A Reaction-diffusion System with Nonlinear Absorption Terms and Boundary Flux
Institute of Scientific and Technical Information of China (English)
2008-01-01
This paper deals with a reaction-diffusion system with nonlinear absorption terms and boundary flux. As results of interactions among the six nonlinear terms in the system, some sufficient conditions on global existence and finite time blow-up of the solutions are described via all the six nonlinear exponents appearing in the six nonlinear terms. In addition, we also show the influence of the coefficients of the absorption terms as well as the geometry of the domain to the global existence and finite time blow-up of the solutions for some cases. At last, some numerical results are given.
Institute of Scientific and Technical Information of China (English)
LI Huiling; WANG Mingxin
2005-01-01
This paper deals with the blow-up properties of the solution to a semilinear parabolic system with localized nonlinear reaction terms, subject to the null Dirichlet boundary condition. We first give sufficient conditions for that the classical solution blows up in the finite time, secondly give necessary conditions and a sufficient condition for that two components blow up simultaneously, and then obtain the uniform blow-up profiles in the interior. Finally we describe the asymptotic behavior of the blow-up solution in the boundary layer.
Indian Academy of Sciences (India)
R S Kaushal; Ranjit Kumar; Awadhesh Prasad
2006-08-01
Attempts have been made to look for the soliton content in the solutions of the recently studied nonlinear diffusion-reaction equations [R S Kaushal, J. Phys. 38, 3897 (2005)] involving quadratic or cubic nonlinearities in addition to the convective flux term which renders the system nonconservative and the corresponding Hamiltonian non-Hermitian.
Turing instability in reaction-diffusion systems with nonlinear diffusion
Energy Technology Data Exchange (ETDEWEB)
Zemskov, E. P., E-mail: zemskov@ccas.ru [Russian Academy of Sciences, Dorodnicyn Computing Center (Russian Federation)
2013-10-15
The Turing instability is studied in two-component reaction-diffusion systems with nonlinear diffusion terms, and the regions in parametric space where Turing patterns can form are determined. The boundaries between super- and subcritical bifurcations are found. Calculations are performed for one-dimensional brusselator and oregonator models.
A Note on a Nonlocal Nonlinear Reaction-Diffusion Model
Walker, Christoph
2011-01-01
We give an application of the Crandall-Rabinowitz theorem on local bifurcation to a system of nonlinear parabolic equations with nonlocal reaction and cross-diffusion terms as well as nonlocal initial conditions. The system arises as steady-state equations of two interacting age-structured populations.
Approximating parameters in nonlinear reaction diffusion equations
Directory of Open Access Journals (Sweden)
Robert R. Ferdinand
2001-07-01
Full Text Available We present a model describing population dynamics in an environment. The model is a nonlinear, nonlocal, reaction diffusion equation with Neumann boundary conditions. An inverse method, involving minimization of a least-squares cost functional, is developed to identify unknown model parameters. Finally, numerical results are presented which display estimates of these parameters using computationally generated data.
Exact solutions of certain nonlinear chemotaxis diffusion reaction equations
Indian Academy of Sciences (India)
MISHRA AJAY; KAUSHAL R S; PRASAD AWADHESH
2016-05-01
Using the auxiliary equation method, we obtain exact solutions of certain nonlinear chemotaxis diffusion reaction equations in the presence of a stimulant. In particular, we account for the nonlinearities arising not only from the density-dependent source terms contributed by the particles and the stimulant but also from the coupling term of the stimulant. In addition to this, the diffusion of the stimulant and the effect of long-range interactions are also accounted for in theconstructed coupled differential equations. The results obtained here could be useful in the studies of several biological systems and processes, e.g., in bacterial infection, chemotherapy, etc.
Nonlinear control of the Salnikov model reaction
DEFF Research Database (Denmark)
Recke, Bodil; Jørgensen, Sten Bay
1999-01-01
This paper explores different nonlinear control schemes, applied to a simple model reaction. The model is the Salnikov model, consisting of two ordinary differential equations. The control strategies investigated are I/O-linearisation, Exact linearisation, exact linearisation combined with LQR...... and Control Lyapunov Functions (CLF's). The results show that based on the lowest possible cost function and shortest settling time, the exact linearisation performs marginally better than the other methods....
Travelling waves in nonlinear diffusion-convection-reaction
Gilding, B.H.; Kersner, R.
2001-01-01
The study of travelling waves or fronts has become an essential part of the mathematical analysis of nonlinear diffusion-convection-reaction processes. Whether or not a nonlinear second-order scalar reaction-convection-diffusion equation admits a travelling-wave solution can be determined by the stu
Implementing Nonlinear Feedback Controllers Using DNA Strand Displacement Reactions.
Sawlekar, Rucha; Montefusco, Francesco; Kulkarni, Vishwesh V; Bates, Declan G
2016-07-01
We show how an important class of nonlinear feedback controllers can be designed using idealized abstract chemical reactions and implemented via DNA strand displacement (DSD) reactions. Exploiting chemical reaction networks (CRNs) as a programming language for the design of complex circuits and networks, we show how a set of unimolecular and bimolecular reactions can be used to realize input-output dynamics that produce a nonlinear quasi sliding mode (QSM) feedback controller. The kinetics of the required chemical reactions can then be implemented as enzyme-free, enthalpy/entropy driven DNA reactions using a toehold mediated strand displacement mechanism via Watson-Crick base pairing and branch migration. We demonstrate that the closed loop response of the nonlinear QSM controller outperforms a traditional linear controller by facilitating much faster tracking response dynamics without introducing overshoots in the transient response. The resulting controller is highly modular and is less affected by retroactivity effects than standard linear designs.
Fluorescence Correlation Spectroscopy and Nonlinear Stochastic Reaction-Diffusion
Del Razo, Mauricio J; Qian, Hong; Lin, Guang
2014-01-01
The currently existing theory of fluorescence correlation spectroscopy(FCS) is based on the linear fluctuation theory originally developed by Einstein, Onsager, Lax, and others as a phenomenological approach to equilibrium fluctuations in bulk solutions. For mesoscopic reaction-diffusion systems with nonlinear chemical reactions among a small number of molecules, a situation often encountered in single-cell biochemistry, it is expected that FCS time correlation functions of a reaction-diffusion system can deviate from the classic results of Elson and Magde. We first discuss this nonlinear effect for reaction systems without diffusion. For nonlinear stochastic reaction-diffusion systems here are no closed solutions; therefore, stochastic Monte-Carlo simulations are carried out. We show that the deviation is small for a simple bimolecular reaction; the most significant deviations occur when the number of molecules is small and of the same order. Our results show that current linear FCS theory could be adequate ...
NONLINEAR SINGULARLY PERTURBED PREDATOR-PREY REACTION DIFFUSION SYSTEMS
Institute of Scientific and Technical Information of China (English)
MoJiaqi; TangRongrong
2004-01-01
A class of nonlinear predator-prey reaction diffusion systems for singularly perturbedproblems are considered. Under suitable conditions, by using theory of differential inequalitiesthe existence and asymptotic behavior of solution for initial boundary value problems arestudied.
Fluorescence Correlation Spectroscopy and Nonlinear Stochastic Reaction-Diffusion
Energy Technology Data Exchange (ETDEWEB)
Del Razo, Mauricio; Pan, Wenxiao; Qian, Hong; Lin, Guang
2014-05-30
The currently existing theory of fluorescence correlation spectroscopy (FCS) is based on the linear fluctuation theory originally developed by Einstein, Onsager, Lax, and others as a phenomenological approach to equilibrium fluctuations in bulk solutions. For mesoscopic reaction-diffusion systems with nonlinear chemical reactions among a small number of molecules, a situation often encountered in single-cell biochemistry, it is expected that FCS time correlation functions of a reaction-diffusion system can deviate from the classic results of Elson and Magde [Biopolymers (1974) 13:1-27]. We first discuss this nonlinear effect for reaction systems without diffusion. For nonlinear stochastic reaction-diffusion systems there are no closed solutions; therefore, stochastic Monte-Carlo simulations are carried out. We show that the deviation is small for a simple bimolecular reaction; the most significant deviations occur when the number of molecules is small and of the same order. Extending Delbrück-Gillespie’s theory for stochastic nonlinear reactions with rapidly stirring to reaction-diffusion systems provides a mesoscopic model for chemical and biochemical reactions at nanometric and mesoscopic level such as a single biological cell.
Nonlinear reaction coordinate analysis in the reweighted path ensemble
Lechner, W.; Rogal, J.; Juraszek, J.; Ensing, B.; Bolhuis, P.G.
2010-01-01
We present a flexible nonlinear reaction coordinate analysis method for the transition path ensemble based on the likelihood maximization approach developed by Peters and Trout [J. Chem. Phys. 125, 054108 (2006)] . By parametrizing the reaction coordinate by a string of images in a collective variab
Bayesian inversion analysis of nonlinear dynamics in surface heterogeneous reactions.
Omori, Toshiaki; Kuwatani, Tatsu; Okamoto, Atsushi; Hukushima, Koji
2016-09-01
It is essential to extract nonlinear dynamics from time-series data as an inverse problem in natural sciences. We propose a Bayesian statistical framework for extracting nonlinear dynamics of surface heterogeneous reactions from sparse and noisy observable data. Surface heterogeneous reactions are chemical reactions with conjugation of multiple phases, and they have the intrinsic nonlinearity of their dynamics caused by the effect of surface-area between different phases. We adapt a belief propagation method and an expectation-maximization (EM) algorithm to partial observation problem, in order to simultaneously estimate the time course of hidden variables and the kinetic parameters underlying dynamics. The proposed belief propagation method is performed by using sequential Monte Carlo algorithm in order to estimate nonlinear dynamical system. Using our proposed method, we show that the rate constants of dissolution and precipitation reactions, which are typical examples of surface heterogeneous reactions, as well as the temporal changes of solid reactants and products, were successfully estimated only from the observable temporal changes in the concentration of the dissolved intermediate product.
Non-Markovian random walks and nonlinear reactions: Subdiffusion and propagating fronts
Fedotov, Sergei
2010-01-01
The main aim of the paper is to incorporate the nonlinear kinetic term into non-Markovian transport equations described by a continuous time random walk (CTRW) with nonexponential waiting time distributions. We consider three different CTRW models with reactions. We derive nonlinear Master equations for the mesoscopic density of reacting particles corresponding to CTRW with arbitrary jump and waiting time distributions. We apply these equations to the problem of front propagation in the reaction-transport systems with Kolmogorov-Petrovskii-Piskunov kinetics and anomalous diffusion. We have found an explicit expression for the speed of a propagating front in the case of subdiffusive transport.
HYPERBOLIC-PARABOLIC CHEMOTAXIS SYSTEM WITH NONLINEAR PRODUCT TERMS
Institute of Scientific and Technical Information of China (English)
Chen Hua; Wu Shaohua
2008-01-01
We prove the local existence and uniqueness of week solution of the hyperbolic-parabolic Chemotaxis system with some nonlinear product terms. For one dimensional case, we prove also the global existence and uniqueness of the solution for the problem.
Asymptotic solution for a class of weakly nonlinear singularly perturbed reaction diffusion problem
Institute of Scientific and Technical Information of China (English)
TANG Rong-rong
2009-01-01
Under appropriate conditions, with the perturbation method and the theory of differential inequalities, a class of weakly nonlinear singularly perturbed reaction diffusion problem is considered. The existence of solution of the original problem is proved by constructing the auxiliary functions. The uniformly valid asymptotic expansions of the solution for arbitrary mth order approximation are obtained through constructing the formal solutions of the original problem, expanding the nonlinear terms to the power in small parameter e and comparing the coefficient for the same powers of ε. Finally, an example is provided, resulting in the error of O(ε2).
Traveling wavefront solutions to nonlinear reaction-diffusion-convection equations
Indekeu, Joseph O.; Smets, Ruben
2017-08-01
Physically motivated modified Fisher equations are studied in which nonlinear convection and nonlinear diffusion is allowed for besides the usual growth and spread of a population. It is pointed out that in a large variety of cases separable functions in the form of exponentially decaying sharp wavefronts solve the differential equation exactly provided a co-moving point source or sink is active at the wavefront. The velocity dispersion and front steepness may differ from those of some previously studied exact smooth traveling wave solutions. For an extension of the reaction-diffusion-convection equation, featuring a memory effect in the form of a maturity delay for growth and spread, also smooth exact wavefront solutions are obtained. The stability of the solutions is verified analytically and numerically.
Nonlinear Kalman Filtering in Affine Term Structure Models
DEFF Research Database (Denmark)
Christoffersen, Peter; Dorion, Christian; Jacobs, Kris;
When the relationship between security prices and state variables in dynamic term structure models is nonlinear, existing studies usually linearize this relationship because nonlinear fi…ltering is computationally demanding. We conduct an extensive investigation of this linearization and analyze...... Monte Carlo experiment demonstrates that the unscented Kalman fi…lter is much more accurate than its extended counterpart in fi…ltering the states and forecasting swap rates and caps. Our fi…ndings suggest that the unscented Kalman fi…lter may prove to be a good approach for a number of other problems...... in fi…xed income pricing with nonlinear relationships between the state vector and the observations, such as the estimation of term structure models using coupon bonds and the estimation of quadratic term structure models....
Indian Academy of Sciences (India)
Aldona Krupska
2015-06-01
In this paper the arduous attempt to find a mathematical solution for the nonlinear autocatalytic chemical processes with a time-varying and oscillating inflow of reactant to the reaction medium has been taken. Approximate analytical solution is proposed. Numerical solutions and analytical attempts to solve the non-linear differential equation indicates a phase shift between the oscillatory influx of intermediate reaction reagent to the medium of chemical reaction and the change of its concentration in this medium. Analytical solutions indicate that this shift may be associated with the reaction rate constants 1 and 2 and the relaxation time . The relationship between the phase shift and the oscillatory flow of reactant seems to be similar to that obtained in the case of linear chemical reactions, as described previously, however, the former is much more complex and different. In this paper, we would like to consider whether the effect of forced phase shift in the case of nonlinear and non-oscillatory chemical processes occurring particularly in the living systems have a practical application in laboratory.
Long term structural dynamics of mechanical systems with local nonlinearities
Fey, R.H.B.; Campen, D.H. van; Kraker, A. de
1996-01-01
This paper deals with the long term behavior of periodically excited mechanical systems consisting of linear components and local nonlinearities. The number of degrees of freedom of the linear components is reduced by applying a component mode synthesis technique. Lyapunov exponents are used to iden
MONOTONE ITERATION FOR ELLIPTIC PDEs WITH DISCONTINUOUS NONLINEAR TERMS
Institute of Scientific and Technical Information of China (English)
Zou Qingsong
2005-01-01
In this paper, we use monotone iterative techniques to show the existence of maximal or minimal solutions of some elliptic PDEs with nonlinear discontinuous terms. As the numerical analysis of this PDEs is concerned, we prove the convergence of discrete extremal solutions.
Adaptive Algorithms of Nonlinear Approximation with Finite Terms
Institute of Scientific and Technical Information of China (English)
Wen Bin WEI; Yue Sheng XU; Pei Xin YE
2007-01-01
This paper deals with realizable adaptive algorithms of the nonlinear approximation with finite terms based on wavelets. We present a concrete algorithm by which we may find the required index set Am for the greedy algorithm GPm(·,ψ). This makes the greedy algorithm realize the near best approximation in practice. Moreover, we study the efficiency of the finite-term approximation of another algorithm introduced by Birge and Massart.
Oscillation criteria for nonlinear fractional differential equation with damping term
Directory of Open Access Journals (Sweden)
Bayram Mustafa
2016-01-01
Full Text Available In this paper, we study the oscillation of solutions to a non-linear fractional differential equation with damping term. The fractional derivative is defined in the sense of the modified Riemann-Liouville derivative. By using a variable transformation, a generalized Riccati transformation, inequalities, and integration average techniquewe establish new oscillation criteria for the fractional differential equation. Several illustrative examples are also given.
Cumulative signal transmission in nonlinear reaction-diffusion networks.
Directory of Open Access Journals (Sweden)
Diego A Oyarzún
Full Text Available Quantifying signal transmission in biochemical systems is key to uncover the mechanisms that cells use to control their responses to environmental stimuli. In this work we use the time-integral of chemical species as a measure of a network's ability to cumulatively transmit signals encoded in spatiotemporal concentrations. We identify a class of nonlinear reaction-diffusion networks in which the time-integrals of some species can be computed analytically. The derived time-integrals do not require knowledge of the solution of the reaction-diffusion equation, and we provide a simple graphical test to check if a given network belongs to the proposed class. The formulae for the time-integrals reveal how the kinetic parameters shape signal transmission in a network under spatiotemporal stimuli. We use these to show that a canonical complex-formation mechanism behaves as a spatial low-pass filter, the bandwidth of which is inversely proportional to the diffusion length of the ligand.
Kumar, Naveen; Hatsagortsyan, Karen Z; Keitel, Christoph H
2013-09-06
Stimulated Raman scattering of an ultraintense laser pulse in plasmas is studied by perturbatively including the leading order term of the Landau-Lifshitz radiation reaction force in the equation of motion for plasma electrons. In this approximation, the radiation reaction force causes a phase shift in nonlinear current densities that drive the two Raman sidebands (anti-Stokes and Stokes waves), manifesting itself into the nonlinear mixing of two sidebands. This mixing results in a strong enhancement in the growth of the forward Raman scattering instability.
Nonlinear Terms of MHD Equations for Homogeneous Magnetized Shear Flow
Dimitrov, Z D; Hristov, T S; Mishonov, T M
2011-01-01
We have derived the full set of MHD equations for incompressible shear flow of a magnetized fluid and considered their solution in the wave-vector space. The linearized equations give the famous amplification of slow magnetosonic waves and describe the magnetorotational instability. The nonlinear terms in our analysis are responsible for the creation of turbulence and self-sustained spectral density of the MHD (Alfven and pseudo-Alfven) waves. Perspectives for numerical simulations of weak turbulence and calculation of the effective viscosity of accretion disks are shortly discussed in k-space.
Fourth order wave equations with nonlinear strain and source terms
Liu, Yacheng; Xu, Runzhang
2007-07-01
In this paper we study the initial boundary value problem for fourth order wave equations with nonlinear strain and source terms. First we introduce a family of potential wells and prove the invariance of some sets and vacuum isolating of solutions. Then we obtain a threshold result of global existence and nonexistence. Finally we discuss the global existence of solutions for the problem with critical initial condition I(u0)[greater-or-equal, slanted]0, E(0)=d. So the Esquivel-Avila's results are generalized and improved.
Tuan, Nguyen Huy; Van Au, Vo; Khoa, Vo Anh; Lesnic, Daniel
2017-05-01
The identification of the population density of a logistic equation backwards in time associated with nonlocal diffusion and nonlinear reaction, motivated by biology and ecology fields, is investigated. The diffusion depends on an integral average of the population density whilst the reaction term is a global or local Lipschitz function of the population density. After discussing the ill-posedness of the problem, we apply the quasi-reversibility method to construct stable approximation problems. It is shown that the regularized solutions stemming from such method not only depend continuously on the final data, but also strongly converge to the exact solution in L 2-norm. New error estimates together with stability results are obtained. Furthermore, numerical examples are provided to illustrate the theoretical results.
Influence of nonlinear chemical reactions on the transport coefficients in oscillatory Couette flow
Barik, Swarup; Dalal, D. C.
2016-10-01
A multiple-scale method of averaging is applied to the study of transport of a chemical species in oscillatory Couette flow where the species may undergoes a reversible phase exchange with the boundary wall and nonlinear chemical reactions both within the fluid and at the boundary wall. Analytical expressions are obtained for transport coefficients. The results shows how the transport coefficients are influenced by the reversible phase exchange reaction kinetics and the rate and degree of the nonlinear decay chemical reaction.
An inverse problem of determining a nonlinear term in an ordinary differential equation
Kamimura, Yutaka
1998-01-01
An inverse problem for a nonlinear ordinary differential equation is discussed. We prove an existence theorem of a nonlinear term with which a boundary value problem admits a solution. This is an improvement of earlier work by A. Lorenzi. We also prove a uniqueness theorem of the nonlinear term.
The constructive technique and its application in solving a nonlinear reaction diffusion equation
Institute of Scientific and Technical Information of China (English)
Lai Shao-Yong; Guo Yun-Xi; Qing Yin; Wu Yong-Hong
2009-01-01
A mathematical technique based on the consideration of a nonlinear partial differential equation together with an additional condition in the form of an ordinary differential equation is employed to study a nonlinear reaction diffusion equation which describes a real process in physics and in chemistry. Several exact solutions for the equation are acquired under certain circumstances.
Nonlinear predator-prey singularly perturbed Robin Problems for reaction diffusion systems
Institute of Scientific and Technical Information of China (English)
莫嘉琪; 韩祥临
2003-01-01
The nonlinear predator-prey reaction diffusion systems for singularly perturbed Robin Problems are considered. Under suitable conditions, the theory of differential inequalities can be used to study the asymptotic behavior of the solution for initial boundary value problems.
Institute of Scientific and Technical Information of China (English)
莫嘉琪
2003-01-01
The nonlinear predator-prey singularly perturbed Robin initial boundary value problems for reaction diffusion systems were considered. Under suitable conditions, using theory of differential inequalities the existence and asymptotic behavior of solution for initial boundary value problems were studied.
Energy Technology Data Exchange (ETDEWEB)
Huang Dingjiang [Department of Applied Mathematics, Dalian University of Technology, Dalian 116024 (China)]. E-mail: hdj8116@163.com; Zhang Hongqing [Department of Applied Mathematics, Dalian University of Technology, Dalian 116024 (China)
2006-08-15
Many travelling wave solutions of nonlinear evolution equations can be written as a polynomial in several elementary or special functions which satisfy a first order nonlinear ordinary differential equation with a sixth-degree nonlinear term. From that property, we deduce an algebraic method for constructing those solutions by determining only a finite number of coefficients. Being concise and straightforward, the method is applied to three nonlinear evolution equations. As a result, many exact travelling wave solutions are obtained which include new bell and kink profile solitary wave solutions, triangular periodic wave solutions and singular solutions.
Institute of Scientific and Technical Information of China (English)
无
2003-01-01
The problem of the process of coupled diffusion and reaction in catalyst pellets is considered for the case of second and half order reactions. The Adomian decomposition method is used to solve the non-linear model. For the second, half and first order reactions, analytical approximate solutions are obtained. The variation of reactant concentration in the catalyst pellet and the effectiveness factors at φ＜10 are determined and compared with those by the BAND's finite difference numerical method developed by Newman. At lower values of φ, the decomposition solution with 3 terms gives satisfactory agreement with the numerical solution; at higher values of φ, as the term number in the decomposition method is increased, an acceptable agreement between the two methods is achieved. In general, the solution with 6 terms gives a satisfactory agreement.
KPP reaction-diffusion equations with a non-linear loss inside a cylinder
Giletti, Thomas
2010-01-01
We consider in this paper a reaction-diffusion system in presence of a flow and under a KPP hypothesis. While the case of a single-equation has been extensively studied since the pioneering Kolmogorov-Petrovski-Piskunov paper, the study of the corresponding system with a Lewis number not equal to 1 is still quite open. Here, we will prove some results about the existence of travelling fronts and generalized travelling fronts solutions of such a system with the presence of a non-linear spacedependent loss term inside the domain. In particular, we will point out the existence of a minimal speed, above which any real value is an admissible speed. We will also give some spreading results for initial conditions decaying exponentially at infinity.
KPP reaction-diffusion system with a nonlinear loss inside a cylinder
Giletti, Thomas
2010-09-01
We consider in this paper a reaction-diffusion system in the presence of a flow and under a KPP hypothesis. While the case of a single-equation has been extensively studied since the pioneering Kolmogorov-Petrovski-Piskunov paper, the study of the corresponding system with a Lewis number not equal to 1 is still quite open. Here, we will prove some results about the existence of travelling fronts and generalized travelling fronts solutions of such a system with the presence of a nonlinear space-dependent loss term inside the domain. In particular, we will point out the existence of a minimal speed, above which any real value is an admissible speed. We will also give some spreading results for initial conditions decaying exponentially at infinity.
Insights into alkali-silica reaction damage in mortar through acoustic nonlinearity
Rashidi, M.; Kim, J.-Y.; Jacobs, L. J.; Kurtis, K. E.
2016-02-01
The progression of damage as a result of alkali-silica reaction in mortar samples is monitored by using the Nonlinear Impact Resonance Acoustic Spectroscopy (NIRAS) method and expansion measurements, which were performed daily. Results of this study show a strong correlation between the cumulative average nonlinearity parameter and expansion for each sample type, and a strong linear relationship between fourteen-day expansion and the cumulative average nonlinearity of among sample types. In addition to the cumulative average nonlinearity parameter, the standard deviation of average nonlinearity parameter shows strong correlation with the fourteen-day expansion of sample types. Results provide insights to the relationship with the acoustic nonlinearity and damage caused by the ASR.
A boundary control problem with a nonlinear reaction term
Directory of Open Access Journals (Sweden)
John R. Cannon
2009-04-01
Full Text Available The authors study the problem $u_t=u_{xx}-au$, $0
Nonlinear Kalman Filtering in Affine Term Structure Models
DEFF Research Database (Denmark)
Christoffersen, Peter; Dorion, Christian; Jacobs, Kris;
2014-01-01
The extended Kalman filter, which linearizes the relationship between security prices and state variables, is widely used in fixed-income applications. We investigate whether the unscented Kalman filter should be used to capture nonlinearities and compare the performance of the Kalman filter...... with that of the particle filter. We analyze the cross section of swap rates, which are mildly nonlinear in the states, and cap prices, which are highly nonlinear. When caps are used to filter the states, the unscented Kalman filter significantly outperforms its extended counterpart. The unscented Kalman filter also...
Nonlinearity degree of short-term heart rate variability signal
Institute of Scientific and Technical Information of China (English)
BIAN Chunhua; NING Xinbao
2004-01-01
A nonlinear autoregressive (NAR) model is built to model the heartbeat interval time series and the optimum model degree is proposed to be taken to evaluate the nonlinearity degree of heart rate variability (HRV). A group of healthy persons are studied and the results indicate that this method can effectively get nonlinear information from short (6-7 min) heartbeat series and consequently reflect the degree of heart rate variability, which supplies convenience in clinical application. Finally, a comparison with the traditional time domain method shows that the NAR model method can reflect the complexity of the whole signal and lessen the influence of noise and instability in the signal.
nonlinear kinetics and mechanism of nile blue reaction
African Journals Online (AJOL)
Prof. S.B. Jonnalagadda
under varied oxidative and reducing media is pivotal in their applications as ... communication, we report the complex mechanism of the reaction between nile blue ... Both the instruments were interfaced for data storage and have ..... The authors acknowledge the financial support received from the University of Durban-.
Cherniha, Roman
2017-01-01
This book presents several fundamental results in solving nonlinear reaction-diffusion equations and systems using symmetry-based methods. Reaction-diffusion systems are fundamental modeling tools for mathematical biology with applications to ecology, population dynamics, pattern formation, morphogenesis, enzymatic reactions and chemotaxis. The book discusses the properties of nonlinear reaction-diffusion systems, which are relevant for biological applications, from the symmetry point of view, providing rigorous definitions and constructive algorithms to search for conditional symmetry (a nontrivial generalization of the well-known Lie symmetry) of nonlinear reaction-diffusion systems. In order to present applications to population dynamics, it focuses mainly on two- and three-component diffusive Lotka-Volterra systems. While it is primarily a valuable guide for researchers working with reaction-diffusion systems and those developing the theoretical aspects of conditional symmetry conception,...
On the study of nonlinear dynamics of complex chemical reaction systems
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
With ever-increasing attentions being paid to complex systems such as the life system, soft matter, and nano-systems, theoretical studies of non-equilibrium nonlinear problems involved in chemical dynamics are now of general interest. In this mini-review, we mainly give a brief introduction to some frontier topics in this field, namely, nonlinear state-state dynamics, nonlinear chemical dynamics on complex networks, and nonlinear dynamics in mesoscopic chemical reaction systems. Deep study of these topics will make great contribution to discovering new laws of chemical dynamics, to exploring new control methods of complex chemical processes, to figuring out the very roles of chemical processes in the life system, and to crosslinking the scientific study of chemistry, physics and biology.
Indian Academy of Sciences (India)
Ranjit Kumar
2012-09-01
Travelling and solitary wave solutions of certain coupled nonlinear diffusion-reaction equations have been constructed using the auxiliary equation method. These equations arise in a variety of contexts not only in biological, chemical and physical sciences but also in ecological and social sciences.
Indian Academy of Sciences (India)
Ranjit Kumar; R S Kaushal; Awadhesh Prasad
2010-10-01
An auto-Bäcklund transformation derived in the homogeneous balance method is employed to obtain several new exact solutions of certain kinds of nonlinear diffusion-reaction (D-R) equations. These equations arise in a variety of problems in physical, chemical, biological, social and ecological sciences.
Directory of Open Access Journals (Sweden)
Kanittha Yimnak
2014-01-01
Full Text Available The meshless local Pretrov-Galerkin method (MLPG with the test function in view of the Heaviside step function is introduced to solve the system of coupled nonlinear reaction-diffusion equations in two-dimensional spaces subjected to Dirichlet and Neumann boundary conditions on a square domain. Two-field velocities are approximated by moving Kriging (MK interpolation method for constructing nodal shape function which holds the Kronecker delta property, thereby enhancing the arrangement nodal shape construction accuracy, while the Crank-Nicolson method is chosen for temporal discretization. The nonlinear terms are treated iteratively within each time step. The developed formulation is verified in two numerical examples with investigating the convergence and the accuracy of numerical results. The numerical experiments revealing the solutions by the developed formulation are stable and more precise.
Long-Term Aging Diagnosis of Rotor Steel Using Acoustic Nonlinearity
Energy Technology Data Exchange (ETDEWEB)
Kim, Chung Seok; Jhang, Kyung Young [Hanyang University, Seoul (Korea, Republic of); Park, Ik Keun; Hyun, Chang Yong [Seoul National University of Science and Tecnology, Seoul (Korea, Republic of)
2011-12-15
The long-term aging of ferritic 2.25CrMo steel was characterized using the acoustic nonlinear effect in order to apply to diagnose the degradation behavior of structural materials. We measured the acoustic nonlinearity parameter for each thermally aged specimen by the higher harmonic-generation technique. The acoustic nonlinearity parameter increased with aging time due to equilibrium M6C carbide precipitation, and has a favorable linear relation with Rockwell hardness. This study suggests that acoustic nonlinearity testing may be applicable to diagnostics on strength degradation in rotor steels.
Indian Academy of Sciences (India)
BHARDWAJ S B; SINGH RAM MEHAR; SHARMA KUSHAL; MISHRA S C
2016-06-01
Attempts have been made to explore the exact periodic and solitary wave solutions of nonlinear reaction diffusion (RD) equation involving cubic–quintic nonlinearity along with timedependent convection coefficients. Effect of varying model coefficients on the physical parameters of solitary wave solutions is demonstrated. Depending upon the parametric condition, the periodic,double-kink, bell and antikink-type solutions for cubic–quintic nonlinear reaction-diffusion equation are extracted. Such solutions can be used to explain various biological and physical phenomena.
On the Cauchy Problem of Evolution p-Laplacian Equation with Nonlinear Gradient Term
Institute of Scientific and Technical Information of China (English)
Mingyu CHEN; Junning ZHAO
2009-01-01
The authors study the existence of solution to p-Laplacian equation with non-linear forcing term under optimal assumptions on the initial data,which are assumed to be measures.The existence of local solution is obtained.
CONFIDENCE REGIONS IN TERMS OF STATISTICAL CURVATURE FOR AR(q) NONLINEAR REGRESSION MODELS
Institute of Scientific and Technical Information of China (English)
刘应安; 韦博成
2004-01-01
This paper constructs a set of confidence regions of parameters in terms of statistical curvatures for AR(q) nonlinear regression models. The geometric frameworks are proposed for the model. Then several confidence regions for parameters and parameter subsets in terms of statistical curvatures are given based on the likelihood ratio statistics and score statistics. Several previous results, such as [1] and [2] are extended to AR(q)nonlinear regression models.
Long-term cavity closure in non-linear rocks
Cornet, Jan; Dabrowski, Marcin; Schmid, Daniel Walter
2017-08-01
The time dependent closure of pressurized cavities in viscous rocks due to far-field loads is a problem encountered in many applications like drilling, cavity abandonment and porosity closure. The non-linear nature of the flow of rocks prevents the use of simple solutions for hole closure and calls for the development of appropriate expressions reproducing all the dependencies observed in nature. An approximate solution is presented for the closure velocity of a pressurized cylindrical cavity in a non-linear viscous medium subjected to a combined pressure and shear stress load in the far field. The embedding medium is treated as homogeneous, isotropic, and incompressible and follows a Carreau viscosity model. We derive analytical solutions for the end-member cases of the pressure and shear loads. The exact analytical solution for pressure loads shows that the closure velocity vR is given by the implicit expression {Δ p}/{2{μ _0D_{II}^*}} = - 1/2B( {{v_R^2}/{RD_{II^* + v_R^2}};1/2, - 1/{2n}} ), where Δp is the pressure load, R is the hole radius, B is the incomplete beta function, and μ0, D_{II}^*, n are, respectively, the threshold viscosity, transition rate and stress exponent of the Carreau model. The closure velocity is dominated by the linear mechanism under pressure loads smaller than 1.8{μ _0}D_{II}^* and by the non-linear one under large pressure loads. In the non-linear regime, pressure variations support an increasing part of the load with increasing degree of non-linearity. The decay of the stress perturbation in the non-linear zone varies as r- 2/n where r is the radial distance to the hole. A solution for the maximum closure velocity at the cavity rim vRmax under far-field shear is given: v_{R\\max} = ( 1 + {\\overline {M_s}} ^{-1/2})R\\overline D_{II}, where \\overline {M_s} = (1 + {\\overline {D_{II}} }^2 \\big/ {nD{_{II}^*}^2}) \\big/ ( 1 + {\\overline {D_{II}}^2} \\big/ D{_{II}^*}^2) and \\overline {D_{II}} is the second invariant of the far
Equivalent Representation Form of Oscillators with Elastic and Damping Nonlinear Terms
Directory of Open Access Journals (Sweden)
Alex Elías-Zúñiga
2013-01-01
Full Text Available In this work we consider the nonlinear equivalent representation form of oscillators that exhibit nonlinearities in both the elastic and the damping terms. The nonlinear damping effects are considered to be described by fractional power velocity terms which provide better predictions of the dissipative effects observed in some physical systems. It is shown that their effects on the system dynamics response are equivalent to a shift in the coefficient of the linear damping term of a Duffing oscillator. Then, its numerical integration predictions, based on its equivalent representation form given by the well-known forced, damped Duffing equation, are compared to the numerical integration values of its original equations of motion. The applicability of the proposed procedure is evaluated by studying the dynamics response of four nonlinear oscillators that arise in some engineering applications such as nanoresonators, microresonators, human wrist movements, structural engineering design, and chain dynamics of polymeric materials at high extensibility, among others.
Radiation reaction reexamined: bound momentum and Schott term
Galtsov, D V; Gal'tsov, Dmitri V.; Spirin, Pavel
2004-01-01
We review and compare two different approaches to radiation reaction in classical electrodynamics of point charges: a local calculation of the self-force using the charge equation of motion and a global calculation consisting in integration of the electromagnetic energy-momentum flux through a hypersurface encircling the world-line. Both approaches are complementary and, being combined together, give rise to an identity relating the locally and globally computed forces. From this identity it follows that the Schott terms in the Abraham force should arise from the bound field momentum and can not be introduced by hand as an additional term in the mechanical momentum of an accelerated charge. This is in perfect agreement with the results of Dirac and Teitelboim, but disagrees with the recent calculation of the bound momentum in the retarded coordinates. We perform an independent calculation of the bound electromagnetic momentum and verify explicitly that the Schott term is the derivative of the finite part of t...
Nonlinear chemical reaction between Na2S2O3 and Peroxide compound
Institute of Scientific and Technical Information of China (English)
高庆宇; 汪跃民; 王贵昌; 张松林; 臧雅茹; 赵学庄
1997-01-01
Kinetics of reaction between Na2S2O3 and peroxide compound ( H2O2 or Na2S2O8) in a batch reactor and in a continuous stirring tank reactor (CSTR) were studied.Steady oscillations in uncatalyzed reactions in a CSTR were first discovered.In Na2S2O3-H2O2-H2SO4 reaction system,Pt potential and pH of higher and lower flow rutes beyond oscillation flow rates were in around the same extreme values.The reaction catalyeed by Cu2+ corsist of the catalyzed oscillation process and the uncatalyzed osciliation one.On the basis of experiment,a reaction mechanism consisting of three stages was put forward.The three stages are H positive-feedback reactions,proton negative-feedba k (uncatalyzed negative-feedback and catalyzed negative-feedback) reactions and transitional reactions.The mechanism is able to explain reasonably the nonlinear chemical phenomena appearing in the thiosulfatc oxidation reaction by peroxide-compounds.
Qian, Hong
2016-01-01
We distinguish a mechanical representation of the world in terms of point masses with positions and momenta and the chemical representation of the world in terms of populations of different individuals, each with intrinsic stochasticity, but population wise with statistical rate laws in their syntheses, degradations, spatial diffusion, individual state transitions, and interactions. Such a formal kinetic system in a small volume $V$, like a single cell, can be rigorously treated in terms of a Markov process describing its nonlinear kinetics as well as nonequilibrium thermodynamics at a mesoscopic scale. We introduce notions such as open, driven chemical systems, entropy production, free energy dissipation, etc. Then in the macroscopic limit, we illustrate how two new "laws", in terms of a generalized free energy of the mesoscopic stochastic dynamics, emerge. Detailed balance and complex balance are two special classes of "simple" nonlinear kinetics. Phase transition is intrinsically related to multi-stability...
ASYMPTOTIC SOLUTION OF ACTIVATOR INHIBITOR SYSTEMS FOR NONLINEAR REACTION DIFFUSION EQUATIONS
Institute of Scientific and Technical Information of China (English)
Jiaqi MO; Wantao LIN
2008-01-01
A nonlinear reaction diffusion equations for activator inhibitor systems is considered. Under suitable conditions, firstly, the outer solution of the original problem is obtained, secondly, using the variables of multiple scales and the expanding theory of power series the formal asymptotic expansions of the solution are constructed, and finally, using the theory of differential inequalities the uniform validity and asymptotic behavior of the solution are studied.
Short- and long-term variations in non-linear dynamics of heart rate variability
DEFF Research Database (Denmark)
Kanters, J K; Højgaard, M V; Agner, E;
1996-01-01
OBJECTIVES: The purpose of the study was to investigate the short- and long-term variations in the non-linear dynamics of heart rate variability, and to determine the relationships between conventional time and frequency domain methods and the newer non-linear methods of characterizing heart rate...... variability. METHODS: Twelve healthy subjects were investigated by 3-h ambulatory ECG recordings repeated on 3 separate days. Correlation dimension, non-linear predictability, mean heart rate, and heart rate variability in the time and frequency domains were measured and compared with the results from...... corresponding surrogate time series. RESULTS: A small significant amount of non-linear dynamics exists in heart rate variability. Correlation dimensions and non-linear predictability are relatively specific parameters for each individual examined. The correlation dimension is inversely correlated to the heart...
A quantum quasi-harmonic nonlinear oscillator with an isotonic term
Energy Technology Data Exchange (ETDEWEB)
Rañada, Manuel F., E-mail: mfran@unizar.es [Dep. de Física Teórica and IUMA, Universidad de Zaragoza, 50009 Zaragoza (Spain)
2014-08-01
The properties of a nonlinear oscillator with an additional term k{sub g}/x², characterizing the isotonic oscillator, are studied. The nonlinearity affects to both the kinetic term and the potential and combines two nonlinearities associated to two parameters, κ and k{sub g}, in such a way that for κ = 0 all the characteristics of the standard isotonic system are recovered. The first part is devoted to the classical system and the second part to the quantum system. This is a problem of quantization of a system with position-dependent mass of the form m(x) = 1/(1 − κx²), with a κ-dependent non-polynomial rational potential and with an additional isotonic term. The Schrödinger equation is exactly solved and the (κ, k{sub g})-dependent wave functions and bound state energies are explicitly obtained for both κ < 0 and κ > 0.
Extending lock-in methods: term isolation detection of nonlinear signals.
Jarvis, Thomas W
2016-08-01
We show that components of a nonlinear signal can be measured using phase-sensitive detection at unconventional demodulation frequencies, allowing us to isolate individual terms from the signal. To demonstrate this technique, autocorrelation measurements of an ultrafast pulsed laser were performed using two-photon absorption. In this example, the isolation of individual autocorrelation terms may provide internal consistency checks to improve the precision and accuracy of pulse characterization. More generally, this scheme can be extended to a range of nonlinear measurements. As a demonstration, we analyze a three-photon autocorrelation model, showing that many nonlinear signals can be studied with this method. We anticipate that term isolation detection will find application in a broad range of experiments, such as multidimensional Fourier transform spectroscopy or coherent anti-Stokes Raman spectroscopy.
On the non-linearity of the master equation describing spin-selective radical-ion-pair reactions
Kominis, I. K.
2010-01-01
We elaborate on the physical meaning of the non-linear master equation that was recently derived to account for spin-selective radical-ion-pair reactions. Based on quite general arguments, we show that such a non-linear master equation is indeed to be expected.
Ge, Hao; Qian, Hong
2017-01-01
This paper studies a mathematical formalism of nonequilibrium thermodynamics for chemical reaction models with N species, M reactions, and general rate law. We establish a mathematical basis for J. W. Gibbs' macroscopic chemical thermodynamics under G. N. Lewis' kinetic law of entire equilibrium (detailed balance in nonlinear chemical kinetics). In doing so, the equilibrium thermodynamics is then naturally generalized to nonequilibrium settings without detailed balance. The kinetic models are represented by a Markovian jumping process. A generalized macroscopic chemical free energy function and its associated balance equation with nonnegative source and sink are the major discoveries. The proof is based on the large deviation principle of this type of Markov processes. A general fluctuation dissipation theorem for stochastic reaction kinetics is also proved. The mathematical theory illustrates how a novel macroscopic dynamic law can emerges from the mesoscopic kinetics in a multi-scale system.
Assessment of Alkali-Silica Reaction Damage in Mortars with Nonlinear Ultrasonic Techniques
Chen, J.; Jayapalan, A. R.; Kurtis, K. E.; Kim, J.-Y.; Jacobs, L. J.
2008-02-01
In this work, a nonlinear ultrasonic modulation technique is employed to assess the damage state of portland cement mortar samples induced by alkali-silica reaction (ASR). Due to the nonlinear interaction of propagating waves caused by distributed microcracks that are agitated from its equilibrium state, the ultrasonic responses of samples produce sideband frequencies around the frequency of propagating waves. The amplitude of the sidebands depends on the amplitude of the input signals and is particularly sensitive to the state of damage evolved in the sample. Therefore, the development of internal microcracks with increasing duration of exposure to aggressive conditions can be quantitatively related to the variation of external ultrasonic measurements. The ultrasonic results are compared with results from standard ASR expansion measurements (ASTM C 1260), and a proportionally increasing relation was found in the early stages. In addition, aggregates with different alkali-reactivity (i.e., low reactivity or high reactivity) were examined in a similar manner. The results indicate that the nonlinear parameter obtained from ultrasonic tests directly reflects the difference of aggregate reactivity. This clearly indicates that the developed nonlinear ultrasonic method is potentially a good alternative for a more rapid and still reliable assessment of aggregate alkali-reactivity.
A Two-grid Method with Expanded Mixed Element for Nonlinear Reaction-diffusion Equations
Institute of Scientific and Technical Information of China (English)
Wei Liu; Hong-xing Rui; Hui Guo
2011-01-01
Expanded mixed finite element approximation of nonlinear reaction-diffusion equations is discussed. The equations considered here are used to model the hydrologic and bio-geochemical phenomena. To linearize the mixed-method equations, we use a two-grid method involving a small nonlinear system on a coarse gird of size H and a linear system on a fine grid of size h. Error estimates are derived which demonstrate that the error is O(△t + hk+1 + H2k+2-d/2) (k ≥ 1), where k is the degree of the approximating space for the primary variable and d is the spatial dimension. The above estimates are useful for determining an appropriate H for the coarse grid problems.
Institute of Scientific and Technical Information of China (English)
Jingsun Yao; Jiaqi Mo
2005-01-01
The nonlinear nonlocal singularly perturbed initial boundary value problems for reaction diffusion equations with a boundary perturbation is considered. Under suitable conditions, the outer solution of the original problem is obtained. Using the stretched variable, the composing expansion method and the expanding theory of power series the initial layer is constructed. And then using the theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems is studied. Finally the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation are discussed.
Directory of Open Access Journals (Sweden)
Morteza Ebrahimi
2012-01-01
Full Text Available The purpose of the present study is to provide a fast and accurate algorithm for identifying the medium temperature and the unknown radiation term from an overspecified condition on the boundary in an inverse problem of linear heat equation with nonlinear boundary condition. The design of the paper is to employ Taylor’s series expansion for linearize nonlinear term and then finite-difference approximation to discretize the problem domain. Owing to the application of the finite difference scheme, a large sparse system of linear algebraic equations is obtained. An approach of Monte Carlo method is employed to solve the linear system and estimate unknown radiation term. The Monte Carlo optimization is adopted to modify the estimated values. Results show that a good estimation on the radiation term can be obtained within a couple of minutes CPU time at pentium IV-2.4 GHz PC.
EXACT SOLUTIONS FOR NONLINEAR TRANSIENT FLOW MODEL INCLUDING A QUADRATIC GRADIENT TERM
Institute of Scientific and Technical Information of China (English)
曹绪龙; 同登科; 王瑞和
2004-01-01
The models of the nonlinear radial flow for the infinite and finite reservoirs including a quadratic gradient term were presented. The exact solution was given in real space for flow equation including quadratic gradiet term for both constant-rate and constant pressure production cases in an infinite system by using generalized Weber transform. Analytical solutions for flow equation including quadratic gradient term were also obtained by using the Hankel transform for a finite circular reservoir case. Both closed and constant pressure outer boundary conditions are considered. Moreover, both constant rate and constant pressure inner boundary conditions are considered. The difference between the nonlinear pressure solution and linear pressure solution is analyzed. The difference may be reached about 8% in the long time. The effect of the quadratic gradient term in the large time well test is considered.
Institute of Scientific and Technical Information of China (English)
Pan Jun-Ting; Gong Lun-Xun
2008-01-01
Based on a first order nonlinear ordinary differential equation with at most a sixth-degree nonlinear term which is extended from a type of elliptic equation,and by converting it into a new expansion form,this paper proposes a new algebraic method to construct exact solutions for nonlinear evolution equations.Being concise and straightforward,themethod is applied to modified Benjamin-Bona-Mahony (mBBM) model,and some new exact solutions to the system are obtained.The algorithm is of important significance in exploring exact solutions for other nonlinear evolution equations.
