains.
Time-domain simulation and nonlinear analysis on ride performance of four-wheel vehicles
Energy Technology Data Exchange (ETDEWEB)
Wang, Y S; He, H; Geng, A L [School of Automobile and Traffic Engineering, Liaoning University of Technology, Jinzhou 121001 (China)], E-mail: jzwbt@163.com
2008-02-15
A nonlinear dynamic model with eight DOFs of a four-wheel vehicle is established in this paper. After detaching the nonlinear characteristics of the leaf springs and shock absorbers, the multi-step linearizing method is used to simulate the vehicle vibration in time domain, under a correlated four-wheel road roughness model. Experimental verifications suggest that the newly built vehicle model and simulation procedure are reasonable and feasible to be used in vehicle vibration analysis. Furthermore, some nonlinear factors of the leaf springs and shock absorbers, which affect the vehicle ride performance (or comfort), are investigated under different vehicle running speeds. Some substaintial rules of the nonlinear vehicle vibrations are revealed in this paper.
Time-domain simulation and nonlinear analysis on ride performance of four-wheel vehicles
International Nuclear Information System (INIS)
Wang, Y S; He, H; Geng, A L
2008-01-01
A nonlinear dynamic model with eight DOFs of a four-wheel vehicle is established in this paper. After detaching the nonlinear characteristics of the leaf springs and shock absorbers, the multi-step linearizing method is used to simulate the vehicle vibration in time domain, under a correlated four-wheel road roughness model. Experimental verifications suggest that the newly built vehicle model and simulation procedure are reasonable and feasible to be used in vehicle vibration analysis. Furthermore, some nonlinear factors of the leaf springs and shock absorbers, which affect the vehicle ride performance (or comfort), are investigated under different vehicle running speeds. Some substaintial rules of the nonlinear vehicle vibrations are revealed in this paper
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).
Large-time asymptotic behaviour of solutions of non-linear Sobolev-type equations
International Nuclear Information System (INIS)
Kaikina, Elena I; Naumkin, Pavel I; Shishmarev, Il'ya A
2009-01-01
The large-time asymptotic behaviour of solutions of the Cauchy problem is investigated for a non-linear Sobolev-type equation with dissipation. For small initial data the approach taken is based on a detailed analysis of the Green's function of the linear problem and the use of the contraction mapping method. The case of large initial data is also closely considered. In the supercritical case the asymptotic formulae are quasi-linear. The asymptotic behaviour of solutions of a non-linear Sobolev-type equation with a critical non-linearity of the non-convective kind differs by a logarithmic correction term from the behaviour of solutions of the corresponding linear equation. For a critical convective non-linearity, as well as for a subcritical non-convective non-linearity it is proved that the leading term of the asymptotic expression for large times is a self-similar solution. For Sobolev equations with convective non-linearity the asymptotic behaviour of solutions in the subcritical case is the product of a rarefaction wave and a shock wave. Bibliography: 84 titles.
High mitogenomic evolutionary rates and time dependency.
Subramanian, S.; Denver, D.R.; Millar, C.D.; Heupink, T.; Aschrafi, A.; Emslie, S.D.; Baroni, C.; Lambert, D.M.
2009-01-01
Using entire modern and ancient mitochondrial genomes of Adelie penguins (Pygoscelis adeliae) that are up to 44000 years old, we show that the rates of evolution of the mitochondrial genome are two to six times greater than those estimated from phylogenetic comparisons. Although the rate of
Williams, G Jackson; Lee, Sooheyong; Walko, Donald A; Watson, Michael A; Jo, Wonhuyk; Lee, Dong Ryeol; Landahl, Eric C
2016-12-22
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.
Symmetries and Invariants of the Time-dependent Oscillator Equation and the Envelope Equation
Qin, Hong
2005-01-01
Single-particle dynamics in a time-dependent focusing field is examined. The existence of the Courant-Snyder invariant* is fundamentally the result of the corresponding symmetry admitted by the oscillator equation with time-dependent frequency.** A careful analysis of the admitted symmetries reveals a deeper connection between the nonlinear envelope equation and the oscillator equation. A general theorem regarding the symmetries and invariants of the envelope equation, which includes the existence of the Courant-Snyder invariant as a special case, is demonstrated. The symmetries of the envelope equation enable a fast algorithm for finding matched solutions without using the conventional iterative shooting method.
Energy Technology Data Exchange (ETDEWEB)
Lasuik, J.; Shalchi, A., E-mail: andreasm4@yahoo.com [Department of Physics and Astronomy, University of Manitoba, Winnipeg, MB R3T 2N2 (Canada)
2017-09-20
Recently, a new theory for the transport of energetic particles across a mean magnetic field was presented. Compared to other nonlinear theories the new approach has the advantage that it provides a full time-dependent description of the transport. Furthermore, a diffusion approximation is no longer part of that theory. The purpose of this paper is to combine this new approach with a time-dependent model for parallel transport and different turbulence configurations in order to explore the parameter regimes for which we get ballistic transport, compound subdiffusion, and normal Markovian diffusion.
Singular perturbation methods for nonlinear dynamic systems with time delays
International Nuclear Information System (INIS)
Hu, H.Y.; Wang, Z.H.
2009-01-01
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-domain Green's Function Method for three-dimensional nonlinear subsonic flows
Tseng, K.; Morino, L.
1978-01-01
The Green's Function Method for linearized 3D unsteady potential flow (embedded in the computer code SOUSSA P) is extended to include the time-domain analysis as well as the nonlinear term retained in the transonic small disturbance equation. The differential-delay equations in time, as obtained by applying the Green's Function Method (in a generalized sense) and the finite-element technique to the transonic equation, are solved directly in the time domain. Comparisons are made with both linearized frequency-domain calculations and existing nonlinear results.
Simulating time-dependent energy transfer between crossed laser beams in an expanding plasma
International Nuclear Information System (INIS)
Hittinger, J.A.F.; Dorr, M.R.; Berger, R.L.; Williams, E.A.
2005-01-01
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
Temporal motifs in time-dependent networks
International Nuclear Information System (INIS)
Kovanen, Lauri; Karsai, Márton; Kaski, Kimmo; Kertész, János; Saramäki, Jari
2011-01-01
Temporal networks are commonly used to represent systems where connections between elements are active only for restricted periods of time, such as telecommunication, neural signal processing, biochemical reaction and human social interaction networks. We introduce the framework of temporal motifs to study the mesoscale topological–temporal structure of temporal networks in which the events of nodes do not overlap in time. Temporal motifs are classes of similar event sequences, where the similarity refers not only to topology but also to the temporal order of the events. We provide a mapping from event sequences to coloured directed graphs that enables an efficient algorithm for identifying temporal motifs. We discuss some aspects of temporal motifs, including causality and null models, and present basic statistics of temporal motifs in a large mobile call network
Tests for nonlinearity in short stationary time series
International Nuclear Information System (INIS)
Chang, T.; Sauer, T.; Schiff, S.J.
1995-01-01
To compare direct tests for detecting determinism in chaotic time series, data from Henon, Lorenz, and Mackey--Glass equations were contaminated with various levels of additive colored noise. These data were analyzed with a variety of recently developed tests for determinism, and the results compared
A Generalized Time-Dependent Harmonic Oscillator at Finite Temperature
International Nuclear Information System (INIS)
Majima, H.; Suzuki, A.
2006-01-01
We show how a generalized time-dependent harmonic oscillator (GTHO) is extended to a finite temperature case by using thermo field dynamics (TFD). We derive the general time-dependent annihilation and creation operators for the system, and obtain the time-dependent quasiparticle annihilation and creation operators for the GTHO by using the temperature-dependent Bogoliubov transformation of TFD. We also obtain the thermal state as a two-mode squeezed vacuum state in the time-dependent case as well as in the time-independent case. The general formula is derived to calculate the thermal expectation value of operators
Fuzzy Control Model and Simulation for Nonlinear Supply Chain System with Lead Times
Directory of Open Access Journals (Sweden)
Songtao Zhang
2017-01-01
Full Text Available A new fuzzy robust control strategy for the nonlinear supply chain system in the presence of lead times is proposed. Based on Takagi-Sugeno fuzzy control system, the fuzzy control model of the nonlinear supply chain system with lead times is constructed. Additionally, we design a fuzzy robust H∞ control strategy taking the definition of maximal overlapped-rules group into consideration to restrain the impacts such as those caused by lead times, switching actions among submodels, and customers’ stochastic demands. This control strategy can not only guarantee that the nonlinear supply chain system is robustly asymptotically stable but also realize soft switching among subsystems of the nonlinear supply chain to make the less fluctuation of the system variables by introducing the membership function of fuzzy system. The comparisons between the proposed fuzzy robust H∞ control strategy and the robust H∞ control strategy are finally illustrated through numerical simulations on a two-stage nonlinear supply chain with lead times.
Chaotification of vibration isolation floating raft system via nonlinear time-delay feedback control
International Nuclear Information System (INIS)
Zhang Jing; Xu Daolin; Zhou Jiaxi; Li Yingli
2012-01-01
Highlights: ► A chaotification method based on nonlinear time-delay feedback control is present. ► An analytical function of nonlinear time-delay feedback control is derived. ► A large range of parametric domain for chaotification is obtained. ► The approach allows using small control gain. ► Design of chaotification becomes a standard process without uncertainty. - Abstract: This paper presents a chaotification method based on nonlinear time-delay feedback control for a two-dimensional vibration isolation floating raft system (VIFRS). An analytical function of nonlinear time-delay feedback control is derived. This approach can theoretically provide a systematic design of chaotification for nonlinear VIFRS and completely avoid blind and inefficient numerical search on the basis of trials and errors. Numerical simulations show that with a proper setting of control parameters the method holds the favorable aspects including the capability of chaotifying across a large range of parametric domain, the advantage of using small control and the flexibility of designing control feedback forms. The effects on chaotification performance are discussed in association with the configuration of the control parameters.
A Time Marching Scheme for Solving Volume Integral Equations on Nonlinear Scatterers
Bagci, Hakan
2015-01-01
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
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
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.
Chaos in Electronic Circuits: Nonlinear Time Series Analysis
Energy Technology Data Exchange (ETDEWEB)
Wheat, Jr., Robert M. [Kennedy Western Univ., Cheyenne, WY (United States)
2003-07-01
Chaos in electronic circuits is a phenomenon that has been largely ignored by engineers, manufacturers, and researchers until the early 1990’s and the work of Chua, Matsumoto, and others. As the world becomes more dependent on electronic devices, the detrimental effects of non-normal operation of these devices becomes more significant. Developing a better understanding of the mechanisms involved in the chaotic behavior of electronic circuits is a logical step toward the prediction and prevention of any potentially catastrophic occurrence of this phenomenon. Also, a better understanding of chaotic behavior, in a general sense, could potentially lead to better accuracy in the prediction of natural events such as weather, volcanic activity, and earthquakes. As a first step in this improvement of understanding, and as part of the research being reported here, methods of computer modeling, identifying and analyzing, and producing chaotic behavior in simple electronic circuits have been developed. The computer models were developed using both the Alternative Transient Program (ATP) and Spice, the analysis techniques have been implemented using the C and C++ programming languages, and the chaotically behaving circuits developed using “off the shelf” electronic components.
DEFF Research Database (Denmark)
Tabatabaeipour, Mojtaba; Blanke, Mogens
2014-01-01
of a system. It must be guaranteed that the trajectory of a system subject to fault remains in the region of attraction (ROA) of the post-fault system during this time. This paper proposes a new algorithm to compute the critical fault recovery time for nonlinear systems with polynomial vector elds using sum...
Detecting nonlinearity in time series driven by non-Gaussian noise: the case of river flows
Directory of Open Access Journals (Sweden)
F. Laio
2004-01-01
Full Text Available Several methods exist for the detection of nonlinearity in univariate time series. In the present work we consider riverflow time series to infer the dynamical characteristics of the rainfall-runoff transformation. It is shown that the non-Gaussian nature of the driving force (rainfall can distort the results of such methods, in particular when surrogate data techniques are used. Deterministic versus stochastic (DVS plots, conditionally applied to the decay phases of the time series, are instead proved to be a suitable tool to detect nonlinearity in processes driven by non-Gaussian (Poissonian noise. An application to daily discharges from three Italian rivers provides important clues to the presence of nonlinearity in the rainfall-runoff transformation.
International Nuclear Information System (INIS)
Tang You-Fu; Liu Shu-Lin; Jiang Rui-Hong; Liu Ying-Hui
2013-01-01
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
A unified nonlinear stochastic time series analysis for climate science.
Moon, Woosok; Wettlaufer, John S
2017-03-13
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.
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
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
Zhang, Shuo; Uecker, Martin; Voit, Dirk; Merboldt, Klaus-Dietmar; Frahm, Jens
2010-07-08
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. 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. 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 degrees 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. Though awaiting thorough clinical evaluation, this work describes a robust and flexible acquisition and reconstruction technique for
Nonlinearities, scale-dependence, and individualism of boreal forest trees to climate forcing
Wolken, J. M.; Mann, D. H.; Grant, T. A., III; Lloyd, A. H.; Hollingsworth, T. N.
2013-12-01
Our understanding of the climate-growth relationships of trees are complicated by the nonlinearity and variability of these responses through space and time. Furthermore, trees growing at the same site may exhibit opposing growth responses to climate, a phenomenon termed growth divergence. To date the majority of dendrochronological studies in Interior Alaska have involved white spruce growing at treeline, even though black spruce is the most abundant tree species. Although changing climate-growth relationships have been observed in black spruce, there is little known about the multivariate responses of individual trees to temperature and precipitation and whether or not black spruce exhibits growth divergences similar to those documented for white spruce. To evaluate the occurrence of growth divergences in black spruce, we collected cores from trees growing on a steep, north-facing toposequence having a gradient in environmental parameters. Our overall goal was to assess how the climate-growth relationships of black spruce change over space and time. Specifically, we evaluated how topography influences the climate-growth relationships of black spruce and if the growth responses to climate are homogeneous. At the site-level most trees responded negatively to temperature and positively to precipitation, while at the tree-level black spruce exhibited heterogenous growth responses to climate that varied in both space (i.e., between sites) and time (i.e., seasonally and annually). There was a dominant response-type at each site, but there was also considerable variability in the proportion of trees exhibiting each response-type combination. Even in a climatically extreme setting like Alaska's boreal forest, tree responses to climate variability are spatially and temporally complex, as well as highly nonlinear.
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.
International Nuclear Information System (INIS)
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
Global format for energy-momentum based time integration in nonlinear dynamics
DEFF Research Database (Denmark)
Krenk, Steen
2014-01-01
A global format is developed for momentum and energy consistent time integration of second‐order dynamic systems with general nonlinear stiffness. The algorithm is formulated by integrating the state‐space equations of motion over the time increment. The internal force is first represented...... of mean value products at the element level or explicit use of a geometric stiffness matrix. An optional monotonic algorithmic damping, increasing with response frequency, is developed in terms of a single damping parameter. In the solution procedure, the velocity is eliminated and the nonlinear...
Comparison of modal spectral and non-linear time history analysis of a piping system
International Nuclear Information System (INIS)
Gerard, R.; Aelbrecht, D.; Lafaille, J.P.
1987-01-01
A typical piping system of the discharge line of the chemical and volumetric control system, outside the containment, between the penetration and the heat exchanger, an operating power plant was analyzed using four different methods: Modal spectral analysis with 2% constant damping, modal spectral analysis using ASME Code Case N411 (PVRC damping), linear time history analysis, non-linear time history analysis. This paper presents an estimation of the conservatism of the linear methods compared to the non-linear analysis. (orig./HP)
On the time-dependent Aharonov–Bohm effect
Directory of Open Access Journals (Sweden)
Jian Jing
2017-11-01
Full Text Available The Aharonov–Bohm effect in the background of a time-dependent vector potential is re-examined for both non-relativistic and relativistic cases. Based on the solutions to the Schrodinger and Dirac equations which contain the time-dependent magnetic vector potential, we find that contrary to the conclusions in a recent paper (Singleton and Vagenas 2013 [4], the interference pattern will be altered with respect to time because of the time-dependent vector potential.
Fully probabilistic control for stochastic nonlinear control systems with input dependent noise.
Herzallah, Randa
2015-03-01
Robust controllers for nonlinear stochastic systems with functional uncertainties can be consistently designed using probabilistic control methods. In this paper a generalised probabilistic controller design for the minimisation of the Kullback-Leibler divergence between the actual joint probability density function (pdf) of the closed loop control system, and an ideal joint pdf is presented emphasising how the uncertainty can be systematically incorporated in the absence of reliable systems models. To achieve this objective all probabilistic models of the system are estimated from process data using mixture density networks (MDNs) where all the parameters of the estimated pdfs are taken to be state and control input dependent. Based on this dependency of the density parameters on the input values, explicit formulations to the construction of optimal generalised probabilistic controllers are obtained through the techniques of dynamic programming and adaptive critic methods. Using the proposed generalised probabilistic controller, the conditional joint pdfs can be made to follow the ideal ones. A simulation example is used to demonstrate the implementation of the algorithm and encouraging results are obtained. Copyright © 2014 Elsevier Ltd. All rights reserved.
History-dependent nonlinear dissipation in superfluid 3He-A
International Nuclear Information System (INIS)
Gay, R.; Bagley, M.; Hook, J.R.; Sandiford, D.J.; Hall, H.E.
1983-01-01
We have studied nonlinear dissipation in oscillatory flow of 3 He-A through 49-μm- and 17-μm-wide channels by means of torsion pendulum experiments at about 50 Hz. The observed effects are strongly history dependent; the dissipation at a given measuring amplitude is strongly increased if the sample is cooled through T/sub c/ while oscillating at large amplitude. Once a highly dissipative state has been created it does not noticeably decay below T/sub c/, though a more dissipative state can be created below T/sub c/ by a period of sufficiently large-amplitude oscillation. The results are described semiquantitatively by a model based on the idea of superflow collapse by motion of the l vector, with consequent orbital dissipation. The history dependence is introduced into this model by postulating the existence of surface singularities in the l texture, the density of which is determined by the previous history of the helium
Weakly intrusive low-rank approximation method for nonlinear parameter-dependent equations
Giraldi, Loic; Nouy, Anthony
2017-01-01
This paper presents a weakly intrusive strategy for computing a low-rank approximation of the solution of a system of nonlinear parameter-dependent equations. The proposed strategy relies on a Newton-like iterative solver which only requires evaluations of the residual of the parameter-dependent equation and of a preconditioner (such as the differential of the residual) for instances of the parameters independently. The algorithm provides an approximation of the set of solutions associated with a possibly large number of instances of the parameters, with a computational complexity which can be orders of magnitude lower than when using the same Newton-like solver for all instances of the parameters. The reduction of complexity requires efficient strategies for obtaining low-rank approximations of the residual, of the preconditioner, and of the increment at each iteration of the algorithm. For the approximation of the residual and the preconditioner, weakly intrusive variants of the empirical interpolation method are introduced, which require evaluations of entries of the residual and the preconditioner. Then, an approximation of the increment is obtained by using a greedy algorithm for low-rank approximation, and a low-rank approximation of the iterate is finally obtained by using a truncated singular value decomposition. When the preconditioner is the differential of the residual, the proposed algorithm is interpreted as an inexact Newton solver for which a detailed convergence analysis is provided. Numerical examples illustrate the efficiency of the method.
Weakly intrusive low-rank approximation method for nonlinear parameter-dependent equations
Giraldi, Loic
2017-06-30
This paper presents a weakly intrusive strategy for computing a low-rank approximation of the solution of a system of nonlinear parameter-dependent equations. The proposed strategy relies on a Newton-like iterative solver which only requires evaluations of the residual of the parameter-dependent equation and of a preconditioner (such as the differential of the residual) for instances of the parameters independently. The algorithm provides an approximation of the set of solutions associated with a possibly large number of instances of the parameters, with a computational complexity which can be orders of magnitude lower than when using the same Newton-like solver for all instances of the parameters. The reduction of complexity requires efficient strategies for obtaining low-rank approximations of the residual, of the preconditioner, and of the increment at each iteration of the algorithm. For the approximation of the residual and the preconditioner, weakly intrusive variants of the empirical interpolation method are introduced, which require evaluations of entries of the residual and the preconditioner. Then, an approximation of the increment is obtained by using a greedy algorithm for low-rank approximation, and a low-rank approximation of the iterate is finally obtained by using a truncated singular value decomposition. When the preconditioner is the differential of the residual, the proposed algorithm is interpreted as an inexact Newton solver for which a detailed convergence analysis is provided. Numerical examples illustrate the efficiency of the method.
Time-dependent theoretical treatments of the dynamics of electrons and nuclei in molecular systems
International Nuclear Information System (INIS)
Deumens, E.; Diz, A.; Longo, R.; Oehrn, Y.
1994-01-01
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
Altitude dependent neutral wind effects on the nonlinear motion of a small barium cloud
International Nuclear Information System (INIS)
Book, D.L.; Ossakow, S.L.; Goldman, S.R.
1975-01-01
The nonlinear motion of a small F region barium release electrostatically coupled to the E region is studied in the presence of a neutral wind with differing values for the E and F regions. In a reference frame moving with the E region neutral wind and F region neutral wind transverse to the background E 0 field is shown to retard or accelerate the evolution of the cloud without otherwise altering the development of the system. When the relative neutral wind has a component parallel to the background E 0 field, there is also a change in the direction of the axis of elongation of the cloud as a function of time, although the final direction is independent of the relative neutral wind. Barium cloud and image behavior are shown to be substantially identical for periodic and Dirichlet boundary conditions
Timing analysis of safety properties using fault trees with time dependencies and timed state-charts
International Nuclear Information System (INIS)
Magott, Jan; Skrobanek, Pawel
2012-01-01
Behavior in time domain is often crucial for safety critical systems. Standard fault trees cannot express time-dependent behavior. In the paper, timing analysis of safety properties using fault trees with time dependencies (FTTDs) and timed state-charts is presented. A new version of timed state-charts (TSCs) is also proposed. These state-charts can model the dynamics of technical systems, e.g. controllers, controlled objects, and people. In TSCs, activity and communication times are represented by time intervals. In the proposed approach the structure of FTTD is fixed by a human. Time properties of events and gates of FTTD are expressed by time intervals, and are calculated using TSCs. The minimal and maximal values of these time intervals of FTTD can be calculated by finding paths with minimal and maximal time lengths in TSCs, which is an NP-hard problem. In order to reduce the practical complexity of computing the FTTD time parameters, some reductions of TSCs are defined in the paper, such as sequential, alternative, loop (iteration), and parallel. Some of the reductions are intuitive, in case of others—theorems are required. Computational complexity of each reduction is not greater than linear in the size of reduced TSC. Therefore, the obtained results enable decreasing of the costs of FTTD time parameters calculation when system dynamics is expressed by TSCs. Case study of a railroad crossing with a controller that controls semaphores, gate, light-audio signal close to the gate will be analyzed.
Propagators for the time-dependent Kohn-Sham equations
International Nuclear Information System (INIS)
Castro, Alberto; Marques, Miguel A. L.; Rubio, Angel
2004-01-01
In this paper we address the problem of the numerical integration of the time-dependent Schroedinger equation i∂ t φ=Hφ. In particular, we are concerned with the important case where H is the self-consistent Kohn-Sham Hamiltonian that stems from time-dependent functional theory. As the Kohn-Sham potential depends parametrically on the time-dependent density, H is in general time dependent, even in the absence of an external time-dependent field. The present analysis also holds for the description of the excited state dynamics of a many-electron system under the influence of arbitrary external time-dependent electromagnetic fields. Our discussion is separated in two parts: (i) First, we look at several algorithms to approximate exp(A), where A is a time-independent operator [e.g., A=-iΔtH(τ) for some given time τ]. In particular, polynomial expansions, projection in Krylov subspaces, and split-operator methods are investigated. (ii) We then discuss different approximations for the time-evolution operator, such as the midpoint and implicit rules, and Magnus expansions. Split-operator techniques can also be modified to approximate the full time-dependent propagator. As the Hamiltonian is time dependent, problem (ii) is not equivalent to (i). All these techniques have been implemented and tested in our computer code OCTOPUS, but can be of general use in other frameworks and implementations
Modified multiple time scale method for solving strongly nonlinear damped forced vibration systems
Razzak, M. A.; Alam, M. Z.; Sharif, M. N.
2018-03-01
In this paper, modified multiple time scale (MTS) method is employed to solve strongly nonlinear forced vibration systems. The first-order approximation is only considered in order to avoid complexicity. The formulations and the determination of the solution procedure are very easy and straightforward. The classical multiple time scale (MS) and multiple scales Lindstedt-Poincare method (MSLP) do not give desire result for the strongly damped forced vibration systems with strong damping effects. The main aim of this paper is to remove these limitations. Two examples are considered to illustrate the effectiveness and convenience of the present procedure. The approximate external frequencies and the corresponding approximate solutions are determined by the present method. The results give good coincidence with corresponding numerical solution (considered to be exact) and also provide better result than other existing results. For weak nonlinearities with weak damping effect, the absolute relative error measures (first-order approximate external frequency) in this paper is only 0.07% when amplitude A = 1.5 , while the relative error gives MSLP method is surprisingly 28.81%. Furthermore, for strong nonlinearities with strong damping effect, the absolute relative error found in this article is only 0.02%, whereas the relative error obtained by MSLP method is 24.18%. Therefore, the present method is not only valid for weakly nonlinear damped forced systems, but also gives better result for strongly nonlinear systems with both small and strong damping effect.
Energy Technology Data Exchange (ETDEWEB)
Solookinejad, G., E-mail: ghsolooki@gmail.com
2016-09-15
In this study, the linear and nonlinear susceptibility of a single-layer graphene nanostructure driven by a weak probe light and an elliptical polarized coupling field is discussed theoretically. The Landau levels of graphene can be separated in infrared or terahertz regions under the strong magnetic field. Therefore, by using the density matrix formalism in quantum optic, the linear and nonlinear susceptibility of the medium can be derived. It is demonstrated that by adjusting the elliptical parameter, one can manipulate the linear and nonlinear absorption as well as Kerr nonlinearity of the medium. It is realized that the enhanced Kerr nonlinearity can be possible with zero linear absorption and nonlinear amplification at some values of elliptical parameter. Our results may be having potential applications in quantum information science based on Nano scales devices.
Wave Functions for Time-Dependent Dirac Equation under GUP
Zhang, Meng-Yao; Long, Chao-Yun; Long, Zheng-Wen
2018-04-01
In this work, the time-dependent Dirac equation is investigated under generalized uncertainty principle (GUP) framework. It is possible to construct the exact solutions of Dirac equation when the time-dependent potentials satisfied the proper conditions. In (1+1) dimensions, the analytical wave functions of the Dirac equation under GUP have been obtained for the two kinds time-dependent potentials. Supported by the National Natural Science Foundation of China under Grant No. 11565009
Prospects for time-dependent asymmetries at LHCb
INSPIRE-00260500
2012-01-01
LHCb is already providing leading measurements of time-dependent CP asymmetries with 1 fb$^{-1}$ of data. With the LHCb detector, and further one with the LHCb upgrade, very high-precision time-dependent CP measurements are expected to stringently test the CKM paradigm and to the search for possible small NP effects. A review of the current precision and the prospects for these time-dependent quantities with the LHCb and LHCb upgraded detectors are summarised in this paper.
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
DEFF Research Database (Denmark)
Backi, Christoph Josef; Bendtsen, Jan Dimon; Leth, John-Josef
2014-01-01
In this work the stability properties of a nonlinear partial differential equation (PDE) with state–dependent parameters is investigated. Among other things, the PDE describes freezing of foodstuff, and is closely related to the (Potential) Burgers’ Equation. We show that for certain forms of coe...
Zhang, Kemei; Zhao, Cong-Ran; Xie, Xue-Jun
2015-12-01
This paper considers the problem of output feedback stabilisation for stochastic high-order feedforward nonlinear systems with time-varying delay. By using the homogeneous domination theory and solving several troublesome obstacles in the design and analysis, an output feedback controller is constructed to drive the closed-loop system globally asymptotically stable in probability.
Gain scheduling for non-linear time-delay systems using approximated model
Pham, H.T.; Lim, J.T
2012-01-01
The authors investigate a regulation problem of non-linear systems driven by an exogenous signal and time-delay in the input. In order to compensate for the input delay, they propose a reduction transformation containing the past information of the control input. Then, by utilising the Euler
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...
Directory of Open Access Journals (Sweden)
Il Young Song
2015-01-01
Full Text Available This paper focuses on estimation of a nonlinear function of state vector (NFS in discrete-time linear systems with time-delays and model uncertainties. The NFS represents a multivariate nonlinear function of state variables, which can indicate useful information of a target system for control. The optimal nonlinear estimator of an NFS (in mean square sense represents a function of the receding horizon estimate and its error covariance. The proposed receding horizon filter represents the standard Kalman filter with time-delays and special initial horizon conditions described by the Lyapunov-like equations. In general case to calculate an optimal estimator of an NFS we propose using the unscented transformation. Important class of polynomial NFS is considered in detail. In the case of polynomial NFS an optimal estimator has a closed-form computational procedure. The subsequent application of the proposed receding horizon filter and nonlinear estimator to a linear stochastic system with time-delays and uncertainties demonstrates their effectiveness.
A sampling approach to constructing Lyapunov functions for nonlinear continuous–time systems
Bobiti, R.V.; Lazar, M.
2016-01-01
The problem of constructing a Lyapunov function for continuous-time nonlinear dynamical systems is tackled in this paper via a sampling-based approach. The main idea of the sampling-based method is to verify a Lyapunov-type inequality for a finite number of points (known state vectors) in the
Inverse chaos synchronization in linearly and nonlinearly coupled systems with multiple time-delays
International Nuclear Information System (INIS)
Shahverdiev, E.M.; Hashimov, R.H.; Nuriev, R.A.; Hashimova, L.H.; Huseynova, E.M.; Shore, K.A.
2005-04-01
We report on inverse chaos synchronization between two unidirectionally linearly and nonlinearly coupled chaotic systems with multiple time-delays and find the existence and stability conditions for different synchronization regimes. We also study the effect of parameter mismatches on synchonization regimes. The method is tested on the famous Ikeda model. Numerical simulations fully support the analytical approach. (author)
Long-Time Asymptotics for the Korteweg-de Vries Equation via Nonlinear Steepest Descent
International Nuclear Information System (INIS)
Grunert, Katrin; Teschl, Gerald
2009-01-01
We apply the method of nonlinear steepest descent to compute the long-time asymptotics of the Korteweg-de Vries equation for decaying initial data in the soliton and similarity region. This paper can be viewed as an expository introduction to this method
Non-linear wave loads and ship responses by a time-domain strip theory
DEFF Research Database (Denmark)
Xia, Jinzhu; Wang, Zhaohui; Jensen, Jørgen Juncher
1998-01-01
. Based on this time-domain strip theory, an efficient non-linear hydroelastic method of wave- and slamming-induced vertical motions and structural responses of ships is developed, where the structure is represented as a Timoshenko beam. Numerical calculations are presented for the S175 Containership...
Non-Linear Wave Loads and Ship responses by a time-domain Strip Theory
DEFF Research Database (Denmark)
Xia, Jinzhu; Wang, Zhaohui; Jensen, Jørgen Juncher
1998-01-01
. Based on this time-domain strip theory, an efficient non-linear hyroelastic method of wave- and slamming-induced vertical motions and structural responses of ships is developed, where the structure is represented by the Timoshenko beam theory. Numerical calculations are presented for the S175...
Direct Adaptive Control of a Class of Nonlinear Discrete-Time Systems
DEFF Research Database (Denmark)
Bendtsen, Jan Dimon
2004-01-01
In this paper we deal with direct adaptive control of a specific class of discrete-time SISO systems, where the nonlinearities are convex and an upper bound is known. We use a control law based on a linear combination of a set of globally uniformly bounded basis functions with compact support, wh...
Intensity-dependent nonlinear optical properties in a modulation-doped single quantum well
International Nuclear Information System (INIS)
Ungan, F.
2011-01-01
In the present work, the changes in the intersubband optical absorption coefficients and the refractive index in a modulation-doped quantum well have been investigated theoretically. Within the envelope function approach and the effective mass approximation, the electronic structure of the quantum well is calculated from the self-consistent numerical solution of the coupled Schroedinger-Poisson equations. The analytical expressions of optical properties are obtained by using the compact density-matrix approach. The numerical results GaAs/Al x Ga 1-x As are presented for typical modulation-doped quantum well system. The linear, third-order nonlinear and total absorption and refractive index changes depending on the doping concentration are investigated as a function of the incident optical intensity and structure parameters, such as quantum well width and stoichiometric ratio. The results show that the doping concentration, the structure parameters and the incident optical intensity have a great effect on the optical characteristics of these structures. - Highlights: → The doping concentration has a great effect on the optical characteristics of these structures. → The structure parameters have a great effect on the optical properties of these structures. → The total absorption coefficients reduced as the incident optical intensity increases. → The RICs reduced as the incident optical intensity increases.
International Nuclear Information System (INIS)
Yuece, Cem
2003-01-01
In this paper, the problem of the charged harmonic plus an inverse harmonic oscillator with time-dependent mass and frequency in a time-dependent electromagnetic field is investigated. It is reduced to the problem of the inverse harmonic oscillator with time-independent parameters and the exact wave function is obtained
International Nuclear Information System (INIS)
Raza, K.S.M.
2004-01-01
This paper demonstrates that if a complicated nonlinear, non-square, state-coupled multi variable system is smartly linearized and subjected to a thorough stability analysis then we can achieve our design objectives via a controller which will be quite simple (in term of resource usage and execution time) and very efficient (in terms of robustness). Further the aim is to implement this controller via computer in a real time environment. Therefore first a nonlinear mathematical model of the system is achieved. An intelligent work is done to decouple the multivariable system. Linearization and stability analysis techniques are employed for the development of a linearized and mathematically sound control law. Nonlinearities like the saturation in actuators are also been catered. The controller is then discretized using Runge-Kutta integration. Finally the discretized control law is programmed in a computer in a real time environment. The programme is done in RT -Linux using GNU C for the real time realization of the control scheme. The real time processes, like sampling and controlled actuation, and the non real time processes, like graphical user interface and display, are programmed as different tasks. The issue of inter process communication, between real time and non real time task is addressed quite carefully. The results of this research pursuit are presented graphically. (author)
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, the ...... present a computational comparison of time-adaptive and a priori route choices, pointing out the effect of travel time and cost distributions. The reported results show that, under realistic distributions, our solution methods are effective.......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...
On quantization of systems with couplings depending on time
International Nuclear Information System (INIS)
Gadzhiev, S.A.; Dzhafarov, R.K.
1990-01-01
Two main moments, on which the Gitman T yutin quantization is based: formal introduction of pulse, conjugated time and postulate of special nonunitary time dependence of the Schroeinger operators, have been interpreted. 4 refs
The accuracy of time dependent transport equation ergodic approximation
International Nuclear Information System (INIS)
Stancic, V.
1995-01-01
In order to predict the accuracy of the ergodic approximation for solving the time dependent transport equation, a comparison with respect to multiple collision and time finite difference methods, has been considered. (author)
Institute of Scientific and Technical Information of China (English)
Jing Lv; Rui-yang Yuan; Hui Yan
2014-01-01
For multi-photon processed with the linear dispersion in the high-intensity terahertz(THz) field,we have systematically investigated the temperature-dependent nonlinear optical response of graphene-based systems, including single layer graphene, graphene superlattice and gapped graphene. In the intrinsic single layer graphene system, it demonstrates that, at low temperature, nonlinear optical conductivities of the thirdand fifth-order are respectively five and ten orders of magnitude larger than the universal conductivity with high-intensity and low frequency THz wave.In the graphene superlattice and gapped graphene systems, the optical responses enhanced because of the anisotropic massless and massive Dirac fermions.
Stability of Nonlinear Systems with Unknown Time-varying Feedback Delay
Chunodkar, Apurva A.; Akella, Maruthi R.
2013-12-01
This paper considers the problem of stabilizing a class of nonlinear systems with unknown bounded delayed feedback wherein the time-varying delay is 1) piecewise constant 2) continuous with a bounded rate. We also consider application of these results to the stabilization of rigid-body attitude dynamics. In the first case, the time-delay in feedback is modeled specifically as a switch among an arbitrarily large set of unknown constant values with a known strict upper bound. The feedback is a linear function of the delayed states. In the case of linear systems with switched delay feedback, a new sufficiency condition for average dwell time result is presented using a complete type Lyapunov-Krasovskii (L-K) functional approach. Further, the corresponding switched system with nonlinear perturbations is proven to be exponentially stable inside a well characterized region of attraction for an appropriately chosen average dwell time. In the second case, the concept of the complete type L-K functional is extended to a class of nonlinear time-delay systems with unknown time-varying time-delay. This extension ensures stability robustness to time-delay in the control design for all values of time-delay less than the known upper bound. Model-transformation is used in order to partition the nonlinear system into a nominal linear part that is exponentially stable with a bounded perturbation. We obtain sufficient conditions which ensure exponential stability inside a region of attraction estimate. A constructive method to evaluate the sufficient conditions is presented together with comparison with the corresponding constant and piecewise constant delay. Numerical simulations are performed to illustrate the theoretical results of this paper.
Time-dependent behavior of positrons in noble gases
International Nuclear Information System (INIS)
Wadehra, J.M.
1990-01-01
Both equilibrium and nonequilibrium behaviors of positrons in several noble gases are reviewed. Our novel procedure for obtaining the time-dependent behavior of various swarm parameters -- such as the positron drift velocity, average positron energy, positron annihilation rate (or equivalently Z eff ) etc. -- for positrons in pure ambient gases subjected to external electrostatic fields is described. Summaries of time-dependent as well as electric field-dependent results for positron swarms in various noble gases are presented. New time-dependent results for positron swarms in neon are also described in detail. 36 refs., 4 figs., 3 tabs
Coherent states for certain time-dependent systems
International Nuclear Information System (INIS)
Pedrosa, I.A.
1989-01-01
Hartley and Ray have constructed and studied coherent states for the time-dependent oscillator. Here we show how to construct states for more general time-dependent systems. We also show that these states are equivalent to the well-known squeezed states. (author) [pt
Energy Technology Data Exchange (ETDEWEB)
Azadi, Mohammad [Sharif University of Technology, Tehran (Iran, Islamic Republic of); Azadi, Mahboobeh [Shiraz University, Shiraz (Iran, Islamic Republic of)
2009-10-15
Nonlinear transient heat transfer and thermoelastic stress analyses of a thick-walled FGM cylinder with temperature dependent materials are performed by using the Hermitian transfinite element method. Temperature-dependency of the material properties has not been taken into account in transient thermoelastic analysis, so far. Due to the mentioned dependency, the resulting governing FEM equations of transient heat transfer are highly nonlinear. Furthermore, in all finite element analysis performed so far in the field, Lagrangian elements have been used. To avoid an artificial local heat source at the mutual boundaries of the elements, Hermitian elements are used instead in the present research. Another novelty of the present paper is simultaneous use of the transfinite element method and updating technique. Time variations of the temperature, displacements, and stresses are obtained through a numerical Laplace inversion. Finally, results obtained considering the temperature-dependency of the material properties are compared with those derived based on temperature independency assumption. Furthermore, the temperature distribution and the radial and circumferential stresses are investigated versus time, geometrical parameters and index of power law. Results reveal that the temperature-dependency effect is significant
Dynamical properties of a particle in a time-dependent double-well potential
International Nuclear Information System (INIS)
Leonel, Edson D; McClintock, P V E
2004-01-01
Some chaotic properties of a classical particle interacting with a time-dependent double-square-well potential are studied. The dynamics of the system is characterized using a two-dimensional nonlinear area-preserving map. Scaling arguments are used to study the chaotic sea in the low-energy domain. It is shown that the distributions of successive reflections and of corresponding successive reflection times obey power laws with the same exponent. If one or both wells move randomly, the particle experiences the phenomenon of Fermi acceleration in the sense that it has unlimited energy growth
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.