A comparison of Eulerian and Lagrangian transport and non-linear reaction algorithms
Benson, David A.; Aquino, Tomás; Bolster, Diogo; Engdahl, Nicholas; Henri, Christopher V.; Fernàndez-Garcia, Daniel
2017-01-01
When laboratory-measured chemical reaction rates are used in simulations at the field-scale, the models typically overpredict the apparent reaction rates. The discrepancy is primarily due to poorer mixing of chemically distinct waters at the larger scale. As a result, realistic field-scale predictions require accurate simulation of the degree of mixing between fluids. The Lagrangian particle-tracking (PT) method is a now-standard way to simulate the transport of conservative or sorbing solutes. The method's main advantage is the absence of numerical dispersion (and its artificial mixing) when simulating advection. New algorithms allow particles of different species to interact in nonlinear (e.g., bimolecular) reactions. Therefore, the PT methods hold a promise of more accurate field-scale simulation of reactive transport because they eliminate the masking effects of spurious mixing due to advection errors inherent in grid-based methods. A hypothetical field-scale reaction scenario is constructed and run in PT and Eulerian (finite-volume/finite-difference) simulators. Grid-based advection schemes considered here include 1st- to 3rd-order spatially accurate total-variation-diminishing flux-limiting schemes, both of which are widely used in current transport/reaction codes. A homogeneous velocity field in which the Courant number is everywhere unity, so that the chosen Eulerian methods incur no error when simulating advection, shows that both the Eulerian and PT methods can achieve convergence in the L1 (integrated concentration) norm, but neither shows stricter pointwise convergence. In this specific case with a constant dispersion coefficient and bimolecular reaction A + B → P , the correct total amount of product is 0.221MA0, where MA0 is the original mass of reactant A. When the Courant number drops, the grid-based simulations can show remarkable errors due to spurious over- and under-mixing. In a heterogeneous velocity field (keeping the same constant and
Luna, Julio; Ocampo-Martinez, Carlos; Serra, Maria
2015-05-01
In this work, a nonlinear model predictive control (NMPC) strategy is proposed to regulate the concentrations of the different gas species inside a Proton Exchange Membrane Fuel Cell (PEMFC) anode gas channel. The purpose of the regulation relies on the rejection of the unmeasurable perturbations that affect the system: the hydrogen reaction and water transport terms. The model of the anode channel is derived from the discretisation of the partial differential equations that define the nonlinear dynamics of the system, taking into account spatial variations along the channel. Forward and backward discretisations of the distributed model are employed to take advantage of the boundary conditions of the problem. A linear observer is designed and implemented to perform output-feedback control of the plant. This information is fed to the controller to regulate the states towards their desired values. Simulation results are presented to show the performance of the proposed control method over a given case study. Different cost functions are compared and the one with minimum state-regulation error is identified. Suitable dynamic responses are obtained facing the different considered disturbances.
Finite Element Solutions for the Space Fractional Diffusion Equation with a Nonlinear Source Term
Directory of Open Access Journals (Sweden)
Y. J. Choi
2012-01-01
Full Text Available We consider finite element Galerkin solutions for the space fractional diffusion equation with a nonlinear source term. Existence, stability, and order of convergence of approximate solutions for the backward Euler fully discrete scheme have been discussed as well as for the semidiscrete scheme. The analytical convergent orders are obtained as O(k+hγ˜, where γ˜ is a constant depending on the order of fractional derivative. Numerical computations are presented, which confirm the theoretical results when the equation has a linear source term. When the equation has a nonlinear source term, numerical results show that the diffusivity depends on the order of fractional derivative as we expect.
Directory of Open Access Journals (Sweden)
Jiang-Tao Li
2015-01-01
Full Text Available The nonlinear dual-porosity flow model, specifically considering the quadratic pressure gradient term, wellbore storage coefficient, well skin factor, and interporosity flow of matrix to natural fractures, was established for well production in a naturally fractured formation and then solved using a semianalytical method, including Laplace transform and a transformation of the pressure function. Analytical solution of the model in Laplace space was converted to numerical solution in real space using Stehfest numerical inversion. Nonlinear flow process for well production in a naturally fractured formation with different external boundaries was simulated and analyzed using standard pressure curves. Influence of the quadratic pressure gradient coefficient on pressure curves was studied qualitatively and quantitatively in conditions of a group of fixed model parameters. The research results show that the semianalytical modelling method is applicable in simulating the nonlinear dual-porosity flow behavior.
Saturations-based nonlinear controllers with integral term: validation in real-time
Alatorre, A. G.; Castillo, P.; Mondié, S.
2016-05-01
Popular saturations-based nonlinear controller usually include proportional and derivative components of the state or output. The fact that in many applications, these components do not suffice to insure the convergence to the desired output values, motivate the addition of an integral term. In this paper, three configurations of nonlinear controllers based on saturation functions are improved with an integral component. The stability of the three algorithms is analysed using the Lyapunov theory. Simulation results validate the proposed control laws when they are applied to nonlinear systems with constant and unknown perturbations. Real-time experiments realised with a quad-rotor aerial vehicle and a hovercraft vehicle show that the proposed scheme can follow autonomously some trajectories, and that it could be robust with respect to delays.
BRST Invariant Theory Of A Generalized 1+1 Dimensional Nonlinear Sigma Model With Topological Term
Huang, Yong-Chang; Lee, Xi-Guo
2006-01-01
We give a generalized Lagrangian density of 1+1 Dimensional O(3) nonlinear sigma model with subsidiary constraints, different Lagrange multiplier fields and topological term, find a lost intrinsic constraint condition, convert the subsidiary constraints into inner constraints in the nonlinear sigma model, give the example of not introducing the lost constraint, by comparing the example with the case of introducing the lost constraint, we obtain that when not introducing the lost constraint, one has to obtain a lot of various non-intrinsic constraints. We further deduce the gauge generator, give general BRST transformation of the model under the general conditions. It is discovered that there exists a gauge parameter originating from the freedom degree of BRST transformation in a general O(3) nonlinear sigma model, and we gain the general commutation relations of ghost field.
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
Kraka, Elfi; Cremer, Dieter
2010-05-18
(A(n,s) reaction complex. URVA can show the mechanism of a reaction expressed in terms of reaction phases, revealing the sequence of chemical processes in the reaction complex and making it possible to determine those electronic factors that control the mechanism and energetics of the reaction. The magnitude of adiabatic curvature coupling coefficients is related to strength and polarizability of the bonds being broken. Transient points along the reaction path are associated with hidden intermediates and hidden transition states, which can be converted into real intermediates and transition states when the reaction conditions or the substitution pattern of the reaction complex are appropriately changed. Accordingly, URVA represents a theoretical tool with tremendous experimental potential, offering the chemist the ability to assert greater control over reactions.
Wright, E. S.; Aleem, T.
2003-12-01
In 1953, G.I.~Taylor published his landmark paper concerning the transport of a contaminant dissolved in a fluid flowing through a pipe of narrow diameter. He demonstrated that an interaction between the transverse variations in the fluid's velocity field and the transverse diffusion of the solute yielded an effective downstream mixing mechanism for the transverse average of the solute. This mechanism has since been dubbed ``Taylor Dispersion.'' Since his original publication, many related studies have surfaced. These include generalizations of channel geometry, generalizations of the velocity field (including turbulent field), applications to sedimentation problems, etc. However, much less attention has been given to the effects of nonlinear chemical reactions upon a system of solutes undergoing Taylor Dispersion. We present a rigorous mathematical model for the evolution of the transverse averages of reacting solutes that travel within a fluid flowing down a pipe of arbitrary cross-section. The technique for deriving this model is a generalization of a multiple scales perturbation approach described by P.C.~Fife for linear (reactionless) problems. The key outcome is that while one still finds an effective mechanism for downstream mixing, but also there is also a effective mechanism for nonlinear advection.
Indian Academy of Sciences (India)
J B ZHOU; J XU; J D WEI; X Q YANG
2017-04-01
This paper is concerned with the existence of travelling wave solutions to a singularly perturbed generalized Gardner equation with nonlinear terms of any order. By using geometric singular perturbation theory and based on the relation between solitary wave solution and homoclinic orbits of the associated ordinary differential equations, the persistence of solitary wave solutions of this equation is proved when the perturbation parameter is sufficiently small. The numerical simulations verify our theoretical analysis.
Removal of Noise Oscillation Term Appearing in the Nonlinear Equation Solution
Directory of Open Access Journals (Sweden)
Yasir Khan
2012-01-01
Full Text Available This paper suggests a novel modified Laplace method for removal of noise oscillation term appearing in the nonlinear equation solutions. The modified method overcomes the noise oscillation during the iteration procedure by suitable choice of an initial solution. Several examples are tested, and the obtained results suggest that this newly developed technique could lead to a promising tool and powerful improvement for many applications in differential and integral equations.
Lattice solitons in nonlinear Schrödinger equation with coupling-to-a-mean-term
Bağcı, Mahmut; Bakırtaş, İlkay; Antar, Nalan
2017-01-01
Wave collapse is arrested in the self-focusing nonlinear Schrödinger equation with coupling to a mean term (NLSM) by adding an external potential (lattice) to the governing equation. It is numerically demonstrated that collapse will eventually occur in a lattice-free system and it can be suppressed by adding an external periodic lattice to the governing system. It is numerically shown that lattice depth provides great controllability on soliton stability and more robust solitons can be obtained.
The dynamics of nonlinear reaction-diffusion equations with small Lévy noise
Debussche, Arnaud; Imkeller, Peter
2013-01-01
This work considers a small random perturbation of alpha-stable jump type nonlinear reaction-diffusion equations with Dirichlet boundary conditions over an interval. It has two stable points whose domains of attraction meet in a separating manifold with several saddle points. Extending a method developed by Imkeller and Pavlyukevich it proves that in contrast to a Gaussian perturbation, the expected exit and transition times between the domains of attraction depend polynomially on the noise intensity in the small intensity limit. Moreover the solution exhibits metastable behavior: there is a polynomial time scale along which the solution dynamics correspond asymptotically to the dynamic behavior of a finite-state Markov chain switching between the stable states.
An improved numerical method for nonlinear terms of spectral model and its applications
Institute of Scientific and Technical Information of China (English)
无
2003-01-01
At present, the spectral model is one of the most widely applied numerical models in the research of numerical prediction and climatic variation. To improve the precision and efficiency of spectral method can greatly contribute to the development of numerical prediction. As the core part of spectral method, the calculating method of nonlinear terms always concentrates on numerical solution of atmospheric dynamical processes in the spectral space. However, there was little study in this field in the late thirty years. According to the principle of nonlinear term calculation with the dimensionality degradation and latitudinal perfect spectral method, we designed a new nonlinear term calculating method and made it compatible well with the common numerical algorithms of the spectral model used internationally. With an own-designed spectral dynamical framework suiting for the numerical application in common uses, theoretical analyses and numerical experiments have also been deeply conducted to compare our new method with the widely-used transform method in an attempt to advance the development of numerical algorithms of spectral model.
Energy Technology Data Exchange (ETDEWEB)
Akiyama, Yasunobu; Imaishi, Nobuyuki [Kyushu University, Fukuoka (Japan)
1999-06-05
The simulation algorithm of step/hole coverage shape which could be applied at the Chemical Vapor Deposition (CVD) system with the nonlinear surface reaction speed was devised. By combining with the conventional simple Monte Carlo calculation technique, the code which could simulate the coverage shape at high speed was made. It was quantitatively explainable in respect of raw material density dependence (fluoridation tungsten (6); WF{sub 6}) of the coverage shape, when this code was applied to the thermal CVD of tungsten (W) with nonlinear surface reaction. (translated by NEDO)
Examining the reaction of monetary policy to exchange rate changes: A nonlinear ARDL approach
Manogaran, Lavaneesvari; Sek, Siok Kun
2017-04-01
Previous studies showed the exchange rate changes can have significant impacts on macroeconomic performance. Over fluctuation of exchange rate may lead to economic instability. Hence, monetary policy rule tends to react to exchange rate changes. Especially, in emerging economies where the policy-maker tends to limit the exchange rate movement through interventions. In this study, we seek to investigate how the monetary policy rule reacts to exchange rate changes. The nonlinear autoregressive distributed lag (NARDL) model is applied to capture the asymmetric effect of exchange rate changes on monetary policy reaction function (interest rate). We focus the study in ASEAN5 countries (Indonesia, Malaysia, Philippines, Thailand and Singapore). The results indicated the existence of asymmetric effect of exchange rates changes on the monetary reaction function for all ASEAN5 countries in the long-run. Where, in majority of the cases the monetary policy is reacting to the appreciation and depreciation of exchange rate by raising the policy rate. This affirms the intervention of policymakers with the `fear of floating' behavior.
Energy Technology Data Exchange (ETDEWEB)
Feng, Wenqiang, E-mail: wfeng1@vols.utk.edu [Department of Mathematics, The University of Tennessee, Knoxville, TN 37996 (United States); Salgado, Abner J., E-mail: asalgad1@utk.edu [Department of Mathematics, The University of Tennessee, Knoxville, TN 37996 (United States); Wang, Cheng, E-mail: cwang1@umassd.edu [Department of Mathematics, The University of Massachusetts, North Dartmouth, MA 02747 (United States); Wise, Steven M., E-mail: swise1@utk.edu [Department of Mathematics, The University of Tennessee, Knoxville, TN 37996 (United States)
2017-04-01
We describe and analyze preconditioned steepest descent (PSD) solvers for fourth and sixth-order nonlinear elliptic equations that include p-Laplacian terms on periodic domains in 2 and 3 dimensions. The highest and lowest order terms of the equations are constant-coefficient, positive linear operators, which suggests a natural preconditioning strategy. Such nonlinear elliptic equations often arise from time discretization of parabolic equations that model various biological and physical phenomena, in particular, liquid crystals, thin film epitaxial growth and phase transformations. The analyses of the schemes involve the characterization of the strictly convex energies associated with the equations. We first give a general framework for PSD in Hilbert spaces. Based on certain reasonable assumptions of the linear pre-conditioner, a geometric convergence rate is shown for the nonlinear PSD iteration. We then apply the general theory to the fourth and sixth-order problems of interest, making use of Sobolev embedding and regularity results to confirm the appropriateness of our pre-conditioners for the regularized p-Lapacian problems. Our results include a sharper theoretical convergence result for p-Laplacian systems compared to what may be found in existing works. We demonstrate rigorously how to apply the theory in the finite dimensional setting using finite difference discretization methods. Numerical simulations for some important physical application problems – including thin film epitaxy with slope selection and the square phase field crystal model – are carried out to verify the efficiency of the scheme.
Feng, Wenqiang; Salgado, Abner J.; Wang, Cheng; Wise, Steven M.
2017-04-01
We describe and analyze preconditioned steepest descent (PSD) solvers for fourth and sixth-order nonlinear elliptic equations that include p-Laplacian terms on periodic domains in 2 and 3 dimensions. The highest and lowest order terms of the equations are constant-coefficient, positive linear operators, which suggests a natural preconditioning strategy. Such nonlinear elliptic equations often arise from time discretization of parabolic equations that model various biological and physical phenomena, in particular, liquid crystals, thin film epitaxial growth and phase transformations. The analyses of the schemes involve the characterization of the strictly convex energies associated with the equations. We first give a general framework for PSD in Hilbert spaces. Based on certain reasonable assumptions of the linear pre-conditioner, a geometric convergence rate is shown for the nonlinear PSD iteration. We then apply the general theory to the fourth and sixth-order problems of interest, making use of Sobolev embedding and regularity results to confirm the appropriateness of our pre-conditioners for the regularized p-Lapacian problems. Our results include a sharper theoretical convergence result for p-Laplacian systems compared to what may be found in existing works. We demonstrate rigorously how to apply the theory in the finite dimensional setting using finite difference discretization methods. Numerical simulations for some important physical application problems - including thin film epitaxy with slope selection and the square phase field crystal model - are carried out to verify the efficiency of the scheme.
Nonlinear optical effects in oxygen-binding reactions of hemoglobin A0.
Ownby, D W; Gill, S J
1990-08-31
Optical spectra have been taken in the Soret band (440-400 nm) under different oxygen partial pressures for hemoglobin (Hb) A0 at pH 7.0, 15 degrees C, 2-3 mM heme, 30 mM inositol hexaphosphate, 0.1 Hepes and 0.1 M NaCl. Application of the matrix method of singular value decomposition (SVD) to the difference spectra for different oxygen pressures shows the presence of at least two distinct optical transitions. From this result one concludes that the optical response to oxygen binding is nonlinear in the Soret band. The degree of nonlinearity has been determined by fitting the data at different wavelengths to the four-step reaction Adair equation with the inclusion of optical parameters that describe the intermediate oxygenated species. It is found that the data are well-represented by two optical parameters at each wavelengths, one which represents the optical change for the addition of the first and second oxygen molecules and the other which corresponds to the change for the addition of the third and fourth oxygen molecules. The ratio of these optical parameters depends only moderately upon wavelength with an average value of 0.8 over the Soret band. Thus, there is an approx. 20% smaller optical response for the first two ligated species than that for the last two ligated species. The overall Adair equilibrium constants are evaluated as follows: beta 1 = 0.081 +/- 0.003 Torr-1, beta 2 = 2.53 x 10(-3) +/- 2.4 x 10(-4) Torr-2, beta 3 = 1.25 x 10(-5) +/- 1.0 x 10(-6) Torr-3, beta 4 = 1.77 x 10(-6) +/- 1.5 x 10(-7) Torr-4.
Hidden attractors in a chaotic system with an exponential nonlinear term
Pham, V.-T.; Vaidyanathan, S.; Volos, C. K.; Jafari, S.
2015-07-01
Studying systems with hidden attractors is new attractive research direction because of its practical and threoretical importance. A novel system with an exponential nonlinear term, which can exhibit hidden attractors, is proposed in this work. Although new system possesses no equilibrium points, it displays rich dynamical behaviors, like chaos. By calculating Lyapunov exponents and bifurcation diagram, the dynamical behaviors of such system are discovered. Moreover, two important features of a chaotic system, the possibility of synchronization and the feasibility of the theoretical model, are also presented by introducing an adaptive synchronization scheme and designing a digital hardware platform-based emulator.
O(3) Non-linear $\\sigma$ model with Hopf term and Higher spin theories
Govindarajan, T R; Shaji, N; Sivakumar, M
1993-01-01
Following our earlier work we argue in detail for the equivalence of the nonlinear $\\sigma$ model with Hopf term at~$\\theta=\\pi/2s$ ~and an interacting spin-s theory. We give an ansatz for spin-s operators in the $\\sigma$ model and show the equivalence of the correlation functions.We also show the relation between topological and Noether currents. We obtain the Lorentz and discrete transformation properties of the spin-s operator from the fields of the $\\sigma$ model. We also explore the connection of this model with Quantum Hall Fluids.
Canonical structure of evolution equations with non-linear dispersive terms
Indian Academy of Sciences (India)
B Talukdar; J Shamanna; S Ghosh
2003-07-01
The inverse problem of the variational calculus for evolution equations characterized by non-linear dispersive terms is analysed with a view to clarify why such a system does not follow from Lagrangians. Conditions are derived under which one could construct similar equations which admit a Lagrangian representation. It is shown that the system of equations thus obtained can be Hamiltonized by making use of the Dirac’s theory of constraints. The speciﬁc results presented refer to the third- and ﬁfth-order equations of the so-called distinguished subclass.
Ge, Hao
2016-01-01
Macroscopic entropy production $\\sigma^{(tot)}$ in the general nonlinear isothermal chemical reaction system with mass action kinetics is decomposed into a free energy dissipation and a house-keeping heat: $\\sigma^{(tot)}=\\sigma^{(fd)}+\\sigma^{(hk)}$; $\\sigma^{(fd)}=-\\rd A/\\rd t$, where $A$ is a generalized free enegy function. This yields a novel nonequilibrium free energy balance equation $\\rd A/\\rd t=-\\sigma^{(tot)}+\\sigma^{(hk)}$, which is on a par with celebrated entropy balance equation $\\rd S/\\rd t=\\sigma^{(tot)}+\\eta^{(ex)}$ where $\\eta^{(ex)}$ is the rate of entropy exchange with the environment.For kinetic system with complex balance,$\\sigma^{(fd)},\\sigma^{(hk)}\\ge 0$: $\\sigma^{(fd)}$ characterizes the irreversibility of a transient relaxation kinetics; while $\\sigma^{(hk)}$ is positive even in a steady state, representing irreversibility in open,driven chemical systems with a chemostat.For kinetic system withoutcomplex balance, negative $\\sigma^{(fd)}$ is a necessary condition for multistability, w...
Guner, Ozkan; Bekir, Ahmet; Unsal, Omer; Cevikel, Adem C.
2017-01-01
In this paper, we pay attention to the analytical method named, ansatz method for finding the exact solutions of the variable-coefficient modified KdV equation and variable coefficient diffusion-reaction equation. As a result the singular 1-soliton solution is obtained. These solutions are important for the explanation of some practical physical problems. The obtained results show that these methods provides a powerful mathematical tool for solving nonlinear equations with variable coefficients. This method can be extended to solve other variable coefficient nonlinear partial differential equations.
Ozone - plant surface reactions an important ozone loss term?
Hansel, Armin; Jud, Werner; Fischer, Lukas; Canaval, Eva; Wohlfahrt, Georg; Tissier, Alain
2015-04-01
Elevated tropospheric ozone concentrations are considered a toxic threat to plants responsible for global crop losses with associated economic costs of several billions dollar per year. Plant injuries have been related to the uptake of ozone through stomatal pores and oxidative effects damaging the internal leaf tissue. But a striking question remains: How much ozone enters the plant through open stomata and how much ozone is lost by chemical reactions at the plant surface? Until now surface losses are estimated from measured total ozone deposition fluxes and calculated stomatal conductance values. While stomatal conductance of CO2 and H2O is well understood and extensively used in describing plant atmosphere gas exchange, stomatal conductance of ozone is not well known. Here we use different Nicotiana tabacum varieties and find that surface reactions of ozone with diterpenoids synthesized by glandular trichomes reduce ozone flux through open stomata. Our measurements reveal that fast ozone loss at the plant surface is accompanied with prompt release of oxygenated volatile compounds. In the ozone fumigation experiments of different Nicotiana tabacum varieties the release of specific volatile oxy-VOCs allowed to identify the semi volatile precursor compounds at the plant surface. Ozone fumigation experiments with Norway spruce (Picea abies) and Scots Pine (Pinus sylvestris), two common species in the Northern Hemisphere, show also a significant ozone loss at the plant surface for Picea abies. Fluid dynamic calculations of ozone transport in the diffusive leaf boundary layer reveal a vertical but no horizontal ozone gradient thus reducing ozone fluxes through the pores in case of efficient ozone scavenging plant surfaces. We explain this efficient ozone protection mechanism by the porous surface architecture of plants in combination with unsaturated semi-volatile compounds deposited at the plant surface. These results show that unsaturated semi-volatile compounds at
The effect of nonlinear thermo-fluid-dynamic terms on free-piston Stirling machine stability
Energy Technology Data Exchange (ETDEWEB)
Benvenuto, G. [Univ. of Genoa (Italy). Dipt. di Ingegneria Navale; Monte, F. de [Univ. of L`Aquila (Italy). Dipt. de Energetica
1996-12-31
In this work a new linearization technique of the dynamic balance equations of a free-piston Stirling machine is developed. It takes into account the nonlinear thermo-fluid-dynamic terms inherent in the machine, although keeping the linearity of the differential dynamic equations. This allows the equations of motion to be solved still analytically and, therefore, useful algebraic relations (already established by the authors in past studies) linking together the various machine parameters to be used. The advantages related to the proposed linearization methodology are the following: (1) it gives a right interpretation of the machine working when the operational parameters vary, because the considered nonlinear terms have a stabilizing effect; (2) it can be used to predict the machine performance not only with more accuracy, but especially in a more exhaustive way, allowing to estimate also the piston stroke and, therefore, the delivered power; (3) it enables to design the machine in such a way to enhance its stability, thus eliminating the necessity of power control systems.
Bahr, J.M.
1990-01-01
This paper extends a four-step derivation procedure, previously presented for cases of transport affected by surface reactions, to transport problems involving homogeneous reactions. Derivations for these classes of reactions are used to illustrate the manner in which mathematical differences between reaction classes are reflected in the mathematical derivation procedures required to identify kinetically influenced terms. Simulation results for a case of transport affected by a single solution phase complexation reaction and for a case of transport affected by a precipitation-dissolution reaction are used to demonstrate the nature of departures from equilibrium-controlled transport as well as the use of kinetically influenced terms in determining criteria for the applicability of the local equilibrium assumption. A final derivation for a multireaction problem demonstrates the application of the generalized procedure to a case of transport affected by reactions of several classes. -from Author
Pyrene-Based Small Molecular Nonlinear Optical Materials Modified by ``Click-Reaction''
Liang, Pengxia; Li, Zhengqiang; Mi, Yongsheng; Yang, Zhou; Wang, Dong; Cao, Hui; He, Wanli; Yang, Huai
2015-08-01
Two pyrene derivatives were successfully synthesized via an efficient copper(I)-catalyzed azide alkyne 1,3-dipolar cycloaddition. The photophysical and electrochemical properties were characterized using ultraviolet-visible absorption spectra, fluorescence spectra, cyclic voltammograms and density functional theory modulations. These results showed that the symmetry structure of these derivatives formed an electron-delocalized organic system, which have larger effects in achieving a third-order nonlinear optical (NLO) response. The third-order nonlinear properties including the nonlinear absorption and the nonlinear susceptibilities investigated by Z-scan technique indicate that the title compounds can serve as a promising candidate for third-order NLO applications.
Kengne, Emmanuel; Saydé, Michel; Ben Hamouda, Fathi; Lakhssassi, Ahmed
2013-11-01
Analytical entire traveling wave solutions to the 1+1 density-dependent nonlinear reaction-diffusion equation via the extended generalized Riccati equation mapping method are presented in this paper. This equation can be regarded as an extension case of the Fisher-Kolmogoroff equation, which is used for studying insect and animal dispersal with growth dynamics. The analytical solutions are then used to investigate the effect of equation parameters on the population distribution.
Investigation of nonlinear models to describe long-term egg production in Japanese quail.
Narinc, Dogan; Karaman, Emre; Aksoy, Tulin; Firat, Mehmet Ziya
2013-06-01
In this study, long-term egg production was monitored in a Japanese quail flock, which had not undergone any genetic improvement, for 52 wk as of the age of sexual maturity. The study aimed to detect some traits with respect to egg production, to determine the cumulative hen-housed egg numbers, and to compare goodness of fit of different nonlinear models for the percentage of hen-day egg production. The mean age at first egg was 38.9 d and the age at 50% egg production was 45.3 d. The quail reached peak production at 15 wk of age (wk 9 of egg production period) when the percentage of hen-day egg production was found to be 94%. The cumulative hen-housed egg number for 52 wk as of the age of sexual maturity was 253.08. The monomolecular function, a nonsigmoid model, was used in the nonlinear regression analysis of the cumulative egg numbers. Parameters a, b, and c of the monomolecular model were estimated to be 461.70, 473.31, and 0.065, respectively. Gamma, McNally, Adams-Bell, and modified compartmental models, widely used in hens previously, were used in the nonlinear regression analysis of the percentages of hen-day egg production. The goodness of fit for these models was compared using the values of pseudo-R², Akaike's information criterion, and Bayesian information criterion. It was determined that all the models are adequate but that the Adams-Bell model displayed a slightly better fit for the percentage of hen-day egg production in Japanese quail than others.
Institute of Scientific and Technical Information of China (English)
Xiang LI; Wei-guo ZHANG; Zheng-ming LI
2014-01-01
This paper aims at analyzing the shapes of the bounded traveling wave solu-tions for a class of nonlinear wave equation with a quintic term and obtaining its damped oscillatory solutions. The theory and method of planar dynamical systems are used to make a qualitative analysis to the planar dynamical system which the bounded traveling wave solutions of this equation correspond to. The shapes, existent number, and condi-tions are presented for all bounded traveling wave solutions. The bounded traveling wave solutions are obtained by the undetermined coefficients method according to their shapes, including exact expressions of bell and kink profile solitary wave solutions and approxi-mate expressions of damped oscillatory solutions. For the approximate damped oscillatory solution, using the homogenization principle, its error estimate is given by establishing the integral equation, which reflects the relation between the exact and approximate so-lutions. It can be seen that the error is infinitesimal decreasing in the exponential form.
Apparently non-invariant terms of nonlinear sigma models in lattice perturbation theory
Harada, Koji; Kubo, Hirofumi; Yamamoto, Yuki
2009-01-01
Apparently non-invariant terms (ANTs) which appear in loop diagrams for nonlinear sigma models (NLSs) are revisited in lattice perturbation theory. The calculations have been done mostly with dimensional regularization so far. In order to establish that the existence of ANTs is independent of the regularization scheme, and of the potential ambiguities in the definition of the Jacobian of the change of integration variables from group elements to "pion" fields, we employ lattice regularization, in which everything (including the Jacobian) is well-defined. We show explicitly that lattice perturbation theory produces ANTs in the four-point functions of the "pion" fields at one-loop and the Jacobian does not play an important role in generating ANTs.
Hyperbilirubinemia Influences Sleep-Wake Cycles of Term Newborns in a Non-Linear Manner
Zhang, Lian; Zhou, Yanxia; Li, Xufang; Cheng, Tingting
2017-01-01
Hyperbilirubinemia is a common cause for irreversible neuronal influence in the brain of term newborns, while the feature of neurological symptoms associated with hyperbilirubinemia has not been well characterized yet. In the present study, we examined a total of 203 neonates suffering from hyperbilirubinemia with a bedside amplitude-integrated Electroencephalography (aEEG) device, in order to determine whether there is any special change in sleep-wake cycles (SWCs). Among these patients, 14 cases showed no recognizable SWCs with the total serum bilirubin (TSB) level at 483.9–996.2 μmol/L; 75 cases exhibited reduced SWCs with the TSB level at 311.2–688.5 μmol/L; and the rest cases had the normal SWCs. The number of the normal SWCs occurrence had a significant negative correlation with the increased TSB level in a non-linear manner (r = -0.689, p <0.001). In addition, the increased TSB reshaped the structure of SWC by narrowing down the broadband and broadening the narrowband. Spearman’s correlation analysis indicated a significant negative correlation between the TSB level and the ratio of broadband (r = -0.618, p < 0.001), a significant positive correlation between the TSB level and the narrowband ratio (r = 0.618, p < 0.001), respectively. Furthermore, the change of SWC seemed like a continuous phenomenon, and the hyperbilirubinemia caused SWC changes was fit into a loess model in this paper. In summary, the hyperbilirubinemia influenced SWC of term newborns significantly at a non-linear manner, and these results revealed the feature of the neurological sequela that is associated with TSB. PMID:28072860
Nonlinear short-term heart rate variability prediction of spontaneous ventricular tachyarrhythmia
Institute of Scientific and Technical Information of China (English)
ZHUANG JianJun; NING XinBao; DU SiDan; WANG ZhenZhou; HUO ChengYu; YANG Xi; FAN AiHua
2008-01-01
As malign ventricular tachyarrhythmias triggering sudden cardiac death (SCD),both ventricular tachycardia (VT) and ventricular fibrillation (VF) are major causes of mortality.The most efficient ther-apy for SCD prevention is implantable cardioverter defibrillators (ICD).The ICD can accurately and ef-fectively identify the forthcoming of fatal ventricular tachyarrhythmias and deliver a shock in order to restore patients' normal sinus rhythm.In this study,two nonlinear complexity measures based on en-tropy:approximate entropy (ApEn) and sample entropy (SampEn) as well as two time linear indices:the mean RR interval (the average of time intervals between consecutive R-waves) and the standard devia-tion of RR intervals were used for short-term forecasting of VT-VF occurrence.The last small sections of interbeat intervals preceding 135 VT-VF episodes from 78 patients stored by the ICD were analyzed and compared with individually acquired control time series (CON series) from the same patients,which are normally intrinsic sinus rhythms.The results demonstrate that in addition to an obvious in-crease in heart rates of the patients,the values of two entropy measures are significantly smaller for VT-VF episodes than those for CON series.Conclusions can be drawn that when a ventricular tach-yarrhythmia approaches,the sympathetic tone of the patients is increased,and the complexity of their RR intervals immediately before the onset of VT-VF events is obviously lower than that of RR Intervals recorded during sinus rhythms.For a better separation,the optimal range of threshold r is determined for two algorithms.ApEn and SampEn measures might be the suitable nonlinear parameters for shod-term prediction of life-threatening ventricular tachyarrhythmias in the application of the cardioversion and defibrillation.
Indian Academy of Sciences (India)
O S IYIOLA; F D ZAMAN
2016-10-01
In this paper, we consider the (2+1) nonlinear fractional heat equation with non-local integral terms and investigate two different cases of such non-local integral terms. The first has to do with the time-dependent non-local integral term and the second is the space-dependent non-local integral term. Apart from the nonlinear nature of these formulations, the complexity due to the presence of the non-local integral terms impelled us to use a relatively new analytical technique called q-homotopy analysis method to obtain analytical solutions to both cases in the form of convergent series with easily computable components. Our numerical analysis enables us to show the effects of non-local terms and the fractional-order derivative on the solutions obtained by this method.
Li, Shukai; Yang, Lixing; Gao, Ziyou; Li, Keping
2014-11-01
In this paper, the stabilization strategies of a general nonlinear car-following model with reaction-time delay of the drivers are investigated. The reaction-time delay of the driver is time varying and bounded. By using the Lyapunov stability theory, the sufficient condition for the existence of the state feedback control strategy for the stability of the car-following model is given in the form of linear matrix inequality, under which the traffic jam can be well suppressed with respect to the varying reaction-time delay. Moreover, by considering the external disturbance for the running cars, the robust state feedback control strategy is designed, which ensures robust stability and a smaller prescribed H∞ disturbance attenuation level for the traffic flow. Numerical examples are given to illustrate the effectiveness of the proposed methods.
Ullah, Imran; Khan, Ilyas; Shafie, Sharidan
2016-11-01
In the present work, the effects of chemical reaction on hydromagnetic natural convection flow of Casson nanofluid induced due to nonlinearly stretching sheet immersed in a porous medium under the influence of thermal radiation and convective boundary condition are performed numerically. Moreover, the effects of velocity slip at stretching sheet wall are also examined in this study. The highly nonlinear-coupled governing equations are converted to nonlinear ordinary differential equations via similarity transformations. The transformed governing equations are then solved numerically using the Keller box method and graphical results for velocity, temperature, and nanoparticle concentration as well as wall shear stress, heat, and mass transfer rate are achieved through MATLAB software. Numerical results for the wall shear stress and heat transfer rate are presented in tabular form and compared with previously published work. Comparison reveals that the results are in good agreement. Findings of this work demonstrate that Casson fluids are better to control the temperature and nanoparticle concentration as compared to Newtonian fluid when the sheet is stretched in a nonlinear way. Also, the presence of suspended nanoparticles effectively promotes the heat transfer mechanism in the base fluid.
Ullah, Imran; Khan, Ilyas; Shafie, Sharidan
2016-12-01
In the present work, the effects of chemical reaction on hydromagnetic natural convection flow of Casson nanofluid induced due to nonlinearly stretching sheet immersed in a porous medium under the influence of thermal radiation and convective boundary condition are performed numerically. Moreover, the effects of velocity slip at stretching sheet wall are also examined in this study. The highly nonlinear-coupled governing equations are converted to nonlinear ordinary differential equations via similarity transformations. The transformed governing equations are then solved numerically using the Keller box method and graphical results for velocity, temperature, and nanoparticle concentration as well as wall shear stress, heat, and mass transfer rate are achieved through MATLAB software. Numerical results for the wall shear stress and heat transfer rate are presented in tabular form and compared with previously published work. Comparison reveals that the results are in good agreement. Findings of this work demonstrate that Casson fluids are better to control the temperature and nanoparticle concentration as compared to Newtonian fluid when the sheet is stretched in a nonlinear way. Also, the presence of suspended nanoparticles effectively promotes the heat transfer mechanism in the base fluid.
Short-term pollution forecasts based on linear and nonlinear methods of time series analysis
Russo, A.; Trigo, R. M.
2012-04-01
Urban air pollution is a complex mixture of toxic components, which may induce acute and chronic responses from sensitive groups, such as children and people with previous heart and respiratory insufficiencies. However, air pollution, presents a highly chaotic and non-linear behavior. In this work we analyzed several pollutants time series recorded in the urban area of Lisbon (Portugal) for the 2002-2006 period. Linear and nonlinear methods were applied in order to assess NO2, PM10 and O3 main trends and fluctuations and finally, to produce daily forecasts of the referred pollutants. Here we evaluate the potential of linear and non-linear neural networks (NN) to produce short-term forecasts, and also the contribution of meteorological variables (daily mean temperature, radiation, wind speed and direction, boundary layer height, humidity) to pollutants dispersion. Additionally, we assess the role of large-scale circulation patterns, usually referred as Weather types (WT) (from the ERA40/ECMWF and ECMWF SLP database) towards the occurrence of critical pollution events identified previously. The presence and importance of trends and fluctuation is addressed by means of two modelling approaches: (1) raw data modelling; (2) residuals modelling (after the removal of the trends from the original data). The relative importance of two periodic components, the weekly and the monthly cycles, is addressed. For the three pollutants, the approach based on the removal of the weekly cycle presents the best results, comparatively to the removal of the monthly cycle or to the use of the raw data. The best predictors are chosen independently for each monitoring station and pollutant through an objective procedure (backward stepwise regression). The analysis reveals that the most significant variables in predicting NO2 concentration are several NO2 measures, wind direction and speed and global radiation, while for O3 correspond to several O3 measures, O3 precursors and WT
DEFF Research Database (Denmark)
Andreasen, Martin Møller; Christensen, Bent Jesper
This paper suggests a new and easy approach to estimate linear and non-linear dynamic term structure models with latent factors. We impose no distributional assumptions on the factors and they may therefore be non-Gaussian. The novelty of our approach is to use many observables (yields or bonds p...
Institute of Scientific and Technical Information of China (English)
张卫国
2003-01-01
In this paper, we have obtained the bell-type and kink-type solitary wave solutions of the generalized symmetric regularized long-wave equations with high-order nonlinear terms by means of proper transformation and undetermined assumption method.
Institute of Scientific and Technical Information of China (English)
HUANG Chunming; ZHANG Shaodong; YI Fan
2005-01-01
By using a three-dimensional fully nonlinear numerical model in spherical coordinates and taking the linear steady solutions of the migrating diurnal and semidiurnal tides in January from the Global-Scale Wave Model (GSWM) as the initial values, we simulate the linear and nonlinear propagations of the migrating diurnal and semidiurnal tides in the atmosphere from the ground to the lower thermosphere. A comparison of our simulations with the results of GSWM is also presented. The simulation results show that affected by the nonlinearity, the migrating diurnal and semidiurnal tides propagating in the middle and upper atmosphere exhibit evident short-term variability. The nonlinear interactions between the migrating tides and the background atmosphere can obviously alter the background wind and temperature fields, which suggests that the nonlinear propagations of the migrating diurnal and semidiurnal tides impact significantly on the transient dynamical and thermal structures of the background middle and upper atmosphere and the nonlinear effect is an important cause of the difference between the results of GSWM and observations.
Directory of Open Access Journals (Sweden)
Hasibun Naher
2012-01-01
Full Text Available We construct new exact traveling wave solutions involving free parameters of the nonlinear reaction diffusion equation by using the improved (G′/G-expansion method. The second-order linear ordinary differential equation with constant coefficients is used in this method. The obtained solutions are presented by the hyperbolic and the trigonometric functions. The solutions become in special functional form when the parameters take particular values. It is important to reveal that our solutions are in good agreement with the existing results.
Directory of Open Access Journals (Sweden)
Felicia Shirly Peace
2014-01-01
Full Text Available A mathematical model of the dynamics of the self-ignition of a reaction-diffusion system is studied in this paper. An approximate analytical method (modified Adomian decomposition method is used to solve nonlinear differential equations under steady-state condition. Analytical expressions for concentrations of the gas reactant and the temperature have been derived for Lewis number (Le and parameters β, γ, and ϕ2. Furthermore, in this work, the numerical simulation of the problem is also reported using MATLAB program. An agreement between analytical and numerical results is noted.
Men, Zhongxian; Yee, Eugene; Lien, Fue-Sang; Yang, Zhiling; Liu, Yongqian
2014-01-01
Short-term wind speed and wind power forecasts (for a 72 h period) are obtained using a nonlinear autoregressive exogenous artificial neural network (ANN) methodology which incorporates either numerical weather prediction or high-resolution computational fluid dynamics wind field information as an exogenous input. An ensemble approach is used to combine the predictions from many candidate ANNs in order to provide improved forecasts for wind speed and power, along with the associated uncertainties in these forecasts. More specifically, the ensemble ANN is used to quantify the uncertainties arising from the network weight initialization and from the unknown structure of the ANN. All members forming the ensemble of neural networks were trained using an efficient particle swarm optimization algorithm. The results of the proposed methodology are validated using wind speed and wind power data obtained from an operational wind farm located in Northern China. The assessment demonstrates that this methodology for wind speed and power forecasting generally provides an improvement in predictive skills when compared to the practice of using an "optimal" weight vector from a single ANN while providing additional information in the form of prediction uncertainty bounds.
Concentration fluctuations in non-isothermal reaction-diffusion systems. II. The nonlinear case
Bedeaux, D.; Ortiz de Zárate, J.M.; Pagonabarraga, I.; Sengers, J.V.; Kjelstrup, S.
2011-01-01
In this paper, we consider a simple reaction-diffusion system, namely, a binary fluid mixture with an association-dissociation reaction between two species. We study fluctuations at hydrodynamic spatiotemporal scales when this mixture is driven out of equilibrium by the presence of a temperature gra
Nonlinearity Role in Long-Term Interaction of the Ocean Gravity Waves
2012-09-30
the Nonlinear Schrodinger equation and its exact solutions. Numerical simulations of the fully nonlinear Euler equation have also been performed in... Schrodinger breathers, Proceedings of ECMWF Workshop on "Ocean Waves" - 25 to 27 June 2012 [published] • Onorato, M. and Proment, D.; Approximate rogue wave
Long-term wave growth and its linear and nonlinear interactions with wind fluctuations
Directory of Open Access Journals (Sweden)
Z. Ge
2008-05-01
Full Text Available Following Ge and Liu (2007, the simultaneously recorded time series of wave elevation and wind velocity are examined for long-term (on Lavrenov's τ_{4}-scale or 3 to 6 h linear and nonlinear interactions between the wind fluctuations and the wave field. Over such long times the detected interaction patterns should reveal general characteristics for the wave growth process. The time series are divided into three episodes, each approximately 1.33 h long, to represent three sequential stages of wave growth. The classic Fourier-domain spectral and bispectral analyses are used to identify the linear and quadratic interactions between the waves and the wind fluctuations as well as between different components of the wave field.
The results show clearly that as the wave field grows the linear interaction becomes enhanced and covers wider range of frequencies. Two different wave-induced components of the wind fluctuations are identified. These components, one at around 0.4 Hz and the other at around 0.15 to 0.2 Hz, are generated and supported by both linear and quadratic wind-wave interactions probably through the distortions of the waves to the wind field. The fact that the higher-frequency wave-induced component always stays with the equilibrium range of the wave spectrum around 0.4 Hz and the lower-frequency one tends to move with the downshifting of the primary peak of the wave spectrum defines the partition of the primary peak and the equilibrium range of the wave spectrum, a characteristic that could not be revealed by short-time wavelet-based analyses in Ge and Liu (2007. Furthermore, these two wave-induced peaks of the wind spectrum appear to have different patterns of feedback to the wave field. The quadratic wave-wave interactions also are assessed using the auto-bispectrum and are found to be especially active during the first and the third episodes. Such directly detected wind-wave interactions, both linear and
Nourazar, S. S.; Nazari-Golshan, A.
2015-01-01
A hybrid of Fourier transform and new modified homotopy perturbation method based on the Adomian method is developed to solve linear and nonlinear partial differential equations. The Taylor series expansion is used to expand nonlinear term of partial differential equation and the Adomian polynomial incorporated into homotopy perturbation method combined with Fourier transform, is used to solve partial differential equations. Three case study problems, partial differential equations, are handled using homotopy perturbation method and Fourier transform modified homotopy perturbation method (FTMHPM). Results obtained are compared with exact solution. The comparison reveals that for same components of recursive sequences, errors associated with Fourier transform modified method are much less than the other and are valid for a large range of x-axis coordinates.
Directory of Open Access Journals (Sweden)
Zoe Rogers
2016-09-01
Full Text Available N-acetyltransferase 2 (NAT2 catalyzes the acetylation of isoniazid to N-acetylisoniazid. NAT2 polymorphism explains 88% of isoniazid clearance variability in adults. We examined the effects of clinical and genetic factors on Michaelis-Menten reaction kinetic constants of maximum velocity (Vmax and affinity (Km in children 0–10 years old. We measured the rates of isoniazid elimination and N-acetylisoniazid production in the blood of 30 children. Since maturation effects could be non-linear, we utilized a pharmacometric approach and the artificial intelligence method, multivariate adaptive regression splines (MARS, to identify factors predicting NAT2 Vmax and Km by examining clinical, genetic, and laboratory factors in toto. Isoniazid concentration predicted both Vmax and Km and superseded the contribution of NAT2 genotype. Age non-linearly modified the NAT2 genotype contribution until maturation at ≥5.3 years. Thus, enzyme efficiency was constrained by substrate concentration, genes, and age. Since MARS output is in the form of basis functions and equations, it allows multiscale systems modeling from the level of cellular chemical reactions to whole body physiological parameters, by automatic selection of significant predictors by the algorithm.
Institute of Scientific and Technical Information of China (English)
胡淑娟; 丑纪范
2004-01-01
The computational uncertainty principle in nonlinear ordinary differential equations makes the numerical solution of the long-term behavior of nonlinear atmospheric equations have no meaning. The main reason is that, in the error analysis theory of present-day computational mathematics, the non-linear process between truncation error and rounding erroris treated as a linear operation. In this paper, based on the operator equations of large-scale atmospheric movement, the above limitation is overcome by using the notion of cell mapping. Through studying the global asymptotic characteristics of the numerical pattern of the large-scale atmospheric equations, the definitions of the global convergence and an appropriate discrete algorithm of the numerical pattern are put forward. Three determinant theorems about the global convergence of the numerical pattern are presented, which provide the theoretical basis for constructing the globally convergent numerical pattern. Further, it is pointed out that only a globally convergent numerical pattern can improve the veracity of climatic prediction.
Reaction Reading: A Tool for Providing Fantasy Imagery for Long-Term Care Facility Residents.
Asmuth, M. Violet
1995-01-01
Describes a project utilizing reaction reading, the choral reading of poetry in small groups. Mentally alert long-term care residents are provided with an opportunity to react to the poetry, and the activity can be led by a nonprofessional. Residents are encouraged to share their memories and fantasies as inspired by poetic images. (JPS)
Werkendam, the Dutch natural analogue for CO2 storage – long-term mineral reactions
Koenen, M.; Wasch, L.J.; Zalinge, M.E. van; Nelskamp, S.
2013-01-01
The Werkendam (WED) and Barendrecht-Ziedewij (BRTZ) gas fields are CO2- and CH4-bearing stratigraphic equivalents in the Netherlands. A comparison in petrographic characteristics and burial histories of the two fields is performed to investigate long-term mineral reactions induced by the presence of
Institute of Scientific and Technical Information of China (English)
Jia-qi Mo; Wan-tao Lin
2006-01-01
In this paper the singularly perturbed initial boundary value problems for the nonlocal reaction diffusion system are considered. Using the iteration method and the comparison theorem, the existence and its asymptotic behavior of the solution for the problem are studied.
Directory of Open Access Journals (Sweden)
Toly Chen
2013-01-01
Full Text Available This study proposes a multiobjective fuzzy nonlinear programming (MOFNP approach to enhance the long-term yield competitiveness of a semiconductor manufacturing factory. By modeling the long-term competitiveness of every product in a semiconductor manufacturing plant with the fuzzy correlation coefficient (FCC between time and instantaneous competitiveness, the proposed model considers the various viewpoints when interpreting the overall competitiveness of the semiconductor manufacturing plant in the long-term. All noninferior solutions of the MOFNP solutions are then derived using a systematic procedure. A real example is employed to illustrate the applicability of the proposed methodology.
Nonlinear and long-term beam dynamics in low energy storage rings
Papash, A. I.; Smirnov, A. V.; Welsch, C. P.