Positive solution of a time and energy dependent neutron transport problem
International Nuclear Information System (INIS)
Pao, C.V.
1975-01-01
A constructive method is given for the determination of a solution and an existence--uniqueness theorem for some nonlinear time and energy dependent neutron transport problems, including the linear transport system. The geometry of the medium under consideration is allowed to be either bounded or unbounded which includes the geometry of a finite or infinite cylinder, a half-space and the whole space R/subm/ (m=1,2,center-dotcenter-dotcenter-dot). Our approach to the problem is by successive approximation which leads to various recursion formulas for the approximations in terms of explicit integrations. It is shown under some Lipschitz conditions on the nonlinear functions, which describe the process of neutrons absorption, fission, and scattering, that the sequence of approximations converges to a unique positive solution. Since these conditions are satisfied by the linear transport equation, all the results for the nonlinear system are valid for the linear transport problem. In the general nonlinear problem, the existence of both local and global solutions are discussed, and an iterative process for the construction of the solution is given
Characterization of Time-Dependent Behavior of Ramming Paste Used in an Aluminum Electrolysis Cell
Orangi, Sakineh; Picard, Donald; Alamdari, Houshang; Ziegler, Donald; Fafard, Mario
2015-12-01
A new methodology was proposed for the characterization of time-dependent behavior of materials in order to develop a constitutive model. The material used for the characterization was ramming paste, a porous material used in an aluminum electrolysis cell, which is baked in place under varying loads induced by the thermal expansion of other components of the cell. In order to develop a constitutive model representing the paste mechanical behavior, it was necessary to get some insight into its behavior using samples which had been baked at different temperatures ranging from 200 to 1000 °C. Creep stages, effect of testing temperature on the creep, creep-recovery, as well as nonlinear creep were observed for designing a constitutive law. Uniaxial creep-recovery tests were carried out at two temperatures on the baked paste: ambient and higher. Results showed that the shape of creep curves was similar to a typical creep; recovery happened and the creep was shown to be nonlinear. Those experimental observations and the identification of nonlinear parameters of developed constitutive model demonstrated that the baked paste experiences nonlinear viscoelastic-viscoplastic behavior at different temperatures.
Fleming, David P.; Poplawski, J. V.
2002-01-01
Rolling-element bearing forces vary nonlinearly with bearing deflection. Thus an accurate rotordynamic transient analysis requires bearing forces to be determined at each step of the transient solution. Analyses have been carried out to show the effect of accurate bearing transient forces (accounting for non-linear speed and load dependent bearing stiffness) as compared to conventional use of average rolling-element bearing stiffness. Bearing forces were calculated by COBRA-AHS (Computer Optimized Ball and Roller Bearing Analysis - Advanced High Speed) and supplied to the rotordynamics code ARDS (Analysis of Rotor Dynamic Systems) for accurate simulation of rotor transient behavior. COBRA-AHS is a fast-running 5 degree-of-freedom computer code able to calculate high speed rolling-element bearing load-displacement data for radial and angular contact ball bearings and also for cylindrical and tapered roller beatings. Results show that use of nonlinear bearing characteristics is essential for accurate prediction of rotordynamic behavior.
Finite-Time Stability and Stabilization of Nonlinear Quadratic Systems with Jumps
Directory of Open Access Journals (Sweden)
Minsong Zhang
2014-01-01
Full Text Available This paper investigates the problems of finite-time stability and finite-time stabilization for nonlinear quadratic systems with jumps. The jump time sequences here are assumed to satisfy some given constraints. Based on Lyapunov function and a particular presentation of the quadratic terms, sufficient conditions for finite-time stability and finite-time stabilization are developed to a set containing bilinear matrix inequalities (BLIMs and linear matrix inequalities (LMIs. Numerical examples are given to illustrate the effectiveness of the proposed methodology.
Fractal analysis and nonlinear forecasting of indoor 222Rn time series
International Nuclear Information System (INIS)
Pausch, G.; Bossew, P.; Hofmann, W.; Steger, F.
1998-01-01
Fractal analyses of indoor 222 Rn time series were performed using different chaos theory based measurements such as time delay method, Hurst's rescaled range analysis, capacity (fractal) dimension, and Lyapunov exponent. For all time series we calculated only positive Lyapunov exponents which is a hint to chaos, while the Hurst exponents were well below 0.5, indicating antipersistent behaviour (past trends tend to reverse in the future). These time series were also analyzed with a nonlinear prediction method which allowed an estimation of the embedding dimensions with some restrictions, limiting the prediction to about three relative time steps. (orig.)
Noise level estimation in weakly nonlinear slowly time-varying systems
International Nuclear Information System (INIS)
Aerts, J R M; Dirckx, J J J; Lataire, J; Pintelon, R
2008-01-01
Recently, a method using multisine excitation was proposed for estimating the frequency response, the nonlinear distortions and the disturbing noise of weakly nonlinear time-invariant systems. This method has been demonstrated on the measurement of nonlinear distortions in the vibration of acoustically driven systems such as a latex membrane, which is a good example of a time-invariant system [1]. However, not all systems are perfectly time invariant, e.g. biomechanical systems. This time variation can be misinterpreted as an elevated noise floor, and the classical noise estimation method gives a wrong result. Two improved methods to retrieve the correct noise information from the measurements are presented. Both of them make use of multisine excitations. First, it is demonstrated that the improved methods give the same result as the classical noise estimation method when applied to a time-invariant system (high-quality microphone membrane). Next, it is demonstrated that the new methods clearly give an improved estimate of the noise level on time-varying systems. As an application example results for the vibration response of an eardrum are shown
International Nuclear Information System (INIS)
Yamashita, Osamu
2009-01-01
The new thermal rate equations were built up by taking the linear and non-linear components in the temperature dependences of the Seebeck coefficient α, the electrical resistivity ρ and thermal conductivity κ of a thermoelectric (TE) material into the thermal rate equations on the assumption that their temperature dependences are expressed by a quadratic function of temperature T. The energy conversion efficiency η for a single TE element was formulated using the new thermal rate ones proposed here. By applying it to the high-performance half-Heusler compound, the non-linear component in the temperature dependence of α among those of the TE properties has the greatest effect on η, so that η/η 0 was increased by 11% under the condition of T = 510 K and ΔT = 440 K, where η 0 is a well-known conventional energy conversion efficiency. It was thus found that the temperature dependences of TE properties have a significant influence on η. When one evaluates the accurate achievement rate of η exp obtained experimentally for a TE generator, therefore, η exp should be compared with η the estimated from the theoretical expression proposed here, not with η 0 , particularly when there is a strong non-linearity in the temperature dependence of TE properties.
DEFF Research Database (Denmark)
Leirs, Herwig; Steneth, Nils Chr.; Nichols, James D.
1997-01-01
, but clear examples of both processes acting in the same population are rare(7,8). Key-factor analysis (regression of population changes on possible causal factors) and time-series analysis are often used to investigate the presence of density dependence, but such approaches may be biased and provide...... no information on actual demographic rates(9,10). Here we report on both density-dependent and density-independent effects in a murid rodent pest species, the multimammute rat Mastomys natalensis (Smith, 1834), using statistical capture-recapture models, Both effects occur simultaneously, but we also demonstrate...
Pepi, John W.
2017-08-01
Thermally induced stress is readily calculated for linear elastic material properties using Hooke's law in which, for situations where expansion is constrained, stress is proportional to the product of the material elastic modulus and its thermal strain. When material behavior is nonlinear, one needs to make use of nonlinear theory. However, we can avoid that complexity in some situations. For situations in which both elastic modulus and coefficient of thermal expansion vary with temperature, solutions can be formulated using secant properties. A theoretical approach is thus presented to calculate stresses for nonlinear, neo-Hookean, materials. This is important for high acuity optical systems undergoing large temperature extremes.
Time-dependent deterministic transport on parallel architectures using PARTISN
International Nuclear Information System (INIS)
Alcouffe, R.E.; Baker, R.S.
1998-01-01
In addition to the ability to solve the static transport equation, the authors have also incorporated time dependence into the parallel S N code PARTISN. Using a semi-implicit scheme, PARTISN is capable of performing time-dependent calculations for both fissioning and pure source driven problems. They have applied this to various types of problems such as shielding and prompt fission experiments. This paper describes the form of the time-dependent equations implemented, their solution strategies in PARTISN including iteration acceleration, and the strategies used for time-step control. Results are presented for a iron-water shielding calculation and a criticality excursion in a uranium solution configuration
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 granular...... situation for soils. That is whether the time-dependent behavior can be characterized as isotach or nonisotach. It seems that the isotach behavior is adequate for describing the time effects in clays in most situations. But for sand, the isotach description is inadequate. Further, the phenomenon...
Ranking paths in stochastic time-dependent networks
DEFF Research Database (Denmark)
Nielsen, Lars Relund; Andersen, Kim Allan; Pretolani, Daniele D.
2014-01-01
In this paper we address optimal routing problems in networks where travel times are both stochastic and time-dependent. In these networks, the best route choice is not necessarily a path, but rather a time-adaptive strategy that assigns successors to nodes as a function of time. Nevertheless, in...
Lam, H K; Leung, Frank H F
2007-10-01
This correspondence presents the stability analysis and performance design of the continuous-time fuzzy-model-based control systems. The idea of the nonparallel-distributed-compensation (non-PDC) control laws is extended to the continuous-time fuzzy-model-based control systems. A nonlinear controller with non-PDC control laws is proposed to stabilize the continuous-time nonlinear systems in Takagi-Sugeno's form. To produce the stability-analysis result, a parameter-dependent Lyapunov function (PDLF) is employed. However, two difficulties are usually encountered: 1) the time-derivative terms produced by the PDLF will complicate the stability analysis and 2) the stability conditions are not in the form of linear-matrix inequalities (LMIs) that aid the design of feedback gains. To tackle the first difficulty, the time-derivative terms are represented by some weighted-sum terms in some existing approaches, which will increase the number of stability conditions significantly. In view of the second difficulty, some positive-definitive terms are added in order to cast the stability conditions into LMIs. In this correspondence, the favorable properties of the membership functions and nonlinear control laws, which allow the introduction of some free matrices, are employed to alleviate the two difficulties while retaining the favorable properties of PDLF-based approach. LMI-based stability conditions are derived to ensure the system stability. Furthermore, based on a common scalar performance index, LMI-based performance conditions are derived to guarantee the system performance. Simulation examples are given to illustrate the effectiveness of the proposed approach.
International Nuclear Information System (INIS)
Densmore, Jeffery D.; Larsen, Edward W.
2004-01-01
The equations of nonlinear, time-dependent radiative transfer are known to yield the equilibrium diffusion equation as the leading-order solution of an asymptotic analysis when the mean-free path and mean-free time of a photon become small. We apply this same analysis to the Fleck-Cummings, Carter-Forest, and N'kaoua Monte Carlo approximations for grey (frequency-independent) radiative transfer. Although Monte Carlo simulation usually does not require the discretizations found in deterministic transport techniques, Monte Carlo methods for radiative transfer require a time discretization due to the nonlinearities of the problem. If an asymptotic analysis of the equations used by a particular Monte Carlo method yields an accurate time-discretized version of the equilibrium diffusion equation, the method should generate accurate solutions if a time discretization is chosen that resolves temperature changes, even if the time steps are much larger than the mean-free time of a photon. This analysis is of interest because in many radiative transfer problems, it is a practical necessity to use time steps that are large compared to a mean-free time. Our asymptotic analysis shows that: (i) the N'kaoua method has the equilibrium diffusion limit, (ii) the Carter-Forest method has the equilibrium diffusion limit if the material temperature change during a time step is small, and (iii) the Fleck-Cummings method does not have the equilibrium diffusion limit. We include numerical results that verify our theoretical predictions
Comparing of the Reaction Time in Substance-Dependent and Non-Dependent Individuals
Directory of Open Access Journals (Sweden)
Mohammad Narimani
2012-11-01
Full Text Available Aim: The aim of this study was to compare the simple, selective, and discrimination reaction time in substance-dependent and non-dependent individuals. Method: In this causal-comparative study, the population included of 425 males (opium and crystal dependents who were referred to addiction rehabilitation centers in Tabriz. By random sampling, 16 opium dependents, 16 crystal dependents, and 16 non-dependent individuals with no history of dependency as the compare group were selected. All groups peered in age, and marital status. For gathering data, “Addicts Admit Questionnaire” and laboratory device known as the "Reaction Time Assay" have been used. Results: The results of this study showed that there are significant differences among all groups in simple reaction time, choice reaction time and reaction time to auditory stimuli, but no significant difference in discrimination reaction time and reaction time to visual stimulus observed. Conclusion: The reaction time of substance-dependent groups is slower than non-dependent groups.
Applications of hybrid time-frequency methods in nonlinear structural dynamics
International Nuclear Information System (INIS)
Politopoulos, I.; Piteau, Ph.; Borsoi, L.; Antunes, J.
2014-01-01
This paper presents a study on methods which may be used to compute the nonlinear response of systems whose linear properties are determined in the frequency or Laplace domain. Typically, this kind of situation may arise in soil-structure and fluid-structure interaction problems. In particular three methods are investigated: (a) the hybrid time-frequency method, (b) the computation of the convolution integral which requires an inverse Fourier or Laplace transform of the system's transfer function, and (c) the identification of an equivalent system defined in the time domain which may be solved with classical time integration methods. These methods are illustrated by their application to some simple, one degree of freedom, non-linear systems and their advantages and drawbacks are highlighted. (authors)
Nonlinear behavior in the time domain in argon atmospheric dielectric-barrier discharges
International Nuclear Information System (INIS)
Shi Hong; Wang Yanhui; Wang Dezhen
2008-01-01
A vast majority of nonlinear behavior in atmospheric pressure discharges has so far been studied in the space domain, and their time-domain characters are often believed to exact the periodicity of the externally applied voltage. In this paper, based on one-dimensional fluid mode, we study complex nonlinear behavior in the time domain in argon atmospheric dielectric-barrier discharges at very broad frequency range from kilohertz to megahertz. Under certain conditions, the discharge not only can be driven to chaos from time-periodic state through period-doubling bifurcation, but also can return stable periodic motion from chaotic state through an inverse period-doubling bifurcation sequence. Upon changing the parameter the discharge undergoes alternatively chaotic and periodic behavior. Some periodic windows embedded in chaos, as well as the secondary bifurcation occurring in the periodic windows can also be observed. The corresponding discharge characteristics are investigated.
Nonlinear Estimation of Discrete-Time Signals Under Random Observation Delay
International Nuclear Information System (INIS)
Caballero-Aguila, R.; Jimenez-Lopez, J. D.; Hermoso-Carazo, A.; Linares-Perez, J.; Nakamori, S.
2008-01-01
This paper presents an approximation to the nonlinear least-squares estimation problem of discrete-time stochastic signals using nonlinear observations with additive white noise which can be randomly delayed by one sampling time. The observation delay is modelled by a sequence of independent Bernoulli random variables whose values, zero or one, indicate that the real observation arrives on time or it is delayed and, hence, the available measurement to estimate the signal is not up-to-date. Assuming that the state-space model generating the signal is unknown and only the covariance functions of the processes involved in the observation equation are ready for use, a filtering algorithm based on linear approximations of the real observations is proposed.
Krasilenko, Vladimir G.; Nikolsky, Alexander I.; Lazarev, Alexander A.; Lazareva, Maria V.
2008-03-01
In the paper the actuality of neurophysiologically motivated neuron arrays with flexibly programmable functions and operations with possibility to select required accuracy and type of nonlinear transformation and learning are shown. We consider neurons design and simulation results of multichannel spatio-time algebraic accumulation - integration of optical signals. Advantages for nonlinear transformation and summation - integration are shown. The offered circuits are simple and can have intellectual properties such as learning and adaptation. The integrator-neuron is based on CMOS current mirrors and comparators. The performance: consumable power - 100...500 μW, signal period- 0.1...1ms, input optical signals power - 0.2...20 μW time delays - less 1μs, the number of optical signals - 2...10, integration time - 10...100 of signal periods, accuracy or integration error - about 1%. Various modifications of the neuron-integrators with improved performance and for different applications are considered in the paper.
Murphy, K. A.
1990-01-01
A parameter estimation algorithm is developed which can be used to estimate unknown time- or state-dependent delays and other parameters (e.g., initial condition) appearing within a nonlinear nonautonomous functional differential equation. The original infinite dimensional differential equation is approximated using linear splines, which are allowed to move with the variable delay. The variable delays are approximated using linear splines as well. The approximation scheme produces a system of ordinary differential equations with nice computational properties. The unknown parameters are estimated within the approximating systems by minimizing a least-squares fit-to-data criterion. Convergence theorems are proved for time-dependent delays and state-dependent delays within two classes, which say essentially that fitting the data by using approximations will, in the limit, provide a fit to the data using the original system. Numerical test examples are presented which illustrate the method for all types of delay.
Yu, Kyung-Hun; Suk, Min-Hwa; Kang, Shin-Woo; Shin, Yun-A
2014-10-01
The purpose of this study was to investigate the effect of combined linear and nonlinear periodic training on physical fitness and competition times in finswimmers. The linear resistance training model (6 days/week) and nonlinear underwater training (4 days/week) were applied to 12 finswimmers (age, 16.08± 1.44 yr; career, 3.78± 1.90 yr) for 12 weeks. Body composition measures included weight, body mass index (BMI), percent fat, and fat-free mass. Physical fitness measures included trunk flexion forward, trunk extension backward, sargent jump, 1-repetition-maximum (1 RM) squat, 1 RM dead lift, knee extension, knee flexion, trunk extension, trunk flexion, and competition times. Body composition and physical fitness were improved after the 12-week periodic training program. Weight, BMI, and percent fat were significantly decreased, and trunk flexion forward, trunk extension backward, sargent jump, 1 RM squat, 1 RM dead lift, and knee extension (right) were significantly increased. The 50- and 100-m times significantly decreased in all 12 athletes. After 12 weeks of training, all finswimmers who participated in this study improved their times in a public competition. These data indicate that combined linear and nonlinear periodic training enhanced the physical fitness and competition times in finswimmers.
Stabilization and tracking controller for a class of nonlinear discrete-time systems
International Nuclear Information System (INIS)
Sharma, B.B.; Kar, I.N.
2011-01-01
Highlights: → We present recursive design of stabilizing controller for nonlinear discrete-time systems. → Problem of stabilizing and tracking control of single link manipulator system is addressed. → We extend the proposed results to output tracking problems. → The proposed methodology is applied satisfactorily to discrete-time chaotic maps. - Abstract: In this paper, stabilization and tracking control problem for parametric strict feedback class of discrete time systems is addressed. Recursive design of control function based on contraction theory framework is proposed instead of traditional Lyapunov based method. Explicit structure of controller is derived for the addressed class of nonlinear discrete-time systems. Conditions for exponential stability of system states are derived in terms of controller parameters. At each stage of recursive procedure a specific structure of Jacobian matrix is ensured so as to satisfy conditions of stability. The closed loop dynamics in this case remains nonlinear in nature. The proposed algorithm establishes global stability results in quite a simple manner as it does not require formulation of error dynamics. Problem of stabilization and output tracking control in case of single link manipulator system with actuator dynamics is analyzed using the proposed strategy. The proposed results are further extended to stabilization of discrete time chaotic systems. Numerical simulations presented in the end show the effectiveness of the proposed approach.
Spectral dependence of third-order nonlinear optical properties in InN
International Nuclear Information System (INIS)
Ahn, H.; Lee, M.-T.; Chang, Y.-M.
2014-01-01
We report on the nonlinear optical properties of InN measured in a wide near-infrared spectral range with the femtosecond Z-scan technique. The above-bandgap nonlinear absorption in InN is found to originate from the saturation of absorption by the band-state-filling and its cross-section increases drastically near the bandgap energy. With below-bandgap excitation, the nonlinear absorption undergoes a transition from saturation absorption (SA) to reverse-SA (RSA), attributed to the competition between SA of band-tail states and two-photon-related RSA. The measured large nonlinear refractive index of the order of 10 −10 cm 2 /W indicates InN as a potential material for all-optical switching and related applications
Arendt, V.; Shalchi, A.
2018-06-01
We explore numerically the transport of energetic particles in a turbulent magnetic field configuration. A test-particle code is employed to compute running diffusion coefficients as well as particle distribution functions in the different directions of space. Our numerical findings are compared with models commonly used in diffusion theory such as Gaussian distribution functions and solutions of the cosmic ray Fokker-Planck equation. Furthermore, we compare the running diffusion coefficients across the mean magnetic field with solutions obtained from the time-dependent version of the unified non-linear transport theory. In most cases we find that particle distribution functions are indeed of Gaussian form as long as a two-component turbulence model is employed. For turbulence setups with reduced dimensionality, however, the Gaussian distribution can no longer be obtained. It is also shown that the unified non-linear transport theory agrees with simulated perpendicular diffusion coefficients as long as the pure two-dimensional model is excluded.
Energy Technology Data Exchange (ETDEWEB)
Verma, Dinkar, E-mail: dinkar@iitk.ac.in [Nuclear Engineering and Technology Program, Indian Institute of Technology Kanpur, Kanpur 208 016 (India); Kalra, Manjeet Singh, E-mail: drmanjeet.singh@dituniversity.edu.in [DIT University, Dehradun 248 009 (India); Wahi, Pankaj, E-mail: wahi@iitk.ac.in [Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur 208 016 (India)
2016-11-15
Highlights: • Simplified models with inclusion of the clad temperature are considered. • Boiling nonlinearity and core power removal have been modeled. • Method of multiple time scales has been used for nonlinear analysis to get the nature and amplitude of oscillations. • Incorporation of modeling complexities enhances the stability of system. • We find that reactors with higher nominal power are more desirable from the point of view of global stability. - Abstract: We study the effect of including boiling nonlinearity, clad temperature and void-dependent power removal from the primary loop in the mathematical modeling of a boiling water reactor (BWR) on its dynamic characteristics. The advanced heavy water reactor (AHWR) is taken as a case study. Towards this end, we have analyzed two different simplified models with different handling of the clad temperature. Each of these models has the necessary modifications pertaining to boiling nonlinearity and power removal from the primary loop. These simplified models incorporate the neutronics and thermal–hydraulic coupling. The effect of successive changes in the modeling assumptions on the linear stability of the reactor has been studied and we find that incorporation of each of these complexities in the model increases the stable operating region of the reactor. Further, the method of multiple time scales (MMTS) is exploited to carry out the nonlinear analysis with a view to predict the bifurcation characteristics of the reactor. Both subcritical and supercritical Hopf bifurcations are present in each model depending on the choice of operating parameters. These analytical observations from MMTS have been verified against numerical simulations. A parametric study on the effect of changing the nominal reactor power on the regions in the parametric space of void coefficient of reactivity and fuel temperature coefficient of reactivity with sub- and super-critical Hopf bifurcations has been performed for all
Time-dependent potential-functional embedding theory
International Nuclear Information System (INIS)
Huang, Chen; Libisch, Florian; Peng, Qing; Carter, Emily A.
2014-01-01
We introduce a time-dependent potential-functional embedding theory (TD-PFET), in which atoms are grouped into subsystems. In TD-PFET, subsystems can be propagated by different suitable time-dependent quantum mechanical methods and their interactions can be treated in a seamless, first-principles manner. TD-PFET is formulated based on the time-dependent quantum mechanics variational principle. The action of the total quantum system is written as a functional of the time-dependent embedding potential, i.e., a potential-functional formulation. By exploiting the Runge-Gross theorem, we prove the uniqueness of the time-dependent embedding potential under the constraint that all subsystems share a common embedding potential. We derive the integral equation that such an embedding potential needs to satisfy. As proof-of-principle, we demonstrate TD-PFET for a Na 4 cluster, in which each Na atom is treated as one subsystem and propagated by time-dependent Kohn-Sham density functional theory (TDDFT) using the adiabatic local density approximation (ALDA). Our results agree well with a direct TDDFT calculation on the whole Na 4 cluster using ALDA. We envision that TD-PFET will ultimately be useful for studying ultrafast quantum dynamics in condensed matter, where key regions are solved by highly accurate time-dependent quantum mechanics methods, and unimportant regions are solved by faster, less accurate methods
Time-dependent reliability sensitivity analysis of motion mechanisms
International Nuclear Information System (INIS)
Wei, Pengfei; Song, Jingwen; Lu, Zhenzhou; Yue, Zhufeng
2016-01-01
Reliability sensitivity analysis aims at identifying the source of structure/mechanism failure, and quantifying the effects of each random source or their distribution parameters on failure probability or reliability. In this paper, the time-dependent parametric reliability sensitivity (PRS) analysis as well as the global reliability sensitivity (GRS) analysis is introduced for the motion mechanisms. The PRS indices are defined as the partial derivatives of the time-dependent reliability w.r.t. the distribution parameters of each random input variable, and they quantify the effect of the small change of each distribution parameter on the time-dependent reliability. The GRS indices are defined for quantifying the individual, interaction and total contributions of the uncertainty in each random input variable to the time-dependent reliability. The envelope function method combined with the first order approximation of the motion error function is introduced for efficiently estimating the time-dependent PRS and GRS indices. Both the time-dependent PRS and GRS analysis techniques can be especially useful for reliability-based design. This significance of the proposed methods as well as the effectiveness of the envelope function method for estimating the time-dependent PRS and GRS indices are demonstrated with a four-bar mechanism and a car rack-and-pinion steering linkage. - Highlights: • Time-dependent parametric reliability sensitivity analysis is presented. • Time-dependent global reliability sensitivity analysis is presented for mechanisms. • The proposed method is especially useful for enhancing the kinematic reliability. • An envelope method is introduced for efficiently implementing the proposed methods. • The proposed method is demonstrated by two real planar mechanisms.
Space-time least-squares Petrov-Galerkin projection in nonlinear model reduction.
Energy Technology Data Exchange (ETDEWEB)
Choi, Youngsoo [Sandia National Laboratories (SNL-CA), Livermore, CA (United States). Extreme-scale Data Science and Analytics Dept.; Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Carlberg, Kevin Thomas [Sandia National Laboratories (SNL-CA), Livermore, CA (United States). Extreme-scale Data Science and Analytics Dept.
2017-09-01
Our work proposes a space-time least-squares Petrov-Galerkin (ST-LSPG) projection method for model reduction of nonlinear dynamical systems. In contrast to typical nonlinear model-reduction methods that first apply Petrov-Galerkin projection in the spatial dimension and subsequently apply time integration to numerically resolve the resulting low-dimensional dynamical system, the proposed method applies projection in space and time simultaneously. To accomplish this, the method first introduces a low-dimensional space-time trial subspace, which can be obtained by computing tensor decompositions of state-snapshot data. The method then computes discrete-optimal approximations in this space-time trial subspace by minimizing the residual arising after time discretization over all space and time in a weighted ℓ^{2}-norm. This norm can be de ned to enable complexity reduction (i.e., hyper-reduction) in time, which leads to space-time collocation and space-time GNAT variants of the ST-LSPG method. Advantages of the approach relative to typical spatial-projection-based nonlinear model reduction methods such as Galerkin projection and least-squares Petrov-Galerkin projection include: (1) a reduction of both the spatial and temporal dimensions of the dynamical system, (2) the removal of spurious temporal modes (e.g., unstable growth) from the state space, and (3) error bounds that exhibit slower growth in time. Numerical examples performed on model problems in fluid dynamics demonstrate the ability of the method to generate orders-of-magnitude computational savings relative to spatial-projection-based reduced-order models without sacrificing accuracy.
Liang, Fayun; Chen, Haibing; Huang, Maosong
2017-07-01
To provide appropriate uses of nonlinear ground response analysis for engineering practice, a three-dimensional soil column with a distributed mass system and a time domain numerical analysis were implemented on the OpenSees simulation platform. The standard mesh of a three-dimensional soil column was suggested to be satisfied with the specified maximum frequency. The layered soil column was divided into multiple sub-soils with a different viscous damping matrix according to the shear velocities as the soil properties were significantly different. It was necessary to use a combination of other one-dimensional or three-dimensional nonlinear seismic ground analysis programs to confirm the applicability of nonlinear seismic ground motion response analysis procedures in soft soil or for strong earthquakes. The accuracy of the three-dimensional soil column finite element method was verified by dynamic centrifuge model testing under different peak accelerations of the earthquake. As a result, nonlinear seismic ground motion response analysis procedures were improved in this study. The accuracy and efficiency of the three-dimensional seismic ground response analysis can be adapted to the requirements of engineering practice.
International Nuclear Information System (INIS)
Lamberti, Alfredo; Semperlotti, Fabio
2013-01-01
Closing delaminations in composite laminated structures exhibit a nonlinear dynamic response when excited by high frequency elastic waves. The contact acoustic nonlinear effects taking place at the damage interface act as a mechanism of energy redistribution from the driving frequency to the nonlinear harmonic frequencies. In this paper, we extend the concept of nonlinear structural intensity (NSI) to the analysis of closing delaminations in composite laminated plates. NSI is calculated using a method based on a combination of finite element and finite difference techniques, which is suitable for processing both numerical and experimental data. NSI is proven to be an effective metric to identify the presence and location of closing delaminations. The highly directional nature of orthotropic composites results in vibrational energy propagating in a different direction from that of the initial elastic wave. This aspect reduces the ability to effectively interrogate the damage and, therefore, the sensitivity to the damage. The time reversal mirror technique is explored as a possible approach to overcome the effect of the material directionality and increase the ability to interrogate the damage. Numerical simulations show that this technique is able to overcome the material directionality and to drastically enhance the ability to interrogate the damage. (paper)
Causal inference in nonlinear systems: Granger causality versus time-delayed mutual information
Li, Songting; Xiao, Yanyang; Zhou, Douglas; Cai, David
2018-05-01
The Granger causality (GC) analysis has been extensively applied to infer causal interactions in dynamical systems arising from economy and finance, physics, bioinformatics, neuroscience, social science, and many other fields. In the presence of potential nonlinearity in these systems, the validity of the GC analysis in general is questionable. To illustrate this, here we first construct minimal nonlinear systems and show that the GC analysis fails to infer causal relations in these systems—it gives rise to all types of incorrect causal directions. In contrast, we show that the time-delayed mutual information (TDMI) analysis is able to successfully identify the direction of interactions underlying these nonlinear systems. We then apply both methods to neuroscience data collected from experiments and demonstrate that the TDMI analysis but not the GC analysis can identify the direction of interactions among neuronal signals. Our work exemplifies inference hazards in the GC analysis in nonlinear systems and suggests that the TDMI analysis can be an appropriate tool in such a case.
Directory of Open Access Journals (Sweden)
Dan Ye
2013-01-01
Full Text Available This paper is concerned with delay-dependent stochastic stability for time-delay Markovian jump systems (MJSs with sector-bounded nonlinearities and more general transition probabilities. Different from the previous results where the transition probability matrix is completely known, a more general transition probability matrix is considered which includes completely known elements, boundary known elements, and completely unknown ones. In order to get less conservative criterion, the state and transition probability information is used as much as possible to construct the Lyapunov-Krasovskii functional and deal with stability analysis. The delay-dependent sufficient conditions are derived in terms of linear matrix inequalities to guarantee the stability of systems. Finally, numerical examples are exploited to demonstrate the effectiveness of the proposed method.
Optimal control of nonlinear continuous-time systems in strict-feedback form.
Zargarzadeh, Hassan; Dierks, Travis; Jagannathan, Sarangapani
2015-10-01
This paper proposes a novel optimal tracking control scheme for nonlinear continuous-time systems in strict-feedback form with uncertain dynamics. The optimal tracking problem is transformed into an equivalent optimal regulation problem through a feedforward adaptive control input that is generated by modifying the standard backstepping technique. Subsequently, a neural network-based optimal control scheme is introduced to estimate the cost, or value function, over an infinite horizon for the resulting nonlinear continuous-time systems in affine form when the internal dynamics are unknown. The estimated cost function is then used to obtain the optimal feedback control input; therefore, the overall optimal control input for the nonlinear continuous-time system in strict-feedback form includes the feedforward plus the optimal feedback terms. It is shown that the estimated cost function minimizes the Hamilton-Jacobi-Bellman estimation error in a forward-in-time manner without using any value or policy iterations. Finally, optimal output feedback control is introduced through the design of a suitable observer. Lyapunov theory is utilized to show the overall stability of the proposed schemes without requiring an initial admissible controller. Simulation examples are provided to validate the theoretical results.
The Fourier decomposition method for nonlinear and non-stationary time series analysis.
Singh, Pushpendra; Joshi, Shiv Dutt; Patney, Rakesh Kumar; Saha, Kaushik
2017-03-01
for many decades, there has been a general perception in the literature that Fourier methods are not suitable for the analysis of nonlinear and non-stationary data. In this paper, we propose a novel and adaptive Fourier decomposition method (FDM), based on the Fourier theory, and demonstrate its efficacy for the analysis of nonlinear and non-stationary time series. The proposed FDM decomposes any data into a small number of 'Fourier intrinsic band functions' (FIBFs). The FDM presents a generalized Fourier expansion with variable amplitudes and variable frequencies of a time series by the Fourier method itself. We propose an idea of zero-phase filter bank-based multivariate FDM (MFDM), for the analysis of multivariate nonlinear and non-stationary time series, using the FDM. We also present an algorithm to obtain cut-off frequencies for MFDM. The proposed MFDM generates a finite number of band-limited multivariate FIBFs (MFIBFs). The MFDM preserves some intrinsic physical properties of the multivariate data, such as scale alignment, trend and instantaneous frequency. The proposed methods provide a time-frequency-energy (TFE) distribution that reveals the intrinsic structure of a data. Numerical computations and simulations have been carried out and comparison is made with the empirical mode decomposition algorithms.
Simulation of time-dependent Heisenberg models in one dimension
DEFF Research Database (Denmark)
Volosniev, A. G.; Hammer, H. -W.; Zinner, N. T.
2016-01-01
In this Letter, we provide a theoretical analysis of strongly interacting quantum systems confined by a time-dependent external potential in one spatial dimension. We show that such systems can be used to simulate spin chains described by Heisenberg Hamiltonians in which the exchange coupling...... constants can be manipulated by time-dependent driving of the shape of the external confinement. As illustrative examples, we consider a harmonic trapping potential with a variable frequency and an infinite square well potential with a time-dependent barrier in the middle....
Van Meer, R.; Gritsenko, O. V.; Baerends, E. J.
2017-01-01
Straightforward interpretation of excitations is possible if they can be described as simple single orbital-to-orbital (or double, etc.) transitions. In linear response time-dependent density functional theory (LR-TDDFT), the (ground state) Kohn-Sham orbitals prove to be such an orbital basis. In
Directory of Open Access Journals (Sweden)
Da Sun
2016-01-01
Full Text Available A novel control algorithm based on the modified wave-variable controllers is proposed to achieve accurate position synchronization and reasonable force tracking of the nonlinear single-master-multiple-slave teleoperation system and simultaneously guarantee overall system’s stability in the presence of large time-varying delays. The system stability in different scenarios of human and environment situations has been analyzed. The proposed method is validated through experimental work based on the 3-DOF trilateral teleoperation system consisting of three different manipulators. The experimental results clearly demonstrate the feasibility of the proposed algorithm to achieve high transparency and robust stability in nonlinear single-master-multiple-slave teleoperation system in the presence of time-varying delays.
Adaptive Neural Tracking Control for Discrete-Time Switched Nonlinear Systems with Dead Zone Inputs
Directory of Open Access Journals (Sweden)
Jidong Wang
2017-01-01
Full Text Available In this paper, the adaptive neural controllers of subsystems are proposed for a class of discrete-time switched nonlinear systems with dead zone inputs under arbitrary switching signals. Due to the complicated framework of the discrete-time switched nonlinear systems and the existence of the dead zone, it brings about difficulties for controlling such a class of systems. In addition, the radial basis function neural networks are employed to approximate the unknown terms of each subsystem. Switched update laws are designed while the parameter estimation is invariable until its corresponding subsystem is active. Then, the closed-loop system is stable and all the signals are bounded. Finally, to illustrate the effectiveness of the proposed method, an example is employed.
Time-Dependent Behaviors of Granite: Loading-Rate Dependence, Creep, and Relaxation
Hashiba, K.; Fukui, K.
2016-07-01
To assess the long-term stability of underground structures, it is important to understand the time-dependent behaviors of rocks, such as their loading-rate dependence, creep, and relaxation. However, there have been fewer studies on crystalline rocks than on tuff, mudstone, and rock salt, because the high strength of crystalline rocks makes the detection of their time-dependent behaviors much more difficult. Moreover, studies on the relaxation, temporal change of stress and strain (TCSS) conditions, and relations between various time-dependent behaviors are scarce for not only granites, but also other rocks. In this study, previous reports on the time-dependent behaviors of granites were reviewed and various laboratory tests were conducted using Toki granite. These tests included an alternating-loading-rate test, creep test, relaxation test, and TCSS test. The results showed that the degree of time dependence of Toki granite is similar to other granites, and that the TCSS resembles the stress-relaxation curve and creep-strain curve. A viscoelastic constitutive model, proposed in a previous study, was modified to investigate the relations between the time-dependent behaviors in the pre- and post-peak regions. The modified model reproduced the stress-strain curve, creep, relaxation, and the results of the TCSS test. Based on a comparison of the results of the laboratory tests and numerical simulations, close relations between the time-dependent behaviors were revealed quantitatively.
Time dependence of magnetization of high temperature superconductors
International Nuclear Information System (INIS)
Larkin, A.I.; Geshkenbein, V.B.
1988-10-01
Magnetization of high T c superconductors logarithmically decreases with time. There is a maximum in the temperature dependence of the coefficient at this logarithm. If one assumes that there do exist two kinds of pinning centers, then this dependence can be described in the Anderson theory of thermal creeps of Abrikosov's vortices. The temperature dependence of the critical current is also discussed. (author). 23 refs
Hydrodynamic perspective on memory in time-dependent density-functional theory
International Nuclear Information System (INIS)
Thiele, M.; Kuemmel, S.
2009-01-01
The adiabatic approximation of time-dependent density-functional theory is studied in the context of nonlinear excitations of two-electron singlet systems. We compare the exact time evolution of these systems to the adiabatically exact one obtained from time-dependent Kohn-Sham calculations relying on the exact ground-state exchange-correlation potential. Thus, we can show under which conditions the adiabatic approximation breaks down and memory effects become important. The hydrodynamic formulation of quantum mechanics allows us to interpret these results and relate them to dissipative effects in the Kohn-Sham system. We show how the breakdown of the adiabatic approximation can be inferred from the rate of change of the ground-state noninteracting kinetic energy.
Regular and chaotic dynamics in time-dependent relativistic mean-field theory
International Nuclear Information System (INIS)
Vretenar, D.; Ring, P.; Lalazissis, G.A.; Poeschl, W.