2013-06-01
Electrostatic storage rings operate at very low energies in the keV range and have proven to be invaluable tools for atomic and molecular physics. Because of the mass independence of electric rigidity, these machines are able to store a wide range of different particles, from light ions to heavy singly charged biomolecules, opening up unique research opportunities. However, earlier measurements have shown strong limitations in maximum beam intensity, fast decay of the stored ion current, and reduced beam lifetime. The nature of these effects has not been fully understood and an improved understanding of the physical processes influencing beam motion and stability in such rings is needed. In this paper, a comprehensive study into nonlinear and long-term beam dynamics studies is presented on the examples of a number of existing and planned electrostatic storage rings using the BETACOOL, OPERA-3D, and MAD-X simulation software. A detailed investigation into ion kinetics, under consideration of effects from electron cooling and multiple scattering of the beam on a supersonic gas jet target, is carried out and yields a consistent explanation of the physical effects in a whole class of storage rings. The lifetime, equilibrium momentum spread, and equilibrium lateral spread during collisions with the target are estimated. In addition, the results from experiments at the Test Storage Ring, where a low-intensity beam of CF+ ions at 93keV/u has been shrunk to extremely small dimensions, are reproduced. Based on these simulations, the conditions for stable ring operation with an extremely low-emittance beam are presented. Finally, results from studies into the interaction of 3-30 keV ions with a gas jet target are summarized.
Nonlinear and long-term beam dynamics in low energy storage rings
Directory of Open Access Journals (Sweden)
A. I. Papash
2013-06-01
Full Text Available Electrostatic storage rings operate at very low energies in the keV range and have proven to be invaluable tools for atomic and molecular physics. Because of the mass independence of electric rigidity, these machines are able to store a wide range of different particles, from light ions to heavy singly charged biomolecules, opening up unique research opportunities. However, earlier measurements have shown strong limitations in maximum beam intensity, fast decay of the stored ion current, and reduced beam lifetime. The nature of these effects has not been fully understood and an improved understanding of the physical processes influencing beam motion and stability in such rings is needed. In this paper, a comprehensive study into nonlinear and long-term beam dynamics studies is presented on the examples of a number of existing and planned electrostatic storage rings using the BETACOOL, OPERA-3D, and MAD-X simulation software. A detailed investigation into ion kinetics, under consideration of effects from electron cooling and multiple scattering of the beam on a supersonic gas jet target, is carried out and yields a consistent explanation of the physical effects in a whole class of storage rings. The lifetime, equilibrium momentum spread, and equilibrium lateral spread during collisions with the target are estimated. In addition, the results from experiments at the Test Storage Ring, where a low-intensity beam of CF^{+} ions at 93 keV/u has been shrunk to extremely small dimensions, are reproduced. Based on these simulations, the conditions for stable ring operation with an extremely low-emittance beam are presented. Finally, results from studies into the interaction of 3–30 keV ions with a gas jet target are summarized.
Nonlinear feedback in a six-dimensional Lorenz Model: impact of an additional heating term
Directory of Open Access Journals (Sweden)
B.-W. Shen
2015-03-01
Full Text Available In this study, a six-dimensional Lorenz model (6DLM is derived, based on a recent study using a five-dimensional (5-D Lorenz model (LM, in order to examine the impact of an additional mode and its accompanying heating term on solution stability. The new mode added to improve the representation of the steamfunction is referred to as a secondary streamfunction mode, while the two additional modes, that appear in both the 6DLM and 5DLM but not in the original LM, are referred to as secondary temperature modes. Two energy conservation relationships of the 6DLM are first derived in the dissipationless limit. The impact of three additional modes on solution stability is examined by comparing numerical solutions and ensemble Lyapunov exponents of the 6DLM and 5DLM as well as the original LM. For the onset of chaos, the critical value of the normalized Rayleigh number (rc is determined to be 41.1. The critical value is larger than that in the 3DLM (rc ~ 24.74, but slightly smaller than the one in the 5DLM (rc ~ 42.9. A stability analysis and numerical experiments obtained using generalized LMs, with or without simplifications, suggest the following: (1 negative nonlinear feedback in association with the secondary temperature modes, as first identified using the 5DLM, plays a dominant role in providing feedback for improving the solution's stability of the 6DLM, (2 the additional heating term in association with the secondary streamfunction mode may destabilize the solution, and (3 overall feedback due to the secondary streamfunction mode is much smaller than the feedback due to the secondary temperature modes; therefore, the critical Rayleigh number of the 6DLM is comparable to that of the 5DLM. The 5DLM and 6DLM collectively suggest different roles for small-scale processes (i.e., stabilization vs. destabilization, consistent with the following statement by Lorenz (1972: If the flap of a butterfly's wings can be instrumental in generating a tornado, it
Attractors and Dimensions for Discretizations of a NLS Equation with a Non-local Nonlinear Term
Institute of Scientific and Technical Information of China (English)
Shu Qing MA; Qian Shun CHANG
2002-01-01
In this paper we consider a semi-dicretized nonlinear Schrodinger (NLS) equation withlocal integral nonlinearity. It is proved that for each mesh size, there exist attractors for the discretizedsystem. The bounds for the Hausdorff and fractal dimensions of the discrete attractors are obtained,and the various bounds are independent of the mesh sizes. Furthermore, numerical experiments aregiven and many interesting phenomena are observed such as limit cycles, chaotic attractors and aso-called crisis of the chaotic attractors.
Synthesis, phase and reaction mechanism of nonlinear optical material MnTeMoO{sub 6}
Energy Technology Data Exchange (ETDEWEB)
Jin, Chengguo; Shao, Juxiang; Yang, Junsheng; Wan, Mingjie [Yibin University, Key Laboratory of Computational Physics of Sichuan Province, Yibin (China); Yibin University, School of Physics and Electronic Engineering, Yibin (China); Luo, Huafeng [Yibin University, College of Chemistry and Chemical Engineering, Yibin (China); Huang, Xingyong [Yibin University, School of Physics and Electronic Engineering, Yibin (China); Wang, Fanhou [Yibin University, Key Laboratory of Computational Physics of Sichuan Province, Yibin (China)
2016-09-15
Pure polycrystalline MnTeMoO{sub 6} is highly desirable to crystal growth. Polycrystalline MnTeMoO{sub 6} has been synthesized by solid-state reaction techniques. The optimized preparation process, phase purity and reaction mechanism of polycrystalline MnTeMoO{sub 6} were investigated. The reaction will be paused if the atoms cannot pass through the grain boundary and restarted after ground intimately. A new method combined with X-ray diffraction and microscopic observation is employed to determine the phase purity of polycrystalline MnTeMoO{sub 6}. Pure polycrystalline MnTeMoO{sub 6} with gray color and single crystalline phase can be obtained after the reactant was calcined at 500 C for 20 h three times and can be used to crystal growth. This method for determining the phase purity of powder sample can be used in the synthesis of other polycrystalline powders. (orig.)
Directory of Open Access Journals (Sweden)
Janmenjoy Nayak
2015-09-01
Full Text Available In this paper, a Chemical Reaction Optimization (CRO based higher order neural network with a single hidden layer called Pi–Sigma Neural Network (PSNN has been proposed for data classification which maintains fast learning capability and avoids the exponential increase of number of weights and processing units. CRO is a recent metaheuristic optimization algorithm inspired by chemical reactions, free from intricate operator and parameter settings such as other algorithms and loosely couples chemical reactions with optimization. The performance of the proposed CRO-PSNN has been tested with various benchmark datasets from UCI machine learning repository and compared with the resulting performance of PSNN, GA-PSNN, PSO-PSNN. The methods have been implemented in MATLAB and the accuracy measures have been tested by using the ANOVA statistical tool. Experimental results show that the proposed method is fast, steady and reliable and provides better classification accuracy than others.
Zhijian, Yang
The paper studies the global existence, asymptotic behavior and blowup of solutions to the initial boundary value problem for a class of nonlinear wave equations with dissipative term. It proves that under rather mild conditions on nonlinear terms and initial data the above-mentioned problem admits a global weak solution and the solution decays exponentially to zero as t→+∞, respectively, in the states of large initial data and small initial energy. In particular, in the case of space dimension N=1, the weak solution is regularized to be a unique generalized solution. And if the conditions guaranteeing the global existence of weak solutions are not valid, then under the opposite conditions, the solutions of above-mentioned problem blow up in finite time. And an example is given.
Institute of Scientific and Technical Information of China (English)
Deng Xi-Jun; Yan Zi-Zong; Han Li-Bo
2009-01-01
In this paper,the travelling wave solutions for the generalized Burgers-Huxley equation with nonlinear terms of any order are studied.By using the first integral method,which is based on the divisor theorem,some exact explicit travelling solitary wave solutions for the above equation are obtained.As a result,some minor errors and some known results in the previousl literature are clarified and improved.
Weakly nonlinear dynamics in reaction-diffusion systems with Levy flights
Energy Technology Data Exchange (ETDEWEB)
Nec, Y; Nepomnyashchy, A A [Department of Mathematics, Technion-Israel Institute of Technology, Haifa 32000 (Israel); Golovin, A A [Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL 60208 (United States)], E-mail: flyby@techunix.technion.ac.il
2008-12-15
Reaction-diffusion equations with a fractional Laplacian are reduced near a long wave Hopf bifurcation. The obtained amplitude equation is shown to be the complex Ginzburg-Landau equation with a fractional Laplacian. Some of the properties of the normal complex Ginzburg-Landau equation are generalized for the fractional analogue. In particular, an analogue of the Kuramoto-Sivashinsky equation is derived.
Jesudason, Christopher G
2011-01-01
The primary emphasis of this work on kinetics is to illustrate the a posteriori approach to applications, where focus on data leads to novel outcomes, rather than the a priori tendencies of applied analysis which imposes constructs on the nature of the observable. The secondary intention is the development of appropriate methods consonant with experimental definitions. By focusing on gradients, it is possible to determine both the average and instantaneous rate constants that can monitor changes in the rate constant with concentration changes as suggested by this theory. Here, methods are developed and discussed utilizing nonlinear analysis which does not require exact knowledge of initial concentrations. These methods are compared with those derived from standard methodology. These gradient methods are shown to be consistent with the ones from standard methods and could readily serve as alternatives for studies where there are limits or unknowns in the initial conditions, such as in the burgeoning fields of ...
Energy Technology Data Exchange (ETDEWEB)
Delaune, X.; Piteau, Ph.; Borsoi, L. [CEA Saclay, Laboratoire d' Etudes de Dynamique, CEA, DEN, DM2S, SEMT, 91 - Gif-sur-Yvette (France); Antunes, J.; Debut, V. [Applied Dynamics Laboratory, Instituto Tecnologico e Nuclear, ITN/ADL, Estrada Nacional 10, 2686 Sacavem Codex (Portugal)
2010-06-15
Predictive computation of the nonlinear dynamical responses of gap-supported tubes subjected to flow excitation has been the subject of very active research. Nevertheless, there is a need for robust techniques capable of extracting, from the actual vibratory response data, information which is relevant for asserting the components integrity. The dynamical contact/impact (vibro-impact) forces are of paramount significance, as are the tube/support gaps. Following our previous studies in this field using wave-propagation techniques, we apply modal methods in the present paper for extracting such information. The dynamical support forces, as well as the vibratory responses at the support locations, are identified from one or several vibratory response measurements at remote transducers, from which the support gaps can be inferred. As for most inverse problems, the identification results prove quite sensitive to noise and modeling error problems. Therefore, topics discussed in the paper include regularization techniques to mitigate the effects of non-measured noise perturbations. In particular, a method is proposed to improve the identification of contact forces at the supports when the system is excited by an unknown distributed turbulence force field. The important topic of dealing with the imperfect knowledge of the modal parameters used to build the inverted transfer functions is addressed elsewhere. Here, the extensive identifications presented are based on the exact modal parameters and performed on realistic numerical simulations of gap-supported tubes subjected to flow excitation. We can thus confront the identified dynamical support contact forces and vibratory motions at the gap-support with the actual values stemming from the original nonlinear computations, with overall satisfying results. (authors)
Long-term evolution of strongly nonlinear internal solitary waves in a rotating channel
Directory of Open Access Journals (Sweden)
J. C. Sánchez-Garrido
2009-09-01
Full Text Available The evolution of internal solitary waves (ISWs propagating in a rotating channel is studied numerically in the framework of a fully-nonlinear, nonhydrostatic numerical model. The aim of modelling efforts was the investigation of strongly-nonlinear effects, which are beyond the applicability of weakly nonlinear theories. Results reveal that small-amplitude waves and sufficiently strong ISWs evolve differently under the action of rotation. At the first stage of evolution an initially two-dimensional ISW transforms according to the scenario described by the rotation modified Kadomtsev-Petviashvili equation, namely, it starts to evolve into a Kelvin wave (with exponential decay of the wave amplitude across the channel with front curved backwards. This transition is accompanied by a permanent radiation of secondary Poincaré waves attached to the leading wave. However, in a strongly-nonlinear limit not all the energy is transmitted to secondary radiated waves. Part of it returns to the leading wave as a result of nonlinear interactions with secondary Kelvin waves generated in the course of time. This leads to the formation of a slowly attenuating quasi-stationary system of leading Kelvin waves, capable of propagating for several hundreds hours as a localized wave packet.
Ultrasonic nonlinearity of AISI316 austenitic steel subjected to long-term isothermal aging
Energy Technology Data Exchange (ETDEWEB)
Gong, Won Sik; Kim, Chung Seok [Dept. of Materials Science and Engineering, Chosun University, Gwangju (Korea, Republic of)
2014-06-15
This study presents the ultrasonic nonlinearity of AISI316 austenitic stainless steels subjected to longterm isothermal aging. These steels are attractive materials for use in industrial mechanical structures because of their strength at high-temperatures and their chemical stability. The test materials were subjected to accelerated heat-treatment in an electrical furnace for a predetermined aging duration. The variations in the ultrasonic nonlinearity and microstructural damage were carefully evaluated through observation of the microstructure. The ultrasonic nonlinearity stiffly dropped after aging for up to 1000 h and, then, monotonously decreased. The polygonal shape of the initial grain structures changed to circular, especially as the annealing twins in the grains dissolved and disappeared. The delta ferrite on the grain boundaries could not be observed at 1000 h of aging, and these continuously transformed into their sigma phases. Consequently, in the intial aging period, the rapid decrease in the ultrasonic nonlinearity was caused by voids, dislocations, and twin annihilation. The continuous monotonic decrease in the ultrasonic nonlinearity after the first drop resulted from the generation of Cr{sub 23}C{sub 6} precipitates and σ phases.
Fernandes, Ryan I
2012-01-01
An alternating direction implicit (ADI) orthogonal spline collocation (OSC) method is described for the approximate solution of a class of nonlinear reaction-diffusion systems. Its efficacy is demonstrated on the solution of well-known examples of such systems, specifically the Brusselator, Gray-Scott, Gierer-Meinhardt and Schnakenberg models, and comparisons are made with other numerical techniques considered in the literature. The new ADI method is based on an extrapolated Crank-Nicolson OSC method and is algebraically linear. It is efficient, requiring at each time level only $O({\\cal N})$ operations where ${\\cal N}$ is the number of unknowns. Moreover,it is shown to produce approximations which are of optimal global accuracy in various norms, and to possess superconvergence properties.
Vaidyanathan, S.
2014-06-01
This paper proposes a eight-term 3-D polynomial chaotic system with three quadratic nonlinearities and describes its properties. The maximal Lyapunov exponent (MLE) of the proposed 3-D chaotic system is obtained as L 1 = 6.5294. Next, new results are derived for the global chaos synchronization of the identical eight-term 3-D chaotic systems with unknown system parameters using adaptive control. Lyapunov stability theory has been applied for establishing the adaptive synchronization results. Numerical simulations are shown using MATLAB to describe the main results derived in this paper.
Ginn, T. R.; Murphy, E. M.; Chilakapati, A.; Seeboonruang, U.
2001-03-01
Aerobic biodegradation of benzoate by Pseudomonas cepacia sp. in a saturated heterogeneous porous medium was simulated using the stochastic-convective reaction (SCR) approach. A laboratory flow cell was randomly packed with low permeability silt-size inclusions in a high permeability sand matrix. In the SCR upscaling approach, the characteristics of the flow field are determined by the breakthrough of a conservative tracer. Spatial information on the actual location of the heterogeneities is not used. The mass balance equations governing the nonlinear and multicomponent reactive transport are recast in terms of reactive transports in each of a finite number of discrete streamtubes. The streamtube ensemble members represent transport via a steady constant average velocity per streamtube and a conventional Fickian dispersion term, and their contributions to the observed breakthroughs are determined by flux-averaging the streamtube solute concentrations. The resulting simulations were compared to those from a high-resolution deterministic simulation of the reactive transport, and to alternative ensemble representations involving (i) effective Fickian travel time distribution function, (ii) purely convective streamtube transport, and (iii) streamtube ensemble subset simulations. The results of the SCR simulation compare favorably to that of a sophisticated high-resolution deterministic approach.
Directory of Open Access Journals (Sweden)
A. A. Kotlyarova
2016-01-01
Full Text Available Lithium preparations are widely used for stabilize mood in case of bipolar affective disorder. Currently neuroprotective and neuroregenerative effects of lithium are of interest as in case of acute brain injury, also in chronic neurodegenerative diseases such as dementia, alcoholism, Alzheimer disease, etc. [1–5]. In clinical practice use of lithium preparations is limited due to difficult adjustment of drug dosage, necessity of monitoring its concentration in blood, side effects development as a result of accumulation of lithium in a body. For the purpose of improvement of pharmacologic properties lithium is combined with other agents (for example modifying sorbent thus it can produce longer-term and more harmless (less side reactions effect in the long view. Lithium immobilization on sorption basis will allow to use sorbent as detoxicant and carrying agent of drugs to body. The purpose of the work is studying the effect of the lithium – containing sorbent on terms of behavioral reactions under chronic alcohol intoxication model.Materials and methods. During the work we used nonlinear mice – males, which weight 25–30 g (180 animals. Chronic alcohol intoxication was precipitated via 40% proof spirit injections (oral supplementation in quantity of 3 g/kg during 2 weeks, additionally mice drunk 5% proof spirit from drinking bowl. Each experimental group consisted of 10 animals. Study drugs were inserted inside while ethanol injecting. Control animals were inserted 0,9% salin solution. Emotional state of animals was assessed through forced swim test, short – term memory assessment was performed through conditioned passive avoidance reflex. Effect of chronic alcohol intoxication on the parameters of conditioned reflex activity was measured every 7 days.Results. It was found that the investigated lithium-containing sorbent increases: the number of mice are trained passive avoidance reflex, remembering percent of electric shock
Institute of Scientific and Technical Information of China (English)
ZHANG Jia-zhong; LIU Yan; CHEN Dang-min
2005-01-01
From viewpoint of nonlinear dynamics, the model reduction and its influence on the long-term behaviours of a class of nonlinear dissipative autonomous dynamical system with higher dimension are investigated theoretically under some assumptions. The system is analyzed in the state space with an introduction of a distance definition which can be used to describe the distance between the full system and the reduced system, and the solution of the full system is then projected onto the complete space spanned by the eigenvectors of the linear operator of the governing equations. As a result, the influence of mode series tnncation on the long-term behaviours and the error estimate are derived, showing that the error is dependent on the first products of frequencies and damping ratios in the subspace spanned by the eigenvectors with higher modal damping. Furthermore, the fundamental understanding for the topological change of the solution due to the application of different model reduction is interpreted in a mathematically precise way, using the qualitative theory of nonlinear dynamics.
Heart rate and blood pressure response to short-term head-down bed rest: a nonlinear approach.
Balocchi, R; Di Garbo, A; Michelassi, C; Chillemi, S; Varanini, M; Barbi, M; Legramante, J M; Raimondi, G; Zbilut, J P
2000-06-01
Although it is well-known that prolonged exposure to microgravity environment such as in space travel results in derangements of orthostasis, recent evidence suggests that even short-term exposure may have similar effects and parallels such common examples as prolonged bed rest. Whereas spectral analysis of heart rate and systolic blood pressure have been unable to detect changes, we hypothesized that nonlinear indexes may be better able to uncover such perturbations. Eighteen healthy subjects were exposed to 4-hour head-down tilt, and of these, 4 exhibited fainting. Two nonlinear indexes, mutual information and recurrence quantification were used to analyze the data. Only recurrence quantification was able to detect a "decoupling" of heart rate and systolic blood pressure at rest using discriminant analysis (p < 0.05). These results suggest that orthostatic intolerance may be due to a decoupling of heart rate from systolic blood pressure reflexive activity occurring at rest.
Long-term non-linear predictability of ENSO events over the 20th century
Astudillo, H F; Borotto, F A
2015-01-01
We show that the monthly recorded history (1878-2013) of the Southern Oscillation Index (SOI), a descriptor of the El Ni\\~no Southern Oscillation (ENSO) phenomenon, can be well described as a dynamic system that supports an average nonlinear predictability well beyond the spring barrier. The predictability is strongly linked to a detailed knowledge of the topology of the attractor obtained by embedding the SOI index in a wavelets base state space. Using the state orbits on the attractor we show that the information contained in the Southern Oscillation Index (SOI) is sufficient to provide average nonlinear predictions for time periods of 2, 3 and 4 years in advance throughout the 20th century with an acceptable error. The simplicity of implementation and ease of use makes it suitable for studying non linear predictability in any area where observations are similar to those that describe the ENSO phenomenon.
Solutions of fractional reaction-diffusion equations in terms of the H-function
Haubold, H. J.; Mathai, A. M.; Saxena, R. K.
2007-12-01
This paper deals with the investigation of the solution of an unified fractional reaction-diffusion equation associated with the Caputo derivative as the time-derivative and Riesz-Feller fractional derivative as the space-derivative. The solution is derived by the application of the Laplace and Fourier transforms in closed form in terms of the H-function. The results derived are of general nature and include the results investigated earlier by many authors, notably by Mainardi et al. (2001, 2005) for the fundamental solution of the space-time fractional diffusion equation, and Saxena et al. (2006a, b) for fractional reaction-diffusion equations. The advantage of using Riesz-Feller derivative lies in the fact that the solution of the fractional reaction-diffusion equation containing this derivative includes the fundamental solution for space-time fractional diffusion, which itself is a generalization of neutral fractional diffusion, space-fractional diffusion, and time-fractional diffusion. These specialized types of diffusion can be interpreted as spatial probability density functions evolving in time and are expressible in terms of the H-functions in compact form.
Wang, Jin-Liang; Wu, Huai-Ning; Huang, Tingwen; Ren, Shun-Yan
2016-04-01
Two types of coupled neural networks with reaction-diffusion terms are considered in this paper. In the first one, the nodes are coupled through their states. In the second one, the nodes are coupled through the spatial diffusion terms. For the former, utilizing Lyapunov functional method and pinning control technique, we obtain some sufficient conditions to guarantee that network can realize synchronization. In addition, considering that the theoretical coupling strength required for synchronization may be much larger than the needed value, we propose an adaptive strategy to adjust the coupling strength for achieving a suitable value. For the latter, we establish a criterion for synchronization using the designed pinning controllers. It is found that the coupled reaction-diffusion neural networks with state coupling under the given linear feedback pinning controllers can realize synchronization when the coupling strength is very large, which is contrary to the coupled reaction-diffusion neural networks with spatial diffusion coupling. Moreover, a general criterion for ensuring network synchronization is derived by pinning a small fraction of nodes with adaptive feedback controllers. Finally, two examples with numerical simulations are provided to demonstrate the effectiveness of the theoretical results.
Effects of Higher Order Dispersion Terms in the Nonlinear Schrodinger Equation
Directory of Open Access Journals (Sweden)
Robert Beech
2005-01-01
Full Text Available This study presents a concise graphical analysis of solitonic solutions to a nonlinear Schrodinger equation (NLSE. A sequence of code using the standard NDSolve function has been developed in Mathematica to investigate the acceptable accuracy of the NLSE in relatively small ranges of the dispersive parameter space. An operator splitting approach was used in the numerical solutions to expand the boundaries and reduce the artifacts for a reliable solution. These numerical routines were implemented through the use with Mathematica and the results give a very clear view of this interesting and important practical phenomenon.
Institute of Scientific and Technical Information of China (English)
DONG Sheng; LI Fengli; JIAO Guiying
2003-01-01
Hydrologic frequency analysis plays an important role in coastal and ocean engineering for structural design and disaster prevention in coastal areas. This paper proposes a Nonlinear Least Squares Method (NLSM), which estimates the three unknown parameters of the Weibull distribution simultaneously by an iteration method. Statistical test shows that the NLSM fits each data sample well. The effects of different parameter-fitting methods, distribution models, and threshold values are also discussed in the statistical analysis of storm set-down elevation. The best-fitting probability distribution is given and the corresponding return values are estimated for engineering design.
Interpreting the nonlinear dielectric response of glass-formers in terms of the coupling model
Energy Technology Data Exchange (ETDEWEB)
Ngai, K. L. [CNR-IPCF, Largo Bruno Pontecorvo 3, I-56127 Pisa, Italy and Dipartimento di Fisica, Università di Pisa, Largo B. Pontecorvo 3, I-56127 Pisa (Italy)
2015-03-21
Nonlinear dielectric measurements at high electric fields of glass-forming glycerol and propylene carbonate initially were carried out to elucidate the dynamic heterogeneous nature of the structural α-relaxation. Recently, the measurements were extended to sufficiently high frequencies to investigate the nonlinear dielectric response of faster processes including the so-called excess wing (EW), appearing as a second power law at high frequencies in the loss spectra of many glass formers without a resolved secondary relaxation. While a strong increase of dielectric constant and loss is found in the nonlinear dielectric response of the α-relaxation, there is a lack of significant change in the EW. A surprise to the experimentalists finding it, this difference in the nonlinear dielectric properties between the EW and the α-relaxation is explained in the framework of the coupling model by identifying the EW investigated with the nearly constant loss (NCL) of caged molecules, originating from the anharmonicity of the intermolecular potential. The NCL is terminated at longer times (lower frequencies) by the onset of the primitive relaxation, which is followed sequentially by relaxation processes involving increasing number of molecules until the terminal Kohlrausch α-relaxation is reached. These intermediate faster relaxations, combined to form the so-called Johari-Goldstein (JG) β-relaxation, are spatially and dynamically heterogeneous, and hence exhibit nonlinear dielectric effects, as found in glycerol and propylene carbonate, where the JG β-relaxation is not resolved and in D-sorbitol where it is resolved. Like the linear susceptibility, χ{sub 1}(f), the frequency dispersion of the third-order dielectric susceptibility, χ{sub 3}(f), was found to depend primarily on the α-relaxation time, and independent of temperature T and pressure P. I show this property of the frequency dispersions of χ{sub 1}(f) and χ{sub 3}(f) is the characteristic of the many
Formalizing MedDRA to support semantic reasoning on adverse drug reaction terms.
Bousquet, Cédric; Sadou, Éric; Souvignet, Julien; Jaulent, Marie-Christine; Declerck, Gunnar
2014-06-01
Although MedDRA has obvious advantages over previous terminologies for coding adverse drug reactions and discovering potential signals using data mining techniques, its terminological organization constrains users to search terms according to predefined categories. Adding formal definitions to MedDRA would allow retrieval of terms according to a case definition that may correspond to novel categories that are not currently available in the terminology. To achieve semantic reasoning with MedDRA, we have associated formal definitions to MedDRA terms in an OWL file named OntoADR that is the result of our first step for providing an "ontologized" version of MedDRA. MedDRA five-levels original hierarchy was converted into a subsumption tree and formal definitions of MedDRA terms were designed using several methods: mappings to SNOMED-CT, semi-automatic definition algorithms or a fully manual way. This article presents the main steps of OntoADR conception process, its structure and content, and discusses problems and limits raised by this attempt to "ontologize" MedDRA.
Directory of Open Access Journals (Sweden)
Guo Haigang
2012-01-01
Full Text Available Combining adaptive fuzzy sliding mode control with fuzzy or variable universe fuzzy switching technique, this study develops two novel direct adaptive schemes for a class of MIMO nonlinear systems with uncertainties and external disturbances. The proposed control schemes consist of fuzzy equivalent control terms, fuzzy switching control terms (in scheme one or variable universe fuzzy switching control terms (in scheme two, and compensation control terms. The compensation control terms are used to relax the assumption on fuzzy approximation error. Based on Lyapunov stability theory, the parameters update laws are adaptively tuned online and the global asymptotic stability of the closed-loop system can be guaranteed. The major contribution of this study is to develop a novel framework for designing direct adaptive fuzzy sliding mode control scheme facing model uncertainties and external disturbances. The derived schemes can effectively solve the chattering problem and the equivalent control calculation in that environment. Simulation results performed on a two-link robotic manipulator demonstrate the feasibility of the proposed control schemes.
DEFF Research Database (Denmark)
Baadsgaard, Mikkel; Nielsen, Jan Nygaard; Madsen, Henrik
2000-01-01
An econometric analysis of continuous-timemodels of the term structure of interest rates is presented. A panel of coupon bond prices with different maturities is used to estimate the embedded parameters of a continuous-discrete state space model of unobserved state variables: the spot interest rate......, the central tendency and stochastic volatility. Emphasis is placed on the particular class of exponential-affine term structure models that permits solving the bond pricing PDE in terms of a system of ODEs. It is assumed that coupon bond prices are contaminated by additive white noise, where the stochastic...
Ramaswamy, Rajesh; Sbalzarini, Ivo F; González-Segredo, Nélido
2011-01-28
Stochastic effects from correlated noise non-trivially modulate the kinetics of non-linear chemical reaction networks. This is especially important in systems where reactions are confined to small volumes and reactants are delivered in bursts. We characterise how the two noise sources confinement and burst modulate the relaxation kinetics of a non-linear reaction network around a non-equilibrium steady state. We find that the lifetimes of species change with burst input and confinement. Confinement increases the lifetimes of all species that are involved in any non-linear reaction as a reactant. Burst monotonically increases or decreases lifetimes. Competition between burst-induced and confinement-induced modulation may hence lead to a non-monotonic modulation. We quantify lifetime as the integral of the time autocorrelation function (ACF) of concentration fluctuations around a non-equilibrium steady state of the reaction network. Furthermore, we look at the first and second derivatives of the ACF, each of which is affected in opposite ways by burst and confinement. This allows discriminating between these two noise sources. We analytically derive the ACF from the linear Fokker-Planck approximation of the chemical master equation in order to establish a baseline for the burst-induced modulation at low confinement. Effects of higher confinement are then studied using a partial-propensity stochastic simulation algorithm. The results presented here may help understand the mechanisms that deviate stochastic kinetics from its deterministic counterpart. In addition, they may be instrumental when using fluorescence-lifetime imaging microscopy (FLIM) or fluorescence-correlation spectroscopy (FCS) to measure confinement and burst in systems with known reaction rates, or, alternatively, to correct for the effects of confinement and burst when experimentally measuring reaction rates.
Directory of Open Access Journals (Sweden)
Victor Kardashov
2002-01-01
Full Text Available This paper has considered a novel approach to structural recognition and control of nonlinear reaction-diffusion systems (systems with density dependent diffusion. The main consistence of the approach is interactive variation of the nonlinear diffusion and sources structural parameters that allows to implement a qualitative control and recognition of transitional system conditions (transients. The method of inverse solutions construction allows formulating the new analytic conditions of compactness and periodicity of the transients that is also available for nonintegrated systems. On the other hand, using of energy conservations laws, allows transfer to nonlinear dynamics models that gives the possiblity to apply the modern deterministic chaos theory (particularly the Feigenboum's universal constants and scenario of chaotic transitions.
Stable and Continuous Long-term Enzymatic Reaction using an Enzyme-Nanofiber Composite
Energy Technology Data Exchange (ETDEWEB)
Lee, Jin Hyung; Hwang, Ee Taek; Kim, Byoung Chan; Lee, Sun Mi; Sang, Byoung-In; Choi, Yong Su; Kim, Jungbae; Gu, Man Bock
2007-07-01
This study shows the preparation and application of enzyme-nanofiber composites for long-term stable operation. The enzyme-nanofiber composite was prepared by coating an enzyme-aggregate, the esterase from Rhizopus oryzae, on the surface of the nanofibers. The activity and stability of the esterase-nanofiber composite was evaluated by measuring the production of p-nitrophenol from the hydrolysis of p-nitrophenyl butyrate. It was found that enzyme-nanofiber was very stable, even when the fibers were shaken in glasses, preserving 80 % of the initial activity for 100 days. In addition, the enzyme nanofiber composite was repeatedly used in 30 cycles of substrate hydrolysis and still remained active. Consequently, the esterase-nanofiber composite was finally employed to find its feasibility of long-term and stable continuous substrate hydrolysis reaction. In the sample reactor, the production of p-nitrophenol was consistent for 400 hr. Additionally, it was found that the production of p-nitrophenol proportionally decreased as the dilution rate was increased, showing the relationship between the efficiency of hydrolysis and the retention time within the reactor. This study demonstrates that the enzyme-nanofiber composite can be used in both repeated-batch and continuous modes for long-term stable operation.
Perkins, Steven E; Jelinek, Herbert F; Al-Aubaidy, Hayder A; de Jong, Berverlie
2017-03-01
Recovery of cardiac autonomic modulation following exercise can be measured using heart rate variability. The objective of this study was to investigate and compare recovery of autonomic cardiac regulation over three days following a single session of high intensity interval training compared to endurance training. Nine untrained students completed two exercise protocols in a one-way crossover design. The endurance protocol consisted of 45min of moderate intensity cycling, and the high intensity interval protocol of six 30s sets of high intensity cycling. Cardiac autonomic activity recovery was measured over three days post-exercise for two hours immediately following each exercise session and each morning thereafter using linear and nonlinear heart rate variability analysis. Both linear and nonlinear measures were significantly decreased immediately following exercise indicating loss of vagal activity. Root mean sum of squared differences (p=0.031) and high frequency (p=0.031) were suppressed following the interval exercise only. The long term correlation of the heart rate applying detrended fluctuation analysis was decreased immediately following endurance training (p=0.039) and trended to increase immediately following the interval protocol (p=0.156). Sample entropy was decreased immediately following both the endurance (p=0.023) and interval (p=0.031) protocols. No exercise effects were noted from 24h post exercise onwards. High intensity interval training had a greater impact on neurocardiac activity than moderate intensity endurance training as indicated by both linear and nonlinear heart rate variability measures. Copyright © 2016 Sports Medicine Australia. Published by Elsevier Ltd. All rights reserved.
Seider, Warren D.; Ungar, Lyle H.
1987-01-01
Describes a course in nonlinear mathematics courses offered at the University of Pennsylvania which provides an opportunity for students to examine the complex solution spaces that chemical engineers encounter. Topics include modeling many chemical processes, especially those involving reaction and diffusion, auto catalytic reactions, phase…
Kutner, Ryszard; Świtała, Filip
2004-12-01
The paper consists of two parts: (i) the empirical one where the non-linear, long-term autocorrelations present in high-frequency data extracting from the Warsaw Stock Exchange were analyzed and (ii) theoretical one where predictions of our model (Quantitative Finance 3 (2003) 201; Physica A (2003); Chem. Phys. 284 (2002) 481; Phys. Comm. 147 (2002) 565; Physica A 264 (1999) 84; Physica A 264 (1999) 107; Lecture Notes in Computer Science 2657 (2003) 407; Eur. Phys. J. B 33 (2003) 495) were shown and discussed. This model introduces the possibility that the Weierstrass (hierarchical) random walk can be occasionally intermitted by momentary localizations; the localizations themselves are again described by the Weierstrass process. In other words, this combined walk is a kind of the non-separable, generalized continuous-time random walk formalism. To adapt the model to the description of empirical data recorded at time horizon Δt=1 min, we applied a discretization procedure into the continuous-time series produced by the model. We observed that such a procedure generates the non-linear, long-term autocorrelations even in the Gaussian regime, as turning points of the random walk trajectory are, most often, incommensurable with discretization time-step. These autocorrelations appear to be similar to those observed in the financial time series (Physica A 287 (2000) 396; Physica A 299 (2001) 1; Physica A 299 (2001) 16; Physica A 299 (2001) 28), although single steps of the walker within continuous time are, by definition, uncorrelated. Our approach suggests a surprising origin of the non-linear, long-term autocorrelations alternative to the one proposed very recently (cf. Phys. Rev. E 67 (2003) 021112 and refs. therein) although both approaches involve related variants of the well-known CTRW formalism applied in yet many different branches of knowledge (Phys. Rep. 158 (1987) 263; Phys. Rep. 195 (1990) 127; in: A. Bunde, S. Havlin (Eds.), Fractals in Science, Springer
Explaining Macroeconomic and Term Structure Dynamics Jointly in a Non-linear DSGE Model
DEFF Research Database (Denmark)
Andreasen, Martin Møller
This paper shows how a standard DSGE model can be extended to reproduce the dynamics in the 10 year yield curve for the post-war US economy with a similar degree of precision as in reduced form term structure models. At the same time, we are able to reproduce the dynamics of four key macro...
Stability and boundedness in terms of two measures for nonlinear impulsive control systems
Institute of Scientific and Technical Information of China (English)
Qiang XI
2009-01-01
In this paper we study stability and boundedness in terms of two measures for impulsive control systems. By using variational Lyapunov method, a new variational comparison principle and some criteria on stability and boundedness are obtained. An example is presented to illustrate the efficiency of proposed result.
Directory of Open Access Journals (Sweden)
MOHAMED BAHITA
2012-02-01
Full Text Available In this paper, a direct adaptive control scheme for a class of nonlinear systems is proposed. The architecture employs a Gaussian radial basis function (RBF network to construct an adaptive controller. The parameters of the adaptive controller are adapted and changed according to a law derived using Lyapunov stability theory. The centres of the RBF network are adapted on line using the k-means algorithm. Asymptotic Lyapunov stability is established without the use of a supervisory (compensatory term in the control law and with the tracking errors converging to a neighbourhood of the origin. Finally, a simulation is provided to explore the feasibility of the proposed neuronal controller design method.
González, Julián J; Pereda, Ernesto
2004-04-01
The short-term cardiovascular control system is reviewed from the analysis of the heart rate, respiration and blood pressure beat-to-beat variability signals. The present state of the art concerning fractal and non-linear techniques as applied to the cardiovascular system and the differences between both approaches are highlighted. We present results obtained in mammals from statistics, such as the fractal exponent, the correlation dimension or the maximal Lyapunov exponent and discuss the convenience of these indexes for characterizing the irregularity present in the signals. Finally, the interdependence between the systems involved in the cardiovascular control is addressed. Recent results obtained from interdependence indexes between the cardio, respiratory and vascular signals are discussed and their convenience in physiological studies and clinical applications are stressed.
An Eight-Term Novel Four-Scroll Chaotic System with Cubic Nonlinearity and its Circuit Simulation
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S. Sampath
2014-11-01
Full Text Available This research work proposes an eight-term novel four-scroll chaotic system with cubic nonlinearity and analyses its fundamental properties such as dissipativity, equilibria, symmetry and invariance, Lyapunov exponents and KaplanYorke dimension. The phase portraits of the novel chaotic system, which are obtained in this work by using MATLAB, depict the four-scroll attractor of the system. For the parameter values and initial conditions chosen in this work, the Lyapunov exponents of the novel four-scroll chaotic system are obtained as L1 = 0.75335, L2 = 0 and L3 = −22.43304. Also, the Kaplan-Yorke dimension of the novel four-scroll chaotic system is obtained as DKY = 2.0336. Finally, an electronic circuit realization of the novel four-scroll chaotic system is presented by using SPICE to confirm the feasibility of the theoretical model.
Energy Technology Data Exchange (ETDEWEB)
Yin, Jiuli, E-mail: yjl@ujs.edu.cn; Zhao, Liuwei
2014-11-07
In this paper, the dynamics from the shock compacton to chaos in the nonlinearly Schrödinger equation with a source term is investigated in detail. The existence of unclosed homoclinic orbits which are not connected with the saddle point indicates that the system has a discontinuous fiber solution which is a shock compacton. We prove that the shock compacton is a weak solution. The Melnikov technique is used to detect the conditions for the occurrence from the shock compacton to chaos and further analysis of the conditions for chaos suppression. The results show that the system turns to chaos easily under external disturbances. The critical parameter values for chaos appearing are obtained analytically and numerically using the Lyapunov exponents and the bifurcation diagrams.
The impact of nonlinear functional responses on the long-term evolution of food web structure.
Drossel, Barbara; McKane, Alan J; Quince, Christopher
2004-08-21
We investigate the long-term web structure emerging in evolutionary food web models when different types of functional responses are used. We find that large and complex webs with several trophic layers arise only if the population dynamics is such that it allows predators to focus on their best prey species. This can be achieved using modified Lotka-Volterra or Holling/Beddington functional responses with effective couplings that depend on the predator's efficiency at exploiting the prey, or a ratio-dependent functional response with adaptive foraging. In contrast, if standard Lotka-Volterra or Holling/Beddington functional responses are used, long-term evolution generates webs with almost all species being basal, and with additionally many links between these species. Interestingly, in all cases studied, a large proportion of weak links result naturally from the evolution of the food webs.
Directory of Open Access Journals (Sweden)
Jaime Buitrago
2017-01-01
Full Text Available Short-term load forecasting is crucial for the operations planning of an electrical grid. Forecasting the next 24 h of electrical load in a grid allows operators to plan and optimize their resources. The purpose of this study is to develop a more accurate short-term load forecasting method utilizing non-linear autoregressive artificial neural networks (ANN with exogenous multi-variable input (NARX. The proposed implementation of the network is new: the neural network is trained in open-loop using actual load and weather data, and then, the network is placed in closed-loop to generate a forecast using the predicted load as the feedback input. Unlike the existing short-term load forecasting methods using ANNs, the proposed method uses its own output as the input in order to improve the accuracy, thus effectively implementing a feedback loop for the load, making it less dependent on external data. Using the proposed framework, mean absolute percent errors in the forecast in the order of 1% have been achieved, which is a 30% improvement on the average error using feedforward ANNs, ARMAX and state space methods, which can result in large savings by avoiding commissioning of unnecessary power plants. The New England electrical load data are used to train and validate the forecast prediction.
Explaining Macroeconomic and Term Structure Dynamics Jointly in a Non-linear DSGE Model
DEFF Research Database (Denmark)
Andreasen, Martin Møller
This paper shows how a standard DSGE model can be extended to reproduce the dynamics in the 10 year yield curve for the post-war US economy with a similar degree of precision as in reduced form term structure models. At the same time, we are able to reproduce the dynamics of four key macro...... variables almost perfectly. Our extension of a standard DSGE model is to introduce three non-stationary shocks which allow us to explain interest rates with medium and long maturities without distorting the dynamics of the macroeconomy....
You, Yi-Zhuang; Bi, Zhen; Mao, Dan; Xu, Cenke
2016-03-01
We propose a series of simple two-dimensional (2D) lattice interacting fermion models that we demonstrate at low energy describe bosonic symmetry-protected topological (SPT) states and quantum phase transitions between them. This is because due to interaction, the fermions are gapped both at the boundary of the SPT states and at the bulk quantum phase transition, thus these models at low energy can be described completely by bosonic degrees of freedom. We show that the bulk of these models is described by a Sp (N ) principal chiral model with a topological Θ term, whose boundary is described by a Sp (N ) principal chiral model with a Wess-Zumino-Witten term at level 1. The quantum phase transition between SPT states in the bulk is tuned by a particular interaction term, which corresponds to tuning Θ in the field theory, and the phase transition occurs at Θ =π . The simplest version of these models with N =1 is equivalent to the familiar O(4) nonlinear sigma model (NLSM) with a topological term, whose boundary is a (1 +1 )D conformal field theory with central charge c =1 . After breaking the O(4) symmetry to its subgroups, this model can be viewed as bosonic SPT states with U(1), or Z2 symmetries, etc. All of these fermion models, including the bulk quantum phase transitions, can be simulated with the determinant quantum Monte Carlo method without the sign problem. Recent numerical results strongly suggest that the quantum disordered phase of the O(4) NLSM with precisely Θ =π is a stable (2 +1 )D conformal field theory with gapless bosonic modes.
Potirakis, S. M.; Contoyiannis, Y.; Melis, N. S.; Kopanas, J.; Antonopoulos, G.; Balasis, G.; Kontoes, C.; Nomicos, C.; Eftaxias, K.
2015-12-01
The preparation process of two recent earthquakes (EQs) occurred in Cephalonia (Kefalonia) island, Greece, (38.22° N, 20.53° E), 26 January 2014, Mw =6.0, depth =21 km, and (38.25° N, 20.39° E), 3 February 2014, Mw =5.9, depth =10 km, respectively, is studied in terms of the critical dynamics revealed in observables of the involved non-linear processes. Specifically, we show, by means of the method of critical fluctuations (MCF), that signatures of critical, as well as tricritical, dynamics were embedded in the fracture-induced electromagnetic emissions (EME) recorded by two stations in locations near the epicenters of these two EQs. It is worth noting that both, the MHz EME recorded by the telemetric stations on the island of Cephalonia and the neighboring island of Zante (Zakynthos), reached simultaneously critical condition a few days before the occurrence of each earthquake. The critical characteristics embedded in the EME signals were further verified using the natural time (NT) method. Moreover, we show, in terms of the NT method, that the foreshock seismic activity also presented critical characteristics before each one of these events. Importantly, the revealed critical process seems to be focused on the area corresponding to the west Cephalonia zone, following the seismotectonic and hazard zoning of the Ionian Islands area near Cephalonia.
Potirakis, Stelios M.; Contoyiannis, Yiannis; Melis, Nikolaos S.; Kopanas, John; Antonopoulos, George; Balasis, Georgios; Kontoes, Charalampos; Nomicos, Constantinos; Eftaxias, Konstantinos
2016-08-01
The preparation process of two recent earthquakes (EQs) that occurred in Cephalonia (Kefalonia), Greece, ((38.22° N, 20.53° E), 26 January 2014, Mw = 6.0, depth ˜ 20 km) and ((38.25° N, 20.39° E), 3 February 2014, Mw = 5.9, depth ˜ 10 km), respectively, is studied in terms of the critical dynamics revealed in observables of the involved non-linear processes. Specifically, we show, by means of the method of critical fluctuations (MCF), that signatures of critical, as well as tricritical, dynamics were embedded in the fracture-induced electromagnetic emissions (EMEs) recorded by two stations in locations near the epicentres of these two EQs. It is worth noting that both the MHz EMEs recorded by the telemetric stations on the island of Cephalonia and the neighbouring island of Zante (Zakynthos) reached a simultaneously critical condition a few days before the occurrence of each earthquake. The critical characteristics embedded in the EME signals were further verified using the natural time (NT) method. Moreover, we show, in terms of the NT method, that the foreshock seismic activity also presented critical characteristics before each event. Importantly, the revealed critical process seems to be focused on the area corresponding to the western Cephalonia zone, following the seismotectonic and hazard zoning of the Ionian Islands area near Cephalonia.
Directory of Open Access Journals (Sweden)
S. M. Potirakis
2015-12-01
Full Text Available The preparation process of two recent earthquakes (EQs occurred in Cephalonia (Kefalonia island, Greece, (38.22° N, 20.53° E, 26 January 2014, Mw =6.0, depth =21 km, and (38.25° N, 20.39° E, 3 February 2014, Mw =5.9, depth =10 km, respectively, is studied in terms of the critical dynamics revealed in observables of the involved non-linear processes. Specifically, we show, by means of the method of critical fluctuations (MCF, that signatures of critical, as well as tricritical, dynamics were embedded in the fracture-induced electromagnetic emissions (EME recorded by two stations in locations near the epicenters of these two EQs. It is worth noting that both, the MHz EME recorded by the telemetric stations on the island of Cephalonia and the neighboring island of Zante (Zakynthos, reached simultaneously critical condition a few days before the occurrence of each earthquake. The critical characteristics embedded in the EME signals were further verified using the natural time (NT method. Moreover, we show, in terms of the NT method, that the foreshock seismic activity also presented critical characteristics before each one of these events. Importantly, the revealed critical process seems to be focused on the area corresponding to the west Cephalonia zone, following the seismotectonic and hazard zoning of the Ionian Islands area near Cephalonia.
Tagantsev, Alexander K.; Stolichnov, Igor; Setter, Nava; Cross, Jeffrey S.