1997-01-01
Isoscalar and isovector monopole oscillations that correspond to giant resonances in spherical nuclei are described in the framework of time-dependent relativistic mean-field theory. Time-dependent and self-consistent calculations that reproduce experimental data on monopole resonances in 208 Pb show that the motion of the collective coordinate is regular for isoscalar oscillations, and that it becomes chaotic when initial conditions correspond to the isovector mode. Regular collective dynamics coexists with chaotic oscillations on the microscopic level. Time histories, Fourier spectra, state-space plots, Poincare sections, autocorrelation functions, and Lyapunov exponents are used to characterize the nonlinear system and to identify chaotic oscillations. Analogous considerations apply to higher multipolarities. copyright 1997 The American Physical Society
Rotating Hele-Shaw cell with a time-dependent angular velocity
Anjos, Pedro H. A.; Alvarez, Victor M. M.; Dias, Eduardo O.; Miranda, José A.
2017-12-01
Despite the large number of existing studies of viscous flows in rotating Hele-Shaw cells, most investigations analyze rotational motion with a constant angular velocity, under vanishing Reynolds number conditions in which inertial effects can be neglected. In this work, we examine the linear and weakly nonlinear dynamics of the interface between two immiscible fluids in a rotating Hele-Shaw cell, considering the action of a time-dependent angular velocity, and taking into account the contribution of inertia. By using a generalized Darcy's law, we derive a second-order mode-coupling equation which describes the time evolution of the interfacial perturbation amplitudes. For arbitrary values of viscosity and density ratios, and for a range of values of a rotational Reynolds number, we investigate how the time-dependent angular velocity and inertia affect the important finger competition events that traditionally arise in rotating Hele-Shaw flows.
Time-dependent local-to-normal mode transition in triatomic molecules
Cruz, Hans; Bermúdez-Montaña, Marisol; Lemus, Renato
2018-01-01
Time-evolution of the vibrational states of two interacting harmonic oscillators in the local mode scheme is presented. A local-to-normal mode transition (LNT) is identified and studied from temporal perspective through time-dependent frequencies of the oscillators. The LNT is established as a polyad-breaking phenomenon from the local standpoint for the stretching degrees of freedom in a triatomic molecule. This study is carried out in the algebraic representation of bosonic operators. The dynamics of the states are determined via the solutions of the corresponding nonlinear Ermakov equation and a local time-dependent polyad is obtained as a tool to identify the LNT. Applications of this formalism to H2O, CO2, O3 and NO2 molecules in the adiabatic, sudden and linear regime are considered.
International Nuclear Information System (INIS)
Xu Ruirui; Chen Tianlun; Gao Chengfeng
2006-01-01
Nonlinear time series prediction is studied by using an improved least squares support vector machine (LS-SVM) regression based on chaotic mutation evolutionary programming (CMEP) approach for parameter optimization. We analyze how the prediction error varies with different parameters (σ, γ) in LS-SVM. In order to select appropriate parameters for the prediction model, we employ CMEP algorithm. Finally, Nasdaq stock data are predicted by using this LS-SVM regression based on CMEP, and satisfactory results are obtained.
Adaptive Neural Control for a Class of Outputs Time-Delay Nonlinear Systems
Directory of Open Access Journals (Sweden)
Ruliang Wang
2012-01-01
Full Text Available This paper considers an adaptive neural control for a class of outputs time-delay nonlinear systems with perturbed or no. Based on RBF neural networks, the radius basis function (RBF neural networks is employed to estimate the unknown continuous functions. The proposed control guarantees that all closed-loop signals remain bounded. The simulation results demonstrate the effectiveness of the proposed control scheme.
Nonlinear techniques for forecasting solar activity directly from its time series
Ashrafi, S.; Roszman, L.; Cooley, J.
1993-01-01
This paper presents numerical techniques for constructing nonlinear predictive models to forecast solar flux directly from its time series. This approach makes it possible to extract dynamical in variants of our system without reference to any underlying solar physics. We consider the dynamical evolution of solar activity in a reconstructed phase space that captures the attractor (strange), give a procedure for constructing a predictor of future solar activity, and discuss extraction of dynamical invariants such as Lyapunov exponents and attractor dimension.
Discussion About Nonlinear Time Series Prediction Using Least Squares Support Vector Machine
International Nuclear Information System (INIS)
Xu Ruirui; Bian Guoxing; Gao Chenfeng; Chen Tianlun
2005-01-01
The least squares support vector machine (LS-SVM) is used to study the nonlinear time series prediction. First, the parameter γ and multi-step prediction capabilities of the LS-SVM network are discussed. Then we employ clustering method in the model to prune the number of the support values. The learning rate and the capabilities of filtering noise for LS-SVM are all greatly improved.
Nonlinearities in Drug Release Process from Polymeric Microparticles: Long-Time-Scale Behaviour
Directory of Open Access Journals (Sweden)
Elena Simona Bacaita
2012-01-01
Full Text Available A theoretical model of the drug release process from polymeric microparticles (a particular type of polymer matrix, through dispersive fractal approximation of motion, is built. As a result, the drug release process takes place through cnoidal oscillations modes of a normalized concentration field. This indicates that, in the case of long-time-scale evolutions, the drug particles assemble in a lattice of nonlinear oscillators occur macroscopically, through variations of drug concentration. The model is validated by experimental results.
Czech Academy of Sciences Publication Activity Database
Dos Santos, S.; Vejvodová, Šárka; Převorovský, Zdeněk
2009-01-01
Roč. 19, č. 2 (2009), s. 14-14 ISSN 1213-3825. [NDT in PROGRESS. 12.11.2009-14.11.2009, Praha] R&D Projects: GA ČR GA106/07/1393; GA MPO(CZ) FR-TI1/274 Institutional research plan: CEZ:AV0Z20760514 Keywords : nonlinear elastic wave spectroscopy (NEWS) * ESAM * time reversal (TR) * TR-NEWS imaging * tomography * DORT Subject RIV: BI - Acoustics
International Nuclear Information System (INIS)
Spears, Robert Edward; Coleman, Justin Leigh
2015-01-01
Currently the Department of Energy (DOE) and the nuclear industry perform seismic soil-structure interaction (SSI) analysis using equivalent linear numerical analysis tools. For lower levels of ground motion, these tools should produce reasonable in-structure response values for evaluation of existing and new facilities. For larger levels of ground motion these tools likely overestimate the in-structure response (and therefore structural demand) since they do not consider geometric nonlinearities (such as gaping and sliding between the soil and structure) and are limited in the ability to model nonlinear soil behavior. The current equivalent linear SSI (SASSI) analysis approach either joins the soil and structure together in both tension and compression or releases the soil from the structure for both tension and compression. It also makes linear approximations for material nonlinearities and generalizes energy absorption with viscous damping. This produces the potential for inaccurately establishing where the structural concerns exist and/or inaccurately establishing the amplitude of the in-structure responses. Seismic hazard curves at nuclear facilities have continued to increase over the years as more information has been developed on seismic sources (i.e. faults), additional information gathered on seismic events, and additional research performed to determine local site effects. Seismic hazard curves are used to develop design basis earthquakes (DBE) that are used to evaluate nuclear facility response. As the seismic hazard curves increase, the input ground motions (DBE's) used to numerically evaluation nuclear facility response increase causing larger in-structure response. As ground motions increase so does the importance of including nonlinear effects in numerical SSI models. To include material nonlinearity in the soil and geometric nonlinearity using contact (gaping and sliding) it is necessary to develop a nonlinear time domain methodology. This
Measuring time-dependent deformations in metallic MEMS
Bergers, L.I.J.C.; Hoefnagels, J.P.M.; Delhey, N.K.R.; Geers, M.G.D.
2011-01-01
The reliability of metallic microelectromechanical systems (MEMS) depends on time-dependent deformation such as creep. Key to this process is the interaction between microstructural length scales and dimensional length scales, so-called size-effects. As a first critical step towards studying these
Energy Technology Data Exchange (ETDEWEB)
Zhang Yu, E-mail: yuzhang@xmu.edu.cn [Key Laboratory of Underwater Acoustic Communication and Marine Information Technology of the Ministry of Education, Xiamen University, Xiamen Fujian 361005 (China); Sprecher, Alicia J. [Department of Surgery, Division of Otolaryngology - Head and Neck Surgery, University of Wisconsin School of Medicine and Public Health, Madison, WI 53792-7375 (United States); Zhao Zongxi [Key Laboratory of Underwater Acoustic Communication and Marine Information Technology of the Ministry of Education, Xiamen University, Xiamen Fujian 361005 (China); Jiang, Jack J. [Department of Surgery, Division of Otolaryngology - Head and Neck Surgery, University of Wisconsin School of Medicine and Public Health, Madison, WI 53792-7375 (United States)
2011-09-15
Highlights: > The VWK method effectively detects the nonlinearity of a discrete map. > The method describes the chaotic time series of a biomechanical vocal fold model. > Nonlinearity in laryngeal pathology is detected from short and noisy time series. - Abstract: In this paper, we apply the Volterra-Wiener-Korenberg (VWK) model method to detect nonlinearity in disordered voice productions. The VWK method effectively describes the nonlinearity of a third-order nonlinear map. It allows for the analysis of short and noisy data sets. The extracted VWK model parameters show an agreement with the original nonlinear map parameters. Furthermore, the VWK mode method is applied to successfully assess the nonlinearity of a biomechanical voice production model simulating irregular vibratory dynamics of vocal folds with a unilateral vocal polyp. Finally, we show the clinical applicability of this nonlinear detection method to analyze the electroglottographic data generated by 14 patients with vocal nodules or polyps. The VWK model method shows potential in describing the nonlinearity inherent in disordered voice productions from short and noisy time series that are common in the clinical setting.
International Nuclear Information System (INIS)
Zhang Yu; Sprecher, Alicia J.; Zhao Zongxi; Jiang, Jack J.
2011-01-01
Highlights: → The VWK method effectively detects the nonlinearity of a discrete map. → The method describes the chaotic time series of a biomechanical vocal fold model. → Nonlinearity in laryngeal pathology is detected from short and noisy time series. - Abstract: In this paper, we apply the Volterra-Wiener-Korenberg (VWK) model method to detect nonlinearity in disordered voice productions. The VWK method effectively describes the nonlinearity of a third-order nonlinear map. It allows for the analysis of short and noisy data sets. The extracted VWK model parameters show an agreement with the original nonlinear map parameters. Furthermore, the VWK mode method is applied to successfully assess the nonlinearity of a biomechanical voice production model simulating irregular vibratory dynamics of vocal folds with a unilateral vocal polyp. Finally, we show the clinical applicability of this nonlinear detection method to analyze the electroglottographic data generated by 14 patients with vocal nodules or polyps. The VWK model method shows potential in describing the nonlinearity inherent in disordered voice productions from short and noisy time series that are common in the clinical setting.
Skinner-Rusk approach to time-dependent mechanics
Cortés, Jorge; Martínez, Sonia; Cantrijn, Frans
2002-01-01
The geometric approach to autonomous classical mechanical systems in terms of a canonical first-order system on the Whitney sum of the tangent and cotangent bundle, developed by Skinner and Rusk, is extended to the time-dependent framework.
Ambiguities in the Lagrangians formalism: the time-dependent case
International Nuclear Information System (INIS)
Moreira, D.T.
1986-01-01
An intrinsic formulation of the equivalence problem for time-dependent Lagrangians is given. A new demostration of a theorem derived by Henneaux (1982) is obtained. The relationship to transformation groups is discussed. (Author) [pt
Selection and scheduling of jobs with time-dependent duration
African Journals Online (AJOL)
†Department of Logistics, University of Stellenbosch, Private Bag X1, ... station must apply to occupy the test station and sometimes may even choose ... are considered where the job duration and cost are dependent on the time and sequence.
Construction of an exact solution of time-dependent Ginzburg ...
Indian Academy of Sciences (India)
time-dependent Ginzburg–Landau (TDGL) equations we have calculated the ... The prototype of such equations is the parabolic reaction diffusion equation [7,8] ..... It may be possible to compare the above results with suitable experiments, ...
Time-dependent pseudo-reciprocity relations in neutronics
International Nuclear Information System (INIS)
Modak, R.S.; Sahni, D.C.
2002-01-01
Earlier, certain reciprocity-like relations have been shown to hold in some restricted steady state cases in neutron diffusion and transport theories. Here, the possibility of existence of similar relations in time-dependent situations is investigated
Nonequilibrium quantum solvation with a time-dependent Onsager cavity
Kirchberg, H.; Nalbach, P.; Thorwart, M.
2018-04-01
We formulate a theory of nonequilibrium quantum solvation in which parameters of the solvent are explicitly depending on time. We assume in a simplest approach a spherical molecular Onsager cavity with a time-dependent radius. We analyze the relaxation properties of a test molecular point dipole in a dielectric solvent and consider two cases: (i) a shrinking Onsager sphere and (ii) a breathing Onsager sphere. Due to the time-dependent solvent, the frequency-dependent response function of the dipole becomes time-dependent. For a shrinking Onsager sphere, the dipole relaxation is in general enhanced. This is reflected in a temporally increasing linewidth of the absorptive part of the response. Furthermore, the effective frequency-dependent response function shows two peaks in the absorptive part which are symmetrically shifted around the eigenfrequency. By contrast, a breathing sphere reduces damping as compared to the static sphere. Interestingly, we find a non-monotonous dependence of the relaxation rate on the breathing rate and a resonant suppression of damping when both rates are comparable. Moreover, the linewidth of the absorptive part of the response function is strongly reduced for times when the breathing sphere reaches its maximal extension.
Directory of Open Access Journals (Sweden)
Bin Wang
2016-01-01
Full Text Available This paper studies the application of frequency distributed model for finite time control of a fractional order nonlinear hydroturbine governing system (HGS. Firstly, the mathematical model of HGS with external random disturbances is introduced. Secondly, a novel terminal sliding surface is proposed and its stability to origin is proved based on the frequency distributed model and Lyapunov stability theory. Furthermore, based on finite time stability and sliding mode control theory, a robust control law to ensure the occurrence of the sliding motion in a finite time is designed for stabilization of the fractional order HGS. Finally, simulation results show the effectiveness and robustness of the proposed scheme.
International Nuclear Information System (INIS)
Goharrizi, Amin Yazdanpanah; Khaki-Sedigh, Ali; Sepehri, Nariman
2009-01-01
A new approach to adaptive control of chaos in a class of nonlinear discrete-time-varying systems, using a delayed state feedback scheme, is presented. It is discussed that such systems can show chaotic behavior as their parameters change. A strategy is employed for on-line calculation of the Lyapunov exponents that will be used within an adaptive scheme that decides on the control effort to suppress the chaotic behavior once detected. The scheme is further augmented with a nonlinear observer for estimation of the states that are required by the controller but are hard to measure. Simulation results for chaotic control problem of Jin map are provided to show the effectiveness of the proposed scheme.
Geometry and dynamics with time-dependent constraints
Evans, Jonathan M.; Jonathan M Evans; Philip A Tuckey
1995-01-01
We describe how geometrical methods can be applied to a system with explicitly time-dependent second-class constraints so as to cast it in Hamiltonian form on its physical phase space. Examples of particular interest are systems which require time-dependent gauge fixing conditions in order to reduce them to their physical degrees of freedom. To illustrate our results we discuss the gauge-fixing of relativistic particles and strings moving in arbitrary background electromagnetic and antisymmetric tensor fields.
Relativistic Photoionization Computations with the Time Dependent Dirac Equation
2016-10-12
Naval Research Laboratory Washington, DC 20375-5320 NRL/MR/6795--16-9698 Relativistic Photoionization Computations with the Time Dependent Dirac... Photoionization Computations with the Time Dependent Dirac Equation Daniel F. Gordon and Bahman Hafizi Naval Research Laboratory 4555 Overlook Avenue, SW...Unclassified Unlimited Unclassified Unlimited 22 Daniel Gordon (202) 767-5036 Tunneling Photoionization Ionization of inner shell electrons by laser
Stationary solution of a time dependent density matrix formalism
International Nuclear Information System (INIS)
Tohyama, Mitsuru
1994-01-01
A stationary solution of a time-dependent density-matrix formalism, which is an extension of the time-dependent Hartree-Fock theory to include the effects of two-body correlations, is obtained for the Lipkin model hamiltonian, using an adiabatic treatment of the two-body interaction. It is found that the obtained result is a reasonable approximation for the exact solution of the model. (author)
Time dependent response of equatorial ionospheric electric fieldsto magnetospheric disturbances
Fejer, Bela G.; Scherliess, L.
1995-01-01
We use extensive radar measurements of F region vertical plasma drifts and auroral electrojet indices to determine the storm time dependence of equatorial zonal electric fields. These disturbance drifts result from the prompt penetration of high latitude electric fields and from the dynamo action of storm time winds which produce largest perturbations a few hours after the onset of magnetic activity. The signatures of the equatorial disturbance electric fields change significantly depending o...
Time-dependent diffusive acceleration of test particles at shocks
Energy Technology Data Exchange (ETDEWEB)
Drury, L.O' C. (Dublin Inst. for Advanced Studies (Ireland))
1991-07-15
The acceleration of test particles at a steady plane non-relativistic shock is considered. Analytic expressions are found for the mean and the variance of the acceleration time distribution in the case where the diffusion coefficient has an arbitrary dependence on position and momentum. These expressions are used as the basis for an approximation scheme which is shown, by comparison with numerical solutions, to give an excellent representation of the time-dependent spectrum. (author).
Time-dependent diffusive acceleration of test particles at shocks
International Nuclear Information System (INIS)
Drury, L.O'C.
1991-01-01
The acceleration of test particles at a steady plane non-relativistic shock is considered. Analytic expressions are found for the mean and the variance of the acceleration time distribution in the case where the diffusion coefficient has an arbitrary dependence on position and momentum. These expressions are used as the basis for an approximation scheme which is shown, by comparison with numerical solutions, to give an excellent representation of the time-dependent spectrum. (author)
Directory of Open Access Journals (Sweden)
G. P. Pavlos
1999-01-01
Full Text Available A long AE index time series is used as a crucial magnetospheric quantity in order to study the underlying dynainics. For this purpose we utilize methods of nonlinear and chaotic analysis of time series. Two basic components of this analysis are the reconstruction of the experimental tiine series state space trajectory of the underlying process and the statistical testing of an null hypothesis. The null hypothesis against which the experimental time series are tested is that the observed AE index signal is generated by a linear stochastic signal possibly perturbed by a static nonlinear distortion. As dis ' ' ating statistics we use geometrical characteristics of the reconstructed state space (Part I, which is the work of this paper and dynamical characteristics (Part II, which is the work a separate paper, and "nonlinear" surrogate data, generated by two different techniques which can mimic the original (AE index signal. lie null hypothesis is tested for geometrical characteristics which are the dimension of the reconstructed trajectory and some new geometrical parameters introduced in this work for the efficient discrimination between the nonlinear stochastic surrogate data and the AE index. Finally, the estimated geometric characteristics of the magnetospheric AE index present new evidence about the nonlinear and low dimensional character of the underlying magnetospheric dynamics for the AE index.
Linear Scaling Solution of the Time-Dependent Self-Consistent-Field Equations
Directory of Open Access Journals (Sweden)
Matt Challacombe
2014-03-01
Full Text Available A new approach to solving the Time-Dependent Self-Consistent-Field equations is developed based on the double quotient formulation of Tsiper 2001 (J. Phys. B. Dual channel, quasi-independent non-linear optimization of these quotients is found to yield convergence rates approaching those of the best case (single channel Tamm-Dancoff approximation. This formulation is variational with respect to matrix truncation, admitting linear scaling solution of the matrix-eigenvalue problem, which is demonstrated for bulk excitons in the polyphenylene vinylene oligomer and the (4,3 carbon nanotube segment.
International Nuclear Information System (INIS)
Lo, C.F.
2009-01-01
By applying the standard analytical techniques of solving partial differential equations, we have obtained the exact solution in terms of the Fourier sine series to the time-dependent Schroedinger equation describing a quantum one-dimensional harmonic oscillator of time-dependent frequency confined in an infinite square well with the two walls moving along some parametric trajectories. Based upon the orthonormal basis of quasi-stationary wave functions, the exact propagator of the system has also been analytically derived. Special cases like (i) a confined free particle, (ii) a confined time-independent harmonic oscillator, and (iii) an aging oscillator are examined, and the corresponding time-dependent wave functions are explicitly determined. Besides, the approach has been extended to solve the case of a confined generalized time-dependent harmonic oscillator for some parametric moving boundaries as well. (general)
International Nuclear Information System (INIS)
Hamann, Jan; Hannestad, Steen; Melchiorri, Alessandro; Wong, Yvonne Y Y
2008-01-01
We explore and compare the performances of two non-linear correction and scale-dependent biasing models for the extraction of cosmological information from galaxy power spectrum data, especially in the context of beyond-ΛCDM (CDM: cold dark matter) cosmologies. The first model is the well known Q model, first applied in the analysis of Two-degree Field Galaxy Redshift Survey data. The second, the P model, is inspired by the halo model, in which non-linear evolution and scale-dependent biasing are encapsulated in a single non-Poisson shot noise term. We find that while the two models perform equally well in providing adequate correction for a range of galaxy clustering data in standard ΛCDM cosmology and in extensions with massive neutrinos, the Q model can give unphysical results in cosmologies containing a subdominant free-streaming dark matter whose temperature depends on the particle mass, e.g., relic thermal axions, unless a suitable prior is imposed on the correction parameter. This last case also exposes the danger of analytic marginalization, a technique sometimes used in the marginalization of nuisance parameters. In contrast, the P model suffers no undesirable effects, and is the recommended non-linear correction model also because of its physical transparency
Hamann, Jan; Hannestad, Steen; Melchiorri, Alessandro; Wong, Yvonne Y. Y.
2008-07-01
We explore and compare the performances of two non-linear correction and scale-dependent biasing models for the extraction of cosmological information from galaxy power spectrum data, especially in the context of beyond-ΛCDM (CDM: cold dark matter) cosmologies. The first model is the well known Q model, first applied in the analysis of Two-degree Field Galaxy Redshift Survey data. The second, the P model, is inspired by the halo model, in which non-linear evolution and scale-dependent biasing are encapsulated in a single non-Poisson shot noise term. We find that while the two models perform equally well in providing adequate correction for a range of galaxy clustering data in standard ΛCDM cosmology and in extensions with massive neutrinos, the Q model can give unphysical results in cosmologies containing a subdominant free-streaming dark matter whose temperature depends on the particle mass, e.g., relic thermal axions, unless a suitable prior is imposed on the correction parameter. This last case also exposes the danger of analytic marginalization, a technique sometimes used in the marginalization of nuisance parameters. In contrast, the P model suffers no undesirable effects, and is the recommended non-linear correction model also because of its physical transparency.
Time-dependent reliability analysis of flood defences
International Nuclear Information System (INIS)
Buijs, F.A.; Hall, J.W.; Sayers, P.B.; Gelder, P.H.A.J.M. van
2009-01-01
This paper describes the underlying theory and a practical process for establishing time-dependent reliability models for components in a realistic and complex flood defence system. Though time-dependent reliability models have been applied frequently in, for example, the offshore, structural safety and nuclear industry, application in the safety-critical field of flood defence has to date been limited. The modelling methodology involves identifying relevant variables and processes, characterisation of those processes in appropriate mathematical terms, numerical implementation, parameter estimation and prediction. A combination of stochastic, hierarchical and parametric processes is employed. The approach is demonstrated for selected deterioration mechanisms in the context of a flood defence system. The paper demonstrates that this structured methodology enables the definition of credible statistical models for time-dependence of flood defences in data scarce situations. In the application of those models one of the main findings is that the time variability in the deterioration process tends to be governed the time-dependence of one or a small number of critical attributes. It is demonstrated how the need for further data collection depends upon the relevance of the time-dependence in the performance of the flood defence system.
Time-dependent Bragg diffraction by multilayer gratings
International Nuclear Information System (INIS)
André, Jean-Michel; Jonnard, Philippe
2016-01-01
Time-dependent Bragg diffraction by multilayer gratings working by reflection or by transmission is investigated. The study is performed by generalizing the time-dependent coupled-wave theory previously developed for one-dimensional photonic crystals (André J-M and Jonnard P 2015 J. Opt. 17 085609) and also by extending the Takagi–Taupin approach of the dynamical theory of diffraction. The indicial response is calculated. It presents a time delay with a transient time that is a function of the extinction length for reflection geometry and of the extinction length combined with the thickness of the grating for transmission geometry. (paper)
Zheng, Xiao; Yam, ChiYung; Wang, Fan; Chen, GuanHua
2011-08-28
We present the time-dependent holographic electron density theorem (TD-HEDT), which lays the foundation of time-dependent density-functional theory (TDDFT) for open electronic systems. For any finite electronic system, the TD-HEDT formally establishes a one-to-one correspondence between the electron density inside any finite subsystem and the time-dependent external potential. As a result, any electronic property of an open system in principle can be determined uniquely by the electron density function inside the open region. Implications of the TD-HEDT on the practicality of TDDFT are also discussed.
Time-dependent mean-field games in the superquadratic case
Gomes, Diogo A.
2016-04-06
We investigate time-dependent mean-field games with superquadratic Hamiltonians and a power dependence on the measure. Such problems pose substantial mathematical challenges as key techniques used in the subquadratic case, which was studied in a previous publication of the authors, do not extend to the superquadratic setting. The main objective of the present paper is to address these difficulties. Because of the superquadratic structure of the Hamiltonian, Lipschitz estimates for the solutions of the Hamilton−Jacobi equation are obtained here through a novel set of techniques. These explore the parabolic nature of the problem through the nonlinear adjoint method. Well-posedness is proven by combining Lipschitz regularity for the Hamilton−Jacobi equation with polynomial estimates for solutions of the Fokker−Planck equation. Existence of classical solutions is then established under conditions depending only on the growth of the Hamiltonian and the dimension. Our results also add to current understanding of superquadratic Hamilton−Jacobi equations.
Time-dependent mean-field games in the superquadratic case
Gomes, Diogo A.; Pimentel, Edgard; Sá nchez-Morgado, Hé ctor
2016-01-01
We investigate time-dependent mean-field games with superquadratic Hamiltonians and a power dependence on the measure. Such problems pose substantial mathematical challenges as key techniques used in the subquadratic case, which was studied in a previous publication of the authors, do not extend to the superquadratic setting. The main objective of the present paper is to address these difficulties. Because of the superquadratic structure of the Hamiltonian, Lipschitz estimates for the solutions of the Hamilton−Jacobi equation are obtained here through a novel set of techniques. These explore the parabolic nature of the problem through the nonlinear adjoint method. Well-posedness is proven by combining Lipschitz regularity for the Hamilton−Jacobi equation with polynomial estimates for solutions of the Fokker−Planck equation. Existence of classical solutions is then established under conditions depending only on the growth of the Hamiltonian and the dimension. Our results also add to current understanding of superquadratic Hamilton−Jacobi equations.
Time-dependent delayed signatures from energetic photon interrogations
International Nuclear Information System (INIS)
Norman, Daren R.; Jones, James L.; Blackburn, Brandon W.; Haskell, Kevin J.; Johnson, James T.; Watson, Scott M.; Hunt, Alan W.; Spaulding, Randy; Harmon, Frank
2007-01-01
Pulsed photonuclear interrogation environments generated by 8-24 MeV electron linac are rich with time-dependent, material-specific, radiation signatures. Nitrogen-based explosives and nuclear materials can be detected by exploiting these signatures in different delayed-time regions. Numerical and experimental results presented in this paper show the unique time and energy dependence of these signatures. It is shown that appropriate delayed-time windows are essential to acquire material-specific signatures in pulsed photonuclear assessment environments. These developments demonstrate that pulsed, high-energy, photon-inspection environments can be exploited for time-dependent, material-specific signatures through the proper operation of specialized detectors and detection methods
Empirical method to measure stochasticity and multifractality in nonlinear time series
Lin, Chih-Hao; Chang, Chia-Seng; Li, Sai-Ping
2013-12-01
An empirical algorithm is used here to study the stochastic and multifractal nature of nonlinear time series. A parameter can be defined to quantitatively measure the deviation of the time series from a Wiener process so that the stochasticity of different time series can be compared. The local volatility of the time series under study can be constructed using this algorithm, and the multifractal structure of the time series can be analyzed by using this local volatility. As an example, we employ this method to analyze financial time series from different stock markets. The result shows that while developed markets evolve very much like an Ito process, the emergent markets are far from efficient. Differences about the multifractal structures and leverage effects between developed and emergent markets are discussed. The algorithm used here can be applied in a similar fashion to study time series of other complex systems.
Watching excitons move: the time-dependent transition density matrix
Ullrich, Carsten
2012-02-01
Time-dependent density-functional theory allows one to calculate excitation energies and the associated transition densities in principle exactly. The transition density matrix (TDM) provides additional information on electron-hole localization and coherence of specific excitations of the many-body system. We have extended the TDM concept into the real-time domain in order to visualize the excited-state dynamics in conjugated molecules. The time-dependent TDM is defined as an implicit density functional, and can be approximately obtained from the time-dependent Kohn-Sham orbitals. The quality of this approximation is assessed in simple model systems. A computational scheme for real molecular systems is presented: the time-dependent Kohn-Sham equations are solved with the OCTOPUS code and the time-dependent Kohn-Sham TDM is calculated using a spatial partitioning scheme. The method is applied to show in real time how locally created electron-hole pairs spread out over neighboring conjugated molecular chains. The coupling mechanism, electron-hole coherence, and the possibility of charge separation are discussed.
Forced phase-locked response of a nonlinear system with time delay after Hopf bifurcation
International Nuclear Information System (INIS)
Ji, J.C.; Hansen, Colin H.
2005-01-01
The trivial equilibrium of a nonlinear autonomous system with time delay may become unstable via a Hopf bifurcation of multiplicity two, as the time delay reaches a critical value. This loss of stability of the equilibrium is associated with two coincident pairs of complex conjugate eigenvalues crossing the imaginary axis. The resultant dynamic behaviour of the corresponding nonlinear non-autonomous system in the neighbourhood of the Hopf bifurcation is investigated based on the reduction of the infinite-dimensional problem to a four-dimensional centre manifold. As a result of the interaction between the Hopf bifurcating periodic solutions and the external periodic excitation, a primary resonance can occur in the forced response of the system when the forcing frequency is close to the Hopf bifurcating periodic frequency. The method of multiple scales is used to obtain four first-order ordinary differential equations that determine the amplitudes and phases of the phase-locked periodic solutions. The first-order approximations of the periodic solutions are found to be in excellent agreement with those obtained by direct numerical integration of the delay-differential equation. It is also found that the steady state solutions of the nonlinear non-autonomous system may lose their stability via either a pitchfork or Hopf bifurcation. It is shown that the primary resonance response may exhibit symmetric and asymmetric phase-locked periodic motions, quasi-periodic motions, chaotic motions, and coexistence of two stable motions
Rational solitons in the parity-time-symmetric nonlocal nonlinear Schrödinger model
International Nuclear Information System (INIS)
Li Min; Xu Tao; Meng Dexin
2016-01-01
In this paper, via the generalized Darboux transformation, rational soliton solutions are derived for the parity-time-symmetric nonlocal nonlinear Schrödinger (NLS) model with the defocusing-type nonlinearity. We find that the first-order solution can exhibit the elastic interactions of rational antidark-antidark, dark-antidark, and antidark-dark soliton pairs on a continuous wave background, but there is no phase shift for the interacting solitons. Also, we discuss the degenerate case in which only one rational dark or antidark soliton survives. Moreover, we reveal that the second-order rational solution displays the interactions between two solitons with combined-peak-valley structures in the near-field regions, but each interacting soliton vanishes or evolves into a rational dark or antidark soliton as |z| → ∞. In addition, we numerically examine the stability of the first- and second-order rational soliton solutions. (author)
Time-Frequency (Wigner Analysis of Linear and Nonlinear Pulse Propagation in Optical Fibers
Directory of Open Access Journals (Sweden)
José Azaña
2005-06-01
Full Text Available Time-frequency analysis, and, in particular, Wigner analysis, is applied to the study of picosecond pulse propagation through optical fibers in both the linear and nonlinear regimes. The effects of first- and second-order group velocity dispersion (GVD and self-phase modulation (SPM are first analyzed separately. The phenomena resulting from the interplay between GVD and SPM in fibers (e.g., soliton formation or optical wave breaking are also investigated in detail. Wigner analysis is demonstrated to be an extremely powerful tool for investigating pulse propagation dynamics in nonlinear dispersive systems (e.g., optical fibers, providing a clearer and deeper insight into the physical phenomena that determine the behavior of these systems.
Esfandiari, Kasra; Abdollahi, Farzaneh; Talebi, Heidar Ali
2017-09-01
In this paper, an identifier-critic structure is introduced to find an online near-optimal controller for continuous-time nonaffine nonlinear systems having saturated control signal. By employing two Neural Networks (NNs), the solution of Hamilton-Jacobi-Bellman (HJB) equation associated with the cost function is derived without requiring a priori knowledge about system dynamics. Weights of the identifier and critic NNs are tuned online and simultaneously such that unknown terms are approximated accurately and the control signal is kept between the saturation bounds. The convergence of NNs' weights, identification error, and system states is guaranteed using Lyapunov's direct method. Finally, simulation results are performed on two nonlinear systems to confirm the effectiveness of the proposed control strategy. Copyright © 2017 Elsevier Ltd. All rights reserved.
Yang, Xiong; Liu, Derong; Wang, Ding
2014-03-01
In this paper, an adaptive reinforcement learning-based solution is developed for the infinite-horizon optimal control problem of constrained-input continuous-time nonlinear systems in the presence of nonlinearities with unknown structures. Two different types of neural networks (NNs) are employed to approximate the Hamilton-Jacobi-Bellman equation. That is, an recurrent NN is constructed to identify the unknown dynamical system, and two feedforward NNs are used as the actor and the critic to approximate the optimal control and the optimal cost, respectively. Based on this framework, the action NN and the critic NN are tuned simultaneously, without the requirement for the knowledge of system drift dynamics. Moreover, by using Lyapunov's direct method, the weights of the action NN and the critic NN are guaranteed to be uniformly ultimately bounded, while keeping the closed-loop system stable. To demonstrate the effectiveness of the present approach, simulation results are illustrated.
International Nuclear Information System (INIS)
Hasegawa, M.; Nakai, S.; Watanabe, T.
1985-01-01
A practical method for elasto-plastic seismic response analysis is described under considerations of nonlinear material law of a structure and dynamic soil-structure interaction. The method is essentially based on the substructure approach of time domain analysis. Verification of the present method is carried out for typical BWR-MARK II type reactor building which is embedded in a soil, and the results are compared with those of the frequency response analysis which gives good accuracy for linear system. As a result, the present method exhibits sufficient accuracy. Furthermore, elasto-plastic analyses considering the soil-structure interaction are made as an application of the present method, and nonlinear behaviors of the structure and embedment effects are discussed. (orig.)
Alabastri, A.; Tuccio, S.; Giugni, A.; Toma, A.; Liberale, Carlo; Das, G.; Angelis, F.D.; Fabrizio, E.D.; Zaccaria, R.P.
2013-01-01
In this paper, we review the principal theoretical models through which the dielectric function of metals can be described. Starting from the Drude assumptions for intraband transitions, we show how this model can be improved by including interband absorption and temperature effect in the damping coefficients. Electronic scattering processes are described and included in the dielectric function, showing their role in determining plasmon lifetime at resonance. Relationships among permittivity, electric conductivity and refractive index are examined. Finally, a temperature dependent permittivity model is presented and is employed to predict temperature and non-linear field intensity dependence on commonly used plasmonic geometries, such as nanospheres. 2013 by the authors; licensee MDPI, Basel, Switzerland.
Alabastri, A.
2013-10-25
In this paper, we review the principal theoretical models through which the dielectric function of metals can be described. Starting from the Drude assumptions for intraband transitions, we show how this model can be improved by including interband absorption and temperature effect in the damping coefficients. Electronic scattering processes are described and included in the dielectric function, showing their role in determining plasmon lifetime at resonance. Relationships among permittivity, electric conductivity and refractive index are examined. Finally, a temperature dependent permittivity model is presented and is employed to predict temperature and non-linear field intensity dependence on commonly used plasmonic geometries, such as nanospheres. 2013 by the authors; licensee MDPI, Basel, Switzerland.
Directory of Open Access Journals (Sweden)
Chuan-Li Zhao
2014-01-01
Full Text Available This paper considers single machine scheduling and due date assignment with setup time. The setup time is proportional to the length of the already processed jobs; that is, the setup time is past-sequence-dependent (p-s-d. It is assumed that a job's processing time depends on its position in a sequence. The objective functions include total earliness, the weighted number of tardy jobs, and the cost of due date assignment. We analyze these problems with two different due date assignment methods. We first consider the model with job-dependent position effects. For each case, by converting the problem to a series of assignment problems, we proved that the problems can be solved in On4 time. For the model with job-independent position effects, we proved that the problems can be solved in On3 time by providing a dynamic programming algorithm.
Non-Linear Dependence and Teleconnections in Climate Data: Sources, Relevance, Nonstationarity
Czech Academy of Sciences Publication Activity Database
Hlinka, Jaroslav; Hartman, David; Vejmelka, Martin; Novotná, Dagmar; Paluš, Milan
2014-01-01
Roč. 42, č. 7-8 (2014), s. 1873-1886 ISSN 0930-7575 R&D Projects: GA ČR GCP103/11/J068 Institutional support: RVO:67985807 ; RVO:68378289 Keywords : climate networks * nonlinearity * mutual information * teleconnections * seasonality in variance * nonstationarity Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 4.673, year: 2014
Directory of Open Access Journals (Sweden)
Hailong Zhu
2012-01-01
Full Text Available The existence and multiplicity of solutions for second-order differential equations with a parameter are discussed in this paper. We are mainly concerned with the semipositone case. The analysis relies on the nonlinear alternative principle of Leray-Schauder and Krasnosel'skii's fixed point theorem in cones.
Nonlinear System Identification via Basis Functions Based Time Domain Volterra Model
Directory of Open Access Journals (Sweden)
Yazid Edwar
2014-07-01
Full Text Available This paper proposes basis functions based time domain Volterra model for nonlinear system identification. The Volterra kernels are expanded by using complex exponential basis functions and estimated via genetic algorithm (GA. The accuracy and practicability of the proposed method are then assessed experimentally from a scaled 1:100 model of a prototype truss spar platform. Identification results in time and frequency domain are presented and coherent functions are performed to check the quality of the identification results. It is shown that results between experimental data and proposed method are in good agreement.
Simplified non-linear time-history analysis based on the Theory of Plasticity
DEFF Research Database (Denmark)
Costa, Joao Domingues
2005-01-01
This paper aims at giving a contribution to the problem of developing simplified non-linear time-history (NLTH) analysis of structures which dynamical response is mainly governed by plastic deformations, able to provide designers with sufficiently accurate results. The method to be presented...... is based on the Theory of Plasticity. Firstly, the formulation and the computational procedure to perform time-history analysis of a rigid-plastic single degree of freedom (SDOF) system are presented. The necessary conditions for the method to incorporate pinching as well as strength degradation...
On solutions of nonlinear time-space fractional Swift–Hohenberg equation: A comparative study
Directory of Open Access Journals (Sweden)
Najeeb Alam Khan
2014-03-01
Full Text Available In this paper, a comparison for the solutions of nonlinear Swift–Hohenberg equation with time-space fractional derivatives has been analyzed. The two most promising techniques, fractional variational iteration method (FVIM and the homotopy analysis method have been chosen for the comparison. The two different definitions of fractional calculus are considered to solve time-fractional derivative separately for the considered approaches. Also, the space fractional derivative is described in the Reisz sense. Analytical and numerical solutions for various combinations of the parameters are obtained. Numerical comparisons have been made for different values of parameters and depicted.