2004-12-01
The phenomenon of polarization imprint consisting of the development of a preferential polarization state in ferroelectric films is known as one of the major issues impacting the development of high density ferroelectric memories. According to the commonly accepted scenario, the imprint is related to the charge injection and charge accumulation in the nearby-electrode passive layer of the ferroelectric film. Recent studies demonstrated that the coercive voltage shift induced by the imprint exhibits a nonlinear time dependence in a logarithmic scale. This result was interpreted as the presence of two different imprint mechanisms characterized by different activation energies. In the present work, an analytical theory of the injection scenario of imprint is developed. The charge accumulation at the interface is shown to provoke a voltage offset and polarization loss which are nonlinearly dependent on the time in logarithmic scale. This result is obtained for different charge injection mechanisms including Schottky, Pool-Frenkel, and tunneling scenarios. Thus, it is shown that a single imprint mechanism can be responsible for a nolinear (in logarithmic scale) time dependence of the voltage offset and polarization loss. Additionally, the temperature dependence of the logarithmic rate of imprint is shown to be nonexponential. The developed model ties together the time and temperature dependences of imprint. For the experimental verification of the model a study of imprint has been performed on (111) Pb(Zr ,Ti)O3 film capacitors with temperatures ranging from 25 to 150°C and exposure times up to 1000h. It has been found that the theory developed adequately describes the obtained experimental data. Based upon the theoretical and experimental results a test for ferroelectric memories is proposed, which enables the long-term prediction of polarization loss caused by imprint for a wide temperature range and for different operating voltages.
Long term stabilization of reaction center protein photochemistry by carbon nanotubes
Energy Technology Data Exchange (ETDEWEB)
Magyar, Melinda; Hajdu, Kata; Szabo, Tibor; Nagy, Laszlo [Department of Medical Physics and Informatics, University of Szeged, 6720 Szeged (Hungary); Hernadi, Klara [Department of Applied and Environmental Chemistry, University of Szeged, 6720 Szeged (Hungary); Dombi, Andras [Institute of Material Sciences and Engineering, University of Szeged, 6701 Szeged (Hungary); Horvath, Endre; Magrez, Arnaud; Forro, Laszlo [Institute of Physics of Complex Matter, Ecole Polytechnique Federale de Lausanne, 1015 Lausanne (Switzerland)
2011-11-15
The long term stability and the redox interaction between single walled carbon nanotubes (SWNTs) and photosynthetic reaction center proteins (RCs) purified from purple bacterium Rhodobacter sphaeroides R-26 in the SWNT/RC complex has been investigated. The binding of SWNT to RC results in an accumulation of positive (the oxidized primary electron donor, P{sup +}) and negative (semiquinone forms, Q{sup -}{sub A} and Q{sup -}{sub B}, the reduced primary and secondary quinones, respectively) charges followed by slow reorganization of the protein structure after excitation. The photochemical activity of the SWNT/RC complexes remains stable for several weeks even in dried form. In the absence of SWNT the secondary quinone activity decays quickly as a function of time after drying the RC onto a glass surface. Polarography measurements substantiate the idea that there is an electronic interaction between the RCs and SWNTs after light excitation, which was suggested earlier by optical measurements. The special electronic properties of the SWNT/protein complexes open the possibility for several applications, e.g., in microelectronics, analytics, or energy conversion and storage. (Copyright copyright 2011 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Kong, Xiangxi; Sun, Wei; Wang, Bo; Wen, Bangchun
2015-06-01
The dynamic behaviors and stability of the linear guide considering contact actions are studied by multi-term incremental harmonic balance method (IHBM). Based on fully considering the parameters of the linear guide, a static model is developed and the contact stiffness is calculated according to Hertz contact theory. A generalized time-varying and piecewise-nonlinear dynamic model of the linear guide is formulated to perform an accurate investigation on its dynamic behaviors and stability. The numerical simulation is used to confirm the feasibility of the approach. The effects of excitation force and mean load on the system are analyzed in low-order nonlinearity. Multi-term IHBM and numerical simulation are employed to the effect of high-order nonlinearity and show the transition to chaos. Additionally, the effects of preload, initial contact angle, the number and diameter of balls are discussed.
Institute of Scientific and Technical Information of China (English)
Li Zi-Liang
2009-01-01
Higher-order Korteweg-de Vries (KdV)-modified KdV (mKdV) equations with a higher-degree of nonlinear terms are derived from a simple incompressible non-hydrostatic Boussinesq equation set in atmosphere and are used to investigate gravity waves in atmosphere. By taking advantage of the auxiliary nonlinear ordinary differential equation, periodic wave and solitary wave solutions of the fifth-order KdV-mKdV models with higher-degree nonlinear terms are obtained under some constraint conditions. The analysis shows that the propagation and the periodic structures of gravity waves depend on the properties of the slope of line of constant phase and atmospheric stability. The Jacobi elliptic function wave and solitary wave solutions with slowly varying amplitude are transformed into triangular waves with the abruptly varying amplitude and breaking gravity waves under the effect of atmospheric instability.
Lapa, Matthew F.; Hughes, Taylor L.
2017-08-01
We canonically quantize O (D +2 ) nonlinear sigma models (NLSMs) with a theta term on arbitrary smooth, closed, connected, oriented D -dimensional spatial manifolds M , with the goal of proving the suitability of these models for describing symmetry-protected topological (SPT) phases of bosons in D spatial dimensions. We show that in the disordered phase of the NLSM, and when the coefficient θ of the theta term is an integer multiple of 2 π , the theory on M has a unique ground state and a finite energy gap to all excitations. We also construct the ground state wave functional of the NLSM in this parameter regime, and we show that it is independent of the metric on M and given by the exponential of a Wess-Zumino term for the NLSM field, in agreement with previous results on flat space. Our results show that the NLSM in the disordered phase and at θ =2 π k , k ∈Z , has a symmetry-preserving ground state but no topological order (i.e., no topology-dependent ground state degeneracy), making it an ideal model for describing SPT phases of bosons. Thus, our work places previous results on SPT phases derived using NLSMs on solid theoretical ground. To canonically quantize the NLSM on M , we use Dirac's method for the quantization of systems with second class constraints, suitably modified to account for the curvature of space. In a series of four Appendixes, we provide the technical background needed to follow the discussion in the main sections of the paper.
Krishnamurthy, M. R.; Gireesha, B. J.; Prasannakumara, B. C.; Gorla, Rama Subba Reddy
2016-09-01
A theoretically investigation has been performed to study the effects of thermal radiation and chemical reaction on MHD velocity slip boundary layer flow and melting heat transfer of nanofluid induced by a nonlinear stretching sheet. The Brownian motion and thermophoresis effects are incorporated in the present nanofluid model. A set of proper similarity variables is used to reduce the governing equations into a system of nonlinear ordinary differential equations. An efficient numerical method like Runge-Kutta-Fehlberg-45 order is used to solve the resultant equations for velocity, temperature and volume fraction of the nanoparticle. The effects of different flow parameters on flow fields are elucidated through graphs and tables. The present results have been compared with existing one for some limiting case and found excellent validation.
Carrillo, J. A.
2009-10-30
Weak solutions of the spatially inhomogeneous (diffusive) Aizenmann-Bak model of coagulation-breakup within a bounded domain with homogeneous Neumann boundary conditions are shown to converge, in the fast reaction limit, towards local equilibria determined by their mass. Moreover, this mass is the solution of a nonlinear diffusion equation whose nonlinearity depends on the (size-dependent) diffusion coefficient. Initial data are assumed to have integrable zero order moment and square integrable first order moment in size, and finite entropy. In contrast to our previous result [5], we are able to show the convergence without assuming uniform bounds from above and below on the number density of clusters. © Taylor & Francis Group, LLC.
Farantos, Stavros C
2014-01-01
This brief presents numerical methods for describing and calculating invariant phase space structures, as well as solving the classical and quantum equations of motion for polyatomic molecules. Examples covered include simple model systems to realistic cases of molecules spectroscopically studied. Vibrationally excited and reacting molecules are nonlinear dynamical systems, and thus, nonlinear mechanics is the proper theory to elucidate molecular dynamics by investigating invariant structures in phase space. Intramolecular energy transfer, and the breaking and forming of a chemical bond have now found a rigorous explanation by studying phase space structures.
Exact solutions for logistic reaction-diffusion equations in biology
Broadbridge, P.; Bradshaw-Hajek, B. H.
2016-08-01
Reaction-diffusion equations with a nonlinear source have been widely used to model various systems, with particular application to biology. Here, we provide a solution technique for these types of equations in N-dimensions. The nonclassical symmetry method leads to a single relationship between the nonlinear diffusion coefficient and the nonlinear reaction term; the subsequent solutions for the Kirchhoff variable are exponential in time (either growth or decay) and satisfy the linear Helmholtz equation in space. Example solutions are given in two dimensions for particular parameter sets for both quadratic and cubic reaction terms.
EL-Dabe, N. T.; Attia, H. A.; Essawy, M. A. I.; Ramadan, A. A.; Abdel-Hamid, A. H.
2016-11-01
The steady MHD axisymmetric flow of an incompressible viscous electrically conducting nanofluid impinging on a permeable plate is investigated with heat and mass transfer. An external uniform magnetic field as well as a uniform inflow, in the presence of either suction or injection, are applied normal to the plate. The effects of heat (generation/absorption) and chemical reaction have been accentuated. This study indicates the incorporated influence of both the thermophoresis phenomenon and the Brownian behavior. Numerical solutions for the governing non-linear momentum, energy and nanoparticle equations have been obtained. The rates of heat and mass transfer are presented and discussed.
Burrill, Gail
This paper is a reaction to a plenary address, "A Research Base Supporting Long Term Algebra Reform?" by James Kaput (SE 057 182). Three dimensions of algebra reform identified by Kaput (breadth, integration, and pedagogy) are discussed and contrasted with the draft version of the Algebra Document from the National Council of Teachers of…
Energy Technology Data Exchange (ETDEWEB)
Chen Yong E-mail: chenyong@dlut.edu.cn; Li Biao E-mail: libiao@dlut.edu.cn
2004-03-01
Applying the improved generalized method, which is a direct and unified algebraic method for constructing multiple travelling wave solutions of nonlinear partial differential equations and implemented in a computer algebraic system, we consider the KdV-type equations and KdV-Burgers-type equations with nonlinear terms of any order. As a result, we can not only successfully recover the previously known travelling wave solutions found by existing various tanh methods and other sophisticated methods, but also obtain some new formal solutions. The solutions obtained include kink-shaped solitons, bell-shaped solitons, singular solitons and periodic solutions.
Chemical-reaction model for Mexican wave
Nagatani, Takashi
2003-05-01
We present a chemical-reaction model to describe the Mexican wave ( La Ola) in football stadia. The spectator's action is described in terms of chemical reactions. The model is governed by three reaction rates k 1, k 2, and k3. We study the nonlinear waves on one- and two-dimensional lattices. The Mexican wave is formulated as a clockwise forwardly propagating wave. Waves are growing or disappear, depending on the values of reaction rates. In the specific case of k1= k2= k3=1, the nonlinear-wave equation produces a propagating pulse like soliton.
Institute of Scientific and Technical Information of China (English)
GAO Hong-Xu; ZHAO Feng-Qi; HU Rong-Zu; ZHANG Hai; DONG Hai-Shan; YAO Pu; XU Zhou; HU Gang
2008-01-01
The thermal behaviour and decomposition reaction kinetics of benzotrifuroxan(BTF)were determined by TG and DSC techniques.The kinetic parameters of the exothermic decomposition reaction in a temperature pro-grammed mode(the apparent activation energy Ea and pre-exponential factor A)were calculated by a single non-isothermal DSC curve.The E values calculated using the Kissinger and Flynn-Wall-Ozawa equations and inte-gral isoconversional non-linear equations were used to check the validity of activation energy by a single non-isothermal DSC curve.The results show that the kinetic model function in integral form and the values of Ea respectively.The critical temperature of thermal explosion of BTF is 257.33 ℃.
Superior long-term activity for a Pt-Re alloy compared to Pt in methanol oxidation reactions
Duke, Audrey S.; Xie, Kangmin; Monnier, John R.; Chen, Donna A.
2017-03-01
Pt-Re bimetallic catalysts have shown enhanced activity compared to pure Pt for reactions involving oxidation, but the origins of this improved activity are not fully understood. Methanol oxidation on a Pt-Re alloy surface and pure Pt foil was studied in a microreactor coupled to an ultrahigh vacuum chamber. For reaction at 60 °C, the Pt-Re alloy surface exhibits superior long-term activity over a 24 h reaction period compared to pure Pt. The initial activity of Pt is 10-15% higher than on Pt-Re; however, the Pt surface gradually loses activity after 10 h online, whereas the activity of Pt-Re does not diminish. Post-reaction XPS shows that more carbon accumulates on the Pt than on Pt-Re, and the improved long-term activity is attributed to a greater ability of Pt-Re to oxidize the carbonaceous intermediates that eventually poison active sites. Both Pt and Pt-Re surfaces have almost no activity for methanol oxidation until a minimum coverage of oxygen is achieved from O2 dissociation. A comparison with methanol oxidation studies on Pt and Pt-Re in a pressure regime that is 150 times lower than in this work demonstrates that more carbon and less oxygen accumulate on the surfaces during reaction at the lower pressures.
The Effect of a Long-Term Artistic Gymnastic Training on Reaction Time of Male Gymnasts
Directory of Open Access Journals (Sweden)
Bahman Aalizadeh
2014-12-01
Full Text Available Since there are variations in the reaction times of athletes in different sports, the aim of the present study was to evaluate the effectiveness of a specific training program on a simple reaction time of male gymnasts. In this longitudinal study, fourteen adolescent gymnasts (mean age 12.6 ± 2.1 years were randomly selected to work out for 15 months in the artistic group. Simple reaction time was assessed by visual and auditory tests using computer software. The training resulted in a significant (P < 0.001 reduction in visual (0.33 ± 0.047 s vs. 0.30 ± 0.048 s and auditory reaction time (0.31 ± 0.056 s vs. 0.27 ± 0.038 s. This study suggested an improvement in both reaction time tests over a long time of specialized training program. Artistic gymnasts had overall developed results of the tests that might be derived from exercise induced arousal, concentration and movement complexity in this sport.
Dratman, Ezequiel
2011-01-01
We study the positive stationary solutions of a standard finite-difference discretization of the semilinear heat equation with nonlinear Neumann boundary conditions. We prove that, if \\emph{the absorption is small enough}, compared with the flux in the boundary, there exists a unique solution of such a discretization, which approximates the unique positive stationary solution of the "continuous" equation. Furthermore, we exhibit an algorithm computing an $\\epsilon$-approximation of such a solution by means of a homotopy continuation method. The cost of our algorithm is {\\em linear} in the number of nodes involved in the discretization and the logarithm of the number of digits of approximation required.
Dratman, Ezequiel
2011-01-01
We study the positive stationary solutions of a standard finite-difference discretization of the semilinear heat equation with nonlinear Neumann boundary conditions. We prove that, if the absorption is large enough, compared with the flux in the boundary, there exists a unique solution of such a discretization, which approximates the unique positive stationary solution of the "continuous" equation. Furthermore, we exhibit an algorithm computing an $\\epsilon$-approximation of such a solution by means of a homotopy continuation method. The cost of our algorithm is {\\em linear} in the number of nodes involved in the discretization and the logarithm of the number of digits of approximation required.
Reaction of monocytes to polystyrene and silica nanoparticles in short-term and long-term exposures†
Mrakovcic, Maria; Meindl, Claudia; Roblegg, Eva; Fröhlich, Eleonore
2015-01-01
Nanoparticles (NPs) are increasingly used in industrial, health and consumer products. In addition to the intended effects, NPs may also cause cell damage. Typical cytotoxicity assays assess short-term effects in adherent cells but do not evaluate longer exposure times and do not focus on cells in suspension. Since NPs are not removed easily from the organism, non-biodegradable NPs may persist in the systemic circulation and affect monocyte function at low concentrations. To mimic this situation, THP-1 monocytes were exposed to low concentrations of plain polystyrene particles (PPP) in different sizes for short (24 h) and prolonged (16 d) time periods. CELLine CL350, a small two-chamber bioreactor, and sub-culturing in flasks were compared regarding prolonged cytotoxicity testing. Uptake rates of the particles, cytotoxicity screening assays, and interleukin secretion were used for the identification of adverse effects. After 24 h, 50 μg ml−1 20 nm PPP did not affect cellular viability and interleukin secretion, while at higher concentrations the cytotoxicity of PPP (20 nm-500 nm) was correlated to surface area. After 16 d of exposure at 50 μg ml−1 20 nm PPP, the decrease in cell number and the increase in interleukins were significant. 200 nm PPP, by contrast, caused only minimal effects. Due to lower reproducibility, CELLine proved to be less suitable for the assessment as compared to sub-culturing in flasks. After prolonged exposure, silica Aerosil OX50 particles also were more cytotoxic towards THP-1 monocytes. The data suggest that prolonged exposure to NPs leads to cytotoxicity at low doses and that induction of cell death may be involved in the observed pro-inflammatory action of NPs. PMID:26005565
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Ryan R Reisinger
Full Text Available Remote tissue biopsy sampling and satellite tagging are becoming widely used in large marine vertebrate studies because they allow the collection of a diverse suite of otherwise difficult-to-obtain data which are critical in understanding the ecology of these species and to their conservation and management. Researchers must carefully consider their methods not only from an animal welfare perspective, but also to ensure the scientific rigour and validity of their results. We report methods for shore-based, remote biopsy sampling and satellite tagging of killer whales Orcinus orca at Subantarctic Marion Island. The performance of these methods is critically assessed using 1 the attachment duration of low-impact minimally percutaneous satellite tags; 2 the immediate behavioural reactions of animals to biopsy sampling and satellite tagging; 3 the effect of researcher experience on biopsy sampling and satellite tagging; and 4 the mid- (1 month and long- (24 month term behavioural consequences. To study mid- and long-term behavioural changes we used multievent capture-recapture models that accommodate imperfect detection and individual heterogeneity. We made 72 biopsy sampling attempts (resulting in 32 tissue samples and 37 satellite tagging attempts (deploying 19 tags. Biopsy sampling success rates were low (43%, but tagging rates were high with improved tag designs (86%. The improved tags remained attached for 26±14 days (mean ± SD. Individuals most often showed no reaction when attempts missed (66% and a slight reaction-defined as a slight flinch, slight shake, short acceleration, or immediate dive-when hit (54%. Severe immediate reactions were never observed. Hit or miss and age-sex class were important predictors of the reaction, but the method (tag or biopsy was unimportant. Multievent trap-dependence modelling revealed considerable variation in individual sighting patterns; however, there were no significant mid- or long-term changes
Tsyganov, Y S
2015-01-01
Sources of non-linear response of PIPS detector, when detecting highly ionizing particles like recoils (EVR), fission fragments and heavy ions, including formation of large pulse-height defect (PHD) are considered. An analytical formula to calculate the recombination component of EVR PHD is proposed on the base of surface recombination model with some empirical correction. PC-based simulation code for generating the spectrum of the measured recoil signal amplitudes of the heavy implanted nuclei is presented. The simulated spectra are compared with the experimental ones for the different facilities: the Dubna Gas Filled Recoil Separator (DGFRS), SHIP and RIKEN gas-filled separator. After the short reviewing of the detection system of the DGFRS, is considered the real-time matrix algorithm application aimed to the radical background suppression in the complete-fusion heavy-ion induced nuclear reactions. Typical examples of application in the long term experiments aimed to the synthesis of superheavy elements Z=...
Wang, Kai; Teng, Zhidong; Jiang, Haijun
2012-10-01
In this paper, the adaptive synchronization in an array of linearly coupled neural networks with reaction-diffusion terms and time delays is discussed. Based on the LaSalle invariant principle of functional differential equations and the adaptive feedback control technique, some sufficient conditions for adaptive synchronization of such a system are obtained. Finally, a numerical example is given to show the effectiveness of the proposed synchronization method.
Long term adverse drug reaction to Efavirenz in a HIV infected ...
African Journals Online (AJOL)
Arun Kumar Agnihotri
2015-08-31
Aug 31, 2015 ... The case of a male HIV Positive Nigerian patient aged 13 years. He presented with five-day history of ... adverse reaction mainly affecting behavior, thought processes and memory. .... and ninety-two (1192 cell/mm3) in a test done on the .... monitoring in HIV-1 infected children receiving efavirenz doses.
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AR. Obac
Full Text Available In forensic medical work, in cases with homicide suspicion, it is important to be able to determine with the greatest possible precision when injuries occurred and whether during vital, or post-mortem conditions. Although several markers of vitality can be employed, it has been attested that components of the extra-cellular matrix, such as fibrin, are among the earliest to be evidenced. In the present study, the histological-histochemical Mallory's Trichrome staining method, previously selected was tested to determine the presence of vital reaction in Wistar rats through fibrin accumulation by testing three short reaction time intervals: 15, 30 and 60 minutes after the skin wound infliction. For all time intervals tested, including the shortest (15 minutes, the presence of fibrin at the edges of the skin wound was evidenced. The accumulation of fibrin was, nevertheless, more pronounced at 30 and 60 minutes after the wound. It could be concluded that fibrin is a good marker for vital reaction and that it can be detected very early, within a few minutes after the injury. It is proposed that histological method coupled to the histochemical staining technique here tested can be incorporated into routine forensic work as a tool for evidencing the existence or not of vital reaction.
Drábek, Pavel; Takáč, Peter
2017-02-14
We consider a one-dimensional population genetics model for the advance of an advantageous gene. The model is described by the semilinear Fisher equation with unbalanced bistable non-Lipschitzian nonlinearity f(u). The "nonsmoothness" of f allows for the appearance of travelling waves with a new, more realistic profile. We study existence, uniqueness, and long-time asymptotic behavior of the solutions u(x, t), [Formula: see text]. We prove also the existence and uniqueness (up to a spatial shift) of a travelling wave U. Our main result is the uniform convergence (for [Formula: see text]) of every solution u(x, t) of the Cauchy problem to a single travelling wave [Formula: see text] as [Formula: see text]. The speed c and the travelling wave U are determined uniquely by f, whereas the shift [Formula: see text] is determined by the initial data.
The numerical dynamic for highly nonlinear partial differential equations
Lafon, A.; Yee, H. C.
1992-01-01
Problems associated with the numerical computation of highly nonlinear equations in computational fluid dynamics are set forth and analyzed in terms of the potential ranges of spurious behaviors. A reaction-convection equation with a nonlinear source term is employed to evaluate the effects related to spatial and temporal discretizations. The discretization of the source term is described according to several methods, and the various techniques are shown to have a significant effect on the stability of the spurious solutions. Traditional linearized stability analyses cannot provide the level of confidence required for accurate fluid dynamics computations, and the incorporation of nonlinear analysis is proposed. Nonlinear analysis based on nonlinear dynamical systems complements the conventional linear approach and is valuable in the analysis of hypersonic aerodynamics and combustion phenomena.
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M.H. Tiwana
2017-04-01
Full Text Available This work investigates the fractional non linear reaction diffusion (FNRD system of Lotka-Volterra type. The system of equations together with the boundary conditions are solved by Homotopy perturbation transform method (HPTM. The series solutions are obtained for the two cases (homogeneous and non-homogeneous of FNRD system. The effect of fractional parameter on the mass concentration of two species are shown and discussed with the help of 3D graphs.
Reactions of Residents to Long-Term Sonic Boom Noise Environments
Fields, James M.
1997-01-01
A combined social survey and noise measurement program has been completed in 14 communities in two regions of the western United States that have been regularly exposed to sonic booms for many years. A total of 1,573 interviews were completed. Three aspects of the sonic booms are most disturbing: being startled, noticing rattles or vibrations, and being concerned about the possibility of damage from the booms. Sonic boom annoyance is greater than that in a conventional aircraft environment with the same continuous equivalent noise exposure. The reactions in the two study regions differ in severity.
Institute of Scientific and Technical Information of China (English)
顾绍泉; 向新民
2005-01-01
Nonlinear Schroedinger equation arises in many physical problems. There are many works in which properties of the solution are studied. In this paper we use fully discrete Fourier spectral method to get an approximation solution of nonlinear weakly dissipative Schroedinger equation with quintic term. We give a large-time error estimate and obtain the existence of the approximate attractor A Nk.
Sokolovski, D; Sen, S K; Aquilanti, V; Cavalli, S; De Fazio, D
2007-02-28
We study the effect of overlapping resonances on the angular distributions of the reaction F+H2(v=0,j=0)-->HF(v=2,j=0)+H in the collision energy range from 5 to 65 meV, i.e., under the reaction barrier. Reactive scattering calculations were performed using the hyperquantization algorithm on the potential energy surface of Stark and Werner [J. Chem. Phys. 104, 6515 (1996)]. The positions of the Regge and complex energy poles are obtained by Pade reconstruction of the scattering matrix element. The Sturmian theory is invoked to relate the Regge and complex energy terms. For two interacting resonances, a two-sheet Riemann surface is contracted and inverted. The semiclassical complex angular momentum analysis is used to decompose the scattering amplitude into the direct and resonance contributions.
Institute of Scientific and Technical Information of China (English)
ZHONG CHENGKUI; SUN CHUNYOU; NIU MINGFEI
2005-01-01
By means of a nonstandard estimation about the energy functional, the authors prove the existence of a global attractor for an abstract nonlinear evolution equation. As an application, the existence of a global attractor for some nonlinear reaction-diffusion equations with some distribution derivatives in inhomogeneous terms is obtained.
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Jarideh S.
2015-05-01
Full Text Available Background: Airport workers are continuously exposed to different levels of radiofrequency microwave (RF/MW radiation emitted by radar equipments. Radars are extensively used in military and aviation industries. Over the past several years, our lab has focused on the health effects of exposure to different sources of electromagnetic fields such as cellular phones, mobile base stations, mobile phone jammers, laptop computers, radars, dentistry cavitrons and MRI. The main goal of this study was to investigate if occupational exposure of Shahid Dastghieb international airport workers to radiofrequency radiation affects their short term memory and reaction time. Methods: Thirty two airport workers involved in duties at control and approach tower (21 males and 11 females, with the age range of 27-67 years old (mean age of 37.38, participated voluntary in this study. On the other hand, 29 workers (13 males, and 16 females whose offices were in the city with no exposure history to radar systems were also participated in this study as the control group. The employees’ reaction time and short term memory were analyzed using a standard visual reaction time (VRT test software and the modified Wechsler memory scale test, respectively. Results: The mean± SD values for the reaction times of the airport employees (N=32 and the control group (N=29 were 0.45±0.12 sec and 0.46±0.17 sec, respectively. Moreover, in the four subset tests; i.e. paired words, forward digit span, backward digit span and word recognition, the following points were obtained for the airport employees and the control group, respectively: (i pair words test: 28.00±13.13 and 32.07±11.65, (ii forward digit span: 8.38±1.40 and 9.03±1.32, (iii backward digit span: 5.54±1.87 and 6.31±1.46, and (iv word recognition: 5.73±2.36 and 6.50±1.93. These differences were not statistically significant. Conclusion: The occupational exposure of the employees to the RF radiation in Shahid
Hervás, C; Toledo, R; Silva, M
2001-01-01
The suitability of pruned computational neural networks (CNNs) for resolving nonlinear multicomponent systems involving synergistic effects by use of oscillating chemical reaction-based methods implemented using the analyte pulse perturbation technique is demonstrated. The CNN input data used for this purpose are estimates provided by the Levenberg-Marquardt method in the form of a three-parameter Gaussian curve associated with the singular profile obtained when the oscillating system is perturbed by an analyte mixture. The performance of the proposed method was assessed by applying it to the resolution of mixtures of pyrogallol and gallic acid based on their perturbating effect on a classical oscillating chemical system, viz. the Belousov-Zhabotinskyi reaction. A straightforward network topology (3:3:2, with 18 connections after pruning) allowed the resolution of mixtures of the two analytes in concentration ratios from 1:7 to 6:2 with a standard error of prediction for the testing set of 4.01 and 8.98% for pyrogallol and gallic acid, respectively. The reduced dimensions of the selected CNN architecture allowed a mathematical transformation of the input vector into the output one that can be easily implemented via software. Finally, the suitability of response surface analysis as an alternative to CNNs was also tested. The results were poor (relative errors were high), which confirms that properly selected pruned CNNs are effective tools for solving the analytical problem addressed in this work.
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Qiankun Song
2007-06-01
Full Text Available Impulsive bidirectional associative memory neural network model with time-varying delays and reaction-diffusion terms is considered. Several sufficient conditions ensuring the existence, uniqueness, and global exponential stability of equilibrium point for the addressed neural network are derived by M-matrix theory, analytic methods, and inequality techniques. Moreover, the exponential convergence rate index is estimated, which depends on the system parameters. The obtained results in this paper are less restrictive than previously known criteria. Two examples are given to show the effectiveness of the obtained results.
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Cao Jinde
2007-01-01
Full Text Available Impulsive bidirectional associative memory neural network model with time-varying delays and reaction-diffusion terms is considered. Several sufficient conditions ensuring the existence, uniqueness, and global exponential stability of equilibrium point for the addressed neural network are derived by M-matrix theory, analytic methods, and inequality techniques. Moreover, the exponential convergence rate index is estimated, which depends on the system parameters. The obtained results in this paper are less restrictive than previously known criteria. Two examples are given to show the effectiveness of the obtained results.
Reaction of sorghum to diverse plant density and rows distance in dependence on sowing terms
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Andrzej Kruczek
2014-03-01
Full Text Available The aim of the study was qualification of optimum plants density on the unit of area and distance of rows for two terms of sowing of sorghum. Field trials were conducted in 2008-2011 in Didactic-Experimental Station in Swadzim that belongs to the Poznań University of Life Sciences. It was shown that sowing of sorghum in III decade of May enlarged the plants density on 1 m2 in comparison to the sowing about two weeks earlier. Enlarging the distance of rows from 30 to 90 cm effectively and gradually limited the number of plants per area unit. The fresh and dry mass yields of whole plants of sorghum and stems, leaves and panicles increased in measure of enlarging the density of sowing from 15 to 25 seeds per 1 m2 and in measure of reducing the distance between rows of plants from 90 to 30 cm. The sowing term of sorghum did not influence fresh and dry mass yields of plants and their components.
Konovalov, I B
2002-01-01
The nonlinear features of the relationships between particulate matter (PM) and volatile organic compounds (VOC) and oxides of nitrogen (NOx) are derived directly from data of long-term routine measurements of NOx, VOC, and total suspended PM. The main idea of the method used for the analysis is creation of special empirical models based on artificial neural networks of the perceptron type. These models which are in essence the nonlinear extension of commonly used linear regression models are believed to provide the best fit for the real nonlinear PM-NOx-VOC relationships under different observed levels of air pollution and various meteorological conditions. It is believed that such models may be useful in context of various scientific and practical problems concerning PM. The method is demonstrated by the example of two empirical models created with independent data-sets collected at two air quality monitoring stations at South Coast Air Basin, California. It is shown that in spite of considerable distance b...
Tsai, Jason S-H; Hsu, Wen-Teng; Lin, Long-Guei; Guo, Shu-Mei; Tann, Joseph W
2014-01-01
A modified nonlinear autoregressive moving average with exogenous inputs (NARMAX) model-based state-space self-tuner with fault tolerance is proposed in this paper for the unknown nonlinear stochastic hybrid system with a direct transmission matrix from input to output. Through the off-line observer/Kalman filter identification method, one has a good initial guess of modified NARMAX model to reduce the on-line system identification process time. Then, based on the modified NARMAX-based system identification, a corresponding adaptive digital control scheme is presented for the unknown continuous-time nonlinear system, with an input-output direct transmission term, which also has measurement and system noises and inaccessible system states. Besides, an effective state space self-turner with fault tolerance scheme is presented for the unknown multivariable stochastic system. A quantitative criterion is suggested by comparing the innovation process error estimated by the Kalman filter estimation algorithm, so that a weighting matrix resetting technique by adjusting and resetting the covariance matrices of parameter estimate obtained by the Kalman filter estimation algorithm is utilized to achieve the parameter estimation for faulty system recovery. Consequently, the proposed method can effectively cope with partially abrupt and/or gradual system faults and input failures by the fault detection.
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Yan Zhao
2014-01-01
Full Text Available This paper is focused on studying approximate damped oscillatory solutions of the compound KdV-Burgers-type equation with nonlinear terms of any order. By the theory and method of planar dynamical systems, existence conditions and number of bounded traveling wave solutions including damped oscillatory solutions are obtained. Utilizing the undetermined coefficients method, the approximate solutions of damped oscillatory solutions traveling to the left are presented. Error estimates of these approximate solutions are given by the thought of homogeneous principle. The results indicate that errors between implicit exact damped oscillatory solutions and approximate damped oscillatory solutions are infinitesimal decreasing in the exponential form.
Energy Technology Data Exchange (ETDEWEB)
Buck, E.C.; Fortner, J.A.; Bates, J.K.; Feng, X.; Dietz, N.L.; Bradley, C.R.; Tani, B.S.
1993-12-31
Alteration phases, found on the leached surfaces and present as colloids in the leachates of 200-based frit (fully active and simulated) nuclear waste glass, reacted under static test conditions, at a surface area to leachate volume ratio of 20,000 m{sup {minus}1} for 15 days to 728 days, have been examined by analytical electron microscopy. The compositions of the secondary phases were determined using x-ray energy dispersive spectroscopy and electron energy loss spectroscopy, and structural analysis was accomplished by electron diffraction. Long-term samples of simulated glass, which had undergone an acceleration of reaction after 182 days, possessed a number of silicate secondary phases, including; smectite (iron silicate and potassium iron alumina-silicate, weeksite (uranium silicate), zeolite (calcium potassium alumino-silicate), tobermorite (calcium silicate), and a pure silica phase. However, uranium silicates and smectite have also been observed in tests, which have not undergone the acceleration of reaction, in both the leachate and leached layer, suggesting that these phases are not responsible for the acceleration of reaction.
Kharkats, Yurij I.; Ulstrup, Jens
1990-02-01
Kinetics of electron transfer between redox metalloproteins and small inorganic reaction partners has become a powerful tool for investigations of protein electron transport. We introduce here a model for metalloprotein electron transfer which incorporates essential features omitted in previous approaches to metalloprotein electron transfer data analysis. The protein is represented by a spherical region of low dielectric constant, with a conducting sphere excentrically located inside the protein simulating the metal centre. A conducting sphere outside the protein represents the small reaction partners, and the whole system is embedded in a dielectric solvent. The inter-reactant work terms and overall protein and solvent reorganization free energy for this model have been calculated. It appears that dielectric image interactions for multiply charged small reactants are important and comparable to interactions with both the protein surface charges and the solvent. The character of work terms and reorganization free energies for proteins is thus different from those of small ionic reactants. Cross relations and other frames where these features are disregarded should therefore be used with care for protein electron transfer.
Chou, Shih-Wei; Lin, Ying-Chieh
2017-08-01
In this paper, we investigate the Cauchy problem for a nonlinear hyperbolic system of balance laws with sources ax g and at h. To get the approximate solutions of our problem, we consider a version of generalized Riemann problem that concentrates the variation of a on a thin T-shaped region of each grid. A new version of Glimm scheme is introduced to construct the approximate solutions and its stability is proved by considering two types of conditions on a. Finally, we verify the consistency of the scheme and the entropy inequality to establish the global existence of entropy solutions.
Hu, Kun; Lo, Men-Tzung; Peng, Chung-Kang; Liu, Yanhui; Novak, Vera
2012-01-01
Cerebral autoregulation (CA) is an important vascular control mechanism responsible for relatively stable cerebral blood flow despite changes of systemic blood pressure (BP). Impaired CA may leave brain tissue unprotected against potentially harmful effects of BP fluctuations. It is generally accepted that CA is less effective or even inactive at frequencies >∼0.1 Hz. Without any physiological foundation, this concept is based on studies that quantified the coupling between BP and cerebral blood flow velocity (BFV) using transfer function analysis. This traditional analysis assumes stationary oscillations with constant amplitude and period, and may be unreliable or even invalid for analysis of nonstationary BP and BFV signals. In this study we propose a novel computational tool for CA assessment that is based on nonlinear dynamic theory without the assumption of stationary signals. Using this method, we studied BP and BFV recordings collected from 39 patients with chronic ischemic infarctions and 40 age-matched non-stroke subjects during baseline resting conditions. The active CA function in non-stroke subjects was associated with an advanced phase in BFV oscillations compared to BP oscillations at frequencies from ∼0.02 to 0.38 Hz. The phase shift was reduced in stroke patients even at > = 6 months after stroke, and the reduction was consistent at all tested frequencies and in both stroke and non-stroke hemispheres. These results provide strong evidence that CA may be active in a much wider frequency region than previously believed and that the altered multiscale CA in different vascular territories following stroke may have important clinical implications for post-stroke recovery. Moreover, the stroke effects on multiscale cerebral blood flow regulation could not be detected by transfer function analysis, suggesting that nonlinear approaches without the assumption of stationarity are more sensitive for the assessment of the coupling of nonstationary
Ahrendt, Andrew; Sprankle, Eric; Kuka, Alex; McPherson, Keagan
2017-01-01
The current study assesses ageism and heterosexism relating to older adult sexual activity within long-term care facilities. To assess caregiver reactions, 153 residential care facility staff members read one of three vignettes. Each vignette described a scenario in which a staff member walks in on two residents (male/female, male/male, or female/female) engaging in sexual activity. Although no main effects were discovered for vignette type, exploratory analyses revealed that the facility where participants were employed was significantly related to their ratings of approval. Furthermore, an interaction effect between vignette and facility types was also discovered for caregivers' approval of sexual activity among residents. Additionally, a strong overall approval rating of older adult sexuality was reported by staff members. The results of this study warrant that further research is necessary regarding older adults' perception of caregiver bias, as well as further investigation of caregivers' perceptions of older adults' sexual activity.
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Palermo Filippo
2009-02-01
Full Text Available Abstract Background Near term infants are a main part of preterms. They are at higher risk for mortality and morbidity than term infants and could show a quite different development of tone and reflexes from them. The aim of the present study was to describe longitudinally, in a large sample of healthy near term infants, the development of the forward parachute reaction (FPR and its correlation with the age of acquisition of independent walking. Methods The assessment of FPR (as absent, incomplete or complete was performed at 3, 6, 9, 12 months of corrected age in 484 infants, with a gestational age between 35.0 and 36.9 weeks. The age of acquisition of independent walking was monitored until its appearance. A correlation analysis was done between the age of walking and the acquisition of a complete or incomplete FPR, using the Spearman Rank correlation. The Mann-Withney U test was used to identify significant gestational age differences for the age of FPR appearance. Results Most of infants had a two-step development pattern. In fact, they showed at first an incomplete and then a complete FPR, which was observed more frequently at 9 months. An incomplete FPR only, without a successive maturation to a complete FPR, was present in the 21% of the whole sample. Infants with a complete FPR walked at a median age of 13 months, whereas those with an incomplete FPR only walked at a median age of 14 months. Conclusion We identified two groups within our sample of near term infants. The first group showed a progressive maturation of FPR, whereas the second one was characterised by the inability to get a complete pattern, within the one year observation's period. Furthermore, we observed a trend toward a delayed acquisition of independent walking in the latter group of infants.
2014-04-01
irreversible deformation, the three-term model allows for residual elastic strains— including dilatation observed in experiments and atomic simulations...residual elastic strains—including dilatation observed in experiments and atomic simulations—not addressed by conventional two-term crystal plasticity...gradient for an element of crystalline material. For simplicity, thermal effects are omitted, gliding dislocations are the only kind of defect considered
Gary, Ronald K.
2004-01-01
The concentration dependence of (delta)S term in the Gibbs free energy function is described in relation to its application to reversible reactions in biochemistry. An intuitive and non-mathematical argument for the concentration dependence of the (delta)S term in the Gibbs free energy equation is derived and the applicability of the equation to…
Schäffer, Beat; Schlittmeier, Sabine J; Pieren, Reto; Heutschi, Kurt; Brink, Mark; Graf, Ralf; Hellbrück, Jürgen
2016-05-01
Current literature suggests that wind turbine noise is more annoying than transportation noise. To date, however, it is not known which acoustic characteristics of wind turbines alone, i.e., without effect modifiers such as visibility, are associated with annoyance. The objective of this study was therefore to investigate and compare the short-term noise annoyance reactions to wind turbines and road traffic in controlled laboratory listening tests. A set of acoustic scenarios was created which, combined with the factorial design of the listening tests, allowed separating the individual associations of three acoustic characteristics with annoyance, namely, source type (wind turbine, road traffic), A-weighted sound pressure level, and amplitude modulation (without, periodic, random). Sixty participants rated their annoyance to the sounds. At the same A-weighted sound pressure level, wind turbine noise was found to be associated with higher annoyance than road traffic noise, particularly with amplitude modulation. The increased annoyance to amplitude modulation of wind turbines is not related to its periodicity, but seems to depend on the modulation frequency range. The study discloses a direct link of different acoustic characteristics to annoyance, yet the generalizability to long-term exposure in the field still needs to be verified.
Park, Joong-Min; Hwang, In Gyu; Suh, Suk-Won; Chi, Kyong-Choun
2011-12-01
TS-1 is an oral anti-cancer agent for gastric cancer with a high response rate and low toxicity. We report a case of long-term drug retention of TS-1 causing interstitial lung disease (ILD) as a fatal adverse reaction. A 65-year-old woman underwent a total gastrectomy with pathologic confirmation of gastric adenocarcinoma. She received 6 cycles of TS-1 and low-dose cisplatin for post-operative adjuvant chemotherapy followed by single-agent maintenance therapy with TS-1. After 8 months, the patient complained of a productive cough with sputum and mild dyspnea. A pulmonary evaluation revealed diffuse ILD in the lung fields, bilaterally. In spite of discontinuing chemotherapy and the administration of corticosteroids, the pulmonary symptoms did not improve, and the patient died of pulmonary failure. TS-1-induced ILD can be caused by long-term drug retention that alters the lung parenchyma irreversibly, the outcome of which can be life-threatening. Pulmonary evaluation for early detection of disease is recommended.
Yu, Hwa-Lung; Chien, Lung-Chang
2016-01-01
Fine particulate matter respiratory disease remain inconsistent. The short-term, population-based association between the respiratory clinic visits of children and PM2.5 exposure levels were investigated by considering both the spatiotemporal distributions of ambient pollution and clinic visit data. We applied a spatiotemporal structured additive regression model to examine the concentration-response (C-R) association between children's respiratory clinic visits and PM2.5 concentrations. This analysis was separately performed on three respiratory disease categories that were selected from the Taiwanese National Health Insurance database, which includes 41 districts in the Taipei area of Taiwan from 2005 to 2007. The findings reveal a non-linear C-R pattern of PM2.5, particularly in acute respiratory infections. However, a PM2.5 increase at relatively lower levels can elevate the same-day respiratory health risks of both preschool children (respiratory risks, except in instances where PM2.5 levels are extremely high, and these occurrences do exhibit a significant positive influence on respiratory health that is especially notable in schoolchildren. A significant high relative rate of respiratory clinic visits are concentrated in highly populated areas. We highlight the non-linearity of the respiratory health effects of PM2.5 on children to investigate this population-based association. The C-R relationship in this study can provide a highly valuable alternative for assessing the effects of ambient air pollution on human health.
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S. Vaidyanathan
2014-11-01
Full Text Available This research work describes a nine-term novel 3-D chaotic system with four quadratic nonlinearities and details its qualitative properties. The phase portraits of the 3-D novel chaotic system simulated using MATLAB, depict the strange chaotic attractor of the system. For the parameter values chosen in this work, the Lyapunov exponents of the novel chaotic system are obtained as L1 = 6.8548, L2 = 0 and L3 = −32.8779. Also, the Kaplan-Yorke dimension of the novel chaotic system is obtained as DKY = 2.2085. Next, an adaptive controller is design to achieve global stabilization of the 3-D novel chaotic system with unknown system parameters. Moreover, an adaptive controller is designed to achieve global chaos synchronization of two identical novel chaotic systems with unknown system parameters. Finally, an electronic circuit realization of the novel chaotic system is presented using SPICE to confirm the feasibility of the theoretical model.
Breatherlike impurity modes in discrete nonlinear lattices
DEFF Research Database (Denmark)
Hennig, D.; Rasmussen, Kim; Tsironis, G. P.
1995-01-01
We investigate the properties of a disordered generalized discrete nonlinear Schrodinger equation, containing both diagonal and nondiagonal nonlinear terms. The equation models a Linear host lattice doped with nonlinear impurities. We find different types of impurity states that form itinerant...
Institute of Scientific and Technical Information of China (English)
徐琛梅
2008-01-01
In the article,the fully discrete finite difference scheme for a type of nonlinear reaction-diffusion equation is established.Then the new function space is introduced and the stability problem for the finite difference scheme is discussed by means of variational approximation method in this function space.The approach used is of a simple characteristic in gaining the stability condition of the scheme.
Directory of Open Access Journals (Sweden)
Wei Khim Ng
2009-02-01
Full Text Available We construct nonlinear extensions of Dirac's relativistic electron equation that preserve its other desirable properties such as locality, separability, conservation of probability and Poincaré invariance. We determine the constraints that the nonlinear term must obey and classify the resultant non-polynomial nonlinearities in a double expansion in the degree of nonlinearity and number of derivatives. We give explicit examples of such nonlinear equations, studying their discrete symmetries and other properties. Motivated by some previously suggested applications we then consider nonlinear terms that simultaneously violate Lorentz covariance and again study various explicit examples. We contrast our equations and construction procedure with others in the literature and also show that our equations are not gauge equivalent to the linear Dirac equation. Finally we outline various physical applications for these equations.
Kratochwil, Nicole A; Meille, Christophe; Fowler, Stephen; Klammers, Florian; Ekiciler, Aynur; Molitor, Birgit; Simon, Sandrine; Walter, Isabelle; McGinnis, Claudia; Walther, Johanna; Leonard, Brian; Triyatni, Miriam; Javanbakht, Hassan; Funk, Christoph; Schuler, Franz; Lavé, Thierry; Parrott, Neil J
2017-03-01
Early prediction of human clearance is often challenging, in particular for the growing number of low-clearance compounds. Long-term in vitro models have been developed which enable sophisticated hepatic drug disposition studies and improved clearance predictions. Here, the cell line HepG2, iPSC-derived hepatocytes (iCell®), the hepatic stem cell line HepaRG™, and human hepatocyte co-cultures (HμREL™ and HepatoPac®) were compared to primary hepatocyte suspension cultures with respect to their key metabolic activities. Similar metabolic activities were found for the long-term models HepaRG™, HμREL™, and HepatoPac® and the short-term suspension cultures when averaged across all 11 enzyme markers, although differences were seen in the activities of CYP2D6 and non-CYP enzymes. For iCell® and HepG2, the metabolic activity was more than tenfold lower. The micropatterned HepatoPac® model was further evaluated with respect to clearance prediction. To assess the in vitro parameters, pharmacokinetic modeling was applied. The determination of intrinsic clearance by nonlinear mixed-effects modeling in a long-term model significantly increased the confidence in the parameter estimation and extended the sensitive range towards 3% of liver blood flow, i.e., >10-fold lower as compared to suspension cultures. For in vitro to in vivo extrapolation, the well-stirred model was used. The micropatterned model gave rise to clearance prediction in man within a twofold error for the majority of low-clearance compounds. Further research is needed to understand whether transporter activity and drug metabolism by non-CYP enzymes, such as UGTs, SULTs, AO, and FMO, is comparable to the in vivo situation in these long-term culture models.
Iyer, C G; Languillon, J; Ramanujam, K; Tarabini-Castellani, G; De las Aguas, J T; Bechelli, L M; Uemura, K; Martinez Dominguez, V; Sundaresan, T
1971-01-01
The treatment of lepra reactions constitutes one of the most serious problems in leprosy. For this reason, the first reports in 1965 of the favourable results obtained with thalidomide aroused considerable interest and led WHO, in 1967, to carry out a trial with the co-operation of four centres. A short-term double-blind trial was designed to study the effect of thalidomide, in comparison with acetylsalicylic acid, in the treatment of acute lepra reactions in male lepromatous patients. Acetylsalicylic acid was used instead of a placebo because of its antipyretic and analgesic activity. Because of the severe adverse reactions that may be caused by thalidomide, mainly the teratogenic effects, only males were included in the trial.The results of this short-term study seem to confirm previous reports of the efficacy of thalidomide and indicate that acetylsalicylic acid also seems to be helpful in the management of certain symptoms of lepra reactions.
Ionescu, Tudor C.; Scherpen, Jacquelien M. A.
We study the notion of cross Gramians for nonlinear gradient systems, using the characterization in terms of prolongation and gradient extension associated to the system. The cross Gramian is given for the variational system associated to the original nonlinear gradient system. We obtain linearization results that correspond to the notion of a cross Gramian for symmetric linear systems. Furthermore, first steps towards relations with the singular value functions of the nonlinear Hankel operator are studied and yield promising results.
De Lucia, Marco; Kempka, Thomas; Kühn, Michael
2014-05-01
Fully-coupled reactive transport simulations involving multiphase hydrodynamics and chemical reactions in heterogeneous settings are extremely challenging from a computational point of view. This often leads to oversimplification of the investigated system: coarse spatial discretization, to keep the number of elements in the order of few thousands; simplified chemistry, disregarding many potentially important reactions. A novel approach for coupling non-reactive hydrodynamic simulations with the outcome of single batch geochemical simulations was therefore introduced to assess the potential long-term mineral trapping at the Ketzin pilot site for underground CO2 storage in Germany [1],[2]. The advantage of the coupling is the ability to use multi-million grid non-reactive hydrodynamics simulations on one side and few batch 0D geochemical simulations on the other, so that the complexity of both systems does not need to be reduced. This contribution shows the approach which was taken to validate this simplified coupling scheme. The procedure involved batch simulations of the reference geochemical model, then performing both non-reactive and fully coupled 1D and 3D reactive transport simulations and finally applying the simplified coupling scheme based on the non-reactive and geochemical batch model. The TOUGHREACT/ECO2N [3] simulator was adopted for the validation. The degree of refinement of the spatial grid and the complexity and velocity of the mineral reactions, along with a cut-off value for the minimum concentration of dissolved CO2 allowed to originate precipitates in the simplified approach were found out to be the governing parameters for the convergence of the two schemes. Systematic discrepancies between the approaches are not reducible, simply because there is no feedback between chemistry and hydrodynamics, and can reach 20 % - 30 % in unfavourable cases. However, even such discrepancy is completely acceptable, in our opinion, given the amount of
Ionescu, T. C.; Scherpen, J. M. A.; Korytowski, A; Malanowski, K; Mitkowski, W; Szymkat, M
2009-01-01
We study the notion of cross Gramians for nonlinear gradient systems, using the characterization in terms of prolongation and gradient extension associated to the system. The cross Gramian is given for the variational system associated to the original nonlinear gradient system. We obtain
Silvers, L J
2007-01-01
For more than a decade, the so-called shearing box model has been used to study the fundamental local dynamics of accretion discs. This approach has proved to be very useful because it allows high resolution and long term studies to be carried out, studies that would not be possible for a global disc. Localised disc studies have largely focused on examining the rate of enhanced transport of angular momentum, essentially a sum of the Reynolds and Maxwell stresses. The dominant radial-azimuthal component of this stress tensor is, in the classic Shakura-Sunayaev model, expressed as a constant alpha times the pressure. Previous studies have estimated alpha based on a modest number of orbital times. Here we use much longer baselines, and perform a cumulative average for alpha. Great care must be exercised when trying to extract numerical alpha values from simulations: dissipation scales, computational box aspect ratio, and even numerical algorithms all affect the result. This study suggests that estimating alpha b...
Watanabe, Saya; Aizawa, Junya; Shimoda, Manabu; Enomoto, Mitsuhiro; Nakamura, Tomomasa; Okawa, Atushi; Yagishita, Kazuyoshi
2016-01-01
[Purpose] Fatigue may be an important contributing factor to non-contact anterior cruciate ligament injuries in sports. The purpose of this study was to evaluate the effects of controlled lower limb fatigue, induced by a short-term, high-intensity exercise protocol, on the profile of the ground reaction force during landings from single-leg anterior drop-jumps. [Subjects and Methods] Twelve healthy males, 18 to 24 years old, performed single-leg anterior drop-jumps, from a 20 cm height, under two conditions, ‘fatigue’ and ‘non-fatigue’. Short-term fatigue was induced by high-intensity interval cycling on an ergometer. Effects of fatigue on peak vertical ground reaction force, time-to-peak of the vertical ground reaction force, and loading rate were evaluated by paired t-test. [Results] Fatigue shortened the time-to-peak duration of the vertical ground reaction force by 10% (non-fatigue, 44.0 ± 16.8 ms; fatigue, 39.6 ± 15.8 ms). Fatigue also yielded a 3.6% lowering in peak vertical ground reaction force and 9.4% increase in loading rate, although these effects were not significant. [Conclusion] The effects of fatigue in reducing time-to-peak of the vertical ground reaction force during single-leg anterior drop-jumps may increase the risk for non-contact anterior cruciate ligament injury in males. PMID:28174454
A hybrid AR-EMD-SVR model for the short-term prediction of nonlinear and non-stationary ship motion
Institute of Scientific and Technical Information of China (English)
Wen-yang DUAN; Li-min HUANG; Yang HAN; Ya-hui ZHANG; Shuo HUANG
2015-01-01
题目：用于非线性非平稳船舶运动极短期预报的一种复合自回归经验模态分解支持向量机回归模型 目的：基于支持向量机回归（SVR）模型在非线时间序列的预测能力及经验模态分解（EMD）方法在处理非线性非平稳性的优势，提出一种复合自回归经验模态分解支持向量机回归（AR-EMD-SVR）模型，提高非线性非平稳船舶运动极短期预报精度。 创新点：1.研究非线性非平稳船舶运动的极短期预报问题，提出一种复合的预报方法；2.基于不同层次的预报模型和模型试验数据，分析非线性非平稳性对极短期预报精度的影响。 方法：1.在SVR模型中引入基于自回归（AR）预报端点延拓的 EMD 方法，形成复合的 AR-EMD-SVR 预报模型；2.基于集装箱船模水池试验运动数据将 AR-EMD-SVR 模型与 AR、SVR 和EMD-AR 三种模型进行比较，分析非线性非平稳性对极短期预报的影响以及不同模型的预报性能。 结论：1. AR-EMD 方法能够有效的克服非平稳对极短期预报模型（AR和 SVR）在精度上所带来的不良影响；2.基于船模试验数据的预报结果表明：相较于 AR、SVR 和 EMD-AR 三种预报模型，基于 AR-EMD-SVR模型的非线性非平稳船舶运动极短期预报结果具有更高的精度。%Accurate and reliable short-term prediction of ship motions offers improvements in both safety and control quality in ship motion sensitive maritime operations. Inspired by the satisfactory nonlinear learning capability of a support vector re-gression (SVR) model and the strong non-stationary processing ability of empirical mode decomposition (EMD), this paper develops a hybrid autoregressive (AR)-EMD-SVR model for the short-term forecast of nonlinear and non-stationary ship motion. The proposed hybrid model is designed by coupling the SVR model with an AR-EMD technique, which employs an AR model in ends
Directory of Open Access Journals (Sweden)
S. Vaidyanathan
2014-11-01
Full Text Available This research work proposes a six-term novel 3-D jerk chaotic system with two exponential nonlinearities. This work also analyses system’s fundamental properties such as dissipativity, equilibria, Lyapunov exponents and Kaplan-Yorke dimension. The phase portraits of the jerk chaotic system simulated using MATLAB, depict the strange chaotic attractor of the system. For the parameter values and initial conditions chosen in this work, the Lyapunov exponents of the novel jerk chaotic system are obtained as L1 = 0.24519, L2 = 0 and L3 = −0.84571. Also, the Kaplan-Yorke dimension of the novel jerk chaotic system is obtained as DKY = 2.2899. Next, an adaptive backstepping controller is designed to stabilize the novel jerk chaotic system having two unknown parameters. Moreover, an adaptive backstepping controller is designed to achieve global chaos anti-synchronization of two identical novel jerk chaotic systems with two unknown system parameters. Finally, an electronic circuit realization of the novel jerk chaotic system is presented using SPICE to confirm the feasibility of the theoretical model.
Al-shyyab, A.; Kahraman, A.
2005-06-01
A non-linear time-varying dynamic model of a typical multi-mesh gear train is proposed in this study. The physical system includes three rigid shafts coupled by two gear pairs. The lumped parameter dynamic model includes the gear backlash in the form of clearance-type displacement functions and parametric variation of gear mesh stiffness values dictated by the gear contact ratios. The system is reduced to a two-degree-of-freedom definite model by using the relative gear mesh displacements as the coordinates. Dimensionless equations of motion are solved for the steady-state period-1 response by using a multi-term Harmonic Balance Method (HBM) in conjunction with discrete Fourier Transforms and a Parametric Continuation scheme. The accuracy of the HBM solutions is demonstrated by comparing them to direct numerical integration solutions. Floquet theory is applied to determine the stability of the steady-state harmonic balance solutions. An example gear train is used to investigate the influence of key system parameters including alternating mesh stiffness amplitudes, gear mesh damping, static torque transmitted, and the gear mesh frequency ratio.
Mortazavi, S M J; Rouintan, M S; Taeb, S; Dehghan, N; Ghaffarpanah, A A; Sadeghi, Z; Ghafouri, F
2012-06-01
The worldwide dramatic increase in mobile phone use has generated great concerns about the detrimental effects of microwave radiations emitted by these communication devices. Reaction time plays a critical role in performing tasks necessary to avoid hazards. As far as we know, this study is the first survey that reports decreased reaction time after exposure to electromagnetic fields generated by a high specific absorption rate mobile phone. It is also the first study in which previous history of mobile phone use is taken into account. The aim of this study was to assess both the acute and chronic effects of electromagnetic fields emitted by mobile phones on reaction time in university students. Visual reaction time (VRT) of young university students was recorded with a simple blind computer-assisted-VRT test, before and after a 10 min real/sham exposure to electromagnetic fields of mobile phones. Participants were 160 right-handed university students aged 18-31. To assess the effect of chronic exposures, the reaction time in sham-exposed phases were compared among low level, moderate and frequent users of mobile phones. The mean ± SD reaction time after real exposure and sham exposure were 286.78 ± 31.35 ms and 295.86 ± 32.17 ms (P students did not significantly alter the reaction time either in talk or in standby mode. The reaction time either in talk or in standby mode was shorter in male students. The students' VRT was significantly affected by exposure to electromagnetic fields emitted by a mobile phone. It can be concluded that these exposures cause decreased reaction time, which may lead to a better response to different hazards. In this light, this phenomenon might decrease the chances of human errors and fatal accidents.
DEFF Research Database (Denmark)
Jeong, Cheol-Ho
2011-01-01
errors of less than 10% if the thickness exceeds 120 mm for a flow resistivity of 5000 Nm-4s. As the flow resistivity doubles, a decrease in the required thickness by 25 mm is observed to achieve the same amount of error. For an absorber backed by an air gap, the thickness ratio between the material...... and air cavity is important, since the thicker the cavity, the more extendedly reacting the absorber. If the absorber thickness is approximately 40% of the cavity depth, the local reaction models give errors below 10% even for a low flow resistivity case....... resistivity and the absorber thickness on the difference between the two surface reaction models are examined and discussed. For a porous absorber backed by a rigid surface, the assumption of local reaction always underestimates the random incidence absorption coefficient and the local reaction models give...
Phillipson, Rebecca; Boyd, Patricia T.; Smale, Alan P.
2016-04-01
The bright low-mass X-ray binary 4U1705-44 exhibits long-term semi-periodic variability with a timescale of several hundred days. The All-Sky Monitor (ASM) aboard the Rossi X-ray Timing Explorer (RXTE) and the Japanese X-ray All-Sky Monitor (MAXI) aboard the International Space Station together have continuously observed the source from December 1995 through the present. The combined ASM-MAXI data provides a continuous time series over fifty times the length of the timescale of interest. The phase space embedding of the flux versus its first derivative shows a strong resemblance to a double-welled nonlinear oscillator. When comparing our time series against well-known nonlinear oscillators, we find that 4U1705-44 exhibits behavior akin to the Duffing oscillator. Topological analysis can help us identify ‘fingerprints’ in the phase space of a system unique to its equations of motion. If such ‘fingerprints’ are the same between two systems, then their equations of motion must be closely related. We therefore found a range of parameters for which the Duffing oscillator closely follows the time evolution of 4U1705-44 and from this range chose 6 different numerical Duffing time series. We can extract low-period, unstable periodic orbits from both the 4U1705-44 and numerical Duffing time series and compare their topological information in phase space, such as their relative rotation rates. We argue that the associated period-1 orbit in 4U1705-44 has a period between 130 and 170 days. The driving periods of our 6 numerical time series correspond to 140 to 175 days. Assigning a logical sequence name to each orbit, the relative rotation rates can be compiled into a unique ‘intertwining’ matrix. The numerical Duffing time series and the 4U1705-44 intertwining matrices are identical, which provides strong evidence that they share the same underlying template. The implications of this equivalence suggests that we can look to the Duffing equation to describe the X
Institute of Scientific and Technical Information of China (English)
莫嘉琪
2006-01-01
A class of nonlinear nonlocal singularly perturbed Robin initial boundary value problems for reaction diffusion equations with boundary perturbation is considered. Under suitable conditions, firstly, the outer solution of the original problem is obtained; secondly, by using the stretched variable, the composing expansion method and the expanding theory of power series, the initial layer is constructed; and finally,by using the theory of differential inequalities the asymptotic behavior of solutions for initial boundary value problems is studied, and including some relational inequalities the existence and uniqueness of solutions for the original problem and the uniformly valid asymptotic estimation are discussed.
Energy Technology Data Exchange (ETDEWEB)
Garcia Velarde, M.
1977-07-01
Thermo convective instabilities in horizontal fluid layers are discussed with emphasis on the Rayleigh-Bernard model problem. Steady solutions and time-dependent phenomena (relaxation oscillations and transition to turbulence) are studied within the nonlinear Boussinesq-Oberbeck approximation. Homogeneous steady solutions, limit cycles, and inhomogeneous (ordered) spatial structures are also studied in simple reaction-diffusion systems. Lastly, the non-periodic attractor that appears at large Rayleigh numbers in the truncated Boussinesq-Oberbeck model of Lorenz, is constructed, and a discussion of turbulent behavior is given. (Author) 105 refs.
Jensen, L; van Duijnen, PT
2005-01-01
We have calculated the frequency-dependent refractive index and the third-order nonlinear susceptibility for C-60 in the condensed phase, which is related to third-harmonic generation (THG) and degenerate four-wave mixing (DFWM) experiments. This was done using the recently developed discrete solven
Triple click reaction strategy for macromolecular diversity.
Tunca, Umit
2013-01-11
This Feature Article focuses on the rapidly emerging concept of the "triple click reactions" towards the design and synthesis of macromolecules with well-defined topology and chemical composition, and also precise molecular weight and narrow molecular weight distribution. The term "triple click reaction" used in this feature article is based on the utilization of three chemically and mechanistically different click reactions for polymer-polymer conjugation and post-modification of the polymers. Three sequential click reactions of which two are identical should not be considered to be triple click reactions. The triple click reaction strategy for polymer conjugation and post-modification of polymers is classified in this article based on the resultant architectures: linear and non-linear structures. Copyright © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Explicit Traveling Wave Solutions to Nonlinear Evolution Equations
Institute of Scientific and Technical Information of China (English)
Linghai ZHANG
2011-01-01
First of all,some technical tools are developed. Then the author studies explicit traveling wave solutions to nonlinear dispersive wave equations,nonlinear dissipative dispersive wave equations,nonlinear convection equations,nonlinear reaction diffusion equations and nonlinear hyperbolic equations,respectively.
denDunnen, WFA; Robinson, PH; vanWessel, R; Pennings, AJ; vanLeeuwen, MBM; Schakenraad, JM
1997-01-01
The aim of this study was to evaluate the degradation and foreign-body reaction of poly(DL-lactide-epsilon-caprolactone) (PLA(85)CL(50)) bars. This specific biomaterial is used for the construction of nerve guides, which can be used in the reconstruction of short nerve gaps. Subcutaneously implanted
Stamova, Ivanka; Stamov, Gani
2017-09-08
In this paper, we propose a fractional-order neural network system with time-varying delays and reaction-diffusion terms. We first develop a new Mittag-Leffler synchronization strategy for the controlled nodes via impulsive controllers. Using the fractional Lyapunov method sufficient conditions are given. We also study the global Mittag-Leffler synchronization of two identical fractional impulsive reaction-diffusion neural networks using linear controllers, which was an open problem even for integer-order models. Since the Mittag-Leffler stability notion is a generalization of the exponential stability concept for fractional-order systems, our results extend and improve the exponential impulsive control theory of neural network system with time-varying delays and reaction-diffusion terms to the fractional-order case. The fractional-order derivatives allow us to model the long-term memory in the neural networks, and thus the present research provides with a conceptually straightforward mathematical representation of rather complex processes. Illustrative examples are presented to show the validity of the obtained results. We show that by means of appropriate impulsive controllers we can realize the stability goal and to control the qualitative behavior of the states. An image encryption scheme is extended using fractional derivatives. Copyright © 2017 Elsevier Ltd. All rights reserved.
Zweig, George
2016-05-01
An earlier paper characterizing the linear mechanical response of the organ of Corti [J. Acoust. Soc. Am. 138, 1102-1121 (2015)] is extended to the nonlinear domain. Assuming the existence of nonlinear oscillators nonlocally coupled through the pressure they help create, the oscillator equations are derived and examined when the stimuli are modulated tones and clicks. The nonlinearities are constrained by the requirements of oscillator stability and the invariance of zero crossings in the click response to changes in click amplitude. The nonlinear oscillator equations for tones are solved in terms of the fluid pressure that drives them, and its time derivative, presumably a proxy for forces created by outer hair cells. The pressure equation is reduced to quadrature, the integrand depending on the oscillators' responses. The resulting nonlocally coupled nonlinear equations for the pressure, and oscillator amplitudes and phases, are solved numerically in terms of the fluid pressure at the stapes. Methods for determining the nonlinear damping directly from measurements are described. Once the oscillators have been characterized from their tone and click responses, the mechanical response of the cochlea to natural sounds may be computed numerically. Signal processing inspired by cochlear mechanics opens up a new area of nonlocal nonlinear time-frequency analysis.
DEFF Research Database (Denmark)
Mosekilde, Erik
Through a significant number of detailed and realistic examples this book illustrates how the insights gained over the past couple of decades in the fields of nonlinear dynamics and chaos theory can be applied in practice. Aomng the topics considered are microbiological reaction systems, ecological...
Bloembergen, Nicolaas
1996-01-01
Nicolaas Bloembergen, recipient of the Nobel Prize for Physics (1981), wrote Nonlinear Optics in 1964, when the field of nonlinear optics was only three years old. The available literature has since grown by at least three orders of magnitude.The vitality of Nonlinear Optics is evident from the still-growing number of scientists and engineers engaged in the study of new nonlinear phenomena and in the development of new nonlinear devices in the field of opto-electronics. This monograph should be helpful in providing a historical introduction and a general background of basic ideas both for expe
Energy Technology Data Exchange (ETDEWEB)
Geniet, F; Leon, J [Physique Mathematique et Theorique, CNRS-UMR 5825, 34095 Montpellier (France)
2003-05-07
A nonlinear system possessing a natural forbidden band gap can transmit energy of a signal with a frequency in the gap, as recently shown for a nonlinear chain of coupled pendulums (Geniet and Leon 2002 Phys. Rev. Lett. 89 134102). This process of nonlinear supratransmission, occurring at a threshold that is exactly predictable in many cases, is shown to have a simple experimental realization with a mechanical chain of pendulums coupled by a coil spring. It is then analysed in more detail. First we go to different (nonintegrable) systems which do sustain nonlinear supratransmission. Then a Josephson transmission line (a one-dimensional array of short Josephson junctions coupled through superconducting wires) is shown to also sustain nonlinear supratransmission, though being related to a different class of boundary conditions, and despite the presence of damping, finiteness, and discreteness. Finally, the mechanism at the origin of nonlinear supratransmission is found to be a nonlinear instability, and this is briefly discussed here.
Directory of Open Access Journals (Sweden)
Salem Abdelmalek
2014-11-01
Full Text Available In this article we construct the invariant regions for m-component reaction-diffusion systems with a tridiagonal symmetric Toeplitz matrix of diffusion coefficients and with nonhomogeneous boundary conditions. We establish the existence of global solutions, and use Lyapunov functional methods. The nonlinear reaction term is assumed to be of polynomial growth.
Directory of Open Access Journals (Sweden)
G. C. Shit
2014-01-01
Full Text Available An analysis has been made to investigate the effects of thermal radiation on the magnetohydrodynamic (MHD flow and heat transfer over an inclined non-linear stretching sheet. The surface velocity of the stretching sheet and the transverse magnetic field are assumed to vary as a power function of the distance from the origin. The effect of internal heat generation/absorption is taken into account. The fluid viscosity is assumed to vary as an inverse linear function of temperature. A generalized similarity transformation is used to reduce the governing partial differential equations to a system of non-linear coupled ordinary differential equations, and is solved numerically by using a finite difference scheme. The numerical results concerned with the velocity, temperature and concentration distributions as well as the skin-friction coefficient and the Nusselt number for various values of the dimensionless parameters of interest are obtained. Some important findings reported in this paper reveal that the effect of thermal radiation and heat generation/absorption have significant role in controlling the rate of heat transfer in the boundary layer region.
Ullah, Imran; Bhattacharyya, Krishnendu; Shafie, Sharidan; Khan, Ilyas
2016-01-01
Numerical results are presented for the effect of first order chemical reaction and thermal radiation on mixed convection flow of Casson fluid in the presence of magnetic field. The flow is generated due to unsteady nonlinearly stretching sheet placed inside a porous medium. Convective conditions on wall temperature and wall concentration are also employed in the investigation. The governing partial differential equations are converted to ordinary differential equations using suitable transformations and then solved numerically via Keller-box method. It is noticed that fluid velocity rises with increase in radiation parameter in the case of assisting flow and is opposite in the case of opposing fluid while radiation parameter has no effect on fluid velocity in the forced convection. It is also seen that fluid velocity and concentration enhances in the case of generative chemical reaction whereas both profiles reduces in the case of destructive chemical reaction. Further, increase in local unsteadiness parameter reduces fluid velocity, temperature and concentration. Over all the effects of physical parameters on fluid velocity, temperature and concentration distribution as well as on the wall shear stress, heat and mass transfer rates are discussed in detail.
Li, Zongxiao; Yuan, Chunlan
2011-08-01
With the help of the kinetic parameters (the rate constant ( k in k p) and the apparent activation energy ( E in E p) of the oscillatory induction period and oscillation period) of the oscillating reaction using thirteen amino acids, leucine (Leu), threonine (Thr), arginine (Arg), lysine (Lys), histidine (His), alanine (Ala), glutamine (Glu), glycine (Gly), methionine (Met), cystine (Cys), tryptophan (Trp), serine (Ser) and tyrosine (Tyr), as organic substrates in amino acid-BrO{3/-}-Mn2+-H2SO4-acetone system, then based on the Oregonator model and the thermodynamics theory on irreversible process, the thermodynamic function (Δ H in, Δ G in, Δ S in and Δ H p, Δ G p, Δ S p) of these oscillating system are studied. The results indicate the entropy Δ S of these oscillating reaction are negative, thereby it is proved that the oscillating reaction is a noequilibrium system with dissipation structure in agreement with the character of the oscillating reaction from disorder to order in irreversible thermodynamics. These are satisfactorily to explain the experimental phenomena.
Dichromatic nonlinear eigenmodes in slab waveguide with chi(2) nonlinearity.
Darmanyan, S A; Nevière, M
2001-03-01
The existence of purely nonlinear eigenmodes in a waveguiding structure composed of a slab with quadratic nonlinearity surrounded by (non)linear claddings is reported. Modes having bright and dark solitonlike shapes and consisting of two mutually locked harmonics are identified. Asymmetrical modes are shown to exist in symmetrical environments. Constraints for the existence of the modes are derived in terms of parameters of guiding structure materials.
Valika, Aziz K; Jain, Dhanpat; Jaffe, Phillip E; Moeckel, Gilbert; Brewster, Ursula C
2016-01-01
A 63-year-old man with HIV (human immunodeficiency virus) infection and end-stage renal disease, treated with lanthanum carbonate phosphate binder for 4 years, presented with anemia and an upper gastrointestinal bleed. Upper endoscopy revealed a nodular hyperplastic epithelium, with an endoscopic ultrasound confirming hyperechoic material within the nodules. Light microscopy showed collections of histiocytes and multinucleated giant cells containing brown granular cytoplasmic material and extracellular crystalline material, a finding confirmed by electron microscopy. Similar pathologic findings associated with lanthanum exposure have been described recently. In our patient, lanthanum carbonate treatment was withdrawn and gastrointestinal bleeding has since ceased. The patient was exposed to a high amount of lanthanum over a long period, which may explain his adverse reaction. However, other contributing factors, such as competing medications or comorbid conditions, also may have increased his sensitivity to the drug.
[Energy reactions in the skeletal muscles of rats after short-term space flight on Kosmos-1514].
Mailian, E S; Chabdarova, R N; Korzun, E I
1988-01-01
Ten hours after the 5-day space flight on Cosmos-1514 rats were examined for oxidative phosphorylation in mitochondria isolated from the posterior femoral muscles as well as for Krebs cycle enzymes and glycolysis in the mitochondrial and cytoplasmic fractions of the muscles. The mitochondrial respiration rate in various metabolic states was similar in flight rats and vivarium controls. After flight calculated parameters of energy efficacy of respiration as well as activity of malate dehydrogenase, isocitrate dehydrogenase and total lactate dehydrogenase remained unchanged. Unlike the flight rats, the synchronous controls showed signs of the stress-reaction: uncoupling of oxidative phosphorylation and oxalacetate inhibition of succinate dehydrogenase. Comparison of these findings with those from prolonged space flights indicates that inhibition of oxidative metabolism and glycolysis in mixed muscles which was demonstrated in the 20-day space flight does not develop immediately after launch but occurs within the time interval between mission days 6 and 18.
Nonlinear Multiantenna Detection Methods
Directory of Open Access Journals (Sweden)
Chen Sheng
2004-01-01
Full Text Available A nonlinear detection technique designed for multiple-antenna assisted receivers employed in space-division multiple-access systems is investigated. We derive the optimal solution of the nonlinear spatial-processing assisted receiver for binary phase shift keying signalling, which we refer to as the Bayesian detector. It is shown that this optimal Bayesian receiver significantly outperforms the standard linear beamforming assisted receiver in terms of a reduced bit error rate, at the expense of an increased complexity, while the achievable system capacity is substantially enhanced with the advent of employing nonlinear detection. Specifically, when the spatial separation expressed in terms of the angle of arrival between the desired and interfering signals is below a certain threshold, a linear beamformer would fail to separate them, while a nonlinear detection assisted receiver is still capable of performing adequately. The adaptive implementation of the optimal Bayesian detector can be realized using a radial basis function network. Two techniques are presented for constructing block-data-based adaptive nonlinear multiple-antenna assisted receivers. One of them is based on the relevance vector machine invoked for classification, while the other on the orthogonal forward selection procedure combined with the Fisher ratio class-separability measure. A recursive sample-by-sample adaptation procedure is also proposed for training nonlinear detectors based on an amalgam of enhanced -means clustering techniques and the recursive least squares algorithm.
Kawai, Yusuke; Yamada, Yoshio
2016-07-01
This paper deals with a free boundary problem for diffusion equation with a certain class of bistable nonlinearity which allows two positive stable equilibrium states as an ODE model. This problem models the invasion of a biological species and the free boundary represents the spreading front of its habitat. Our main interest is to study large-time behaviors of solutions for the free boundary problem. We will completely classify asymptotic behaviors of solutions and, in particular, observe two different types of spreading phenomena corresponding to two positive stable equilibrium states. Moreover, it will be proved that, if the free boundary expands to infinity, an asymptotic speed of the moving free boundary for large time can be uniquely determined from the related semi-wave problem.
2016-07-01
Advanced Research Projects Agency (DARPA) Dynamics-Enabled Frequency Sources (DEFYS) program is focused on the convergence of nonlinear dynamics and...Early work in this program has shown that nonlinear dynamics can provide performance advantages. However, the pathway from initial results to...dependent nonlinear stiffness observed in these devices. This work is ongoing, and will continue through the final period of this program . Reference 9
Gan, Qintao
2017-01-01
In this paper, the exponential synchronization problem of generalized reaction-diffusion neural networks with mixed time-varying delays is investigated concerning Dirichlet boundary conditions in terms of p-norm. Under the framework of the Lyapunov stability method, stochastic theory, and mathematical analysis, some novel synchronization criteria are derived, and an aperiodically intermittent control strategy is proposed simultaneously. Moreover, the effects of diffusion coefficients, diffusion space, and stochastic perturbations on the synchronization process are explicitly expressed under the obtained conditions. Finally, some numerical simulations are performed to illustrate the feasibility of the proposed control strategy and show different synchronization dynamics under a periodically/aperiodically intermittent control.
Leburn, Christopher; Reid, Derryck
2013-01-01
The field of ultrafast nonlinear optics is broad and multidisciplinary, and encompasses areas concerned with both the generation and measurement of ultrashort pulses of light, as well as those concerned with the applications of such pulses. Ultrashort pulses are extreme events – both in terms of their durations, and also the high peak powers which their short durations can facilitate. These extreme properties make them powerful experiment tools. On one hand, their ultrashort durations facilitate the probing and manipulation of matter on incredibly short timescales. On the other, their ultrashort durations can facilitate high peak powers which can drive highly nonlinear light-matter interaction processes. Ultrafast Nonlinear Optics covers a complete range of topics, both applied and fundamental in nature, within the area of ultrafast nonlinear optics. Chapters 1 to 4 are concerned with the generation and measurement of ultrashort pulses. Chapters 5 to 7 are concerned with fundamental applications of ultrasho...
Nonlinear Stokes Mueller Polarimetry
Samim, Masood; Barzda, Virginijus
2015-01-01
The Stokes Mueller polarimetry is generalized to include nonlinear optical processes such as second- and third-harmonic generation, sum- and difference-frequency generations. The overall algebraic form of the polarimetry is preserved, where the incoming and outgoing radiations are represented by column vectors and the intervening medium is represented by a matrix. Expressions for the generalized nonlinear Stokes vector and the Mueller matrix are provided in terms of coherency and correlation matrices, expanded by higher-dimensional analogues of Pauli matrices. In all cases, the outgoing radiation is represented by the conventional $4\\times 1$ Stokes vector, while dimensions of the incoming radiation Stokes vector and Mueller matrix depend on the order of the process being examined. In addition, relation between nonlinear susceptibilities and the measured Mueller matrices are explicitly provided. Finally, the approach of combining linear and nonlinear optical elements is discussed within the context of polarim...
Nayfeh, Ali Hasan
1995-01-01
Nonlinear Oscillations is a self-contained and thorough treatment of the vigorous research that has occurred in nonlinear mechanics since 1970. The book begins with fundamental concepts and techniques of analysis and progresses through recent developments and provides an overview that abstracts and introduces main nonlinear phenomena. It treats systems having a single degree of freedom, introducing basic concepts and analytical methods, and extends concepts and methods to systems having degrees of freedom. Most of this material cannot be found in any other text. Nonlinear Oscillations uses sim
Yoshida, Zensho
2010-01-01
This book gives a general, basic understanding of the mathematical structure "nonlinearity" that lies in the depths of complex systems. Analyzing the heterogeneity that the prefix "non" represents with respect to notions such as the linear space, integrability and scale hierarchy, "nonlinear science" is explained as a challenge of deconstruction of the modern sciences. This book is not a technical guide to teach mathematical tools of nonlinear analysis, nor a zoology of so-called nonlinear phenomena. By critically analyzing the structure of linear theories, and cl
Nanda, Sudarsan
2013-01-01
"Nonlinear analysis" presents recent developments in calculus in Banach space, convex sets, convex functions, best approximation, fixed point theorems, nonlinear operators, variational inequality, complementary problem and semi-inner-product spaces. Nonlinear Analysis has become important and useful in the present days because many real world problems are nonlinear, nonconvex and nonsmooth in nature. Although basic concepts have been presented here but many results presented have not appeared in any book till now. The book could be used as a text for graduate students and also it will be useful for researchers working in this field.
Directory of Open Access Journals (Sweden)
Carolyn Granier-Deferre
Full Text Available BACKGROUND: Human hearing develops progressively during the last trimester of gestation. Near-term fetuses can discriminate acoustic features, such as frequencies and spectra, and process complex auditory streams. Fetal and neonatal studies show that they can remember frequently recurring sounds. However, existing data can only show retention intervals up to several days after birth. METHODOLOGY/PRINCIPAL FINDINGS: Here we show that auditory memories can last at least six weeks. Experimental fetuses were given precisely controlled exposure to a descending piano melody twice daily during the 35(th, 36(th, and 37(th weeks of gestation. Six weeks later we assessed the cardiac responses of 25 exposed infants and 25 naive control infants, while in quiet sleep, to the descending melody and to an ascending control piano melody. The melodies had precisely inverse contours, but similar spectra, identical duration, tempo and rhythm, thus, almost identical amplitude envelopes. All infants displayed a significant heart rate change. In exposed infants, the descending melody evoked a cardiac deceleration that was twice larger than the decelerations elicited by the ascending melody and by both melodies in control infants. CONCLUSIONS/SIGNIFICANCE: Thus, 3-weeks of prenatal exposure to a specific melodic contour affects infants 'auditory processing' or perception, i.e., impacts the autonomic nervous system at least six weeks later, when infants are 1-month old. Our results extend the retention interval over which a prenatally acquired memory of a specific sound stream can be observed from 3-4 days to six weeks. The long-term memory for the descending melody is interpreted in terms of enduring neurophysiological tuning and its significance for the developmental psychobiology of attention and perception, including early speech perception, is discussed.
Institute of Scientific and Technical Information of China (English)
吴一凡
2011-01-01
In this paper, we propose a differential geometric framework for nonlinear models with Bayes conditions. The framework may be regarded as an extension of that presented by Bates & Watts for nonlinear regression models. On this basis,we use this geometric framework to discuss about the confidence regions for parameter and parameter subset in terms of curvature.%给出了Bayes条件下非线性模型的参数估计,建立了该模型的几何结构,推广了Bates&Wates关于非线性回归模型的几何框架,在此基础上,用几何方法探讨了关于参数与子集参数置信域的曲率表示.
Directory of Open Access Journals (Sweden)
Márcia Cristina Aquino Teixeira
2011-03-01
Full Text Available Domestic dogs are considered to be the main reservoirs of zoonotic visceral leishmaniasis. In this work, we evaluated a protocol to induce Leishmania infantum/Leishmania chagasi-specific cellular and humoral immune responses in dogs, which consisted of two injections of Leishmania promastigote lysate followed by a subcutaneous inoculation of viable promastigotes. The primary objective was to establish a canine experimental model to provide positive controls for testing immune responses to Leishmania in laboratory conditions. After inoculation of viable promastigotes, specific proliferative responses of peripheral blood mononuclear cells (PBMCs to either Leishmania lysate or recombinant proteins, the in vitro production of interferon-γ by antigen-stimulated PBMCs and a significant increase in circulating levels of anti-Leishmania antibodies were observed. The immunized dogs also displayed positive delayed-type hypersensitivity reactions to Leishmania crude antigens and to purified recombinant proteins. An important finding that supports the suitability of the dogs as positive controls is that they remained healthy for the entire observation period, i.e., more than seven years after infection. Following the Leishmania antigen lysate injections, the infection of dogs by the subcutaneous route appears to induce a sustained cellular immune response, leading to an asymptomatic infection. This provides a useful model for both the selection of immunogenic Leishmania antigens and for immunobiological studies on their possible immunoprotective activities.
Chaos in the Belousov-Zhabotinsky reaction
Field, Richard J.
The dynamics of reacting chemical systems is governed by typically polynomial differential equations that may contain nonlinear terms and/or embedded feedback loops. Thus the dynamics of such systems may exhibit features associated with nonlinear dynamical systems, including (among others): temporal oscillations, excitability, multistability, reaction-diffusion-driven formation of spatial patterns, and deterministic chaos. These behaviors are exhibited in the concentrations of intermediate chemical species. Bifurcations occur between particular dynamic behaviors as system parameters are varied. The governing differential equations of reacting chemical systems have as variables the concentrations of all chemical species involved, as well as controllable parameters, including temperature, the initial concentrations of all chemical species, and fixed reaction-rate constants. A discussion is presented of the kinetics of chemical reactions as well as some thermodynamic considerations important to the appearance of temporal oscillations and other nonlinear dynamic behaviors, e.g., deterministic chaos. The behavior, chemical details, and mechanism of the oscillatory Belousov-Zhabotinsky Reaction (BZR) are described. Furthermore, experimental and mathematical evidence is presented that the BZR does indeed exhibit deterministic chaos when run in a flow reactor. The origin of this chaos seems to be in toroidal dynamics in which flow-driven oscillations in the control species bromomalonic acid couple with the BZR limit cycle...
Puķīte, Jānis; Wagner, Thomas
2016-05-01
We address the application of differential optical absorption spectroscopy (DOAS) of scattered light observations in the presence of strong absorbers (in particular ozone), for which the absorption optical depth is a non-linear function of the trace gas concentration. This is the case because Beer-Lambert law generally does not hold for scattered light measurements due to many light paths contributing to the measurement. While in many cases linear approximation can be made, for scenarios with strong absorptions non-linear effects cannot always be neglected. This is especially the case for observation geometries, for which the light contributing to the measurement is crossing the atmosphere under spatially well-separated paths differing strongly in length and location, like in limb geometry. In these cases, often full retrieval algorithms are applied to address the non-linearities, requiring iterative forward modelling of absorption spectra involving time-consuming wavelength-by-wavelength radiative transfer modelling. In this study, we propose to describe the non-linear effects by additional sensitivity parameters that can be used e.g. to build up a lookup table. Together with widely used box air mass factors (effective light paths) describing the linear response to the increase in the trace gas amount, the higher-order sensitivity parameters eliminate the need for repeating the radiative transfer modelling when modifying the absorption scenario even in the presence of a strong absorption background. While the higher-order absorption structures can be described as separate fit parameters in the spectral analysis (so-called DOAS fit), in practice their quantitative evaluation requires good measurement quality (typically better than that available from current measurements). Therefore, we introduce an iterative retrieval algorithm correcting for the higher-order absorption structures not yet considered in the DOAS fit as well as the absorption dependence on
J. Puķīte; T. Wagner
2016-01-01
We address the application of differential optical absorption spectroscopy (DOAS) of scattered light observations in the presence of strong absorbers (in particular ozone), for which the absorption optical depth is a non-linear function of the trace gas concentration. This is the case because Beer–Lambert law generally does not hold for scattered light measurements due to many light paths contributing to the measurement. While in many cases linear approximation can be made, ...
Leyva, J. Francisco; Malaga, Carlos; Plaza, Ramon G.
2013-01-01
This paper introduces a reaction-diffusion-chemotaxis model for bacterial aggregation patterns on the surface of thin agar plates. It is based on the non-linear degenerate cross diffusion model proposed by Kawasaki et al. (J. of Theor. Biol. 188(2) 1997) and it includes a suitable nutrient chemotactic term compatible with such type of diffusion. High resolution numerical simulations using Graphic Processing Units (GPUs) of the new model are presented, showing that the chemotactic term enhance...
BRST charge for nonlinear algebras
Buchbinder, I L
2007-01-01
We study the construction of the classical nilpotent canonical BRST charge for the nonlinear gauge algebras where a commutator (in terms of Poisson brackets) of the constraints is a finite order polynomial of the constraints.
Zhu, Hong-Ming; Pen, Ue-Li; Chen, Xuelei; Yu, Hao-Ran
2016-01-01
We present a direct approach to non-parametrically reconstruct the linear density field from an observed non-linear map. We solve for the unique displacement potential consistent with the non-linear density and positive definite coordinate transformation using a multigrid algorithm. We show that we recover the linear initial conditions up to $k\\sim 1\\ h/\\mathrm{Mpc}$ with minimal computational cost. This reconstruction approach generalizes the linear displacement theory to fully non-linear fields, potentially substantially expanding the BAO and RSD information content of dense large scale structure surveys, including for example SDSS main sample and 21cm intensity mapping.
Boyd, Robert W
2013-01-01
Nonlinear Optics is an advanced textbook for courses dealing with nonlinear optics, quantum electronics, laser physics, contemporary and quantum optics, and electrooptics. Its pedagogical emphasis is on fundamentals rather than particular, transitory applications. As a result, this textbook will have lasting appeal to a wide audience of electrical engineering, physics, and optics students, as well as those in related fields such as materials science and chemistry.Key Features* The origin of optical nonlinearities, including dependence on the polarization of light* A detailed treatment of the q
Nonlinear scattering in plasmonic nanostructures
Chu, Shi-Wei
2016-09-01
Nonlinear phenomena provide novel light manipulation capabilities and innovative applications. Recently, we discovered nonlinear saturation on single-particle scattering of gold nanospheres by continuous-wave laser excitation and innovatively applied to improve microscopic resolution down to λ/8. However, the nonlinearity was limited to the green-orange plasmonic band of gold nanosphere, and the underlying mechanism has not yet been fully understood. In this work, we demonstrated that nonlinear scattering exists for various material/geometry combinations, thus expanding the applicable wavelength range. For near-infrared, gold nanorod is used, while for blue-violet, silver nanospheres are adopted. In terms of mechanism, the nonlinearity may originate from interband/intraband absorption, hot electron, or hot lattice, which are spectrally mixed in the case of gold nanosphere. For gold nanorod and silver nanosphere, nonlinear scattering occurs at plasmonic resonances, which are spectrally far from interband/intraband absorptions, so they are excluded. We found that the nonlinear index is much larger than possible contributions from hot electrons in literature. Therefore, we conclude that hot lattice is the major mechanism. In addition, we propose that similar to z-scan, which is the standard method to characterize nonlinearity of a thin sample, laser scanning microscopy should be adopted as the standard method to characterize nonlinearity from a nanostructure. Our work not only provides the physical mechanism of the nonlinear scattering, but also paves the way toward multi-color superresolution imaging based on non-bleaching plasmonic scattering.
Studies of Nonlinear Problems. I
Fermi, E.; Pasta, J.; Ulam, S.
1955-05-01
A one-dimensional dynamical system of 64 particles with forces between neighbors containing nonlinear terms has been studied on the Los Alamos computer MANIAC I. The nonlinear terms considered are quadratic, cubic, and broken linear types. The results are analyzed into Fourier components and plotted as a function of time. The results show very little, if any, tendency toward equipartition of energy among the degrees of freedom.
Nonlinear parametric instability of wind turbine wings
DEFF Research Database (Denmark)
Larsen, Jesper Winther; Nielsen, Søren R.K.
2006-01-01
Nonlinear rotor dynamic is characterized by parametric excitation of both linear and nonlinear terms caused by centrifugal and Coriolis forces when formulated in a moving frame of reference. Assuming harmonically varying support point motions from the tower, the nonlinear parametric instability...
Nonlinear parametric instability of wind turbine wings
DEFF Research Database (Denmark)
Larsen, Jesper Winther; Nielsen, Søren R.K.
2006-01-01
Nonlinear rotor dynamic is characterized by parametric excitation of both linear and nonlinear terms caused by centrifugal and Coriolis forces when formulated in a moving frame of reference. Assuming harmonically varying support point motions from the tower, the nonlinear parametric instability o...
UV Nano-Lights: Nonlinear Quantum Dot-Plasmon Coupling
2014-08-01
method is also applicable to bare nanoparticles in polar solvents. 15. SUBJECT TERMS Quantum Dots, Nonlinear Optical Materials , Energy...TERMS Quantum Dots, Nonlinear Optical Materials , Energy Conservation, Up-conversion 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT
Energy Technology Data Exchange (ETDEWEB)
Belmonte-Beitia, Juan [Departamento de Matematicas, E. T. S. de Ingenieros Industriales and Instituto de Matematica Aplicada a la Ciencia y la IngenierIa (IMACI), E. T. S. I. Industriales, Avda. Camilo Jose Cela, s/n Universidad de Castilla-La Mancha 13071 Ciudad Real (Spain)
2009-01-23
We introduce a model of a Bose-Einstein condensate based on the one-dimensional nonlinear Schroedinger equation, in which the nonlinear term depends on the domain. The nonlinear term changes a cubic term into a quintic term, according to the domain considered. We study the existence, stability and bifurcation of solutions, and use the qualitative theory of dynamical systems to study certain properties of such solutions.
Ruszczynski, Andrzej
2011-01-01
Optimization is one of the most important areas of modern applied mathematics, with applications in fields from engineering and economics to finance, statistics, management science, and medicine. While many books have addressed its various aspects, Nonlinear Optimization is the first comprehensive treatment that will allow graduate students and researchers to understand its modern ideas, principles, and methods within a reasonable time, but without sacrificing mathematical precision. Andrzej Ruszczynski, a leading expert in the optimization of nonlinear stochastic systems, integrates t
Størseth, Fred
2006-12-01
The objective was to identify focus areas for possible reduction of job insecurity and its outcomes. A model was specified and tested as a prediction model for health and safety. First, a parsimonious model was specified. The model consisted of perceived job insecurity (as a stressor), organizational factors (information quality, leadership style, work task administration), and short-term stress reactions (job dissatisfaction, reduced work motivation). Second, the model was tested as a prediction model in three separate path analyses, in order to examine the model's contribution in explaining (1) physical health complaints, (2) mental health complaints, and (3) risk taking behavior. A quota sample of Norwegian employees (N= 1,002) was obtained by means of a self-completion questionnaire survey. The results of the structural equation modeling (path analyses) supported the hypothesized model. Mental health complaints and employee risk taking behavior were significantly predicted (not physical health complaints).
Institute of Scientific and Technical Information of China (English)
李瑞斋; 耿范
2015-01-01
在动力系统理论中,二次非线性项复差分方程的正解存在性问题,在解决动力系统的稳定性控制方面具有重要意义.在相空间的一个子集上构建二次非线性项复差分方程,采用Lyapunov-Kraso-vskii泛函进行交叉项干扰的临界阈值确定,对方程正解的收敛性问题看作是时频对偶问题,通过多迹B?cklund变换,分析接收数据矩阵与阵列流型张成的空间之间的时频耦合性,得到方程的所有正解向量的递归计算式,构建差分方程的正解约束模型,进行二次非线性项复差分方程正解的稳定性证明,保证了非线性动力系统的稳定性和有界性,推导结论真实有效.%In the theory of dynamical systems, quadratic nonlinear term complex difference equations for the existence of positive solution of problems and solve the stability of the power system control plays an important role in. In a subset of the phase space construction of quadratic nonlinear complex differential equations, of cross term interference in the determina-tion of threshold value by using Lyapunov Krasovskii functional, convergence problem of positive solutions of the equation as the time-frequency duality problems, through the multi track from B cklund transformation, analyzes the received data matrix and array manifold piece into the space between the time-frequency coupling, equations are obtained for all positive solutions vectors of a recursive formula, constructs difference constraint model of positive solutions of differential equations, proof of quadratic nonlinear term complex differential equation positive solution stability, to ensure the stability and bound-edness of nonlinear dynamic system, conclusion derived from the real and effective.
Recent topics in non-linear partial differential equations 4
Mimura, M
1989-01-01
This fourth volume concerns the theory and applications of nonlinear PDEs in mathematical physics, reaction-diffusion theory, biomathematics, and in other applied sciences. Twelve papers present recent work in analysis, computational analysis of nonlinear PDEs and their applications.
Nonlinear metrology with a quantum interface
Napolitano, M.; Mitchell, M. W.
2009-01-01
We describe nonlinear quantum atom-light interfaces and nonlinear quantum metrology in the collective continuous variable formalism. We develop a nonlinear effective Hamiltonian in terms of spin and polarization collective variables and show that model Hamiltonians of interest for nonlinear quantum metrology can be produced in $^{87}$Rb ensembles. With these Hamiltonians, metrologically relevant atomic properties, e.g. the collective spin, can be measured better than the "Heisenberg limit" $\\...