Finite-time output feedback stabilization of high-order uncertain nonlinear systems
Jiang, Meng-Meng; Xie, Xue-Jun; Zhang, Kemei
2018-06-01
This paper studies the problem of finite-time output feedback stabilization for a class of high-order nonlinear systems with the unknown output function and control coefficients. Under the weaker assumption that output function is only continuous, by using homogeneous domination method together with adding a power integrator method, introducing a new analysis method, the maximal open sector Ω of output function is given. As long as output function belongs to any closed sector included in Ω, an output feedback controller can be developed to guarantee global finite-time stability of the closed-loop system.
Student Understanding of Time Dependence in Quantum Mechanics
Emigh, Paul J.; Passante, Gina; Shaffer, Peter S.
2015-01-01
The time evolution of quantum states is arguably one of the more difficult ideas in quantum mechanics. In this article, we report on results from an investigation of student understanding of this topic after lecture instruction. We demonstrate specific problems that students have in applying time dependence to quantum systems and in recognizing…
Simulation of compressible viscous flow in time-dependent domains
Czech Academy of Sciences Publication Activity Database
Česenek, J.; Feistauer, M.; Horáček, Jaromír; Kučera, V.; Prokopova, J.
2013-01-01
Roč. 219, č. 13 (2013), s. 7139-7150 ISSN 0096-3003 R&D Projects: GA ČR(CZ) GAP101/11/0207 Institutional support: RVO:61388998 Keywords : time dependent domain * ALE method * semi-implicit time discretization * shock indicator Subject RIV: BI - Acoustics Impact factor: 1.600, year: 2013
Investment horizons : A time-dependent measure of asset performance
Ingve Simonsen; Anders Johansen; Mogens H. Jensen
2005-01-01
We review a resent {\\em time-dependent} performance measure for economical time series -- the (optimal) investment horizon approach. For stock indices, the approach shows a pronounced gain-loss asymmetry that is {\\em not} observed for the individual stocks that comprise the index. This difference may hint towards an synchronize of the draw downs of the stocks.
Propagator of a time-dependent unbound quadratic Hamiltonian system
International Nuclear Information System (INIS)
Yeon, K.H.; Kim, H.J.; Um, C.I.; George, T.F.; Pandey, L.N.
1996-01-01
The propagator for a time-dependent unbound quadratic Hamiltonian system is explicitly evaluated using the path integral method. Two time-invariant quantities of the system are found where these invariants determine whether or not the system is bound. Several examples are considered to illustrate that the propagator obtained for the unbound systems is correct
The evolution of streams in a time-dependent potential
Buist, Hans J. T.; Helmi, Amina
2015-01-01
We study the evolution of streams in a time-dependent spherical gravitational potential. Our goal is to establish what are the imprints of this time evolution on the properties of streams as well as their observability. To this end, we have performed a suite of test-particle experiments for a host
Asymptotic time dependent neutron transport in multidimensional systems
International Nuclear Information System (INIS)
Nagy, M.E.; Sawan, M.E.; Wassef, W.A.; El-Gueraly, L.A.
1983-01-01
A model which predicts the asymptotic time behavior of the neutron distribution in multi-dimensional systems is presented. The model is based on the kernel factorization method used for stationary neutron transport in a rectangular parallelepiped. The accuracy of diffusion theory in predicting the asymptotic time dependence is assessed. The use of neutron pulse experiments for predicting the diffusion parameters is also investigated
Stability of orbits in nonlinear mechanics for finite but very long times
International Nuclear Information System (INIS)
Warnock, R.L.; Ruth, R.D.
1990-07-01
In various applications of nonlinear mechanics, especially in accelerator design, it would be useful to set bounds on the motion for finite but very long times. Such bounds can be sought with the help of a canonical transformation to new action-angle variables (J, Ψ), such that action J is nearly constant while the angle Ψ advances almost linearly with the time. By examining the change in J during a time T 0 from many initial conditions in the open domain Ω of phase space, one can estimate the change in J during a much larger time T, on any orbit starting in a smaller open domain Ω 0 contained-in Ω. A numerical realization of this idea is described. The canonical transformations, equivalent to close approximations to invariant tori, are constructed by an effective new method in which surfaces are fitted to orbit data. In a first application to a model sextupole lattice in a region of strong nonlinearity, we predict stability of betatron motion in two degrees of freedom for a time comparable to the storage time in a proton storage ring (10 8 turns). 10 refs., 6 figs., 1 tab
Stability of orbits in nonlinear mechanics for finite but very long times
Energy Technology Data Exchange (ETDEWEB)
Warnock, R.L.; Ruth, R.D.
1990-07-01
In various applications of nonlinear mechanics, especially in accelerator design, it would be useful to set bounds on the motion for finite but very long times. Such bounds can be sought with the help of a canonical transformation to new action-angle variables (J, {Psi}), such that action J is nearly constant while the angle {Psi} advances almost linearly with the time. By examining the change in J during a time T{sub 0} from many initial conditions in the open domain {Omega} of phase space, one can estimate the change in J during a much larger time T, on any orbit starting in a smaller open domain {Omega}{sub 0} {contained in} {Omega}. A numerical realization of this idea is described. The canonical transformations, equivalent to close approximations to invariant tori, are constructed by an effective new method in which surfaces are fitted to orbit data. In a first application to a model sextupole lattice in a region of strong nonlinearity, we predict stability of betatron motion in two degrees of freedom for a time comparable to the storage time in a proton storage ring (10{sup 8} turns). 10 refs., 6 figs., 1 tab.
Characterization of Models for Time-Dependent Behavior of Soils
DEFF Research Database (Denmark)
Liingaard, Morten; Augustesen, Anders; Lade, Poul V.
2004-01-01
Different classes of constitutive models have been developed to capture the time-dependent viscous phenomena ~ creep, stress relaxation, and rate effects ! observed in soils. Models based on empirical, rheological, and general stress-strain-time concepts have been studied. The first part....... Special attention is paid to elastoviscoplastic models that combine inviscid elastic and time-dependent plastic behavior. Various general elastoviscoplastic models can roughly be divided into two categories: Models based on the concept of overstress and models based on nonstationary flow surface theory...
Time-dependent massless Dirac fermions in graphene
Energy Technology Data Exchange (ETDEWEB)
Khantoul, Boubakeur, E-mail: bobphys@gmail.com [Department of Mathematics, City University London, Northampton Square, London EC1V 0HB (United Kingdom); Department of Physics, University of Jijel, BP 98, Ouled Aissa, 18000 Jijel (Algeria); Fring, Andreas, E-mail: a.fring@city.ac.uk [Department of Mathematics, City University London, Northampton Square, London EC1V 0HB (United Kingdom)
2015-10-30
Using the Lewis–Riesenfeld method of invariants we construct explicit analytical solutions for the massless Dirac equation in 2+1 dimensions describing quasi-particles in graphene. The Hamiltonian of the system considered contains some explicit time-dependence in addition to one resulting from being minimally coupled to a time-dependent vector potential. The eigenvalue equations for the two spinor components of the Lewis–Riesenfeld invariant are found to decouple into a pair of supersymmetric invariants in a similar fashion as the known decoupling for the time-independent Dirac Hamiltonians. - Highlights: • An explicit analytical solution for a massless 2+1 dimensional time-dependent Dirac equation is found. • All steps of the Lewis–Riesenfeld method have been carried out.
Fundamental Constants in Physics and their Time Dependence
CERN. Geneva
2008-01-01
In the Standard Model of Particle Physics we are dealing with 28 fundamental constants. In the experiments these constants can be measured, but theoretically they are not understood. I will discuss these constants, which are mostly mass parameters. Astrophysical measurements indicate that the finestructure constant is not a real constant, but depends on time. Grand unification then implies also a time variation of the QCD scale. Thus the masses of the atomic nuclei and the magnetic moments of the nuclei will depend on time. I proposed an experiment, which is currently done by Prof. Haensch in Munich and his group. The first results indicate a time dependence of the QCD scale. I will discuss the theoretical implications.
Computational complexity of time-dependent density functional theory
International Nuclear Information System (INIS)
Whitfield, J D; Yung, M-H; Tempel, D G; Aspuru-Guzik, A; Boixo, S
2014-01-01
Time-dependent density functional theory (TDDFT) is rapidly emerging as a premier method for solving dynamical many-body problems in physics and chemistry. The mathematical foundations of TDDFT are established through the formal existence of a fictitious non-interacting system (known as the Kohn–Sham system), which can reproduce the one-electron reduced probability density of the actual system. We build upon these works and show that on the interior of the domain of existence, the Kohn–Sham system can be efficiently obtained given the time-dependent density. We introduce a V-representability parameter which diverges at the boundary of the existence domain and serves to quantify the numerical difficulty of constructing the Kohn-Sham potential. For bounded values of V-representability, we present a polynomial time quantum algorithm to generate the time-dependent Kohn–Sham potential with controllable error bounds. (paper)
Directory of Open Access Journals (Sweden)
Maximilian B Maier
Full Text Available The effect of high pressure thermal (HPT processing on the inactivation of spores of proteolytic type B Clostridium botulinum TMW 2.357 in four differently composed low-acid foods (green peas with ham, steamed sole, vegetable soup, braised veal was studied in an industrially feasible pressure range and temperatures between 100 and 120°C. Inactivation curves exhibited rapid inactivation during compression and decompression followed by strong tailing effects. The highest inactivation (approx. 6-log cycle reduction was obtained in braised veal at 600 MPa and 110°C after 300 s pressure-holding time. In general, inactivation curves exhibited similar negative exponential shapes, but maximum achievable inactivation levels were lower in foods with higher fat contents. At high treatment temperatures, spore inactivation was more effective at lower pressure levels (300 vs. 600 MPa, which indicates a non-linear pressure/temperature-dependence of the HPT spore inactivation efficiency. A comparison of spore inactivation levels achievable using HPT treatments versus a conventional heat sterilization treatment (121.1°C, 3 min illustrates the potential of combining high pressures and temperatures to replace conventional retorting with the possibility to reduce the process temperature or shorten the processing time. Finally, experiments using varying spore inoculation levels suggested the presence of a resistant fraction comprising approximately 0.01% of a spore population as reason for the pronounced tailing effects in survivor curves. The loss of the high resistance properties upon cultivation indicates that those differences develop during sporulation and are not linked to permanent modifications at the genetic level.
Donges, Jonathan; Heitzig, Jobst; Beronov, Boyan; Wiedermann, Marc; Runge, Jakob; Feng, Qing Yi; Tupikina, Liubov; Stolbova, Veronika; Donner, Reik; Marwan, Norbert; Dijkstra, Henk; Kurths, Jürgen
2016-04-01
We introduce the pyunicorn (Pythonic unified complex network and recurrence analysis toolbox) open source software package for applying and combining modern methods of data analysis and modeling from complex network theory and nonlinear time series analysis. pyunicorn is a fully object-oriented and easily parallelizable package written in the language Python. It allows for the construction of functional networks such as climate networks in climatology or functional brain networks in neuroscience representing the structure of statistical interrelationships in large data sets of time series and, subsequently, investigating this structure using advanced methods of complex network theory such as measures and models for spatial networks, networks of interacting networks, node-weighted statistics, or network surrogates. Additionally, pyunicorn provides insights into the nonlinear dynamics of complex systems as recorded in uni- and multivariate time series from a non-traditional perspective by means of recurrence quantification analysis, recurrence networks, visibility graphs, and construction of surrogate time series. The range of possible applications of the library is outlined, drawing on several examples mainly from the field of climatology. pyunicorn is available online at https://github.com/pik-copan/pyunicorn. Reference: J.F. Donges, J. Heitzig, B. Beronov, M. Wiedermann, J. Runge, Q.-Y. Feng, L. Tupikina, V. Stolbova, R.V. Donner, N. Marwan, H.A. Dijkstra, and J. Kurths, Unified functional network and nonlinear time series analysis for complex systems science: The pyunicorn package, Chaos 25, 113101 (2015), DOI: 10.1063/1.4934554, Preprint: arxiv.org:1507.01571 [physics.data-an].
New insights into soil temperature time series modeling: linear or nonlinear?
Bonakdari, Hossein; Moeeni, Hamid; Ebtehaj, Isa; Zeynoddin, Mohammad; Mahoammadian, Abdolmajid; Gharabaghi, Bahram
2018-03-01
Soil temperature (ST) is an important dynamic parameter, whose prediction is a major research topic in various fields including agriculture because ST has a critical role in hydrological processes at the soil surface. In this study, a new linear methodology is proposed based on stochastic methods for modeling daily soil temperature (DST). With this approach, the ST series components are determined to carry out modeling and spectral analysis. The results of this process are compared with two linear methods based on seasonal standardization and seasonal differencing in terms of four DST series. The series used in this study were measured at two stations, Champaign and Springfield, at depths of 10 and 20 cm. The results indicate that in all ST series reviewed, the periodic term is the most robust among all components. According to a comparison of the three methods applied to analyze the various series components, it appears that spectral analysis combined with stochastic methods outperformed the seasonal standardization and seasonal differencing methods. In addition to comparing the proposed methodology with linear methods, the ST modeling results were compared with the two nonlinear methods in two forms: considering hydrological variables (HV) as input variables and DST modeling as a time series. In a previous study at the mentioned sites, Kim and Singh Theor Appl Climatol 118:465-479, (2014) applied the popular Multilayer Perceptron (MLP) neural network and Adaptive Neuro-Fuzzy Inference System (ANFIS) nonlinear methods and considered HV as input variables. The comparison results signify that the relative error projected in estimating DST by the proposed methodology was about 6%, while this value with MLP and ANFIS was over 15%. Moreover, MLP and ANFIS models were employed for DST time series modeling. Due to these models' relatively inferior performance to the proposed methodology, two hybrid models were implemented: the weights and membership function of MLP and
Predicting long-term catchment nutrient export: the use of nonlinear time series models
Valent, Peter; Howden, Nicholas J. K.; Szolgay, Jan; Komornikova, Magda
2010-05-01
After the Second World War the nitrate concentrations in European water bodies changed significantly as the result of increased nitrogen fertilizer use and changes in land use. However, in the last decades, as a consequence of the implementation of nitrate-reducing measures in Europe, the nitrate concentrations in water bodies slowly decrease. This causes that the mean and variance of the observed time series also changes with time (nonstationarity and heteroscedascity). In order to detect changes and properly describe the behaviour of such time series by time series analysis, linear models (such as autoregressive (AR), moving average (MA) and autoregressive moving average models (ARMA)), are no more suitable. Time series with sudden changes in statistical characteristics can cause various problems in the calibration of traditional water quality models and thus give biased predictions. Proper statistical analysis of these non-stationary and heteroscedastic time series with the aim of detecting and subsequently explaining the variations in their statistical characteristics requires the use of nonlinear time series models. This information can be then used to improve the model building and calibration of conceptual water quality model or to select right calibration periods in order to produce reliable predictions. The objective of this contribution is to analyze two long time series of nitrate concentrations of the rivers Ouse and Stour with advanced nonlinear statistical modelling techniques and compare their performance with traditional linear models of the ARMA class in order to identify changes in the time series characteristics. The time series were analysed with nonlinear models with multiple regimes represented by self-exciting threshold autoregressive (SETAR) and Markov-switching models (MSW). The analysis showed that, based on the value of residual sum of squares (RSS) in both datasets, SETAR and MSW models described the time-series better than models of the
DEFF Research Database (Denmark)
Jimenez, M.J.; Madsen, Henrik; Bloem, J.J.
2008-01-01
This paper focuses on a method for linear or non-linear continuous time modelling of physical systems using discrete time data. This approach facilitates a more appropriate modelling of more realistic non-linear systems. Particularly concerning advanced building components, convective and radiati...... that a description of the non-linear heat transfer is essential. The resulting model is a non-linear first order stochastic differential equation for the heat transfer of the PV component....... heat interchanges are non-linear effects and represent significant contributions in a variety of components such as photovoltaic integrated facades or roofs and those using these effects as passive cooling strategies, etc. Since models are approximations of the physical system and data is encumbered...
Time dependence of the pH of rain
John A. Kadlecek; Volkar A. Mohnen
1976-01-01
Standard procedures for determining the pH of rain samples usually involve substantial delays from the time of rainfall to the time of analysis. This assumes that no change in pH occurs during the storage period. We have found that this is not always true. We have determined that individual rain water samples possess a time dependent pH which can be correlated with the...
Analysis of multimedian problems on time dependent networks
Salman, F Sibel
1994-01-01
Ankara : The Department of Industrial Engineering and the Institute of Enginering and Science of Bilkent Univ., 1994. Thesis (Master's) -- Bilkent University, 1994. Includes bibliographical references leaves 81-85. Time dependency arises in transportation and computer-communication networks due to factors such as time varying demand, traffic intensity, and road conditions. This necessitates a locational decision to be based on an analysis involving a time horizon. In this st...
International Nuclear Information System (INIS)
Haug, E.; Rouvray, A.L. de; Nguyen, Q.S.
1977-01-01
This study proposes a general nonlinear algorithm stability criterion; it introduces a nonlinear algorithm, easily implemented in existing incremental/iterative codes, and it applies the new scheme beneficially to problems of linear elastic dynamic snap buckling. Based on the concept of energy conservation, the paper outlines an algorithm which degenerates into the trapezoidal rule, if applied to linear systems. The new algorithm conserves energy in systems having elastic potentials up to the fourth order in the displacements. This is true in the important case of nonlinear total Lagrange formulations where linear elastic material properties are substituted. The scheme is easily implemented in existing incremental-iterative codes with provisions for stiffness reformation and containing the basic Newmark scheme. Numerical analyses of dynamic stability can be dramatically sensitive to amplitude errors, because damping algorithms may mask, and overestimating schemes may numerically trigger, the physical instability. The newly proposed scheme has been applied with larger time steps and less cost to the dynamic snap buckling of simple one and multi degree-of-freedom structures for various initial conditions
Optimum Control for Nonlinear Dynamic Radial Deformation of Turbine Casing with Time-Varying LSSVM
Directory of Open Access Journals (Sweden)
Cheng-Wei Fei
2015-01-01
Full Text Available With the development of the high performance and high reliability of aeroengine, the blade-tip radial running clearance (BTRRC of high pressure turbine seriously influences the reliability and performance of aeroengine, wherein the radial deformation control of turbine casing has to be concerned in BTRRC design. To improve BTRRC design, the optimum control-based probabilistic optimization of turbine casing radial deformation was implemented using time-varying least square support vector machine (T-LSSVM by considering nonlinear material properties and dynamic thermal load. First the T-LSSVM method was proposed and its mathematical model was established. And then the nonlinear dynamic optimal control model of casing radial deformation was constructed with T-LSSVM. Thirdly, through the numerical experiments, the T-LSSVM method is demonstrated to be a promising approach in reducing additional design samples and improving computational efficiency with acceptable computational precision. Through the optimum control-based probabilistic optimization for nonlinear dynamic radial turbine casing deformation, the optimum radial deformation is 7.865 × 10−4 m with acceptable reliability degree 0.995 6, which is reduced by 7.86 × 10−5 m relative to that before optimization. These results validate the effectiveness and feasibility of the proposed T-LSSVM method, which provides a useful insight into casing radial deformation, BTRRC control, and the development of gas turbine with high performance and high reliability.
Cao, Jiguo; Huang, Jianhua Z.; Wu, Hulin
2012-01-01
Ordinary differential equations (ODEs) are widely used in biomedical research and other scientific areas to model complex dynamic systems. It is an important statistical problem to estimate parameters in ODEs from noisy observations. In this article we propose a method for estimating the time-varying coefficients in an ODE. Our method is a variation of the nonlinear least squares where penalized splines are used to model the functional parameters and the ODE solutions are approximated also using splines. We resort to the implicit function theorem to deal with the nonlinear least squares objective function that is only defined implicitly. The proposed penalized nonlinear least squares method is applied to estimate a HIV dynamic model from a real dataset. Monte Carlo simulations show that the new method can provide much more accurate estimates of functional parameters than the existing two-step local polynomial method which relies on estimation of the derivatives of the state function. Supplemental materials for the article are available online.