The Nonlinear Analytical Envelope Equation in quadratic nonlinear crystals
Bache, Morten
2016-01-01
We here derive the so-called Nonlinear Analytical Envelope Equation (NAEE) inspired by the work of Conforti et al. [M. Conforti, A. Marini, T. X. Tran, D. Faccio, and F. Biancalana, "Interaction between optical fields and their conjugates in nonlinear media," Opt. Express 21, 31239-31252 (2013)], whose notation we follow. We present a complete model that includes $\\chi^{(2)}$ terms [M. Conforti, F. Baronio, and C. De Angelis, "Nonlinear envelope equation for broadband optical pulses in quadratic media," Phys. Rev. A 81, 053841 (2010)], $\\chi^{(3)}$ terms, and then extend the model to delayed Raman effects in the $\\chi^{(3)}$ term. We therefore get a complete model for ultrafast pulse propagation in quadratic nonlinear crystals similar to the Nonlinear Wave Equation in Frequency domain [H. Guo, X. Zeng, B. Zhou, and M. Bache, "Nonlinear wave equation in frequency domain: accurate modeling of ultrafast interaction in anisotropic nonlinear media," J. Opt. Soc. Am. B 30, 494-504 (2013)], but where the envelope is...
Nonlinear airship aeroelasticity
Bessert, N.; Frederich, O.
2005-12-01
The aeroelastic derivatives for today's aircraft are calculated in the concept phase using a standard procedure. This scheme has to be extended for large airships, due to various nonlinearities in structural and aerodynamic behaviour. In general, the structural model of an airship is physically as well as geometrically nonlinear. The main sources of nonlinearity are large deformations and the nonlinear material behaviour of membranes. The aerodynamic solution is also included in the nonlinear problem, because the deformed airship influences the surrounding flow. Due to these nonlinearities, the aeroelastic problem for airships can only be solved by an iterative procedure. As one possibility, the coupled aerodynamic and structural dynamic problem was handled using linked standard solvers. On the structural side, the Finite-Element program package ABAQUS was extended with an interface to the aerodynamic solver VSAERO. VSAERO is based on the aerodynamic panel method using potential flow theory. The equilibrium of the internal structural and the external aerodynamic forces leads to the structural response and a trimmed flight state for the specified flight conditions (e.g. speed, altitude). The application of small perturbations around a trimmed state produces reaction forces and moments. These constraint forces are then transferred into translational and rotational acceleration fields by performing an inertia relief analysis of the disturbed structural model. The change between the trimmed flight state and the disturbed one yields the respective aeroelastic derivatives. By including the calculated derivatives in the linearised equation of motion system, it is possible to judge the stability and controllability of the investigated airship.
In, Visarath; Longhini, Patrick; Kho, Andy; Neff, Joseph D.; Leung, Daniel; Liu, Norman; Meadows, Brian K.; Gordon, Frank; Bulsara, Adi R.; Palacios, Antonio
2012-12-01
The nonlinear channelizer is an integrated circuit made up of large parallel arrays of analog nonlinear oscillators, which, collectively, serve as a broad-spectrum analyzer with the ability to receive complex signals containing multiple frequencies and instantaneously lock-on or respond to a received signal in a few oscillation cycles. The concept is based on the generation of internal oscillations in coupled nonlinear systems that do not normally oscillate in the absence of coupling. In particular, the system consists of unidirectionally coupled bistable nonlinear elements, where the frequency and other dynamical characteristics of the emergent oscillations depend on the system's internal parameters and the received signal. These properties and characteristics are being employed to develop a system capable of locking onto any arbitrary input radio frequency signal. The system is efficient by eliminating the need for high-speed, high-accuracy analog-to-digital converters, and compact by making use of nonlinear coupled systems to act as a channelizer (frequency binning and channeling), a low noise amplifier, and a frequency down-converter in a single step which, in turn, will reduce the size, weight, power, and cost of the entire communication system. This paper covers the theory, numerical simulations, and some engineering details that validate the concept at the frequency band of 1-4 GHz.
Nonlinear diffusion and viral spread through the leaf of a plant
Edwards, Maureen P.; Waterhouse, Peter M.; Munoz-Lopez, María Jesús; Anderssen, Robert S.
2016-10-01
The spread of a virus through the leaf of a plant is both spatially and temporally causal in that the present status depends on the past and the spatial spread is compactly supported and progresses outwards. Such spatial spread is known to occur for certain nonlinear diffusion processes. The first compactly supported solution for nonlinear diffusion equations appears to be that of Pattle published in 1959. In that paper, no explanation is given as to how the solution was derived. Here, we show how the solution can be derived using Lie symmetry analysis. This lays a foundation for exploring the behavior of other choices for nonlinear diffusion and exploring the addition of reaction terms which do not eliminate the compactly supported structure. The implications associated with using the reaction-diffusion equation to model the spatial-temporal spread of a virus through the leaf of a plant are discussed.
Directory of Open Access Journals (Sweden)
E. M. E. Zayed
2014-01-01
Full Text Available We apply the generalized projective Riccati equations method to find the exact traveling wave solutions of some nonlinear evolution equations with any-order nonlinear terms, namely, the nonlinear Pochhammer-Chree equation, the nonlinear Burgers equation and the generalized, nonlinear Zakharov-Kuznetsov equation. This method presents wider applicability for handling many other nonlinear evolution equations in mathematical physics.
Energy Technology Data Exchange (ETDEWEB)
Turchetti, G. (Bologna Univ. (Italy). Dipt. di Fisica)
1989-01-01
Research in nonlinear dynamics is rapidly expanding and its range of applications is extending beyond the traditional areas of science where it was first developed. Indeed while linear analysis and modelling, which has been very successful in mathematical physics and engineering, has become a mature science, many elementary phenomena of intrinsic nonlinear nature were recently experimentally detected and investigated, suggesting new theoretical work. Complex systems, as turbulent fluids, were known to be governed by intrinsically nonlinear laws since a long time ago, but received purely phenomenological descriptions. The pioneering works of Boltzmann and Poincare, probably because of their intrinsic difficulty, did not have a revolutionary impact at their time; it is only very recently that their message is reaching a significant number of mathematicians and physicists. Certainly the development of computers and computer graphics played an important role in developing geometric intuition of complex phenomena through simple numerical experiments, while a new mathematical framework to understand them was being developed.
Nonlinear biochemical signal processing via noise propagation.
Kim, Kyung Hyuk; Qian, Hong; Sauro, Herbert M
2013-10-14
Single-cell studies often show significant phenotypic variability due to the stochastic nature of intra-cellular biochemical reactions. When the numbers of molecules, e.g., transcription factors and regulatory enzymes, are in low abundance, fluctuations in biochemical activities become significant and such "noise" can propagate through regulatory cascades in terms of biochemical reaction networks. Here we develop an intuitive, yet fully quantitative method for analyzing how noise affects cellular phenotypes based on identifying a system's nonlinearities and noise propagations. We observe that such noise can simultaneously enhance sensitivities in one behavioral region while reducing sensitivities in another. Employing this novel phenomenon we designed three biochemical signal processing modules: (a) A gene regulatory network that acts as a concentration detector with both enhanced amplitude and sensitivity. (b) A non-cooperative positive feedback system, with a graded dose-response in the deterministic case, that serves as a bistable switch due to noise-induced ultra-sensitivity. (c) A noise-induced linear amplifier for gene regulation that requires no feedback. The methods developed in the present work allow one to understand and engineer nonlinear biochemical signal processors based on fluctuation-induced phenotypes.
Kumar, Sanjiv; Merwade, Venkatesh; Rao, P Suresh C; Pijanowski, Bryan C
2013-04-01
We relate the historical (1850-2000) spatial and temporal changes in cropland cover in the conterminous United States to several socio-economic and biophysical determinants using an eco-region based spatial framework. Results show population density as a major determinant during the nineteenth century, and biophysical suitability as the major determinant during the twentieth century. We further examine the role of technological innovations, socio-economic and socio-ecological feedbacks that have either sustained or altered the cropland trajectories in different eco-regions. The cropland trajectories for each of the 84 level-III eco-regions were analyzed using a nonlinear bi-analytical model. In the Eastern United States, low biophysically suitable eco-regions, e.g., New England, have shown continual decline in the cropland after reaching peak levels. The cropland trajectories in high biophysically suitable regions, e.g., Corn Belt, have stabilized after reaching peak levels. In the Western United States, low-intensity crop cover (land conversion was found in the industrial period. Significant effect of Conservation Reserve Program on planted crop area is found in last two decades (1990-2010).
Günther, U; Bezerra, V; Romero, C; Guenther, Uwe; Zhuk, Alexander; Bezerra, Valdir; Romero, Carlos
2004-01-01
We study multidimensional gravitational models with scalar curvature nonlinearities of the type 1/R and R^4. It is assumed that the corresponding higher dimensional spacetime manifolds undergo a spontaneous compactification to manifolds with warped product structure. Special attention is paid to the stability of the extra-dimensional factor spaces. It is shown that for certain parameter regions the systems allow for a freezing stabilization of these spaces. In particular, we find for the 1/R model that configurations with stabilized extra dimensions do not provide a late-time acceleration (they are AdS), whereas the solution branch which allows for accelerated expansion (the dS branch) is incompatible with stabilized factor spaces. In the case of the R^4 model, we obtain that the stability region in parameter space depends on the total dimension D=dim(M) of the higher dimensional spacetime M. For D>8 the stability region consists of a single (absolutely stable) sector which is shielded from a conformal singul...
Fast Numerical Nonlinear Fourier Transforms
Wahls, Sander
2014-01-01
The nonlinear Fourier transform, which is also known as the forward scattering transform, decomposes a periodic signal into nonlinearly interacting waves. In contrast to the common Fourier transform, these waves no longer have to be sinusoidal. Physically relevant waveforms are often available for the analysis instead. The details of the transform depend on the waveforms underlying the analysis, which in turn are specified through the implicit assumption that the signal is governed by a certain evolution equation. For example, water waves generated by the Korteweg-de Vries equation can be expressed in terms of cnoidal waves. Light waves in optical fiber governed by the nonlinear Schr\\"dinger equation (NSE) are another example. Nonlinear analogs of classic problems such as spectral analysis and filtering arise in many applications, with information transmission in optical fiber, as proposed by Yousefi and Kschischang, being a very recent one. The nonlinear Fourier transform is eminently suited to address them ...
Cubication of conservative nonlinear oscillators
Energy Technology Data Exchange (ETDEWEB)
Belendez, Augusto; Alvarez, Mariela L [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Fernandez, Elena; Pascual, Inmaculada [Departamento de Optica, FarmacologIa y Anatomia, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)], E-mail: a.belendez@ua.es
2009-09-15
A cubication procedure of the nonlinear differential equation for conservative nonlinear oscillators is analysed and discussed. This scheme is based on the Chebyshev series expansion of the restoring force, and this allows us to approximate the original nonlinear differential equation by a Duffing equation in which the coefficients for the linear and cubic terms depend on the initial amplitude, A, while in a Taylor expansion of the restoring force these coefficients are independent of A. The replacement of the original nonlinear equation by an approximate Duffing equation allows us to obtain an approximate frequency-amplitude relation as a function of the complete elliptic integral of the first kind. Some conservative nonlinear oscillators are analysed to illustrate the usefulness and effectiveness of this scheme.
Analysis of Nonlinear Electromagnetic Metamaterials
Poutrina, Ekaterina; Smith, David R
2010-01-01
We analyze the properties of a nonlinear metamaterial formed by integrating nonlinear components or materials into the capacitive regions of metamaterial elements. A straightforward homogenization procedure leads to general expressions for the nonlinear susceptibilities of the composite metamaterial medium. The expressions are convenient, as they enable inhomogeneous system of scattering elements to be described as a continuous medium using the standard notation of nonlinear optics. We illustrate the validity and accuracy of our theoretical framework by performing measurements on a fabricated metamaterial sample composed of an array of split ring resonators (SRRs) with packaged varactors embedded in the capacitive gaps in a manner similar to that of Wang et al. [Opt. Express 16, 16058 (2008)]. Because the SRRs exhibit a predominant magnetic response to electromagnetic fields, the varactor-loaded SRR composite can be described as a magnetic material with nonlinear terms in its effective magnetic susceptibility...
Some Asymptotic Inference in Multinomial Nonlinear Models (a Geometric Approach)
Institute of Scientific and Technical Information of China (English)
WEIBOCHENG
1996-01-01
A geometric framework is proposed for multinomlat nonlinear modelsbased on a modified vemlon of the geometric structure presented by Bates & Watts[4]. We use this geometric framework to study some asymptotic inference in terms ofcurvtures for multlnomial nonlinear models. Our previous results [15] for ordlnary nonlinear regression models are extended to multlnomlal nonlinear models.
The myth about nonlinear differential equations
Radhakrishnan, C.
2002-01-01
Taking the example of Koretweg--de Vries equation, it is shown that soliton solutions need not always be the consequence of the trade-off between the nonlinear terms and the dispersive term in the nonlinear differential equation. Even the ordinary one dimensional linear partial differential equation can produce a soliton.
Retarded Integral Inequality With Multiple Nonlinear Terms and Its Application%含多个非线性项的时滞积分不等式及其应用
Institute of Scientific and Technical Information of China (English)
王五生; 李自尊
2012-01-01
本文在文献[Agarwal et al，J.Inequ．Appl．，2008，Art．ID908784，15pages]和文献[Chen et al．，J．Inequ．Appl．，2009，Art．ID258569，15pages]的基础上，建立了一类新的非线性时滞积分不等式．第一个参考文献中不等式的未知函数u是一元函数，右端第一项是正常数c；第二个参考文献中不等式右端第一项也是正常数c，第二项的被积函数中只含未知函数线性因子；本文研究的不等式中未知函数是二元函数，右端第一项是不减的正函数，第二项被积函数中含有未知函数的非线性因子，积分号外还有一个非常数因子．最后， 本文用研究不等式得到的结果讨论了时滞偏微分方程初边值问题的有界性．%On the basis of [Agarwal et al., J. Inequ. Appl., 2008, Art. ID 908784, 15 pages] and [Chen et al., J. Inequ. Appl., 2009, Art. ID 258569, 15 pages], this paper establishes a new nonlinear retarded integral inequality. In the first literature the unknown function u of the inequality is a single variable function, the first term of the right hand of the inequality is positive constant c; in the second literature the first term of the right hand of the inequality is also a positive constant, and the integrand of the second term only contains linear factors of unknown function. In this paper, the unknown function of the inequality is a two-variable function, the first term of the right hand of the inequality is a nondecreasing and positive function, and the integrand of the second term contains a nonlinear factor of unknown function, and it also contains a nonconstant factor outside the integral sign. Finally, We apply our result to the discussion of boundedness for the initial-boundary value problem of retarded partial differential equation.
Institute of Scientific and Technical Information of China (English)
郝平平; 冯春华
2012-01-01
本文利用分析不等式方法来研究Berezansky等人在2010年提出的公开问题之一:一类具有非线性物种密度制约死亡率的Nicholson模型的解的有界性、稳定性和振动性.通过这个方法证明了这个模型解的有界性、振动性,并部分解决了解的稳定性.%By using the method of analysis inequality ,this paper mainly deals with the open problem provided by Berezansky et al. The boundedness and oscillations of the solutions for this Nicholson's model with a nonlinear density-dependent mortality term are investigated,and the stability of the solutions for this model is solved partially.
On Nonlinear Higher Spin Curvature
Manvelyan, Ruben(Yerevan Physics Institute, Alikhanian Br. St. 2, Yerevan, 0036, Armenia); Mkrtchyan, Karapet; Rühl, Werner; Tovmasyan, Murad
2011-01-01
We present the first nonlinear term of the higher spin curvature which is covariant with respect to deformed gauge transformations that are linear in the field. We consider in detail the case of spin 3 after presenting spin 2 as an example, and then construct the general spin s quadratic term of the deWit-Freedman curvature.
On nonlinear higher spin curvature
Energy Technology Data Exchange (ETDEWEB)
Manvelyan, Ruben, E-mail: manvel@physik.uni-kl.d [Department of Physics, Erwin Schroedinger Strasse, Technical University of Kaiserslautern, Postfach 3049, 67653 Kaiserslautern (Germany); Yerevan Physics Institute, Alikhanian Br. Str. 2, 0036 Yerevan (Armenia); Mkrtchyan, Karapet, E-mail: karapet@yerphi.a [Department of Physics, Erwin Schroedinger Strasse, Technical University of Kaiserslautern, Postfach 3049, 67653 Kaiserslautern (Germany); Yerevan Physics Institute, Alikhanian Br. Str. 2, 0036 Yerevan (Armenia); Ruehl, Werner, E-mail: ruehl@physik.uni-kl.d [Department of Physics, Erwin Schroedinger Strasse, Technical University of Kaiserslautern, Postfach 3049, 67653 Kaiserslautern (Germany); Tovmasyan, Murad, E-mail: mtovmasyan@ysu.a [Yerevan Physics Institute, Alikhanian Br. Str. 2, 0036 Yerevan (Armenia)
2011-05-09
We present the first nonlinear term of the higher spin curvature which is covariant with respect to deformed gauge transformations that are linear in the field. We consider the case of spin 3 after presenting spin 2 as an example, and then construct the general spin s quadratic term of the de Wit-Freedman curvature.
The Effective AC Response of Nonlinear Composites
Institute of Scientific and Technical Information of China (English)
WEI En-Bo; GU Guo-Qing
2001-01-01
A perturbative approach is used to study the AC response of nonlinear composite media, which obey a current-field relation of the form J = σ E + χ|E|2 E with components having nonlinear response at finite frequencies. For a sinusoidal applied field, we extend the local potential in terms of sinusoidal components at fundamental frequency and high-order harmonic frequencies to treat the nonlinear composites. For nonlinear composite media vith a low concentrations of spherical inclusions, we give the formulae of the nonlinear effective AC susceptibility χ*3ω at the third harmonic frequency.
The nonlinear piezoelectric tuned vibration absorber
Soltani, P.; Kerschen, G.
2015-07-01
This paper proposes a piezoelectric vibration absorber, termed the nonlinear piezoelectric tuned vibration absorber (NPTVA), for the mitigation of nonlinear resonances of mechanical systems. The new feature of the NPTVA is that its nonlinear restoring force is designed according to a principle of similarity, i.e., the NPTVA should be an electrical analog of the nonlinear host system. Analytical formulas for the NPTVA parameters are derived using the homotopy perturbation method. Doing so, a nonlinear generalization of Den Hartog’s equal-peak tuning rule is developed for piezoelectric vibration absorbers.
Arun, N K; Mohan, B M
2017-09-01
The mathematical models reported in the literature so far have been found using Center of Sums (CoS) defuzzification method only. It appears that no one has found models using Center of Area (CoA) or Center of Gravity (CoG) defuzzification method. Although there have been some works reported to deal with modeling of fuzzy controllers via Centroid method, all of them have in fact used CoS method only. In this paper, for the first time mathematical models of the simplest Mamdani type fuzzy Proportional Integral (PI)/Proportional Derivative (PD) controllers via CoG defuzzification are presented. L-type and Γ-type membership functions over different Universes of Discourse (UoDs) are considered for the input variables. L-type, Π-type and Γ-type membership functions are considered for the output variable. Three linear fuzzy control rules relating all four input fuzzy sets to three output fuzzy sets are chosen. Two triangular norms namely Algebraic Product (AP) and Minimum (Min), Maximum (Max) triangular co-norm, and two inference methods, Larsen Product (LP) and Mamdani Minimum (MM), are used. Properties of the models are studied. Stability analysis of closed-loop systems containing one of these controller models in the loop is done using the Small Gain theorem. Since digital controllers are implemented using digital processors, computational and memory requirements of these fuzzy controllers and conventional (nonfuzzy) controllers are compared. A rough estimate of the computational time taken by the digital computer while implementing any of these discrete-time fuzzy controllers is given. Two nonlinear plants are considered to show the superiority of the simplest fuzzy controller obtained using CoA or CoG defuzzification method over the simplest fuzzy controller obtained using CoS method and reported recently. Real-time implementation of one of the developed controller models is done on coupled tank experimental setup to show the feasibility of the developed model
Energy Technology Data Exchange (ETDEWEB)
Huang Dingjiang [Department of Applied Mathematics, Dalian University of Technology, Dalian 116024 (China)]. E-mail: hdj8116@163.com; Zhang Hongqing [Department of Applied Mathematics, Dalian University of Technology, Dalian 116024 (China)
2005-09-05
In this Letter, an extended first kind elliptic sub-equation method and its algorithm are proposed by studying a first order nonlinear ordinary differential equation with a sixth-degree nonlinear term. Being concise and straightforward, the method is applied to the generalized reaction Duffing model. As a consequence, more types of exact travelling wave solutions are obtained which include new bell and kink profile solitary wave solutions, triangular periodic wave solutions and singular solutions. The method can be also extended to many other nonlinear wave equations.
2015-01-01
From the Back Cover: The emphasis throughout the present volume is on the practical application of theoretical mathematical models helping to unravel the underlying mechanisms involved in processes from mathematical physics and biosciences. It has been conceived as a unique collection of abstract methods dealing especially with nonlinear partial differential equations (either stationary or evolutionary) that are applied to understand concrete processes involving some important applications re...
Yamada, H; Ito, M
1998-01-01
The amoeboid organism, the plasmodium of Physarum polycephalum, behaves on the basis of spatio-temporal pattern formation by local contraction-oscillators. This biological system can be regarded as a reaction-diffusion system which has spatial interaction by active flow of protoplasmic sol in the cell. Paying attention to the physiological evidence that the flow is determined by contraction pattern in the plasmodium, a reaction-diffusion system having self-determined flow arises. Such a coupling of reaction-diffusion-advection is a characteristic of the biological system, and is expected to relate with control mechanism of amoeboid behaviours. Hence, we have studied effects of the self-determined flow on pattern formation of simple reaction-diffusion systems. By weakly nonlinear analysis near a trivial solution, the envelope dynamics follows the complex Ginzburg-Landau type equation just after bifurcation occurs at finite wave number. The flow term affects the nonlinear term of the equation through the critic...
Essentials of nonlinear optics
Murti, Y V G S
2014-01-01
Current literature on Nonlinear Optics varies widely in terms of content, style, and coverage of specific topics, relative emphasis of areas and the depth of treatment. While most of these books are excellent resources for the researchers, there is a strong need for books appropriate for presenting the subject at the undergraduate or postgraduate levels in Universities. The need for such a book to serve as a textbook at the level of the bachelors and masters courses was felt by the authors while teaching courses on nonlinear optics to students of both science and engineering during the past two decades. This book has emerged from an attempt to address the requirement of presenting the subject at college level. A one-semester course covering the essentials can effectively be designed based on this.
Östh, Jan; Krajnović, Siniša
2013-01-01
We investigate a hierarchy of eddy-viscosity terms in POD Galerkin models to account for a large fraction of unresolved fluctuation energy. These Galerkin methods are applied to Large Eddy Simulation data for a flow around the vehicle-like bluff body call Ahmed body. This flow has three challenges for any reduced-order model: a high Reynolds number, coherent structures with broadband frequency dynamics, and meta-stable asymmetric base flow states. The Galerkin models are found to be most accurate with modal eddy viscosities as proposed by Rempfer & Fasel (1994). Robustness of the model solution with respect to initial conditions, eddy viscosity values and model order is only achieved for state-dependent eddy viscosities as proposed by Noack, Morzynski & Tadmor (2011). Only the POD system with state-dependent modal eddy viscosities can address all challenges of the flow characteristics. All parameters are analytically derived from the Navier-Stokes based balance equations with the available data. We ar...
Modal Identification Using OMA Techniques: Nonlinearity Effect
Directory of Open Access Journals (Sweden)
E. Zhang
2015-01-01
Full Text Available This paper is focused on an assessment of the state of the art of operational modal analysis (OMA methodologies in estimating modal parameters from output responses of nonlinear structures. By means of the Volterra series, the nonlinear structure excited by random excitation is modeled as best linear approximation plus a term representing nonlinear distortions. As the nonlinear distortions are of stochastic nature and thus indistinguishable from the measurement noise, a protocol based on the use of the random phase multisine is proposed to reveal the accuracy and robustness of the linear OMA technique in the presence of the system nonlinearity. Several frequency- and time-domain based OMA techniques are examined for the modal identification of simulated and real nonlinear mechanical systems. Theoretical analyses are also provided to understand how the system nonlinearity degrades the performance of the OMA algorithms.
A nonlinear plate control without linearization
Directory of Open Access Journals (Sweden)
Yildirim Kenan
2017-03-01
Full Text Available In this paper, an optimal vibration control problem for a nonlinear plate is considered. In order to obtain the optimal control function, wellposedness and controllability of the nonlinear system is investigated. The performance index functional of the system, to be minimized by minimum level of control, is chosen as the sum of the quadratic 10 functional of the displacement. The velocity of the plate and quadratic functional of the control function is added to the performance index functional as a penalty term. By using a maximum principle, the nonlinear control problem is transformed to solving a system of partial differential equations including state and adjoint variables linked by initial-boundary-terminal conditions. Hence, it is shown that optimal control of the nonlinear systems can be obtained without linearization of the nonlinear term and optimal control function can be obtained analytically for nonlinear systems without linearization.
Fast Stiffness Matrix Calculation for Nonlinear Finite Element Method
Directory of Open Access Journals (Sweden)
Emir Gülümser
2014-01-01
Full Text Available We propose a fast stiffness matrix calculation technique for nonlinear finite element method (FEM. Nonlinear stiffness matrices are constructed using Green-Lagrange strains, which are derived from infinitesimal strains by adding the nonlinear terms discarded from small deformations. We implemented a linear and a nonlinear finite element method with the same material properties to examine the differences between them. We verified our nonlinear formulation with different applications and achieved considerable speedups in solving the system of equations using our nonlinear FEM compared to a state-of-the-art nonlinear FEM.
Boundary control of long waves in nonlinear dispersive systems
DEFF Research Database (Denmark)
Hasan, Agus; Foss, Bjarne; Aamo, Ole Morten
2011-01-01
Unidirectional propagation of long waves in nonlinear dispersive systems may be modeled by the Benjamin-Bona-Mahony-Burgers equation, a third order partial differential equation incorporating linear dissipative and dispersive terms, as well as a term covering nonlinear wave phenomena. For higher...... orders of the nonlinearity, the equation may have unstable solitary wave solutions. Although it is a one dimensional problem, achieving a global result for this equation is not trivial due to the nonlinearity and the mixed partial derivative. In this paper, two sets of nonlinear boundary control laws...... that achieve global exponential stability and semi-global exponential stability are derived for both linear and nonlinear cases....
Block, Daniel J; Spong, Mark W
2007-01-01
This monograph describes the Reaction Wheel Pendulum, the newest inverted-pendulum-like device for control education and research. We discuss the history and background of the reaction wheel pendulum and other similar experimental devices. We develop mathematical models of the reaction wheel pendulum in depth, including linear and nonlinear models, and models of the sensors and actuators that are used for feedback control. We treat various aspects of the control problem, from linear control of themotor, to stabilization of the pendulum about an equilibrium configuration using linear control, t
Recursive design of nonlinear H∞ excitation controller
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
This work is concerned with the problem of L2 gain disturbance attenuation for nonlinear systems and nonlinear robust control for power systems. In terms of the recurrence design approach proposed, the nonnegative solution of dissipative inequality and the storage function of nonlinear H∞ control for a generator excitation system are acquired. From this storage function, the excitation controller is constructed. Moreover, simulation results manifest the effectiveness of this design method.
Nonlinear cross Gramians and gradient systems
Ionescu, T. C.; Scherpen, J.M.A.
2007-01-01
We study the notion of cross Gramians for nonlinear gradient systems, using the characterization in terms of prolongation and gradient extension associated to the system. The cross Gramian is given for the variational system associated to the original nonlinear gradient system. We obtain linearization results that precisely correspond to the notion of a cross Gramian for symmetric linear systems. Furthermore, first steps towards relations with the singular value functions of the nonlinear Han...
Quantum Dynamics of Nonlinear Cavity Systems
Nation, Paul D.
2010-01-01
We investigate the quantum dynamics of three different configurations of nonlinear cavity systems. To begin, we carry out a quantum analysis of a dc superconducting quantum interference device (SQUID) mechanical displacement detector comprised of a SQUID with a mechanically compliant loop segment. The SQUID is approximated by a nonlinear current-dependent inductor, inducing a flux tunable nonlinear Duffing term in the cavity equation of motion. Expressions are derived for the detector signal ...
Studies in nonlinear problems of energy
Matkowsky, B. J.
1992-07-01
Emphasis has been on combustion and flame propagation. The research program was on modeling, analysis and computation of combustion phenomena, with emphasis on transition from laminar to turbulent combustion. Nonlinear dynamics and pattern formation were investigated in the transition. Stability of combustion waves, and transitions to complex waves are described. Combustion waves possess large activation energies, so that chemical reactions are significant only in thin layers, or reaction zones. In limit of infinite activation energy, the zones shrink to moving surfaces, termed fronts which must be found during the analysis, so that the problems are moving free boundary problems. The studies are carried out for limiting case with fronts, while the numerical studies are carried out for finite, though large, activation energy. Accurate resolution of the solution in the reaction zones is essential, otherwise false predictions of dynamics are possible. Since the the reaction zones move, adaptive pseudo-spectral methods were developed. The approach is based on a synergism of analytical and computational methods. The numerical computations build on and extend the analytical information. Furthermore, analytical solutions serve as benchmarks for testing the accuracy of the computation. Finally, ideas from analysis (singular perturbation theory) have induced new approaches to computations. The computational results suggest new analysis to be considered. Among the recent interesting results, was spatio-temporal chaos in combustion. One goal is extension of the adaptive pseudo-spectral methods to adaptive domain decomposition methods. Efforts have begun to develop such methods for problems with multiple reaction zones, corresponding to problems with more complex, and more realistic chemistry. Other topics included stochastics, oscillators, Rysteretic Josephson junctions, DC SQUID, Markov jumps, laser with saturable absorber, chemical physics, Brownian movement, combustion
Global existence and asymptotic stability of equilibria to reaction-diffusion systems
Wang, Rong-Nian; Tang, Zhong Wei
2009-06-01
In this paper, we study weakly coupled reaction-diffusion systems in unbounded domains of {\\bb R}^2 or {\\bb R}^3 , where the reaction terms are sums of quasimonotone nondecreasing and nonincreasing functions. Such systems are more complicated than those in many previous publications and little is known about them. A comparison principle and global existence, and boundedness theorems for solutions to these systems are established. Sufficient conditions on the nonlinearities, ensuring the positively Ljapunov stability of the zero solution with respect to H2-perturbations, are also obtained. As samples of applications, these results are applied to an autocatalytic chemical model and a concrete problem, whose nonlinearities are nonquasimonotone. Our results are novel. In particular, we present a solution to an open problem posed by Escher and Yin (2005 J. Nonlinear Anal. Theory Methods Appl. 60 1065-84).
Rajasekar, Shanmuganathan
2016-01-01
This introductory text presents the basic aspects and most important features of various types of resonances and anti-resonances in dynamical systems. In particular, for each resonance, it covers the theoretical concepts, illustrates them with case studies, and reviews the available information on mechanisms, characterization, numerical simulations, experimental realizations, possible quantum analogues, applications and significant advances made over the years. Resonances are one of the most fundamental phenomena exhibited by nonlinear systems and refer to specific realizations of maximum response of a system due to the ability of that system to store and transfer energy received from an external forcing source. Resonances are of particular importance in physical, engineering and biological systems - they can prove to be advantageous in many applications, while leading to instability and even disasters in others. The book is self-contained, providing the details of mathematical derivations and techniques invo...
Institute of Scientific and Technical Information of China (English)
1996-01-01
3.1 A Unified Nonlinear Feedback Functional Method for Study Both Control and Synchronization of Spatiotemporal Chaos Fang Jinqing Ali M. K. (Department of Physics, The University of Lethbridge,Lethbridge, Alberta T1K 3M4,Canada) Two fundamental questions dominate future chaos control theories.The first is the problem of controlling hyperchaos in higher dimensional systems.The second question has yet to be addressed:the problem of controlling spatiotemporal chaos in a spatiotemporal system.In recent years, control and synchronization of spatiotemporal chaos and hyperchaos have became a much more important and challenging subject. The reason for this is the control and synchronism of such behaviours have extensive and great potential of interdisciplinary applications, such as security communication, information processing, medicine and so on. However, this subject is not much known and remains an outstanding open.
Nonlinear cross Gramians and gradient systems
Ionescu, T. C.; Scherpen, J. M. A.
2007-01-01
We study the notion of cross Gramians for nonlinear gradient systems, using the characterization in terms of prolongation and gradient extension associated to the system. The cross Gramian is given for the variational system associated to the original nonlinear gradient system. We obtain
Nonlinear dynamics of the left ventricle.
Munteanu, Ligia; Chiroiu, Calin; Chiroiu, Veturia
2002-05-01
The cnoidal method is applied to solve the set of nonlinear dynamic equations of the left ventricle. By using the theta-function representation of the solutions and a genetic algorithm, the ventricular motion can be described as a linear superposition of cnoidal pulses and additional terms, which include nonlinear interactions among them.
Bankole, Owolabi M.; Nyokong, Tebello
2017-05-01
We report on the conjugation of azide-derivatized gold nanoparticles (AuNPs) to alkyne moieties of ZnPc and InPc via azide-alkyne Huisgen cycloaddition reaction to form phthalocyanines-AuNPs (MPc-AuNPs) conjugates. The detailed structural characterizations of the composites were in good agreement with the expected results. The nonlinear absorption coefficients and other nonlinear optical limiting parameters were almost two times larger for the conjugates compared to free phthalocyanines. We established direct relationship between improved photophysical characterizations and enhanced nonlinear effects of reverse saturable absorption mechanisms favoured by excited triplet absorption of the phthalocyanines in the presence of AuNPs. The combination of InPc with AuNPs resulted in the lowest limiting intensity value of 0.06 J/cm2, hence the best performance in terms of optical limiting.
Directory of Open Access Journals (Sweden)
Hector Vazquez-Leal
2013-01-01
Full Text Available A new tool for the solution of nonlinear differential equations is presented. The Fixed-Term Homotopy (FTH delivers a high precision representation of the nonlinear differential equation using only a few linear algebraic terms. In addition to this tool, a procedure based on Laplace-Padé to deal with the truncate power series resulting from the FTH method is also proposed. In order to assess the benefits of this proposal, two nonlinear problems are solved and compared against other semianalytic methods. The obtained results show that FTH is a power tool capable of generating highly accurate solutions compared with other methods of literature.
Institute of Scientific and Technical Information of China (English)
黄祖达
2012-01-01
In this paper, we study a generalized Nicholson' s blowflies model with a nonlinear density-dependent mortality term. Under the admissible initial conditions, by using continuous dependence theorem, some criteria to guarantee the positivity and global existence of solutions are obtained. Then, by applying differential inequality techniques, we give the positive lower bound and upper bound of solutions, and get the permanence of this model. Moreover, we present an example to illustrate our main results.%研究了一类具有非线性死亡率的广义时滞Nicholson飞蝇方程.在容许初值的条件下,利用解的延拓定理,首先证明了该方程的所有解是正的并且是整体存在的,然后利用微分不等式的技巧,证明了该方程所有解具有正的上下确界,获得了该方程所有解具有持久性的充分条件.由于所考虑的模型比同类文献中的模型更加广泛,从而改进和推广了已有文献中的相关结果,并给出了一个具体的例子.
Coexistence of competitors mediated by nonlinear noise
Siekmann, Ivo; Bengfort, Michael; Malchow, Horst
2017-06-01
Stochastic reaction-diffusion equations are a popular modelling approach for studying interacting populations in a heterogeneous environment under the influence of environmental fluctuations. Although the theoretical basis of alternative models such as Fokker-Planck diffusion is not less convincing, movement of populations is most commonly modelled using the diffusion law due to Fick. An interesting feature of Fokker-Planck diffusion is the fact that for spatially varying diffusion coefficients the stationary solution is not a homogeneous distribution - in contrast to Fick's law of diffusion. Instead, concentration accumulates in regions of low diffusivity and tends to lower levels for areas of high diffusivity. Thus, we may interpret the stationary distribution of the Fokker-Planck diffusion as a reflection of different levels of habitat quality. Moreover, the most common model for environmental fluctuations, linear multiplicative noise, is based on the assumption that individuals respond independently to stochastic environmental fluctuations. For large population densities the assumption of independence is debatable and the model further implies that noise intensities can increase to arbitrarily high levels. Therefore, instead of the commonly used linear multiplicative noise model, we implement environmental variability by an alternative nonlinear noise term which never exceeds a certain maximum noise intensity. With Fokker-Planck diffusion and the nonlinear noise model replacing the classical approaches we investigate a simple invasive system based on the Lotka-Volterra competition model. We observe that the heterogeneous stationary distribution generated by Fokker-Planck diffusion generally facilitates the formation of segregated habitats of resident and invader. However, this segregation can be broken by nonlinear noise leading to coexistence of resident and invader across the whole spatial domain, an effect that would not be possible in the non
Practical stability of nonlinear systems
Lakshmikantham, Vangipuram; Martynyuk, Anatolii Andreevich
1990-01-01
This is the first book that deals with practical stability and its development. It presents a systematic study of the theory of practical stability in terms of two different measures and arbitrary sets and demonstrates the manifestations of general Lyapunov's method by showing how this effective technique can be adapted to investigate various apparently diverse nonlinear problems including control systems and multivalued differential equations.
A single-ion nonlinear mechanical oscillator
Akerman, Nitzan; Glickamn, Yinnon; Dallal, Yehonatan; Keselman, Anna; Ozeri, Roee
2010-01-01
We study the steady state motion of a single trapped ion oscillator driven to the nonlinear regime. Damping is achieved via Doppler laser-cooling. The ion motion is found to be well described by the Duffing oscillator model with an additional nonlinear damping term. We demonstrate a unique ability of tuning both the linear as well as the nonlinear damping coefficients by controlling the cooling laser parameters. Our observations open a way for the investigation of nonlinear dynamics on the quantum-to-classical interface as well as mechanical noise squeezing in laser-cooling dynamics.
NONLINEAR ELASTICITY OF BLOOD ARTERIAL DUCT
Institute of Scientific and Technical Information of China (English)
黄孟才; 顾忠; 沈俊; 唐复勇
1991-01-01
The paper deals with nonlinear elasticity of blood arterial duct, in which the artery is modeled to bea locally triclinic, transverse isotropic, incorapressible, axisymmetric and thickwalled tube with large deformations, The nonlinear coustitutive relationship of arterial tissues is based on the theorv of Green and Adkins. A nonlinear strain energy density function is introduced for nonlinear stress-strain relationship of second order, in which the coefficient of each term is expressed by means of a Lame’s constant, The elasticity constants are nqcessary to describe such a uonlinear finite strain etastieity of the second order, These constants are determined by means of the stress-strain increment theory.
Nonlinear Materials Characterization Facility
Federal Laboratory Consortium — The Nonlinear Materials Characterization Facility conducts photophysical research and development of nonlinear materials operating in the visible spectrum to protect...
Nonlinear optical properties of ultrathin metal layers
DEFF Research Database (Denmark)
Lysenko, Oleg
2016-01-01
. The optical characterization of the plasmonic waveguides is performed using femtosecond and picosecond optical pulses. Two nonlinear optical effects in the strip plasmonic waveguides are experimentally observed and reported. The first effect is the nonlinear power transmission of the plasmonic mode......-order nonlinear susceptibility of the plasmonic mode in the gold strip waveguides significantly depends on the metal layer thickness and laser pulse duration. This dependence is explained in detail in terms of the free-electron temporal dynamics in gold. The third-order nonlinear susceptibility of the gold layer...... duration dependence of the third-order nonlinear susceptibility of gold is calculated in the broad range from tens of femtoseconds to tens of picoseconds using the two-temperature model of the free-electron temporal dynamics of gold, and shows the saturation of the thirdorder nonlinear susceptibility...
Nonlinear singular vectors and nonlinear singular values
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
A novel concept of nonlinear singular vector and nonlinear singular value is introduced, which is a natural generalization of the classical linear singular vector and linear singular value to the nonlinear category. The optimization problem related to the determination of nonlinear singular vectors and singular values is formulated. The general idea of this approach is demonstrated by a simple two-dimensional quasigeostrophic model in the atmospheric and oceanic sciences. The advantage and its applications of the new method to the predictability, ensemble forecast and finite-time nonlinear instability are discussed. This paper makes a necessary preparation for further theoretical and numerical investigations.
Synchronization between two different chaotic systems with nonlinear feedback control
Institute of Scientific and Technical Information of China (English)
Lü Ling; Guo Zhi-An; Zhang Chao
2007-01-01
This paper presents chaos synchronization between two different chaotic systems by using a nonlinear controller, in which the nonlinear functions of the system are used as a nonlinear feedback term. The feedback controller is designed on the basis of stability theory, and the area of feedback gain is determined. The artificial simulation results show that this control method is commendably effective and feasible.
Exact Solution of a Generalized Nonlinear Schrodinger Equation Dimer
DEFF Research Database (Denmark)
Christiansen, Peter Leth; Maniadis, P.; Tsironis, G.P.
1998-01-01
We present exact solutions for a nonlinear dimer system defined throught a discrete nonlinear Schrodinger equation that contains also an integrable Ablowitz-Ladik term. The solutions are obtained throught a transformation that maps the dimer into a double Sine-Gordon like ordinary nonlinear...... differential equation....
The rigid-flexible nonlinear robotic manipulator: Modeling and control
Fenili, André; Balthazar, José Manoel
2011-05-01
The State-Dependent Riccati Equation (SDRE) control of a nonlinear rigid-flexible two link robotic manipulator is investigated. Different cases are considered assuming small deviations and large deviations from the desired final states. The nonlinear governing equations of motion are coupled, providing considerable excitation of all the nonlinear terms. The results present satisfactory final states but also undesirable overshoot.
Nonlinear Resistivity for Magnetohydrodynamical Models
Lingam, Manasvi; Pfefferlé, David; Comisso, Luca; Bhattacharjee, Amitava
2016-01-01
A nonlinear current-dependent resistivity that accurately accounts for the collisional electron-ion momentum transfer rate is derived. It is shown that the Spitzer resistivity overestimates the resistivity in certain observationally relevant regimes. The nonlinear resistivity computed herein is a strictly decreasing function of the current, in contrast to some notable previous proposals. The relative importance of the new expression with respect to the well-established electron inertia and Hall terms is also examined. The subtle implications of this current-dependent resistivity are discussed in the context of plasma systems and phenomena such as magnetic reconnection.
Time Series with Tailored Nonlinearities
Raeth, C
2015-01-01
It is demonstrated how to generate time series with tailored nonlinearities by inducing well- defined constraints on the Fourier phases. Correlations between the phase information of adjacent phases and (static and dynamic) measures of nonlinearities are established and their origin is explained. By applying a set of simple constraints on the phases of an originally linear and uncor- related Gaussian time series, the observed scaling behavior of the intensity distribution of empirical time series can be reproduced. The power law character of the intensity distributions being typical for e.g. turbulence and financial data can thus be explained in terms of phase correlations.
Edge detection by nonlinear dynamics
Energy Technology Data Exchange (ETDEWEB)
Wong, Yiu-fai
1994-07-01
We demonstrate how the formulation of a nonlinear scale-space filter can be used for edge detection and junction analysis. By casting edge-preserving filtering in terms of maximizing information content subject to an average cost function, the computed cost at each pixel location becomes a local measure of edgeness. This computation depends on a single scale parameter and the given image data. Unlike previous approaches which require careful tuning of the filter kernels for various types of edges, our scheme is general enough to be able to handle different edges, such as lines, step-edges, corners and junctions. Anisotropy in the data is handled automatically by the nonlinear dynamics.
Stability analysis of nonlinear systems
Lakshmikantham, Vangipuram; Martynyuk, Anatoly A
2015-01-01
The book investigates stability theory in terms of two different measure, exhibiting the advantage of employing families of Lyapunov functions and treats the theory of a variety of inequalities, clearly bringing out the underlying theme. It also demonstrates manifestations of the general Lyapunov method, showing how this technique can be adapted to various apparently diverse nonlinear problems. Furthermore it discusses the application of theoretical results to several different models chosen from real world phenomena, furnishing data that is particularly relevant for practitioners. Stability Analysis of Nonlinear Systems is an invaluable single-sourse reference for industrial and applied mathematicians, statisticians, engineers, researchers in the applied sciences, and graduate students studying differential equations.
Higher dimensional nonlinear massive gravity
Do, Tuan Q
2016-01-01
Inspired by a recent ghost-free nonlinear massive gravity in four-dimensional spacetime, we study its higher dimensional scenarios. As a result, we are able to show the constant-like behavior of massive graviton terms for some well-known metrics such as the Friedmann-Lemaitre-Robertson-Walker, Bianchi type I, and Schwarzschild-Tangherlini-(A)dS metrics in a specific five-dimensional nonlinear massive gravity under an assumption that its fiducial metrics are compatible with physical ones. In addition, some simple cosmological solutions of the five-dimensional massive gravity will be figured out consistently.
Spectral theory and nonlinear functional analysis
Lopez-Gomez, Julian
2001-01-01
This Research Note addresses several pivotal problems in spectral theory and nonlinear functional analysis in connection with the analysis of the structure of the set of zeroes of a general class of nonlinear operators. It features the construction of an optimal algebraic/analytic invariant for calculating the Leray-Schauder degree, new methods for solving nonlinear equations in Banach spaces, and general properties of components of solutions sets presented with minimal use of topological tools. The author also gives several applications of the abstract theory to reaction diffusion equations and systems.The results presented cover a thirty-year period and include recent, unpublished findings of the author and his coworkers. Appealing to a broad audience, Spectral Theory and Nonlinear Functional Analysis contains many important contributions to linear algebra, linear and nonlinear functional analysis, and topology and opens the door for further advances.
Behar, M.; Filevich, A.; Macchiavelli, A. O.; Szybisz, L.; Thieberger, P.
1982-10-01
Nuclear states of 79Kr were studied through the 78Se(α, 3n) reaction at an energy of 45 MeV. Excitation functions, γ-ray angular distributions, and γ-γ coincidences were performed. Three bands based on the g.s. (12-), 147.1 keV (52-), and 129.7 keV (72+) states were identified. Leading order analysis and quasiparticle-plus-rotor model calculations were performed. A good overall agreement was found between the experimental data and the theoretical predictions. NUCLEAR REACTIONS 78Se(α, 3n), E=30-55 MeV; measured σ(E, Eγ, θ), Eγ, Iγ, γ-γ coin. 79Kr deduced levels J. Enriched targets.
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
investigated through chlorophyll fluorescence parameters in morning glory (Ipomoea setosa) leaves, which were dipped into water, dithiothreitol (DTT) and lincomycin (LM), respectively. During the stress, both the xanthophyll cycle and D1 protein turnover could protect PSI from photoinhibition. In DTT leaves, non-photochemical quenching (NPQ) was inhibited greatly and the oxidation level of P700 (P700+) was the lowest one. However, the maximal photochemical efficiency of PSII (Fv/Fm) in DTT leaves was higher than that of LM leaves and was lower than that of control leaves. These results suggested that PSI was more sensitive to the loss of the xanthophyll cycle than PSII under high irradiance. In LM leaves, NPQ was partly inhibited, Fv/Fm was the lowest one among three treatments under high irradiance and P700+ was at a similar level as that of control leaves. These results implied that inactivation of PSII reaction centers could protect PSI from further photoinhibition. Additionally, the lowest of the number of active reaction centers to one inactive reaction center for a PSII cross-section (RC/CSo), maximal trapping rate in a PSII cross-section (TRo/CSo), electron transport in a PSII cross-section (ETo/CSo) and the highest of 1-qP in LM leaves further indicated that severe photoinhibition of PSII in LM leaves was mainly induced by inactivation of PSII reaction centers, which limited electrons transporting to PSI. However, relative to the LM leaves the higher level of RC/CSo, TRo/CSo, Fv/Fm and the lower level of 1-qP in DTT leaves indicated that PSI photoinhibition was mainly induced by the electron accumulation at the PSI acceptor side, which induced the decrease of P700+ under high irradiance.
Thermodynamics of random reaction networks.
Directory of Open Access Journals (Sweden)
Jakob Fischer
Full Text Available Reaction networks are useful for analyzing reaction systems occurring in chemistry, systems biology, or Earth system science. Despite the importance of thermodynamic disequilibrium for many of those systems, the general thermodynamic properties of reaction networks are poorly understood. To circumvent the problem of sparse thermodynamic data, we generate artificial reaction networks and investigate their non-equilibrium steady state for various boundary fluxes. We generate linear and nonlinear networks using four different complex network models (Erdős-Rényi, Barabási-Albert, Watts-Strogatz, Pan-Sinha and compare their topological properties with real reaction networks. For similar boundary conditions the steady state flow through the linear networks is about one order of magnitude higher than the flow through comparable nonlinear networks. In all networks, the flow decreases with the distance between the inflow and outflow boundary species, with Watts-Strogatz networks showing a significantly smaller slope compared to the three other network types. The distribution of entropy production of the individual reactions inside the network follows a power law in the intermediate region with an exponent of circa -1.5 for linear and -1.66 for nonlinear networks. An elevated entropy production rate is found in reactions associated with weakly connected species. This effect is stronger in nonlinear networks than in the linear ones. Increasing the flow through the nonlinear networks also increases the number of cycles and leads to a narrower distribution of chemical potentials. We conclude that the relation between distribution of dissipation, network topology and strength of disequilibrium is nontrivial and can be studied systematically by artificial reaction networks.
Improved fiber nonlinearity mitigation in dispersion managed optical OFDM links
Tamilarasan, Ilavarasan; Saminathan, Brindha; Murugappan, Meenakshi
2017-02-01
Fiber nonlinearity is seen as a capacity limiting factor in OFDM based dispersion managed links since the Four Wave Mixing effects become enhanced due to the high PAPR. In this paper, the authors have compared the linear and nonlinear PAPR reduction techniques for fiber nonlinearity mitigation in OFDM based dispersion managed links. In the existing optical systems, linear transform techniques such as SLM and PTS have been implemented to reduce nonlinear effects. In the proposed study, superior performance of the L2-by-3 nonlinear transform technique is demonstrated for PAPR reduction to mitigate fiber nonlinearities. The performance evaluation is carried out by interfacing multiple simulators. The results of both linear and nonlinear transform techniques have been compared and the results show that nonlinear transform technique outperforms the linear transform in terms of nonlinearity mitigation and improved BER performance.
Nonlinear Multigrid for Reservoir Simulation
DEFF Research Database (Denmark)
Christensen, Max la Cour; Eskildsen, Klaus Langgren; Engsig-Karup, Allan Peter
2016-01-01
A feasibility study is presented on the effectiveness of applying nonlinear multigrid methods for efficient reservoir simulation of subsurface flow in porous media. A conventional strategy modeled after global linearization by means of Newton’s method is compared with an alternative strategy...... modeled after local linearization, leading to a nonlinear multigrid method in the form of the full-approximation scheme (FAS). It is demonstrated through numerical experiments that, without loss of robustness, the FAS method can outperform the conventional techniques in terms of algorithmic and numerical...... efficiency for a black-oil model. Furthermore, the use of the FAS method enables a significant reduction in memory usage compared with conventional techniques, which suggests new possibilities for improved large-scale reservoir simulation and numerical efficiency. Last, nonlinear multilevel preconditioning...
Nonlinear Filtering Preserves Chaotic Synchronization via Master-Slave System
Directory of Open Access Journals (Sweden)
J. S. González-Salas
2013-01-01
Full Text Available We present a study on a class of interconnected nonlinear systems and give some criteria for them to behave like a filter. Some chaotic systems present this kind of interconnected nonlinear structure, which enables the synchronization of a master-slave system. Interconnected nonlinear filters have been defined in terms of interconnected nonlinear systems. Furthermore, their behaviors have been studied numerically and theoretically on different input signals.
Model of anisotropic nonlinearity in self-defocusing photorefractive media.
Barsi, C; Fleischer, J W
2015-09-21
We develop a phenomenological model of anisotropy in self-defocusing photorefractive crystals. In addition to an independent term due to nonlinear susceptibility, we introduce a nonlinear, non-separable correction to the spectral diffraction operator. The model successfully describes the crossover between photovoltaic and photorefractive responses and the spatially dispersive shock wave behavior of a nonlinearly spreading Gaussian input beam. It should prove useful for characterizing internal charge dynamics in complex materials and for accurate image reconstruction through nonlinear media.
On the multiplicity of solutions of the nonlinear reactive transport model
Directory of Open Access Journals (Sweden)
Elyas Shivanian
2014-06-01
Full Text Available The generalization of the nonlinear reaction–diffusion model in porous catalysts the so called one dimensional steady state reactive transport model is revisited. This model, which originates also in fluid and solute transport in soft tissues and microvessels, has been recently given analytical solution in terms of Taylor’s series for different families of reaction terms. This article considers the mentioned model without advective transport in the case of including Michaelis–Menten reaction term and shows that it is exactly solvable and furthermore, gives analytical exact solution in the implicit form for further physical interpretation. It is also revealed that the problem may admit unique or dual or even more triple solutions in some domains for the parameters of the model.
Traveling Wave Solutions of Reaction-Diffusion Equations Arising in Atherosclerosis Models
Directory of Open Access Journals (Sweden)
Narcisa Apreutesei
2014-05-01
Full Text Available In this short review article, two atherosclerosis models are presented, one as a scalar equation and the other one as a system of two equations. They are given in terms of reaction-diffusion equations in an infinite strip with nonlinear boundary conditions. The existence of traveling wave solutions is studied for these models. The monostable and bistable cases are introduced and analyzed.
Interactive optomechanical coupling with nonlinear polaritonic systems
Bobrovska, N; Liew, T C H; Kyriienko, O
2016-01-01
We study a system of interacting matter quasiparticles strongly coupled to photons inside an optomechanical cavity. The resulting normal modes of the system are represented by hybrid polaritonic quasiparticles, which acquire effective nonlinearity. Its strength is influenced by the presence of the mechanical mode and depends on the resonance frequency of the cavity. This leads to an interactive type of optomechanical coupling, being distinct from the previously studied dispersive and dissipative couplings in optomechanical systems. The emergent interactive coupling is shown to generate effective optical nonlinearity terms of high order, being quartic in the polariton number. We consider particular systems of exciton-polaritons and dipolaritons, and show that the induced effective optical nonlinearity due to the interactive coupling can exceed in magnitude the strength of Kerr nonlinear terms, such as those arising from polariton-polariton interactions. As applications, we show that the higher order terms give...
Jansen, Koen; Meek, Marcel F; van der Werff, John F A; van Wachem, Pauline B; van Luyn, Marja J A
2004-05-01
Long-term studies on nerve-guide regeneration are scarce. Therefore, in rats, long-term (16 months) sciatic nerve regeneration through poly(DL-lactide-epsilon-caprolactone) [poly(DLLA-epsilon-CL)] nerve guides was studied and compared with the nonoperated control side. Poly(DLLA-epsilon-CL) degradation and possible long-term foreign body reaction against poly(DLLA-epsilon-CL) nerve guides, as well as the distribution of both collagen type III and IV were studied. In vivo poly(DLLA-epsilon-CL) studies have been performed before but not for such long time points; also, a detailed analysis of collagen III/IV has not been presented before. The results demonstrate that biodegradable poly(DLLA-epsilon-CL) nerve guides yield good nerve regeneration and collagen III/IV deposition relative to the anatomy of the control side. Regenerated nerve showed almost similar collagen type III/IV distribution patterns as compared with the nonoperated control side, although the delineation of matrix was clearer in the control side. The relative amount of collagen III and IV immunostaining in nerve cross-sections did not, however, differ between the control nerve tissue and the operated side after 16 months. After 16 months of implantation, however, some very small fragments of biomaterial could still be found on the edge of the epineurium of the regenerated nerve, indicating remnants of a secondary foreign body reaction. The biomaterial fragments and foreign body reaction did not influence the nerve regeneration process after 16 months. Biodegradable poly(DLLA-epsilon-CL) nerve guides are useful for long-term bridging of short peripheral nerve gaps.
The entropy dissipation method for spatially inhomogeneous reaction-diffusion-type systems
Di Francesco, M.
2008-12-08
We study the long-time asymptotics of reaction-diffusion-type systems that feature a monotone decaying entropy (Lyapunov, free energy) functional. We consider both bounded domains and confining potentials on the whole space for arbitrary space dimensions. Our aim is to derive quantitative expressions for (or estimates of) the rates of convergence towards an (entropy minimizing) equilibrium state in terms of the constants of diffusion and reaction and with respect to conserved quantities. Our method, the so-called entropy approach, seeks to quantify convergence to equilibrium by using functional inequalities, which relate quantitatively the entropy and its dissipation in time. The entropy approach is well suited to nonlinear problems and known to be quite robust with respect to model variations. It has already been widely applied to scalar diffusion-convection equations, and the main goal of this paper is to study its generalization to systems of partial differential equations that contain diffusion and reaction terms and admit fewer conservation laws than the size of the system. In particular, we successfully apply the entropy approach to general linear systems and to a nonlinear example of a reaction-diffusion-convection system arising in solid-state physics as a paradigm for general nonlinear systems. © 2008 The Royal Society.
NONLINEAR EXPECTATIONS AND NONLINEAR MARKOV CHAINS
Institute of Scientific and Technical Information of China (English)
PENG SHIGE
2005-01-01
This paper deals with nonlinear expectations. The author obtains a nonlinear generalization of the well-known Kolmogorov's consistent theorem and then use it to construct filtration-consistent nonlinear expectations via nonlinear Markov chains. Compared to the author's previous results, i.e., the theory of g-expectations introduced via BSDE on a probability space, the present framework is not based on a given probability measure. Many fully nonlinear and singular situations are covered. The induced topology is a natural generalization of Lp-norms and L∞-norm in linear situations.The author also obtains the existence and uniqueness result of BSDE under this new framework and develops a nonlinear type of von Neumann-Morgenstern representation theorem to utilities and present dynamic risk measures.
Directory of Open Access Journals (Sweden)
Mersedeh Jahanseir
2014-11-01
Full Text Available Background: In neurofeedback systems, people are able to reinforce or hinder their basic EEG rhythms according to operant conditioninin recent studies the effect of neurofeedback training on improvement of working memory has been shown on the healthy subjects. Disadvantage of neurofeedback is the high number of training sessions and high cost. In previous studies, alpha band power within (8-12 Hz has been considered for all subjects. Previous research reached the conclusion that by using individual upper alpha in neurofeedback, learning rate will increase, so the training sessions and the cost of training will be reduced. Material and Methods: In this study, all participants were female, 10 adults (10 women, mean age 33.8 years, SD=3.56 years. Randomly assigned to control and test group, five in test group and five in control group. Each subject performed the memory test four times, two times before the start of the first neurofeedback training and two times after the end of the last neurofeedback session. Eight training sessions were held, each session had three trials. Results: Discriminate response to the color of the drawing, as well as reaction time hadsignificant effects for test group (p0.05. Before and after eight training sessions by individual upper alpha power neurofeedback, reaction time of discriminate response to the color of the drawing for test group decreased and had significant effects (p0.05. Conclusion: Increasing relative individual upper alpha power, caused by neurofeedback training during eight sessions, indicated that this method increases the memory of women employees, and improves the ability of discriminative response to the color (red & green of the drawing as well as reducing reaction time.
Judd, S L; Judd, Stephen L.; Silber, Mary
1998-01-01
This paper investigates the competition between both simple (e.g. stripes, hexagons) and ``superlattice'' (super squares, super hexagons) Turing patterns in two-component reaction-diffusion systems. ``Superlattice'' patterns are formed from eight or twelve Fourier modes, and feature structure at two different length scales. Using perturbation theory, we derive simple analytical expressions for the bifurcation equation coefficients on both rhombic and hexagonal lattices. These expressions show that, no matter how complicated the reaction kinectics, the nonlinear reaction terms reduce to just four effective terms within the bifurcation equation coefficients. Moreover, at the hexagonal degeneracy -- when the quadratic term in the hexagonal bifurcation equation disappears -- the number of effective system parameters drops to two, allowing a complete characterization of the possible bifurcation results at this degeneracy. The general results are then applied to specific model equations, to investigate the stabilit...
Nonlinear ion acoustic waves scattered by vortexes
Ohno, Yuji; Yoshida, Zensho
2016-09-01
The Kadomtsev-Petviashvili (KP) hierarchy is the archetype of infinite-dimensional integrable systems, which describes nonlinear ion acoustic waves in two-dimensional space. This remarkably ordered system resides on a singular submanifold (leaf) embedded in a larger phase space of more general ion acoustic waves (low-frequency electrostatic perturbations). The KP hierarchy is characterized not only by small amplitudes but also by irrotational (zero-vorticity) velocity fields. In fact, the KP equation is derived by eliminating vorticity at every order of the reductive perturbation. Here, we modify the scaling of the velocity field so as to introduce a vortex term. The newly derived system of equations consists of a generalized three-dimensional KP equation and a two-dimensional vortex equation. The former describes 'scattering' of vortex-free waves by ambient vortexes that are determined by the latter. We say that the vortexes are 'ambient' because they do not receive reciprocal reactions from the waves (i.e., the vortex equation is independent of the wave fields). This model describes a minimal departure from the integrable KP system. By the Painlevé test, we delineate how the vorticity term violates integrability, bringing about an essential three-dimensionality to the solutions. By numerical simulation, we show how the solitons are scattered by vortexes and become chaotic.
Chemisorption And Precipitation Reactions
The transport and bioavailability of chemical components within soils is, in part, controlled by partitioning between solids and solution. General terms used to describe these partitioning reactions include chemisorption and precipitation. Chemisorption is inclusive of the suit...
Energy Technology Data Exchange (ETDEWEB)
Lallart, Mickael; Guyomar, Daniel, E-mail: mickael.lallart@insa-lyon.fr [LGEF, INSA-Lyon, Universite de Lyon, 8 rue de la Physique, F-69621 (France)
2011-10-29
The proliferation of wearable and left-behind devices has raised the issue of powering such systems. While primary batteries have been widely used in order to address this issue, recent trends have focused on energy harvesting products that feature high reliability and low maintenance issues. Among all the ambient sources available for energy harvesting, vibrations and heat have been of significant interest among the research community for small-scale devices. However, the conversion abilities of materials are still limited when dealing with systems featuring small dimensions. The purpose of this paper is to presents an up-to-date view of nonlinear approaches for increasing the efficiency of electromechanical and electrocaloric conversion mechanisms. From the modeling of the operation principles of the different architectures, a comparative analysis will be exposed, emphasizing the advantages and drawbacks of the presented concepts, in terms of maximal output power (under constant vibration magnitude or taking into account the damping effect), load independence, and implementation easiness.
2016-01-01
This volume brings together four lecture courses on modern aspects of water waves. The intention, through the lectures, is to present quite a range of mathematical ideas, primarily to show what is possible and what, currently, is of particular interest. Water waves of large amplitude can only be fully understood in terms of nonlinear effects, linear theory being not adequate for their description. Taking advantage of insights from physical observation, experimental evidence and numerical simulations, classical and modern mathematical approaches can be used to gain insight into their dynamics. The book presents several avenues and offers a wide range of material of current interest. Due to the interdisciplinary nature of the subject, the book should be of interest to mathematicians (pure and applied), physicists and engineers. The lectures provide a useful source for those who want to begin to investigate how mathematics can be used to improve our understanding of water wave phenomena. In addition, some of the...
Nonlinear estimation and classification
Hansen, Mark; Holmes, Christopher; Mallick, Bani; Yu, Bin
2003-01-01
Researchers in many disciplines face the formidable task of analyzing massive amounts of high-dimensional and highly-structured data This is due in part to recent advances in data collection and computing technologies As a result, fundamental statistical research is being undertaken in a variety of different fields Driven by the complexity of these new problems, and fueled by the explosion of available computer power, highly adaptive, non-linear procedures are now essential components of modern "data analysis," a term that we liberally interpret to include speech and pattern recognition, classification, data compression and signal processing The development of new, flexible methods combines advances from many sources, including approximation theory, numerical analysis, machine learning, signal processing and statistics The proposed workshop intends to bring together eminent experts from these fields in order to exchange ideas and forge directions for the future
Directory of Open Access Journals (Sweden)
Roman M. Baevsky
2013-05-01
Full Text Available The paper presents the results of the long-term medical & ecological investigations conducted during the experiment Mars-500. Methodology of conducting the long-term medical & ecological investigations and the applied methods are considered. The results are presented in the materials of the research conducted in Russian Federation and Republic of Belarus (Moscow, Syktyvkar, Yekaterinburg, Izhevsk, Magadan and Minsk. For comparative evaluation of the functional state of different reference groups the notion of “ecological stress” was introduced. It depends upon the degree of dominance of the activity of the sympathetic member of the regulatory system over the parasympathetic member. Application of probabilistic approach to the assessment of the functional state and adaptation level with the FR (functional reserve and the DT (the degree of tension of the regulatory mechanisms proved the detected peculiarities of the heart rhythm vegetative regulation. Clear dependency of the functional state of the volunteers on geographic location of regions and climatic parameters is observed. Almost every HRV indicator is characterized by seasonal dynamics. Seasonal dynamics data is exemplified by the research conducted in Yekaterinburg and Syktyvkar. During the earth-bound experiment Mars-500 flight conditions to Mars were simulated. Results of the long-term medical & ecological investigations conducted simultaneously with the experiment Mars-500 showed that health changes in practically healthy people do not usually exceed the limits of the prenosological state.
Development of a Nonlinear Internal Wave Tactical Decision Aid
2016-06-07
of a Nonlinear Internal Wave Tactical Decision Aid 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER...Development of a Nonlinear Internal Wave Tactical Decision Aid Christopher R. Jackson Global Ocean Associates 6220 Jean Louise Way Alexandria...www.internalwaveatlas.com LONG-TERM GOALS The long term goal of the project is to develop a prediction methodology for the occurrence of nonlinear
Nonlinear effects in asymmetric catalysis.
Satyanarayana, Tummanapalli; Abraham, Susan; Kagan, Henri B
2009-01-01
There is a need for the preparation of enantiomerically pure compounds for various applications. An efficient approach to achieve this goal is asymmetric catalysis. The chiral catalyst is usually prepared from a chiral auxiliary, which itself is derived from a natural product or by resolution of a racemic precursor. The use of non-enantiopure chiral auxiliaries in asymmetric catalysis seems unattractive to preparative chemists, since the anticipated enantiomeric excess (ee) of the reaction product should be proportional to the ee value of the chiral auxiliary (linearity). In fact, some deviation from linearity may arise. Such nonlinear effects can be rich in mechanistic information and can be synthetically useful (asymmetric amplification). This Review documents the advances made during the last decade in the use of nonlinear effects in the area of organometallic and organic catalysis.
Freezing of nonlinear Bloch oscillations in the generalized discrete nonlinear Schrödinger equation.
Cao, F J
2004-09-01
The dynamics in a nonlinear Schrödinger chain in a homogeneous electric field is studied. We show that discrete translational invariant integrability-breaking terms can freeze the Bloch nonlinear oscillations and introduce new faster frequencies in their dynamics. These phenomena are studied by direct numerical integration and through an adiabatic approximation. The adiabatic approximation allows a description in terms of an effective potential that greatly clarifies the phenomena.
Transformation design and nonlinear Hamiltonians
Brougham, Thomas; Jex, Igor
2009-01-01
We study a class of nonlinear Hamiltonians, with applications in quantum optics. The interaction terms of these Hamiltonians are generated by taking a linear combination of powers of a simple `beam splitter' Hamiltonian. The entanglement properties of the eigenstates are studied. Finally, we show how to use this class of Hamiltonians to perform special tasks such as conditional state swapping, which can be used to generate optical cat states and to sort photons.
Design of a nonlinear torsional vibration absorber
Tahir, Ammaar Bin
larger than that in the latter. A nonlinear absorber design has been proposed comprising of thin beams as elastic elements. The geometric configuration of the proposed design has been shown to provide cubic stiffness nonlinearity in torsion. The values of design variables, namely the strength of nonlinearity alpha and torsional stiffness kalpha, were obtained by optimizing dimensions and material properties of the beams for a maximum vibration energy dissipation in the nonlinear absorber. A parametric study has also been conducted to analyze the effect of the magnitude of excitation provided to the system on the performance of a nonlinear absorber. It has been shown that the nonlinear absorber turns out to be more effective in terms of energy dissipation as compared to a linear absorber with an increase in the excitation level applied to the system.
Institute of Scientific and Technical Information of China (English)
张炎涛
2012-01-01
运用Hansen和Seo的两区制阈值协整理论,研究了1953—2010年中国经济增长与碳排放之间的关系及其关系的短期非线性调整。结果表明：经济增长与碳排放之间存在非线性协整关系;当两者的长期均衡关系出现短期偏离时,在正常区制中,主要依靠碳排放的调整使两者间关系恢复到长期均衡状态,在极端区制中,碳排放和经济增长都会向均衡状态做出调整,且碳排放的调整速度更快。%This paper applies the theory of two-regime threshold cointegration developed by Hansen and Seo to investigate the relationship between economic growth and carbon emission during 1953-2010 in China and its short-term nonlinear adjustment.The results show as follows：there exists a threshold co-integration relationship between economic growth and carbon emission;when the deviation from the long-run equilibrium between economic growth and carbon emission,short-run response is mainly executed by the adjustment of carbon emission in typical regime,while both economic growth and carbon emission are all moving toward long-term equilibrium in extreme regime,and the adjustment speed of carbon emission is faster than that of economic growth.
Souissi, Makram; Chtourou, Hamdi; Abedelmalek, Salma; Ghozlane, Imen Ben; Sahnoun, Zouhair
2014-05-28
The aim of the present study was to investigate the effects of caffeine ingestion on cognitive and physical performances after 36h of sleep deprivation. In randomized order, thirteen healthy male physical education students (age: 21.1±1.1years, body mass: 77.1±7.2kg, height: 1.77±0.06m) completed four test sessions at 18:00h: after placebo or 5mg·kg(-1) of caffeine ingestion during a baseline night (RN) (bed time: from 22:30h to 07:00h) or a night of 36h of sleep deprivation (TSD). During each test session, participants performed the squat jump (SJ), the reaction time, and the 30-s Wingate tests (i.e., for the measurement of the peak (PP) and mean (MP) powers and the fatigue index (FI)). The results showed that PP and MP decreased and FI increased during the TSD compared to RN in the placebo condition (pcaffeine ingestion improved PP after TSD compared to RN (pcaffeine ingestions (pcaffeine ingestion during RN and TSD (pcaffeine ingestion only during the TSD (pcaffeine is an effective strategy to counteract the effect of 36h of sleep loss on physical and cognitive performances.
Chen, Xianfeng; Zeng, Heping; Guo, Qi; She, Weilong
2015-01-01
This book presents an overview of the state of the art of nonlinear optics from weak light nonlinear optics, ultrafast nonlinear optics to electro-optical theory and applications. Topics range from the fundamental studies of the interaction between matter and radiation to the development of devices, components, and systems of tremendous commercial interest for widespread applications in optical telecommunications, medicine, and biotechnology.
Distributed nonlinear optical response
DEFF Research Database (Denmark)
Nikolov, Nikola Ivanov
2005-01-01
The purpose of the research presented here is to investigate basic physical properties in nonlinear optical materials with delayed or nonlocal nonlinearity. Soliton propagation, spectral broadening and the influence of the nonlocality or delay of the nonlinearity are the main focusses in the work...
Noncommutative Nonlinear Supersymmetry
Nishino, H; Nishino, Hitoshi; Rajpoot, Subhash
2002-01-01
We present noncommutative nonlinear supersymmetric theories. The first example is a non-polynomial Akulov-Volkov-type lagrangian with noncommutative nonlinear global supersymmetry in arbitrary space-time dimensions. The second example is the generalization of this lagrangian to Dirac-Born-Infeld lagrangian with nonlinear supersymmetry realized in dimensions D=2,3,4 and 6 (mod 8).
Fiber Nonlinearities: A Tutorial
Institute of Scientific and Technical Information of China (English)
Govind P. Agrawal
2003-01-01
Fiber nonlinearities have long been regarded as being mostly harmful for fiber-optic communication systems. Over the last few years, however, the nonlinear effects are increasingly being used for practical telecommunications applications,the Raman amplification being only one of the recent examples. In this tutorial I review the vario us nonlinear effects occurring in optical fibers from both standpoints..
Fiber Nonlinearities: A Tutorial
Institute of Scientific and Technical Information of China (English)
Govind; P.; Agrawal
2003-01-01
Fiber nonlinearities have long been regarded as being mostly harmful for fiber-optic communication systems. Over the last few years, however, the nonlinear effects are increasingly being used for practical telecommunications applications, the Raman amplification being only one of the recent examples. In this tutorial I review the various nonlinear effects occurring in optical fibers from both standpoints..
Euclidean Quantum Mechanics and Universal Nonlinear Filtering
Directory of Open Access Journals (Sweden)
Bhashyam Balaji
2009-02-01
Full Text Available An important problem in applied science is the continuous nonlinear filtering problem, i.e., the estimation of a Langevin state that is observed indirectly. In this paper, it is shown that Euclidean quantum mechanics is closely related to the continuous nonlinear filtering problem. The key is the configuration space Feynman path integral representation of the fundamental solution of a Fokker-Planck type of equation termed the Yau Equation of continuous-continuous filtering. A corollary is the equivalence between nonlinear filtering problem and a time-varying Schr¨odinger equation.
BRST structure of non-linear superalgebras
Asorey, M; Radchenko, O V; Sugamoto, A
2008-01-01
In this paper we analyse the structure of the BRST structure of nonlinear superalgebras. We consider quadratic non-linear superalgebras where a commutator (in terms of (super) Poisson brackets) of the generators is a quadratic polynomial of the generators. We find the explicit form of the BRST charge up to cubic order in Faddeev-Popov ghost fields for arbitrary quadratic nonlinear superalgebras. We point out the existence of constraints on structure constants of the superalgebra when the nilpotent BRST charge is quadratic in Faddeev-Popov ghost fields. The general results are illustrated by simple examples of superalgebras.
Structural optimization for nonlinear dynamic response.
Dou, Suguang; Strachan, B Scott; Shaw, Steven W; Jensen, Jakob S
2015-09-28
Much is known about the nonlinear resonant response of mechanical systems, but methods for the systematic design of structures that optimize aspects of these responses have received little attention. Progress in this area is particularly important in the area of micro-systems, where nonlinear resonant behaviour is being used for a variety of applications in sensing and signal conditioning. In this work, we describe a computational method that provides a systematic means for manipulating and optimizing features of nonlinear resonant responses of mechanical structures that are described by a single vibrating mode, or by a pair of internally resonant modes. The approach combines techniques from nonlinear dynamics, computational mechanics and optimization, and it allows one to relate the geometric and material properties of structural elements to terms in the normal form for a given resonance condition, thereby providing a means for tailoring its nonlinear response. The method is applied to the fundamental nonlinear resonance of a clamped-clamped beam and to the coupled mode response of a frame structure, and the results show that one can modify essential normal form coefficients by an order of magnitude by relatively simple changes in the shape of these elements. We expect the proposed approach, and its extensions, to be useful for the design of systems used for fundamental studies of nonlinear behaviour as well as for the development of commercial devices that exploit nonlinear behaviour.
Nonlinear Krylov acceleration of reacting flow codes
Energy Technology Data Exchange (ETDEWEB)
Kumar, S.; Rawat, R.; Smith, P.; Pernice, M. [Univ. of Utah, Salt Lake City, UT (United States)
1996-12-31
We are working on computational simulations of three-dimensional reactive flows in applications encompassing a broad range of chemical engineering problems. Examples of such processes are coal (pulverized and fluidized bed) and gas combustion, petroleum processing (cracking), and metallurgical operations such as smelting. These simulations involve an interplay of various physical and chemical factors such as fluid dynamics with turbulence, convective and radiative heat transfer, multiphase effects such as fluid-particle and particle-particle interactions, and chemical reaction. The governing equations resulting from modeling these processes are highly nonlinear and strongly coupled, thereby rendering their solution by traditional iterative methods (such as nonlinear line Gauss-Seidel methods) very difficult and sometimes impossible. Hence we are exploring the use of nonlinear Krylov techniques (such as CMRES and Bi-CGSTAB) to accelerate and stabilize the existing solver. This strategy allows us to take advantage of the problem-definition capabilities of the existing solver. The overall approach amounts to using the SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) method and its variants as nonlinear preconditioners for the nonlinear Krylov method. We have also adapted a backtracking approach for inexact Newton methods to damp the Newton step in the nonlinear Krylov method. This will be a report on work in progress. Preliminary results with nonlinear GMRES have been very encouraging: in many cases the number of line Gauss-Seidel sweeps has been reduced by about a factor of 5, and increased robustness of the underlying solver has also been observed.
Analytic solutions of nonlinear Cournot duopoly game
Directory of Open Access Journals (Sweden)
Akio Matsumoto
2005-01-01
Full Text Available We construct a Cournot duopoly model with production externality in which reaction functions are unimodal. We consider the case of a Cournot model which has a stable equilibrium point. Then we show the existence of analytic solutions of the model. Moreover, we seek general solutions of the model in the form of nonlinear second-order difference equation.
Asymptotic Behaviour Near a Nonlinear Sink
Calder, Matt S
2010-01-01
In this paper, we will explore an iterative procedure to determine the detailed asymptotic behaviour of solutions of a certain class of nonlinear vector differential equations which approach a nonlinear sink as time tends to infinity. This procedure is indifferent to resonance in the eigenvalues. Moreover, we will address the writing of one component in terms of the other in the case of a planar system. Examples will be given, notably the Michaelis-Menten mechanism of enzyme kinetics.
PBH tests for nonlinear systems
Kawano, Yu; Ohtsuka, Toshiyuki
2017-01-01
Recently, concepts of nonlinear eigenvalues and eigenvectors are introduced. In this paper, we establish connections between the nonlinear eigenvalues and nonlinear accessibility/observability. In particular, we provide a generalization of Popov- Belevitch-Hautus (PBH) test to nonlinear accessibilit
Nonlinear Process Fault Diagnosis Based on Serial Principal Component Analysis.
Deng, Xiaogang; Tian, Xuemin; Chen, Sheng; Harris, Chris J
2016-12-22
Many industrial processes contain both linear and nonlinear parts, and kernel principal component analysis (KPCA), widely used in nonlinear process monitoring, may not offer the most effective means for dealing with these nonlinear processes. This paper proposes a new hybrid linear-nonlinear statistical modeling approach for nonlinear process monitoring by closely integrating linear principal component analysis (PCA) and nonlinear KPCA using a serial model structure, which we refer to as serial PCA (SPCA). Specifically, PCA is first applied to extract PCs as linear features, and to decompose the data into the PC subspace and residual subspace (RS). Then, KPCA is performed in the RS to extract the nonlinear PCs as nonlinear features. Two monitoring statistics are constructed for fault detection, based on both the linear and nonlinear features extracted by the proposed SPCA. To effectively perform fault identification after a fault is detected, an SPCA similarity factor method is built for fault recognition, which fuses both the linear and nonlinear features. Unlike PCA and KPCA, the proposed method takes into account both linear and nonlinear PCs simultaneously, and therefore, it can better exploit the underlying process's structure to enhance fault diagnosis performance. Two case studies involving a simulated nonlinear process and the benchmark Tennessee Eastman process demonstrate that the proposed SPCA approach is more effective than the existing state-of-the-art approach based on KPCA alone, in terms of nonlinear process fault detection and identification.
Nonlinear generalization of Den Hartog's equal-peak method
Habib, G.; Detroux, T.; Viguié, R.; Kerschen, G.
2015-02-01
This study addresses the mitigation of a nonlinear resonance of a mechanical system. In view of the narrow bandwidth of the classical linear tuned vibration absorber, a nonlinear absorber, termed the nonlinear tuned vibration absorber (NLTVA), is introduced in this paper. An unconventional aspect of the NLTVA is that the mathematical form of its restoring force is tailored according to the nonlinear restoring force of the primary system. The NLTVA parameters are then determined using a nonlinear generalization of Den Hartog's equal-peak method. The mitigation of the resonant vibrations of a Duffing oscillator is considered to illustrate the proposed developments.
Nonlinear dynamics and complexity
Luo, Albert; Fu, Xilin
2014-01-01
This important collection presents recent advances in nonlinear dynamics including analytical solutions, chaos in Hamiltonian systems, time-delay, uncertainty, and bio-network dynamics. Nonlinear Dynamics and Complexity equips readers to appreciate this increasingly main-stream approach to understanding complex phenomena in nonlinear systems as they are examined in a broad array of disciplines. The book facilitates a better understanding of the mechanisms and phenomena in nonlinear dynamics and develops the corresponding mathematical theory to apply nonlinear design to practical engineering.
Institute of Scientific and Technical Information of China (English)
孙皓; 俞来雷
2012-01-01
基于MS—VECM模型对预期理论调整作用下的中国利率期限结构非线性动态过程进行的实证研究，结果表明：预期理论在中国利率期限结构中是成立的；中国利率期限结构具有两区制的非线性动态特征，可以按预期理论的调整强度将两种区制分别描述为“强调整区制”与“弱调整区制”；不同期限利率的平均变动幅度和平均风险溢价水平会随区制状态变化而发生变化，具有区制相依性，区制间的转移具有非对称性；利率期限结构与物价压力的非线性区制划分具有相似性，物价波动是利率期限结构非线性动态变化的重要原因。%This paper conducts an empirical study of the nonlinear dynamic process of China＇s term structure of interest rates under the adjustment of the expectation theory with MS-VECM model. The results indicate that the expectation theory is tenable in China＇s term structure of interest rates. The term structure of interest rates in China has the nonlinear dynamic characteristics of two regimes, which can be described as ＂strong adjustment regime＂ and ＂weak adjustment regime＂ according to the intensity of adjustment of the expectation theory. The average interest rate changes and the aver- age risk premium level at different terms will change along with the changes of the regimes, and the changing of each regime is asymmetric. The term structure of interest rates has some similarity as the non-linear zone partition of price pressure; the price fluctuation is one of the important reasons for the nonlinear dynamic changes of the term structure of interest rates.
Nonlinear field space cosmology
Mielczarek, Jakub; Trześniewski, Tomasz
2017-08-01
We consider the FRW cosmological model in which the matter content of the Universe (playing the role of an inflaton or quintessence) is given by a novel generalization of the massive scalar field. The latter is a scalar version of the recently introduced nonlinear field space theory, where the physical phase space of a given field is assumed to be compactified at large energies. For our analysis, we choose the simple case of a field with the spherical phase space and endow it with the generalized Hamiltonian analogous to the XXZ Heisenberg model, normally describing a system of spins in condensed matter physics. Subsequently, we study both the homogenous cosmological sector and linear perturbations of such a test field. In the homogenous sector, we find that nonlinearity of the field phase space is becoming relevant for large volumes of the Universe and can lead to a recollapse, and possibly also at very high energies, leading to the phase of a bounce. Quantization of the field is performed in the limit where the nontrivial nature of its phase space can be neglected, while there is a nonvanishing contribution from the Lorentz symmetry breaking term of the Hamiltonian. As a result, in the leading order of the XXZ anisotropy parameter, we find that the inflationary spectral index remains unmodified with respect to the standard case but the total amplitude of perturbations is subject to a correction. The Bunch-Davies vacuum state also becomes appropriately corrected. The proposed new approach is bringing cosmology and condensed matter physics closer together, which may turn out to be beneficial for both disciplines.
An Enhanced Asymptotic Expansion for the Stability of Nonlinear Elastic Structures
DEFF Research Database (Denmark)
Christensen, Claus Dencker; Byskov, Esben
2010-01-01
A new, enhanced asymptotic expansion applicable to stability of structures made of nonlinear elastic materials is established. The method utilizes “hyperbolic” terms instead of the conventional polynomial terms, covers full kinematic nonlinearity and is applied to nonlinear elastic Euler columns ...
Topological approximation of the nonlinear Anderson model
Milovanov, Alexander V.; Iomin, Alexander
2014-06-01
We study the phenomena of Anderson localization in the presence of nonlinear interaction on a lattice. A class of nonlinear Schrödinger models with arbitrary power nonlinearity is analyzed. We conceive the various regimes of behavior, depending on the topology of resonance overlap in phase space, ranging from a fully developed chaos involving Lévy flights to pseudochaotic dynamics at the onset of delocalization. It is demonstrated that the quadratic nonlinearity plays a dynamically very distinguished role in that it is the only type of power nonlinearity permitting an abrupt localization-delocalization transition with unlimited spreading already at the delocalization border. We describe this localization-delocalization transition as a percolation transition on the infinite Cayley tree (Bethe lattice). It is found in the vicinity of the criticality that the spreading of the wave field is subdiffusive in the limit t →+∞. The second moment of the associated probability distribution grows with time as a power law ∝ tα, with the exponent α =1/3 exactly. Also we find for superquadratic nonlinearity that the analog pseudochaotic regime at the edge of chaos is self-controlling in that it has feedback on the topology of the structure on which the transport processes concentrate. Then the system automatically (without tuning of parameters) develops its percolation point. We classify this type of behavior in terms of self-organized criticality dynamics in Hilbert space. For subquadratic nonlinearities, the behavior is shown to be sensitive to the details of definition of the nonlinear term. A transport model is proposed based on modified nonlinearity, using the idea of "stripes" propagating the wave process to large distances. Theoretical investigations, presented here, are the basis for consistency analysis of the different localization-delocalization patterns in systems with many coupled degrees of freedom in association with the asymptotic properties of the
Solution of continuous nonlinear PDEs through order completion
Oberguggenberger, MB
1994-01-01
This work inaugurates a new and general solution method for arbitrary continuous nonlinear PDEs. The solution method is based on Dedekind order completion of usual spaces of smooth functions defined on domains in Euclidean spaces. However, the nonlinear PDEs dealt with need not satisfy any kind of monotonicity properties. Moreover, the solution method is completely type independent. In other words, it does not assume anything about the nonlinear PDEs, except for the continuity of their left hand term, which includes the unkown function. Furthermore the right hand term of such nonlinear PDEs can in fact be given any discontinuous and measurable function.
Nonlinear Elliptic Differential Equations with Multivalued Nonlinearities
Indian Academy of Sciences (India)
Antonella Fiacca; Nikolaos Matzakos; Nikolaos S Papageorgiou; Raffaella Servadei
2001-11-01
In this paper we study nonlinear elliptic boundary value problems with monotone and nonmonotone multivalued nonlinearities. First we consider the case of monotone nonlinearities. In the first result we assume that the multivalued nonlinearity is defined on all $\\mathbb{R}$. Assuming the existence of an upper and of a lower solution, we prove the existence of a solution between them. Also for a special version of the problem, we prove the existence of extremal solutions in the order interval formed by the upper and lower solutions. Then we drop the requirement that the monotone nonlinearity is defined on all of $\\mathbb{R}$. This case is important because it covers variational inequalities. Using the theory of operators of monotone type we show that the problem has a solution. Finally in the last part we consider an eigenvalue problem with a nonmonotone multivalued nonlinearity. Using the critical point theory for nonsmooth locally Lipschitz functionals we prove the existence of at least two nontrivial solutions (multiplicity theorem).
Nonlinear ion acoustic waves scattered by vortexes
Ohno, Yuji
2015-01-01
The Kadomtsev--Petviashvili (KP) hierarchy is the archetype of infinite-dimensional integrable systems, which describes nonlinear ion acoustic waves in two-dimensional space. This remarkably ordered system resides on a singular submanifold (leaf) embedded in a larger phase space of more general ion acoustic waves (low-frequency electrostatic perturbations). The KP hierarchy is characterized not only by small amplitudes but also by irrotational (zero-vorticity) velocity fields. In fact, the KP equation is derived by eliminating vorticity at every order of the reductive perturbation. Here we modify the scaling of the velocity field so as to introduce a vortex term. The newly derived system of equations consists of a generalized three-dimensional KP equation and a two-dimensional vortex equation. The former describes `scattering' of vortex-free waves by ambient vortexes that are determined by the latter. We say that the vortexes are `ambient' because they do not receive reciprocal reactions from the waves (i.e.,...
DEFF Research Database (Denmark)
Christiansen, Peter Leth; Gaididei, Yuri Borisovich; Rasmussen, Kim
1996-01-01
We study the effect of adding noise and nonlinear damping in the two-dimensional nonlinear Schrodinger equation (NLS). Using a collective approach, we find that for initial conditions where total collapse occurs in the unperturbed NLS, the presence of the damping term will instead in an exponenti......We study the effect of adding noise and nonlinear damping in the two-dimensional nonlinear Schrodinger equation (NLS). Using a collective approach, we find that for initial conditions where total collapse occurs in the unperturbed NLS, the presence of the damping term will instead...
Traveling waves in a nonlocal, piecewise linear reaction-diffusion population model
Autry, E. A.; Bayliss, A.; Volpert, V. A.
2017-08-01
We consider an analytically tractable switching model that is a simplification of a nonlocal, nonlinear reaction-diffusion model of population growth where we take the source term to be piecewise linear. The form of this source term allows us to consider both the monostable and bistable versions of the problem. By transforming to a traveling frame and choosing specific kernel functions, we are able to reduce the problem to a system of algebraic equations. We construct solutions and examine the propagation speed and monotonicity of the resulting waves.
Nonlinear Chemical Dynamics and Synchronization
Li, Ning
Alan Turing's work on morphogenesis, more than half a century ago, continues to motivate and inspire theoretical and experimental biologists even today. That said, there are very few experimental systems for which Turing's theory is applicable. In this thesis we present an experimental reaction-diffusion system ideally suited for testing Turing's ideas in synthetic "cells" consisting of microfluidically produced surfactant-stabilized emulsions in which droplets containing the Belousov-Zhabotinsky (BZ) oscillatory chemical reactants are dispersed in oil. The BZ reaction has become the prototype of nonlinear dynamics in chemistry and a preferred system for exploring the behavior of coupled nonlinear oscillators. Our system consists of a surfactant stabilized monodisperse emulsion of drops of aqueous BZ solution dispersed in a continuous phase of oil. In contrast to biology, here the chemistry is understood, rate constants are measured and interdrop coupling is purely diffusive. We explore a large set of parameters through control of rate constants, drop size, spacing, and spatial arrangement of the drops in lines and rings in one-dimension (1D) and hexagonal arrays in two-dimensions (2D). The Turing model is regarded as a metaphor for morphogenesis in biology but not for prediction. Here, we develop a quantitative and falsifiable reaction-diffusion model that we experimentally test with synthetic cells. We quantitatively establish the extent to which the Turing model in 1D describes both stationary pattern formation and temporal synchronization of chemical oscillators via reaction-diffusion and in 2D demonstrate that chemical morphogenesis drives physical differentiation in synthetic cells.
Blow-up of a hyperbolic equation of viscoelasticity with supercritical nonlinearities
Guo, Yanqiu; Rammaha, Mohammad A.; Sakuntasathien, Sawanya
2017-02-01
We investigate a hyperbolic PDE, modeling wave propagation in viscoelastic media, under the influence of a linear memory term of Boltzmann type, and a nonlinear damping modeling friction, as well as an energy-amplifying supercritical nonlinear source:
Nonlinear modeling of thermoacoustically driven energy cascade
Gupta, Prateek; Scalo, Carlo; Lodato, Guido
2016-11-01
We present an investigation of nonlinear energy cascade in thermoacoustically driven high-amplitude oscillations, from the initial weakly nonlinear regime to the shock wave dominated limit cycle. We develop a first principle based quasi-1D model for nonlinear wave propagation in a canonical minimal unit thermoacoustic device inspired by the experimental setup of Biwa et al.. Retaining up to quadratic nonlinear terms in the governing equations, we develop model equations for nonlinear wave propagation in the proximity of differentially heated no-slip boundaries. Furthermore, we discard the effects of acoustic streaming in the present study and focus on nonlinear energy cascade due to high amplitude wave propagation. Our model correctly predicts the observed exponential growth of the thermoacoustically amplified second harmonic, as well as the energy transfer rate to higher harmonics causing wave steepening. Moreover, we note that nonlinear coupling of local pressure with heat transfer reduces thermoacoustic amplification gradually thus causing the system to reach limit cycle exhibiting shock waves. Throughout, we verify the results from the quasi-1D model with fully compressible Navier-Stokes simulations.
PREFACE Integrability and nonlinear phenomena Integrability and nonlinear phenomena
Gómez-Ullate, David; Lombardo, Sara; Mañas, Manuel; Mazzocco, Marta; Nijhoff, Frank; Sommacal, Matteo
2010-10-01
includes two papers devoted to the subject. Konopelchenko et al [8] describe critical and degenerate critical points of a scalar function which obeys the Euler-Poisson-Darboux equation in terms of the hodograph solutions of the dispersionless coupled Korteweg-de Vries hierarchies. Finally, Bogdanov [9] considers 2-component integrable generalizations of the dispersionless 2D Toda lattice hierarchy connected with non-Hamiltonian vector fields, similar to the Manakov-Santini hierarchy generalizing the dKP hierarchy. He presents the simplest 2-component generalization of the dispersionless 2DTL equation, being its differential reduction analogous to the Dunajski interpolating system. Some papers in the issue are concerned with methods to construct solutions of integrable systems, while others place more emphasis on studying properties of specific solutions of applicative interest. Among the first approach, the paper by Kaup and van Gorder [10] describes perturbation theory applied to the Inverse Scattering Transform in 3x eigenvalue problems of Zakharov-Shabat's type. Schiebold [11] studies a projection method to construct solutions of the Ablowitz-Kaup-Newell-Segur (AKNS) system, which enables her to write explicit N-soliton solutions in closed form. An example of the second kind is the paper by Biondini and Wang [12], who study in detail the behaviour of line soliton solutions of the 2DTL, describing their directions and amplitudes and also the richness of their interactions, which include resonant soliton interactions and web structure. An important field of study in integrable systems relates to the singularity structure of the solutions to nonlinear equations. When all movable singularities are poles, the system is said to have the Painleve property. The solutions may be multivalued but they can be analytically continued to meromorphic functions on the universal cover of the punctured Riemann sphere (the punctures being the fixed singularities) and the spectral curve is
A nonlinear RDF model for waves propagating in shallow water
Institute of Scientific and Technical Information of China (English)
王厚杰; 杨作升; 李瑞杰; 张军
2001-01-01
In this paper, a composite explicit nonlinear dispersion relation is presented with reference to Stokes 2nd order dispersion relation and the empirical relation of Hedges. The explicit dispersion relation has such advantages that it can smoothly match the Stokes relation in deep and intermediate water and Hedgs’s relation in shallow water. As an explicit formula, it separates the nonlinear term from the linear dispersion relation. Therefore it is convenient to obtain the numerical solution of nonlinear dispersion relation. The present formula is combined with the modified mild-slope equation including nonlinear effect to make a Refraction-Diffraction (RDF) model for wave propagating in shallow water. This nonlinear model is verified over a complicated topography with two submerged elliptical shoals resting on a slope beach. The computation results compared with those obtained from linear model show that at present the nonlinear RDF model can predict the nonlinear characteristics and the combined refracti
Extended models of nonlinear waves in liquid with gas bubbles
Kudryashov, Nikolay A
2016-01-01
In this work we generalize the models for nonlinear waves in a gas--liquid mixture taking into account an interphase heat transfer, a surface tension and a weak liquid compressibility simultaneously at the derivation of the equations for nonlinear waves. We also take into consideration high order terms with respect to the small parameter. Two new nonlinear differential equations are derived for long weakly nonlinear waves in a liquid with gas bubbles by the reductive perturbation method considering both high order terms with respect to the small parameter and the above mentioned physical properties. One of these equations is the perturbation of the Burgers equation and corresponds to main influence of dissipation on nonlinear waves propagation. The other equation is the perturbation of the Burgers--Korteweg--de Vries equation and corresponds to main influence of dispersion on nonlinear waves propagation.