Induced voltage due to time-dependent magnetisation textures
International Nuclear Information System (INIS)
Kudtarkar, Santosh Kumar; Dhadwal, Renu
2010-01-01
We determine the induced voltage generated by spatial and temporal magnetisation textures (inhomogeneities) in metallic ferromagnets due to the spin diffusion of non-equilibrium electrons. Using time dependent semi-classical theory as formulated in Zhang and Li and the drift-diffusion model of transport it is shown that the voltage generated depends critically on the difference in the diffusion constants of up and down spins. Including spin relaxation results in a crucial contribution to the induced voltage. We also show that the presence of magnetisation textures results in the modification of the conductivity of the system. As an illustration, we calculate the voltage generated due to a time dependent field driven helimagnet by solving the Landau-Lifshitz equation with Gilbert damping and explicitly calculate the dependence on the relaxation and damping parameters.
Solution of the time-dependent, three-dimensional resistive magnetohydrodynamic equations
International Nuclear Information System (INIS)
Finan, C.H. III; Killeen, J.; California Univ., Davis
1981-01-01
Resistive magnetohydrodynamics (MHD) is described by a set of eight coupled, nonlinear, three-dimensional, time-dependent, partial differential equations. A computer code, IMP (Implicit MHD Program), has been developed to solve these equations numerically by the method of finite differences on an Eulerian mesh. In this model, the equations are expressed in orthogonal curvilinear coordinates, making the code applicable to a variety of coordinate systems. The Douglas-Gunn algorithm for Alternating-Direction Implicit (ADI) temporal advancement is used to avoid the limitations in timestep size imposed by explicit methods. The equations are expressed as conservation laws, the momentum and energy equations are nonconservative. This is to: (1) provide enhanced numerical stability by eliminating errors introduced by the nonvanishing of nabla x B on the finite difference mesh; and, (2) allow the simulation of low β plasmas. The resulting finite difference equations are a coupled system of nonlinear algebraic equations which are solved by the Newton-Raphson iteration technique. We apply our model to a number of problems of importance in magnetic fusion research. Ideal and resistive internal kink instabilities are simulated in a Cartesian geometry. Growth rates and nonlinear saturation amplitudes are found to be in agreement with previous analytic and numerical predictions. We also simulate these instabilities in a torus, which demonstrates the versatility of the orthogonal curvilinear coordinate representation. (orig.)
Examining the time dependence of DAMA's modulation amplitude
Kelso, Chris; Savage, Christopher; Sandick, Pearl; Freese, Katherine; Gondolo, Paolo
2018-03-01
If dark matter is composed of weakly interacting particles, Earth's orbital motion may induce a small annual variation in the rate at which these particles interact in a terrestrial detector. The DAMA collaboration has identified at a 9.3σ confidence level such an annual modulation in their event rate over two detector iterations, DAMA/NaI and DAMA/LIBRA, each with ˜ 7 years of observations. This data is well fit by a constant modulation amplitude for the two iterations of the experiment. We statistically examine the time dependence of the modulation amplitudes, which "by eye" appear to be decreasing with time in certain energy ranges. We perform a chi-squared goodness of fit test of the average modulation amplitudes measured by the two detector iterations which rejects the hypothesis of a consistent modulation amplitude at greater than 80, 96, and 99.6% for the 2-4, 2-5 and 2-6 keVee energy ranges, respectively. We also find that among the 14 annual cycles there are three ≳ 3σ departures from the average in our estimated data in the 5-6 keVee energy range. In addition, we examined several phenomenological models for the time dependence of the modulation amplitude. Using a maximum likelihood test, we find that descriptions of the modulation amplitude as decreasing with time are preferred over a constant modulation amplitude at anywhere between 1σ and 3σ , depending on the phenomenological model for the time dependence and the signal energy range considered. A time dependent modulation amplitude is not expected for a dark matter signal, at least for dark matter halo morphologies consistent with the DAMA signal. New data from DAMA/LIBRA-phase2 will certainly aid in determining whether any apparent time dependence is a real effect or a statistical fluctuation.
Directory of Open Access Journals (Sweden)
Xiaohui Mo
2017-01-01
Full Text Available In this paper, finite-time stabilization problem for a class of nonlinear differential-algebraic systems (NDASs subject to external disturbance is investigated via a composite control manner. A composite finite-time controller (CFTC is proposed with a three-stage design procedure. Firstly, based on the adding a power integrator technique, a finite-time control (FTC law is explicitly designed for the nominal NDAS by only using differential variables. Then, by using homogeneous system theory, a continuous finite-time disturbance observer (CFTDO is constructed to estimate the disturbance generated by an exogenous system. Finally, a composite controller which consists of a feedforward compensation part based on CFTDO and the obtained FTC law is proposed. Rigorous analysis demonstrates that not only the proposed composite controller can stabilize the NDAS in finite time, but also the proposed control scheme exhibits nominal performance recovery property. Simulation examples are provided to illustrate the effectiveness of the proposed control approach.
Identification of time-varying nonlinear systems using differential evolution algorithm
DEFF Research Database (Denmark)
Perisic, Nevena; Green, Peter L; Worden, Keith
2013-01-01
(DE) algorithm for the identification of time-varying systems. DE is an evolutionary optimisation method developed to perform direct search in a continuous space without requiring any derivative estimation. DE is modified so that the objective function changes with time to account for the continuing......, thus identification of time-varying systems with nonlinearities can be a very challenging task. In order to avoid conventional least squares and gradient identification methods which require uni-modal and double differentiable objective functions, this work proposes a modified differential evolution...... inclusion of new data within an error metric. This paper presents results of identification of a time-varying SDOF system with Coulomb friction using simulated noise-free and noisy data for the case of time-varying friction coefficient, stiffness and damping. The obtained results are promising and the focus...
Relan, Rishi; Tiels, Koen; Marconato, Anna; Dreesen, Philippe; Schoukens, Johan
2018-05-01
Many real world systems exhibit a quasi linear or weakly nonlinear behavior during normal operation, and a hard saturation effect for high peaks of the input signal. In this paper, a methodology to identify a parsimonious discrete-time nonlinear state space model (NLSS) for the nonlinear dynamical system with relatively short data record is proposed. The capability of the NLSS model structure is demonstrated by introducing two different initialisation schemes, one of them using multivariate polynomials. In addition, a method using first-order information of the multivariate polynomials and tensor decomposition is employed to obtain the parsimonious decoupled representation of the set of multivariate real polynomials estimated during the identification of NLSS model. Finally, the experimental verification of the model structure is done on the cascaded water-benchmark identification problem.
Nonlinear plasma waves excited near resonance
International Nuclear Information System (INIS)
Cohen, B.I.; Kaufman, A.N.
1977-01-01
The nonlinear resonant response of a uniform plasma to an external plane-wave field is formulated in terms of the mismatch Δ/sub n l/ between the driving frequency and the time-dependent, complex, nonlinear normal mode frequency at the driving wavenumber. This formalism is applied to computer simulations of this process, yielding a deduced nonlinear frequency shift. The time dependence of the nonlinear phenomena, at frequency Δ/sub n l/ and at the bounce frequency of the resonant particles, is analyzed. The interdependence of the nonlinear features is described by means of energy and momentum relations
Semiclassical approximation to time-dependent Hartree--Fock theory
International Nuclear Information System (INIS)
Dworzecka, M.; Poggioli, R.
1976-01-01
Working within a time-dependent Hartree-Fock framework, one develops a semiclassical approximation appropriate for large systems. It is demonstrated that the standard semiclassical approach, the Thomas-Fermi approximation, is inconsistent with Hartree-Fock theory when the basic two-body interaction is short-ranged (as in nuclear systems, for example). However, by introducing a simple extension of the Thomas-Fermi approximation, one overcomes this problem. One also discusses the infinite nuclear matter problem and point out that time-dependent Hartree-Fock theory yields collective modes of the zero sound variety instead of ordinary hydrodynamic (first) sound. One thus emphasizes that one should be extremely circumspect when attempting to cast the equations of motion of time-dependent Hartree-Fock theory into a hydrodynamic-like form
Time dependent convection electric fields and plasma injection
International Nuclear Information System (INIS)
Kaye, S.M.; Kivelson, M.G.
1979-01-01
Large-scale electric fields associated with storms or substorms are responsible for inward convection and energization of plasma sheet plasma. Calculations based on steady state convection theory show that the response to such electric fields qualitatively accounts for many features of the injected particle distribution, but quantitative agreement with the theory has not yet been obtained. It is known that the predictions can be improved by introducing the concept of convection in response to a time dependent electric field. On the other hand, time dependent calculations are sensitive to the choice of initial conditions, and most models have failed to incorporate these conditions in a realistic and self-consistent manner. In this paper we present a more complete model consisting of realisic initial conditions and time dependent convection to explain a typical substorm-associated electron injection event. We find very good agreement between the observed electron flux changes and those predicted by our model
Quadratic time dependent Hamiltonians and separation of variables
Anzaldo-Meneses, A.
2017-06-01
Time dependent quantum problems defined by quadratic Hamiltonians are solved using canonical transformations. The Green's function is obtained and a comparison with the classical Hamilton-Jacobi method leads to important geometrical insights like exterior differential systems, Monge cones and time dependent Gaussian metrics. The Wei-Norman approach is applied using unitary transformations defined in terms of generators of the associated Lie groups, here the semi-direct product of the Heisenberg group and the symplectic group. A new explicit relation for the unitary transformations is given in terms of a finite product of elementary transformations. The sequential application of adequate sets of unitary transformations leads naturally to a new separation of variables method for time dependent Hamiltonians, which is shown to be related to the Inönü-Wigner contraction of Lie groups. The new method allows also a better understanding of interacting particles or coupled modes and opens an alternative way to analyze topological phases in driven systems.
Wenger, Elisabeth; Kühn, Simone; Verrel, Julius; Mårtensson, Johan; Bodammer, Nils Christian; Lindenberger, Ulman; Lövdén, Martin
2017-05-01
Evidence for experience-dependent structural brain change in adult humans is accumulating. However, its time course is not well understood, as intervention studies typically consist of only 2 imaging sessions (before vs. after training). We acquired up to 18 structural magnetic resonance images over a 7-week period while 15 right-handed participants practiced left-hand writing and drawing. After 4 weeks, we observed increases in gray matter of both left and right primary motor cortices relative to a control group; 3 weeks later, these differences were no longer reliable. Time-series analyses revealed that gray matter in the primary motor cortices expanded during the first 4 weeks and then partially renormalized, in particular in the right hemisphere, despite continued practice and increasing task proficiency. Similar patterns of expansion followed by partial renormalization are also found in synaptogenesis, cortical map plasticity, and maturation, and may qualify as a general principle of structural plasticity. Research on human brain plasticity needs to encompass more than 2 measurement occasions to capture expansion and potential renormalization processes over time. © The Author 2016. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.
Real-time simulation of the nonlinear visco-elastic deformations of soft tissues.
Basafa, Ehsan; Farahmand, Farzam
2011-05-01
Mass-spring-damper (MSD) models are often used for real-time surgery simulation due to their fast response and fairly realistic deformation replication. An improved real time simulation model of soft tissue deformation due to a laparoscopic surgical indenter was developed and tested. The mechanical realization of conventional MSD models was improved using nonlinear springs and nodal dampers, while their high computational efficiency was maintained using an adapted implicit integration algorithm. New practical algorithms for model parameter tuning, collision detection, and simulation were incorporated. The model was able to replicate complex biological soft tissue mechanical properties under large deformations, i.e., the nonlinear and viscoelastic behaviors. The simulated response of the model after tuning of its parameters to the experimental data of a deer liver sample, closely tracked the reference data with high correlation and maximum relative differences of less than 5 and 10%, for the tuning and testing data sets respectively. Finally, implementation of the proposed model and algorithms in a graphical environment resulted in a real-time simulation with update rates of 150 Hz for interactive deformation and haptic manipulation, and 30 Hz for visual rendering. The proposed real time simulation model of soft tissue deformation due to a laparoscopic surgical indenter was efficient, realistic, and accurate in ex vivo testing. This model is a suitable candidate for testing in vivo during laparoscopic surgery.
2014-12-18
liquid. Since the diffusive nature of the relaxation follows the Debye –Stokes–Einstein relation [39], this mechanism is referred to as diffusive...Sigma-Aldrich, 270660, ≥99.9%) are conducted using 1 mm path length , fused silica cuvettes. Using the refractive index measurements of [46], we find...studies of molecular liquids,” Ann. Rev. Phys. Chem. 31, 523–558 (1980). 38. R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic/Elsevier, 2008). 39. P. Debye
Vacuum radiation induced by time dependent electric field
Directory of Open Access Journals (Sweden)
Bo Zhang
2017-04-01
Full Text Available Many predictions of new phenomena given by strong field quantum electrodynamics (SFQED will be tested on next generation multi-petawatt laser facilities in the near future. These new phenomena are basis to understand physics in extremely strong electromagnetic fields therefore have attracted wide research interest. Here we discuss a new SFQED phenomenon that is named as vacuum radiation. In vacuum radiation, a virtual electron loop obtain energy from time dependent external electric field and radiate an entangled photon pair. Features of vacuum radiation in a locally time dependent electric field including spectrum, characteristic temperature, production rate and power are given.
Vacuum radiation induced by time dependent electric field
Energy Technology Data Exchange (ETDEWEB)
Zhang, Bo, E-mail: zhangbolfrc@caep.cn [Department of High Energy Density Physics, Research Center of Laser Fusion, 621900, Mianyang, Sichuan (China); Laboratory of Science and Technology on Plasma Physics, Research Center of Laser Fusion, 621900, Mianyang, Sichuan (China); Zhang, Zhi-meng; Hong, Wei; He, Shu-Kai; Teng, Jian [Department of High Energy Density Physics, Research Center of Laser Fusion, 621900, Mianyang, Sichuan (China); Laboratory of Science and Technology on Plasma Physics, Research Center of Laser Fusion, 621900, Mianyang, Sichuan (China); Gu, Yu-qiu, E-mail: yqgu@caep.cn [Department of High Energy Density Physics, Research Center of Laser Fusion, 621900, Mianyang, Sichuan (China); Laboratory of Science and Technology on Plasma Physics, Research Center of Laser Fusion, 621900, Mianyang, Sichuan (China)
2017-04-10
Many predictions of new phenomena given by strong field quantum electrodynamics (SFQED) will be tested on next generation multi-petawatt laser facilities in the near future. These new phenomena are basis to understand physics in extremely strong electromagnetic fields therefore have attracted wide research interest. Here we discuss a new SFQED phenomenon that is named as vacuum radiation. In vacuum radiation, a virtual electron loop obtain energy from time dependent external electric field and radiate an entangled photon pair. Features of vacuum radiation in a locally time dependent electric field including spectrum, characteristic temperature, production rate and power are given.
Time dependent density matrix theory and effective interaction
Energy Technology Data Exchange (ETDEWEB)
Tohyama, Mitsuru [Kyorin Univ., Mitaka, Tokyo (Japan). School of Medicine
1998-07-01
A correlated ground state of {sup 16}O and an E2 giant resonance built on it are calculated using an extended version of the time-dependent Hartree-Fock theory called the time-dependent density-matrix theory (TDDM). The Skyrme force is used in the calculation of both a mean field and two-body correlations. It is found that TDDM gives reasonable ground-state correlations and a large spreading width of the E2 giant resonance when single-particle states in the continuum are treated appropriately. (author)
Radhakrishnan, Srinivasan; Duvvuru, Arjun; Sultornsanee, Sivarit; Kamarthi, Sagar
2016-02-01
The cross correlation coefficient has been widely applied in financial time series analysis, in specific, for understanding chaotic behaviour in terms of stock price and index movements during crisis periods. To better understand time series correlation dynamics, the cross correlation matrices are represented as networks, in which a node stands for an individual time series and a link indicates cross correlation between a pair of nodes. These networks are converted into simpler trees using different schemes. In this context, Minimum Spanning Trees (MST) are the most favoured tree structures because of their ability to preserve all the nodes and thereby retain essential information imbued in the network. Although cross correlations underlying MSTs capture essential information, they do not faithfully capture dynamic behaviour embedded in the time series data of financial systems because cross correlation is a reliable measure only if the relationship between the time series is linear. To address the issue, this work investigates a new measure called phase synchronization (PS) for establishing correlations among different time series which relate to one another, linearly or nonlinearly. In this approach the strength of a link between a pair of time series (nodes) is determined by the level of phase synchronization between them. We compare the performance of phase synchronization based MST with cross correlation based MST along selected network measures across temporal frame that includes economically good and crisis periods. We observe agreement in the directionality of the results across these two methods. They show similar trends, upward or downward, when comparing selected network measures. Though both the methods give similar trends, the phase synchronization based MST is a more reliable representation of the dynamic behaviour of financial systems than the cross correlation based MST because of the former's ability to quantify nonlinear relationships among time
Directory of Open Access Journals (Sweden)
Pedro A. Galvani
2016-08-01
Full Text Available The work presented in this paper has two major aspects: (i investigation of a simple, yet efficient model of the NREL (National Renewable Energy Laboratory 5-MW reference wind turbine; (ii nonlinear control system development through a real-time nonlinear receding horizon control methodology with application to wind turbine control dynamics. In this paper, the results of our simple wind turbine model and a real-time nonlinear control system implementation are shown in comparison with conventional control methods. For this purpose, the wind turbine control problem is converted into an optimization problem and is directly solved by the nonlinear backwards sweep Riccati method to generate the control protocol, which results in a non-iterative algorithm. One main contribution of this paper is that we provide evidence through simulations, that such an advanced control strategy can be used for real-time control of wind turbine dynamics. Examples are provided to validate and demonstrate the effectiveness of the presented scheme.
You, Yue; Zhang, Wenjia; Sun, Lin; Du, Jiangbing; Liang, Chenyu; Yang, Fan; He, Zuyuan
2018-03-01
The vertical cavity surface emitting laser (VCSEL)-based multimode optical transceivers enabled by pulse amplitude modulation (PAM)-4 will be commercialized in near future to meet the 400-Gbps standard short reach optical interconnects. It is still challenging to achieve over 56/112-Gbps with the multilevel signaling as the multimode property of the device and link would introduce the nonlinear temporal response for the different levels. In this work, we scrutinize the distortions that relates to the multilevel feature of PAM-4 modulation, and propose an effective feedback equalization scheme for 56-Gbps VCSEL-based PAM-4 optical interconnects system to mitigate the distortions caused by eye timing-skew and nonlinear power-dependent noise. Level redistribution at Tx side is theoretically modeled and constructed to achieve equivalent symbol error ratios (SERs) of four levels and improved BER performance. The cause of the eye skewing and the mitigation approach are also simulated at 100-Gbps and experimentally investigated at 56-Gbps. The results indicate more than 2-dB power penalty improvement has been achieved by using such a distortion aware equalizer.
Conservative fourth-order time integration of non-linear dynamic systems
DEFF Research Database (Denmark)
Krenk, Steen
2015-01-01
An energy conserving time integration algorithm with fourth-order accuracy is developed for dynamic systems with nonlinear stiffness. The discrete formulation is derived by integrating the differential state-space equations of motion over the integration time increment, and then evaluating...... the resulting time integrals of the inertia and stiffness terms via integration by parts. This process introduces the time derivatives of the state space variables, and these are then substituted from the original state-space differential equations. The resulting discrete form of the state-space equations...... is a direct fourth-order accurate representation of the original differential equations. This fourth-order form is energy conserving for systems with force potential in the form of a quartic polynomial in the displacement components. Energy conservation for a force potential of general form is obtained...