Energy Technology Data Exchange (ETDEWEB)
Hagstrom, T. [Univ. of New Mexico, Albuquerque, NM (United States); Radhakrishnan, K. [Sverdrup Technology, Brook Park, OH (United States)
1994-12-31
The authors report on some iterative methods which they have tested for use in combustion simulations. In particular, they have developed a code to solve zero Mach number reacting flow equations with complex reaction and diffusion physics. These equations have the form of a nonlinear parabolic system coupled with constraints. In semi-discrete form, one obtains DAE`s of index two or three depending on the number of spatial dimensions. The authors have implemented a fourth order (fully implicit) BDF method in time, coupled with a suite of fourth order explicit and implicit spatial difference approximations. Most codes they know of for simulating reacting flows use a splitting strategy to march in time. This results in a sequence of nonlinear systems to solve, each of which has a simpler structure than the one they are faced with. The rapid and robust solution of the coupled system is the essential requirement for the success of their approach. They have implemented and analyzed nonlinear generalizations of conjugate gradient-like methods for nonsymmetric systems, including CGS and the quasi-Newton based method of Eirola and Nevanlinna. They develop a general framework for the nonlinearization of linear methods in terms of the acceleration of fixed-point iterations, where the latter is assumed to include the {open_quote}preconditioning{open_quote}. Their preconditioning is a single step of a split method, using lower order spatial difference approximations as well as simplified (Fickian) approximations of the diffusion physics.
Directory of Open Access Journals (Sweden)
W. L. Fouché
1983-03-01
Full Text Available In this article we discuss some aspects of nonlinear functional analysis. It included reviews of Banach’s contraction theorem, Schauder’s fixed point theorem, globalising techniques and applications of homotopy theory to nonlinear functional analysis. The author emphasises that fundamentally new ideas are required in order to achieve a better understanding of phenomena which contain both nonlinear and definite infinite dimensional features.
Nonlinear Electrodynamics and QED
2003-01-01
The limits of linear electrodynamics are reviewed, and possible directions of nonlinear extension are explored. The central theme is that the qualitative character of the empirical successes of quantum electrodynamics must be used as a guide for understanding the nature of the nonlinearity of electrodynamics at the subatomic level. Some established theories of nonlinear electrodynamics, namely, those of Mie, Born, and Infeld are presented in the language of the modern geometrical and topologi...
Institute of Scientific and Technical Information of China (English)
田慧洁; 李艳玲; 郭改慧
2016-01-01
研究了具有饱和项和毒素影响的反应扩散模型的平衡态方程,在齐次Neumann边界条件下常数平衡解的分歧与稳定性.利用谱分析和分歧理论的方法,分别以r1、r2为分歧参数,讨论了系统在常数平衡解附近出现分歧现象;同时运用线性算子的扰动理论和分歧解的稳定理论给出分歧解的稳定性.%The steady-states of reaction diffusion model with saturating terms and effects of toxic substances is studied, the bifurcation and the stability of a reaction-diffusion system with homogeneous Neumann boundary are investigated by the method of spectral analysis and bifurcation theory. The bifurcation at the steady-state solutions is acquired by treating r1, r2 as bifurcation parameters. Moreover, some stability results of the bifurcation solutions are obtained by using pertur-bation theory of linear operators and stability theory of bifurcation solutions.
Structural optimization for nonlinear dynamic response
DEFF Research Database (Denmark)
Dou, Suguang; Strachan, B. Scott; Shaw, Steven W.
2015-01-01
condition, thereby providing a means for tailoring its nonlinear response. The method is applied to the fundamental nonlinear resonance of a clamped–clamped beam and to the coupled mode response of a frame structure, and the results show that one can modify essential normal form coefficients by an order...... resonant behaviour is being used for a variety of applications in sensing and signal conditioning. In this work, we describe a computational method that provides a systematic means for manipulating and optimizing features of nonlinear resonant responses of mechanical structures that are described...... by a single vibrating mode, or by a pair of internally resonant modes. The approach combines techniques from nonlinear dynamics, computational mechanics and optimization, and it allows one to relate the geometric and material properties of structural elements to terms in the normal form for a given resonance...
Kim, Daesang
2013-11-01
We have extended reactive flow simulation in pore-network models to include geometric changes in the medium from dissolution effects. These effects include changes in pore volume and reactive surface area, as well as topological changes that open new connections. The computed changes were based upon a mineral map from an X-ray computed tomography image of a sandstone core. We studied the effect of these changes on upscaled (pore-scale to core-scale) reaction rates and compared against the predictions of a continuum model. Specifically, we modeled anorthite and kaolinite reactions under acidic flow conditions during which the anorthite reactions remain far from equilibrium (dissolution only), while the kaolinite reactions can be near-equilibrium. Under dissolution changes, core-scale reaction rates continuously and nonlinearly evolved in time. At higher injection rates, agreement with predictions of the continuum model degraded significantly. For the far-from-equilibrium reaction, our results indicate that the ability to correctly capture the heterogeneity in dissolution changes in the reactive mineral surface area is critical to accurately predict upscaled reaction rates. For the near-equilibrium reaction, the ability to correctly capture the heterogeneity in the saturation state remains critical. Inclusion of a Nernst-Planck term to ensure neutral ionic currents under differential diffusion resulted in at most a 9% correction in upscaled rates.
Kono, Mitsuo
2010-01-01
A nonlinearity is one of the most important notions in modern physics. A plasma is rich in nonlinearities and provides a variety of behaviors inherent to instabilities, coherent wave structures and turbulence. The book covers the basic concepts and mathematical methods, necessary to comprehend nonlinear problems widely encountered in contemporary plasmas, but also in other fields of physics and current research on self-organized structures and magnetized plasma turbulence. The analyses make use of strongly nonlinear models solved by analytical techniques backed by extensive simulations and available experiments. The text is written for senior undergraduates, graduate students, lecturers and researchers in laboratory, space and fusion plasmas.
Nonlinear magnetic metamaterials.
Shadrivov, Ilya V; Kozyrev, Alexander B; van der Weide, Daniel W; Kivshar, Yuri S
2008-12-08
We study experimentally nonlinear tunable magnetic metamaterials operating at microwave frequencies. We fabricate the nonlinear metamaterial composed of double split-ring resonators where a varactor diode is introduced into each resonator so that the magnetic resonance can be tuned dynamically by varying the input power. We demonstrate that at higher powers the transmission of the metamaterial becomes power-dependent and, as a result, such metamaterial can demonstrate various nonlinear properties. In particular, we study experimentally the power-dependent shift of the transmission band and demonstrate nonlinearity-induced enhancement (or suppression) of wave transmission. (c) 2008 Optical Society of America
Organic nonlinear optical materials
Umegaki, S.
1987-01-01
Recently, it became clear that organic compounds with delocalized pi electrons show a great nonlinear optical response. Especially, secondary nonlinear optical constants of more than 2 digits were often seen in the molecular level compared to the existing inorganic crystals such as LiNbO3. The crystallization was continuously tried. Organic nonlinear optical crystals have a new future as materials for use in the applied physics such as photomodulation, optical frequency transformation, opto-bistabilization, and phase conjugation optics. Organic nonlinear optical materials, e.g., urea, O2NC6H4NH2, I, II, are reviewed with 50 references.
Nonlinearity-reduced interferometer
Wu, Chien-ming
2007-12-01
Periodic nonlinearity is a systematic error limiting the accuracy of displacement measurements at the nanometer level. It results from many causes such as the frequency mixing, polarization mixing, polarization-frequency mixing, and the ghost reflections. An interferometer having accuracy in displacement measurement of less than one-nanometer is necessary in nanometrology. To meet the requirement, the periodic nonlinearity should be less than deep sub-nanometer. In this paper, a nonlinearity-reduced interferometry has been proposed. Both the linear- and straightness-interferometer were tested. The developed interferometer demonstrated of a residual nonlinearity less than 25 pm.
Recursive design of nonlinear H _∞ excitation controller
Institute of Scientific and Technical Information of China (English)
卢强; 梅生伟; 申铁龙; 胡伟
2000-01-01
This work is concerned with the problem of L2 gain disturbance attenuation for nonlinear systems and nonlinear robust control for power systems. In terms of the recurrence design approach proposed, the nonnegative solution of dissipative inequality and the storage function of nonlinear H∞ control for a generator excitation system are acquired. From this storage function, the excitation controller is constructed. Moreover, simulation results manifest the effectiveness of this design method.
A simplified NARMAX method using nonlinear input-output data
Institute of Scientific and Technical Information of China (English)
Jie CHEN; Sheng FENG
2007-01-01
A system identification method for nonlinear systems with unknown structure is presented using short input-output data. The method simplifies the original NARMAX method. It introduces more general model structures for nonlinear systems. The group method of data handling (GMDH) method is employed to obtain the model terms and parameters. Effectiveness of the proposed method is illustrated by a typical nonlinear system with unknown structure and deficient input-output data.
Logarithmic singularities of solutions to nonlinear partial differential equations
Tahara, Hidetoshi
2007-01-01
We construct a family of singular solutions to some nonlinear partial differential equations which have resonances in the sense of a paper due to T. Kobayashi. The leading term of a solution in our family contains a logarithm, possibly multiplied by a monomial. As an application, we study nonlinear wave equations with quadratic nonlinearities. The proof is by the reduction to a Fuchsian equation with singular coefficients.
Directory of Open Access Journals (Sweden)
Yacouba Simporé
2016-01-01
Full Text Available We first prove a null controllability result for a nonlinear system derived from a nonlinear population dynamics model. In order to tackle the controllability problem we use an adapted Carleman inequality. Next we consider the nonlinear population dynamics model with a source term called the pollution term. In order to obtain information on the pollution term we use the method of sentinel.
Energy Technology Data Exchange (ETDEWEB)
Nguyen, Ba Phi [Central University of Construction, Tuy Hoa (Viet Nam); Kim, Ki Hong [Ajou University, Suwon (Korea, Republic of)
2014-02-15
We study numerically the dynamics of an initially localized wave packet in one-dimensional nonlinear Schroedinger lattices with both local and nonlocal nonlinearities. Using the discrete nonlinear Schroedinger equation generalized by including a nonlocal nonlinear term, we calculate four different physical quantities as a function of time, which are the return probability to the initial excitation site, the participation number, the root-mean-square displacement from the excitation site and the spatial probability distribution. We investigate the influence of the nonlocal nonlinearity on the delocalization to self-trapping transition induced by the local nonlinearity. In the non-self-trapping region, we find that the nonlocal nonlinearity compresses the soliton width and slows down the spreading of the wave packet. In the vicinity of the delocalization to self-trapping transition point and inside the self-trapping region, we find that a new kind of self-trapping phenomenon, which we call partial self-trapping, takes place when the nonlocal nonlinearity is sufficiently strong.
Nonlinear Parabolic Equations with Singularities in Colombeau Vector Spaces
Institute of Scientific and Technical Information of China (English)
Mirjana STOJANOVI(C)
2006-01-01
We consider nonlinear parabolic equations with nonlinear non-Lipschitz's term and singular initial data like Dirac measure, its derivatives and powers. We prove existence-uniqueness theorems in Colombeau vector space gC1,w2,2([O,T),Rn),n ≤ 3. Due to high singularity in a case of parabolic equation with nonlinear conservative term we employ the regularized derivative for the conservative term, in order to obtain the global existence-uniqueness result in Colombeau vector space gC1,L2([O,T),Rn),n ≤ 3.
Institute of Scientific and Technical Information of China (English)
傅育熙
1998-01-01
The paper proposes reaction graphs as graphical representations of computational objects.A reaction graph is a directed graph with all its arrows and some of its nodes labeled.Computations are modled by graph rewriting of a simple nature.The basic rewriting rules embody the essence of both the communications among processes and cut-eliminations in proofs.Calculi of graphs are ideentified to give a formal and algebraic account of reaction graphs in the spirit of process algebra.With the help of the calculi,it is demonstrated that reaction graphs capture many interesting aspects of computations.
Lasers for nonlinear microscopy.
Wise, Frank
2013-03-01
Various versions of nonlinear microscopy are revolutionizing the life sciences, almost all of which are made possible because of the development of ultrafast lasers. In this article, the main properties and technical features of short-pulse lasers used in nonlinear microscopy are summarized. Recent research results on fiber lasers that will impact future instruments are also discussed.
Eaton, D F
1991-07-19
The current state of materials development in nonlinear optics is summarized, and the promise of these materials is critically evaluated. Properties and important materials constants of current commercial materials and of new, promising, inorganic and organic molecular and polymeric materials with potential in second- and third-order nonlinear optical applications are presented.
Billings, S. A.
1988-03-01
Time and frequency domain identification methods for nonlinear systems are reviewed. Parametric methods, prediction error methods, structure detection, model validation, and experiment design are discussed. Identification of a liquid level system, a heat exchanger, and a turbocharge automotive diesel engine are illustrated. Rational models are introduced. Spectral analysis for nonlinear systems is treated. Recursive estimation is mentioned.
DEFF Research Database (Denmark)
Clausen, Carl A. Balslev; Christiansen, Peter Leth; Torner, L.
1999-01-01
We show that with the quasi-phase-matching technique it is possible to fabricate stripes of nonlinearity that trap and guide light like waveguides. We investigate an array of such stripes and find that when the stripes are sufficiently narrow, the beam dynamics is governed by a quadratic nonlinear...
Controllability in nonlinear systems
Hirschorn, R. M.
1975-01-01
An explicit expression for the reachable set is obtained for a class of nonlinear systems. This class is described by a chain condition on the Lie algebra of vector fields associated with each nonlinear system. These ideas are used to obtain a generalization of a controllability result for linear systems in the case where multiplicative controls are present.
Menon, P. K. A.; Badgett, M. E.; Walker, R. A.
1992-01-01
Trajectory-control laws based on singular-perturbation theory and nonlinear dynamical modeling. Nonlinear maneuver autopilot commands flight-test trajectories of F-15 airplane. Underlying theory of controller enables separation of variables processed in fast and slow control loops, reducing amount of computation required.
Nonlinear and stochastic dynamics of coherent structures
DEFF Research Database (Denmark)
Rasmussen, Kim
1997-01-01
system described by a tight-binding Hamiltonian and a harmonic lattice coupled b y a deformation-type potential. This derivation results in a two-dimensional nonline ar Schrödinger model, and considering the harmonic lattice to be in thermal contact with a heat bath w e show that the nonlinear...... phenomenon. We find numerically and analytically that the collapse can be delayed and ultimatively arrested by the fluctuations. Allowing the system to reach thermal equilibrium we further augment the model by a nonlineardamping term and find that this prohibits collapse in the strict mathematical se nse....... However a collapse like behavior still persists in the presence of the nonlinear damping . Apart from the absence of the collapse in the strict mathematical sense we find that the nonlinear damping term has rather weak influence on the interplay between fluctuations and self-focusing. The study...
Nonlinear behavior of Helmholtz resonators
Hersh, A. S.
1990-10-01
A semi-empirical fluid mechanical model has been derived to predict the nonlinear acoustic behavior of thin-walled, single-orifice Helmholtz resonators. The model assumed that the sound particle velocity field approaches the resonator in a spherically symmetric manner. The incident and cavity sound pressure fields are connected in terms of an orifice discharge coefficient and an end correction parameter whose values are determined empirically. The accuracy of the model was verified by comparing predicted with measured impedance over a wide range of sound amplitudes and frequencies for two different resonator geometries and with measurements conducted by Ingard and Ising.
Wase, Nishikant; Pham, Trong Khoa; Ow, Saw Yen; Wright, Phillip C
2014-09-23
A quantitative proteomics and metabolomics analysis was performed using iTRAQ, HPLC and GC-MS in the filamentous cyanobacterium Nostoc punctiforme ATCC 29133 to understand the effect of short and long term UV-A exposure. Changes in the proteome were measured for short-term stress (4-24h) using iTRAQ. Changes in the photosynthetic pigments and intracellular metabolites were observed at exposures of up to 7days (pigments) and up to 11days (intracellular metabolites). To assess iTRAQ measurement quality, pseudo selected reaction monitoring (pSRM) was used, with this confirming underestimation of protein abundance levels by iTRAQ. Our results suggest that short term UV-A radiation lowers the abundance of PS-I and PS-II proteins. We also observed an increase in abundance of intracellular redox homeostasis proteins and plastocyanin. Additionally, we observed statistically significant changes in scytonemin, Chlorophyll A, astaxanthin, zeaxanthin, and β-carotene. Assessment of intracellular metabolites showed significant changes in several, suggesting their potential role in the Nostoc's stress mitigation strategy. Cyanobacteria under UV-A radiation have reduced growth due to intensive damage to essential functions, but the organism shows a defense response by remodeling bioenergetics pathway, induction of the UV protection compound scytonemin and increased levels of proline and tyrosine as a mitigation response. The effect of UV-A radiation on the proteome and intracellular metabolites of N. punctiforme ATCC 29133 including photosynthetic pigments has been described. We also verify the expression of 13 iTRAQ quantified protein using LC-pSRM. Overall we observed that UV-A radiation has a drastic effect on the photosynthetic machinery, photosynthetic pigments and intracellular amino acids. As a mitigation strategy against UV-A radiation, proline, glycine, and tyrosine were accumulated. Copyright © 2014. Published by Elsevier B.V.
Nonlinear optics and photonics
He, Guang S
2015-01-01
This book provides a comprehensive presentation on most of the major topics in nonlinear optics and photonics, with equal emphasis on principles, experiments, techniques, and applications. It covers many major new topics including optical solitons, multi-photon effects, nonlinear photoelectric effects, fast and slow light , and Terahertz photonics. Chapters 1-10 present the fundamentals of modern nonlinear optics, and could be used as a textbook with problems provided at the end of each chapter. Chapters 11-17 cover the more advanced topics of techniques and applications of nonlinear optics and photonics, serving as a highly informative reference for researchers and experts working in related areas. There are also 16 pages of color photographs to illustrate the visual appearances of some typical nonlinear optical effects and phenomena. The book could be adopted as a textbook for both undergraduates and graduate students, and serve as a useful reference work for researchers and experts in the fields of physics...
Lugiato, Luigi; Brambilla, Massimo
2015-01-01
Guiding graduate students and researchers through the complex world of laser physics and nonlinear optics, this book provides an in-depth exploration of the dynamics of lasers and other relevant optical systems, under the umbrella of a unitary spatio-temporal vision. Adopting a balanced approach, the book covers traditional as well as special topics in laser physics, quantum electronics and nonlinear optics, treating them from the viewpoint of nonlinear dynamical systems. These include laser emission, frequency generation, solitons, optically bistable systems, pulsations and chaos and optical pattern formation. It also provides a coherent and up-to-date treatment of the hierarchy of nonlinear optical models and of the rich variety of phenomena they describe, helping readers to understand the limits of validity of each model and the connections among the phenomena. It is ideal for graduate students and researchers in nonlinear optics, quantum electronics, laser physics and photonics.
Analytical Solutions to Non-linear Mechanical Oscillation Problems
DEFF Research Database (Denmark)
Kaliji, H. D.; Ghadimi, M.; Barari, Amin
2011-01-01
In this paper, the Max-Min Method is utilized for solving the nonlinear oscillation problems. The proposed approach is applied to three systems with complex nonlinear terms in their motion equations. By means of this method, the dynamic behavior of oscillation systems can be easily approximated u...
A Unified Approach for Solving Nonlinear Regular Perturbation Problems
Khuri, S. A.
2008-01-01
This article describes a simple alternative unified method of solving nonlinear regular perturbation problems. The procedure is based upon the manipulation of Taylor's approximation for the expansion of the nonlinear term in the perturbed equation. An essential feature of this technique is the relative simplicity used and the associated unified…
On absolute stability of nonlinear systems with small delays
Directory of Open Access Journals (Sweden)
M. I. Gil
1998-01-01
Full Text Available Nonlinear nonautonomous retarded systems with separated autonomous linear parts and continuous nonlinear ones are considered. It is assumed that deviations of the argument are sufficiently small. Absolute stability conditions are derived. They are formulated in terms of eigenvalues of auxiliary matrices.
Nonlocal description of X waves in quadratic nonlinear materials
DEFF Research Database (Denmark)
Larsen, Peter Ulrik Vingaard; Sørensen, Mads Peter; Bang, Ole
2006-01-01
We study localized light bullets and X-waves in quadratic media and show how the notion of nonlocality can provide an alternative simple physical picture of both types of multi-dimensional nonlinear waves. For X-waves we show that a local cascading limit in terms of a nonlinear Schrodinger equation...
Asymptotic stability and stabilizability of nonlinear systems with delay.
Srinivasan, V; Sukavanam, N
2016-11-01
This paper is concerned with asymptotic stability and stabilizability of a class of nonlinear dynamical systems with fixed delay in state variable. New sufficient conditions are established in terms of the system parameters such as the eigenvalues of the linear operator, delay parameter, and bounds on the nonlinear parts. Finally, examples are given to testify the effectiveness of the proposed theory.
Prolongation Structure of Semi-discrete Nonlinear Evolution Equations
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
Based on noncommutative differential calculus, we present a theory of prolongation structure for semi-discrete nonlinear evolution equations. As an illustrative example, a semi-discrete model of the nonlinear Schr(o)dinger equation is discussed in terms of this theory and the corresponding Lax pairs are also given.
A Photonic Basis for Deriving Nonlinear Optical Response
Andrews, David L.; Bradshaw, David S.
2009-01-01
Nonlinear optics is generally first presented as an extension of conventional optics. Typically the subject is introduced with reference to a classical oscillatory electric polarization, accommodating correction terms that become significant at high intensities. The material parameters that quantify the extent of the nonlinear response are cast as…
Richter, Otto; Moenickes, Sylvia; Suhling, Frank
2012-02-01
The spatial dynamics of range expansion is studied in dependence of temperature. The main elements population dynamics, competition and dispersal are combined in a coherent approach based on a system of coupled partial differential equations of the reaction-diffusion type. The nonlinear reaction terms comprise population dynamic models with temperature dependent reproduction rates subject to an Allee effect and mutual competition. The effect of temperature on travelling wave solutions is investigated for a one dimensional model version. One main result is the importance of the Allee effect for the crossing of regions with unsuitable habitats. The nonlinearities of the interaction terms give rise to a richness of spatio-temporal dynamic patterns. In two dimensions, the resulting non-linear initial boundary value problems are solved over geometries of heterogeneous landscapes. Geo referenced model parameters such as mean temperature and elevation are imported into the finite element tool COMSOL Multiphysics from a geographical information system. The model is applied to the range expansion of species at the scale of middle Europe.
The Homoclinic Orbits in Nonlinear Schroedinger Equation
Institute of Scientific and Technical Information of China (English)
PengchengXU; BolingGUO; 等
1998-01-01
The persistence of Homoclinic orbits for perturbed nonlinear Schroedinger equation with five degree term under een periodic boundary conditions is considered.The exstences of the homoclinic orbits for the truncation equation is established by Melnikov's analysis and geometric singular perturbation theory.
EXACT SOLUTIONS TO NONLINEAR WAVE EQUATION
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
In this paper,we use an invariant set to construct exact solutions to a nonlinear wave equation with a variable wave speed. Moreover,we obtain conditions under which the equation admits a nonclassical symmetry. Several different nonclassical symmetries for equations with different diffusion terms are presented.
Nonlinear second order elliptic equations involving measures
Marcus, Moshe
2013-01-01
This book presents a comprehensive study of boundary value problems for linear and semilinear second order elliptic equations with measure data,especially semilinear equations with absorption. The interactions between the diffusion operator and the absorption term give rise to a large class of nonlinear phenomena in the study of which singularities and boundary trace play a central role.
Estimating the uncertainty in underresolved nonlinear dynamics
Energy Technology Data Exchange (ETDEWEB)
Chorin, Alelxandre; Hald, Ole
2013-06-12
The Mori-Zwanzig formalism of statistical mechanics is used to estimate the uncertainty caused by underresolution in the solution of a nonlinear dynamical system. A general approach is outlined and applied to a simple example. The noise term that describes the uncertainty turns out to be neither Markovian nor Gaussian. It is argued that this is the general situation.
A polynomial approach to nonlinear system controllability
Zheng, YF; Willems, JC; Zhang, CH
2001-01-01
This note uses a polynomial approach to present a necessary and sufficient condition for local controllability of single-input-single-output (SISO) nonlinear systems. The condition is presented in terms of common factors of a noncommutative polynomial expression. This result exposes controllability
A Second Generation Nonlinear Factor Analysis.
Etezadi-Amoli, Jamshid; McDonald, Roderick P.
1983-01-01
Nonlinear common factor models with polynomial regression functions, including interaction terms, are fitted by simultaneously estimating the factor loadings and common factor scores, using maximum likelihood and least squares methods. A Monte Carlo study gives support to a conjecture about the form of the distribution of the likelihood ratio…
NONLINEAR APPROXIMATION WITH GENERAL WAVE PACKETS
Institute of Scientific and Technical Information of China (English)
L. Borup; M. Nielsen
2005-01-01
We study nonlinear approximation in the Triebel-Lizorkin spaces with dictionaries formed by dilating and translating one single function g. A general Jackson inequality is derived for best m-term approximation with such dictionaries. In some special cases where g has a special structure, a complete characterization of the approximation spaces is derived.
Nonlinear approximation with general wave packets
DEFF Research Database (Denmark)
Borup, Lasse; Nielsen, Morten
2005-01-01
We study nonlinear approximation in the Triebel-Lizorkin spaces with dictionaries formed by dilating and translating one single function g. A general Jackson inequality is derived for best m-term approximation with such dictionaries. In some special cases where g has a special structure, a complete...... characterization of the approximation spaces is derived....
Nonlinear terahertz metamaterials with active electrical control
Keiser, G. R.; Karl, N.; Liu, P. Q.; Tulloss, C.; Chen, H.-T.; Taylor, A. J.; Brener, I.; Reno, J. L.; Mittleman, D. M.
2017-09-01
We present a study of an electrically modulated nonlinear metamaterial consisting of an array of split-ring resonators fabricated on n-type gallium arsenide. The resonant metamaterial nonlinearity appears as an intensity-dependent transmission minimum at terahertz frequencies and arises from the interaction between local electric fields in the split-ring resonator (SRR) capacitive gaps and charge carriers in the n-type substrate. We investigate the active tuning range of the metamaterial device as the incident terahertz field intensity is increased and conversely the effect of an applied DC bias on the terahertz field-induced nonlinear modulation of the metamaterial response. Applying a DC bias to the metamaterial sample alters the nonlinear response and reduces the net nonlinear modulation. Similarly, increasing the incident terahertz field intensity decreases the net modulation induced by an applied DC bias. We interpret these results in terms of DC and terahertz-field-assisted carrier acceleration, scattering, and multiplication processes, highlighting the unique nature of this DC-field modulated terahertz nonlinearity.
Alternative Forms of Enhanced Boussinesq Equations with Improved Nonlinearity
Directory of Open Access Journals (Sweden)
Kezhao Fang
2013-01-01
Full Text Available We propose alternative forms of the Boussinesq equations which extend the equations of Madsen and Schäffer by introducing extra nonlinear terms during enhancement. Theoretical analysis shows that nonlinear characteristics are considerably improved. A numerical implementation of one-dimensional equations is described. Three tests involving strongly nonlinear evolution, namely, regular waves propagating over an elevated bar feature in a tank with an otherwise constant depth, wave group transformation over constant water depth, and nonlinear shoaling of unsteady waves over a sloping beach, are simulated by the model. The model is found to be effective.
Recovering map static nonlinearities from chaotic data using dynamical models
Aguirre, Luis Antonio
1997-02-01
This paper is concerned with the estimation from chaotic data of maps with static nonlinearities. A number of issues concerning model construction such as structure selection, over-parametrization and model validation are discussed in the light of the shape of the static non-linearities reproduced by the estimated maps. A new interpretation of term clusters and cluster coefficients of polynomial models is provided based on this approach. The paper discusses model limitations and some useful principles to select the structure of nonlinear maps. Some of the ideas have been tested using several nonlinear systems including a boost voltage regulator map and a set of real data from a chaotic circuit.
Lattice Boltzmann model for nonlinear convection-diffusion equations.
Shi, Baochang; Guo, Zhaoli
2009-01-01
A lattice Boltzmann model for convection-diffusion equation with nonlinear convection and isotropic-diffusion terms is proposed through selecting equilibrium distribution function properly. The model can be applied to the common real and complex-valued nonlinear evolutionary equations, such as the nonlinear Schrödinger equation, complex Ginzburg-Landau equation, Burgers-Fisher equation, nonlinear heat conduction equation, and sine-Gordon equation, by using a real and complex-valued distribution function and relaxation time. Detailed simulations of these equations are performed, and it is found that the numerical results agree well with the analytical solutions and the numerical solutions reported in previous studies.
Nonlinear analysis and prediction of time series in multiphase reactors
Liu, Mingyan
2014-01-01
This book reports on important nonlinear aspects or deterministic chaos issues in the systems of multi-phase reactors. The reactors treated in the book include gas-liquid bubble columns, gas-liquid-solid fluidized beds and gas-liquid-solid magnetized fluidized beds. The authors take pressure fluctuations in the bubble columns as time series for nonlinear analysis, modeling and forecasting. They present qualitative and quantitative non-linear analysis tools which include attractor phase plane plot, correlation dimension, Kolmogorov entropy and largest Lyapunov exponent calculations and local non-linear short-term prediction.
Nonlinear approximation in alpha-modulation spaces
DEFF Research Database (Denmark)
Borup, Lasse; Nielsen, Morten
2006-01-01
The α-modulation spaces are a family of spaces that contain the Besov and modulation spaces as special cases. In this paper we prove that brushlet bases can be constructed to form unconditional and even greedy bases for the α-modulation spaces. We study m -term nonlinear approximation with brushlet...... bases, and give complete characterizations of the associated approximation spaces in terms of α-modulation spaces....
DEFF Research Database (Denmark)
Thomsen, Ingrid K; Pedersen, Asger R; Nyord, Tavs
2010-01-01
method, and N2O emissions from untreated, digested and separated slurry were similar, although higher N2O emissions from treated slurry were indicated. A conceptual model to explain the observed patterns of N2O is discussed. Accounting for the indirect emissions of N2O associated with NH3 volatilization...... or straight tines. In 2008, three slurry types (digested, separated or untreated) were applied by straight tine injection. In both years band spreading of the slurries by trail-hose application was included as reference. Nitrous oxide emissions were quantified using static chambers for up to 44 days after...... slurry application. A new flux calculation method (HMR) was applied. With HMR, flux estimation is based on non-linear regression using a single-parameter criterion. In connection with gas samplings, soil cores were collected to 20-cm depth within and between bands for analysis of mineral N. Short...
Ouyang, Canbin; Liu, Jialei; Liu, Qi; Li, Yuan; Yan, Dongdong; Wang, Qiuxia; Guo, Meixia; Cao, Aocheng
2017-03-29
Main-chain nonlinear optical polymers based on novel chromophores with special structures presented good solubility in most of the organic solvents. Polymers PE-1 and PE-2 attained the thermal decomposition temperatures of 305 and 223 °C and glass transition temperatures of 113 and 108 °C, and exhibited only negligible decay in the SHG signal baked at 85 °C over hundreds of hours, respectively. The SHG coefficients of poled films from polymers PE-1 and PE-2 were 26.3 and 35.8 pm/V, respectively. These results indicated that this class of polymers can be used in the preparation of organic electro-optic devices.
Nonlinear inversion schemes for fluorescence optical tomography.
Freiberger, Manuel; Egger, Herbert; Scharfetter, Hermann
2010-11-01
Fluorescence optical tomography is a non-invasive imaging modality that employs the absorption and re-emission of light by fluorescent dyes. The aim is to reconstruct the fluorophore distribution in a body from measurements of light intensities at the boundary. Due to the diffusive nature of light propagation in tissue, fluorescence tomography is a nonlinear and severely ill-posed problem, and some sort of regularization is required for a stable solution. In this paper we investigate reconstruction methods based on Tikhonov regularization with nonlinear penalty terms, namely total-variation regularization and a levelset-type method using a nonlinear parameterization of the unknown function. Moreover, we use the full threedimensional nonlinear forward model, which arises from the governing system of partial differential equations. We discuss the numerical realization of the regularization schemes by Newtontype iterations, present some details of the discretization by finite element methods, and outline the efficient implementation of sensitivity systems via adjoint methods. As we will demonstrate in numerical tests, the proposed nonlinear methods provide better reconstructions than standard methods based on linearized forward models and linear penalty terms. We will additionally illustrate, that the careful discretization of the methods derived on the continuous level allows to obtain reliable, mesh independent reconstruction algorithms.
Nonlinear Fourier analysis with cnoidal waves
Energy Technology Data Exchange (ETDEWEB)
Osborne, A.R. [Dipt. di Fisica Generale dell`Universita, Torino (Italy)
1996-12-31
Fourier analysis is one of the most useful tools to the ocean engineer. The approach allows one to analyze wave data and thereby to describe a dynamical motion in terms of a linear superposition of ordinary sine waves. Furthermore, the Fourier technique allows one to compute the response function of a fixed or floating structure: each sine wave in the wave or force spectrum yields a sine wave in the response spectrum. The counting of fatigue cycles is another area where the predictable oscillations of sine waves yield procedures for the estimation of the fatigue life of structures. The ocean environment, however, is a source of a number of nonlinear effects which must also be included in structure design. Nonlinearities in ocean waves deform the sinusoidal shapes into other kinds of waves such as the Stokes wave, cnoidal wave or solitary wave. A key question is: Does there exist a generalization of linear Fourier analysis which uses nonlinear basis functions rather than the familiar sine waves? Herein addresses the dynamics of nonlinear wave motion in shallow water where the basis functions are cnoidal waves and discuss nonlinear Fourier analysis in terms of a linear superposition of cnoidal waves plus their mutual nonlinear interactions. He gives a number of simple examples of nonlinear Fourier wave motion and then analyzes an actual surface-wave time series obtained on an offshore platform in the Adriatic Sea. Finally, he briefly discusses application of the cnoidal wave spectral approach to the computation of the frequency response function of a floating vessel. The results given herein will prove useful in future engineering studies for the design of fixed, floating and complaint offshore structures.
Applications of Nonlinear Electrochemical Impedance Spectroscopy (NLEIS)
Adler, S. B.
2013-08-31
This paper reviews the use of nonlinear electrochemical impedance spectroscopy (NLEIS) in the analysis of SOFC electrode reactions. By combining EIS and NLEIS, as well as other independent information about an electrode material, it becomes possible to establish quantitative links between electrochemical kinetics and materials properties, even when systems are unstable with time. After a brief review of the method, this paper summarizes recent results analyzing the effects of Sr segregation in thin-film LSC electrodes. © The Electrochemical Society.
The Nonlinear Convection—Reaction—Diffusion Equation
Institute of Scientific and Technical Information of China (English)
ShiminTANG; MaochangCUI; 等
1996-01-01
A nonlinear convection-reaction-diffusion equation is used as a model equation of the El Nino events.In this model,the effects of convection,turbulent diffusion,linear feed-back and nolinear radiation on the anomaly of Sea Surface Temperature(SST) are considered.In the case of constant convection,this equation has exact kink-like travelling wave solutions,which can be used to explain the history of an El Nino event.
Agrawal, Govind P
2001-01-01
The Optical Society of America (OSA) and SPIE - The International Society for Optical Engineering have awarded Govind Agrawal with an honorable mention for the Joseph W. Goodman Book Writing Award for his work on Nonlinear Fiber Optics, 3rd edition.Nonlinear Fiber Optics, 3rd Edition, provides a comprehensive and up-to-date account of the nonlinear phenomena occurring inside optical fibers. It retains most of the material that appeared in the first edition, with the exception of Chapter 6, which is now devoted to the polarization effects relevant for light propagation in optical
Will Nonlinear Backcalculation Help?
DEFF Research Database (Denmark)
Ullidtz, Per
2000-01-01
demonstrates, that treating the subgrade as a nonlinear elastic material, can result in more realistic moduli and a much better agreement between measured and calculated stresses and strains.The response of nonlinear elastic materials can be calculated using the Finite Element Method (FEM). A much simpler...... approach is to use the Method of Equivalent Thicknesses (MET), modified for a nonlinear subgrade. The paper includes an example where moduli backcalculated using FEM, linear elastic theory and MET are compared. Stresses and strains predicted by the three methods are also compared to measured values...
Nonlinear graphene metamaterial
Nikolaenko, Andrey E; Atmatzakis, Evangelos; Luo, Zhiqiang; Shen, Ze Xiang; De Angelis, Francesco; Boden, Stuart A; Di Fabrizio, Enzo; Zheludev, Nikolay I
2012-01-01
We demonstrate that the broadband nonlinear optical response of graphene can be resonantly enhanced by more than an order of magnitude through hybridization with a plasmonic metamaterial,while retaining an ultrafast nonlinear response time of ~1 ps. Transmission modulation close to ~1% is seen at a pump uence of ~0.03 mJ/cm^2 at the wavelength of ~1600 nm. This approach allows to engineer and enhance graphene's nonlinearity within a broad wavelength range enabling applications in optical switching, mode-locking and pulse shaping.
DEFF Research Database (Denmark)
Chin, Selena K.; Sunderland, Peter B.; Jomaas, Grunde
2017-01-01
Nozzle reaction and hose tension are analyzed using conservation of fluid momentum and assuming steady, inviscid flow and a flexible hose in frictionless contact with the ground. An expression that is independent of the bend angle is derived for the hose tension. If this tension is exceeded owing...... to anchor forces, the hose becomes straight. The nozzle reaction is found to equal the jet momentum flow rate, and it does not change when an elbow connects the hose to the nozzle. A forward force must be exerted by a firefighter or another anchor that matches the forward force that the jet would exert...... on a perpendicular wall. Three reaction expressions are derived, allowing it to be determined in terms of hose diameter, jet diameter, flow rate, and static pressure upstream of the nozzle. The nozzle reaction predictions used by the fire service are 56% to 90% of those obtained here for typical firefighting hand...
Nonlinear normal modes and their application in structural dynamics
Directory of Open Access Journals (Sweden)
2006-01-01
Full Text Available Recent progress in the area of nonlinear modal analysis for structural systems is reported. Systematic methods are developed for generating minimally sized reduced-order models that accurately describe the vibrations of large-scale nonlinear engineering structures. The general approach makes use of nonlinear normal modes that are defined in terms of invariant manifolds in the phase space of the system model. An efficient Galerkin projection method is developed, which allows for the construction of nonlinear modes that are accurate out to large amplitudes of vibration. This approach is successfully extended to the generation of nonlinear modes for systems that are internally resonant and for systems subject to external excitation. The effectiveness of the Galerkin-based construction of the nonlinear normal modes is also demonstrated for a realistic model of a rotating beam.
Geometric nonlinearities in field theory, condensed matter and analytical mechanics
Directory of Open Access Journals (Sweden)
J.J. Sławianowski
2010-01-01
Full Text Available There are two very important subjects in physics: Symmetry of dynamical models and nonlinearity. All really fundamental models are invariant under some particular symmetry groups. There is also no true physics, no our Universe and life at all, without nonlinearity. Particularly interesting are essential, non-perturbative nonlinearities which are not described by correction terms imposed on some well-defined linear background. Our idea in this paper is that there exists some mysterious, still incomprehensible link between essential, physically relevant nonlinearity and dynamical symmetry, first of all, of large symmetry groups. In some sense the problem is known even in soliton theory, where the essential nonlinearity is often accompanied by the infinite system of integrals of motion, thus, by infinite-dimensional symmetry groups. Here we discuss some more familiar problems from the realm of field theory, condensed matter physics, and analytical mechanics, where the link between essential nonlinearity and high symmetry is obvious, although not fully understandable.
The Power of Unit Root Tests Against Nonlinear Local Alternatives
DEFF Research Database (Denmark)
Demetrescu, Matei; Kruse, Robinson
of Econometrics 112, 359-379) in comparison to the linear Dickey-Fuller test. To this end, we consider different adjustment schemes for deterministic terms. We provide asymptotic results which imply that the error variance has a severe impact on the behavior of the tests in the nonlinear case; the reason...... by simulation. Furthermore, our own simulation results suggest that the user-specied adjustment scheme for deterministic components (e.g. OLS, GLS, or recursive adjustment) has a much higher impact on the power of unit root tests than accounting for nonlinearity, at least under local (linear or nonlinear......This article extends the analysis of local power of unit root tests in a nonlinear direction by considering local nonlinear alternatives and tests built specically against stationary nonlinear models. In particular, we focus on the popular test proposed by Kapetanios et al. (2003, Journal...
Nonlinear I-V characteristics of nanoparticle compacts and nanocomposites
Energy Technology Data Exchange (ETDEWEB)
Herth, Simone [Rensselaer Polytechnic Institute, Troy, NY (United States); Bielefeld University, Bielefeld (Germany); Wang, Xiaoping; Hugener, Teresa; Schadler, Linda; Siegel, Richard [Rensselaer Polytechnic Institute, Troy, NY (United States); Hillborg, Henrik; Auletta, Tommaso [ABB AB, Corporate Research, Schweden (Sweden)
2007-07-01
Materials with nonlinear I-V characteristics are commonly used as field grading materials. In many cases, the non-linearity is achieved through the addition of equiaxed fillers to a polymer matrix. These composite field grading materials are optimized in terms of nonlinearity, conductivity, and breakdown strength. One limitation in designing new field grading materials is a robust understanding of the relationship between powder morphology, composition and electrical characteristics of the powder, as well as a robust understanding of the relationship between powder conductivity and non-linearity and composite non-linearity. In this work, treatment of ZnO powder with a SnF{sub 2} solution resulted in a powder that yielded highly non-linear behavior. The highest non-linearity was achieved for powders with at least two different phases and a rough surface, as indicated by transmission electron micrographs. In contrast, the non-linearity of the nanocomposite conductivity is mainly determined by the conductivity of the nanofiller. The electrical behavior of the non-linear powder can be understood by a polarization of the nanoparticles at the interfaces, whereas the nonlinearity of the nanocomposites can be explained by a tunnelling mechanism between two particles.
Nonlinear regime-switching state-space (RSSS) models.
Chow, Sy-Miin; Zhang, Guangjian
2013-10-01
Nonlinear dynamic factor analysis models extend standard linear dynamic factor analysis models by allowing time series processes to be nonlinear at the latent level (e.g., involving interaction between two latent processes). In practice, it is often of interest to identify the phases--namely, latent "regimes" or classes--during which a system is characterized by distinctly different dynamics. We propose a new class of models, termed nonlinear regime-switching state-space (RSSS) models, which subsumes regime-switching nonlinear dynamic factor analysis models as a special case. In nonlinear RSSS models, the change processes within regimes, represented using a state-space model, are allowed to be nonlinear. An estimation procedure obtained by combining the extended Kalman filter and the Kim filter is proposed as a way to estimate nonlinear RSSS models. We illustrate the utility of nonlinear RSSS models by fitting a nonlinear dynamic factor analysis model with regime-specific cross-regression parameters to a set of experience sampling affect data. The parallels between nonlinear RSSS models and other well-known discrete change models in the literature are discussed briefly.
Optical rogue waves and soliton turbulence in nonlinear fibre optics
DEFF Research Database (Denmark)
Genty, G.; Dudley, J. M.; de Sterke, C. M.
2009-01-01
We examine optical rogue wave generation in nonlinear fibre propagation in terms of soliton turbulence. We show that higher-order dispersion is sufficient to generate localized rogue soliton structures, and Raman scattering effects are not required.......We examine optical rogue wave generation in nonlinear fibre propagation in terms of soliton turbulence. We show that higher-order dispersion is sufficient to generate localized rogue soliton structures, and Raman scattering effects are not required....
Linear and nonlinear stiffness and friction in biological rhythmic movements.
Beek, P J; Schmidt, R C; Morris, A W; Sim, M Y; Turvey, M T
1995-11-01
Biological rhythmic movements can be viewed as instances of self-sustained oscillators. Auto-oscillatory phenomena must involve a nonlinear friction function, and usually involve a nonlinear elastic function. With respect to rhythmic movements, the question is: What kinds of nonlinear friction and elastic functions are involved? The nonlinear friction functions of the kind identified by Rayleigh (involving terms such as theta3) and van der Pol (involving terms such as theta2theta), and the nonlinear elastic functions identified by Duffing (involving terms such as theta3), constitute elementary nonlinear components for the assembling of self-sustained oscillators, Recently, additional elementary nonlinear friction and stiffness functions expressed, respectively, through terms such as theta2theta3 and thetatheta2, and a methodology for evaluating the contribution of the elementary components to any given cyclic activity have been identified. The methodology uses a quantification of the continuous deviation of oscillatory motion from ideal (harmonic) motion. Multiple regression of this quantity on the elementary linear and nonlinear terms reveals the individual contribution of each term to the oscillator's non-harmonic behavior. In the present article the methodology was applied to the data from three experiments in which human subjects produced pendular rhythmic movements under manipulations of rotational inertia (experiment 1), rotational inertia and frequency (experiment 2), and rotational inertia and amplitude (experiment 3). The analysis revealed that the pendular oscillators assembled in the three experiments were compositionally rich, braiding linear and nonlinear friction and elastic functions in a manner that depended on the nature of the task.
Multipolar nonlinear nanophotonics
Smirnova, Daria
2016-01-01
Nonlinear nanophotonics is a rapidly developing field with many useful applications for a design of nonlinear nanoantennas, light sources, nanolasers, sensors, and ultrafast miniature metadevices. A tight confinement of the local electromagnetic fields in resonant photonic nanostructures can boost nonlinear optical effects, thus offering versatile opportunities for subwavelength control of light. To achieve the desired functionalities, it is essential to gain flexible control over the near- and far-field properties of nanostructures. Thus, both modal and multipolar analyses are widely exploited for engineering nonlinear scattering from resonant nanoscale elements, in particular for enhancing the near-field interaction, tailoring the far-field multipolar interference, and optimization of the radiation directionality. Here, we review the recent advances in this recently emerged research field ranging from metallic structures exhibiting localized plasmonic resonances to hybrid metal-dielectric and all-dielectric...
Solitons in nonlinear lattices
Kartashov, Yaroslav V; Torner, Lluis
2010-01-01
This article offers a comprehensive survey of results obtained for solitons and complex nonlinear wave patterns supported by purely nonlinear lattices (NLs), which represent a spatially periodic modulation of the local strength and sign of the nonlinearity, and their combinations with linear lattices. A majority of the results obtained, thus far, in this field and reviewed in this article are theoretical. Nevertheless, relevant experimental settings are surveyed too, with emphasis on perspectives for implementation of the theoretical predictions in the experiment. Physical systems discussed in the review belong to the realms of nonlinear optics (including artificial optical media, such as photonic crystals, and plasmonics) and Bose-Einstein condensation (BEC). The solitons are considered in one, two, and three dimensions (1D, 2D, and 3D). Basic properties of the solitons presented in the review are their existence, stability, and mobility. Although the field is still far from completion, general conclusions c...
Directory of Open Access Journals (Sweden)
Shakeeb Bin Hasan
2014-12-01
Full Text Available Contrary to traditional optical elements, plasmonic antennas made from nanostructured metals permit the localization of electromagnetic fields on length scales much smaller than the wavelength of light. This results in huge amplitudes for the electromagnetic field close to the antenna being conducive for the observation of nonlinear effects already at moderate pump powers. Thus, these antennas exhibit a promising potential to achieve optical frequency conversion and all-optical control of light at the nano-scale. This opens unprecedented opportunities for ultrafast nonlinear spectroscopy, sensing devices, on-chip optical frequency conversion, nonlinear optical metamaterials, and novel photon sources. Here, we review some of the recent advances in exploiting the potential of plasmonic antennas to realize robust nonlinear applications.
DEFF Research Database (Denmark)
Nguyen-Duy, Khiem
and remains the prime source of energy in non-terrestrial applications such as those in sky-explorers. However, a renewable energy source is expensive, bulky, and its performance is weather dependent, which make testing of downstream converters very difficult. As a result, a nonlinear source emulator (NSE......) is a good solution to solve the problems associated with the use of real nonlinear sources in testing phases. However, a recent technical survey conducted during this work shows that most existing NSEs have only been concerned with simulating nonlinear systems in terrestrial applications. Furthermore......, their dynamic performance were not fast enough in order to imitate how a real nonlinear energy source would react under extreme conditions and operation modes. Particularly, a system in the sky can experience a step change of sunlight irradiation. Moreover, operation modes may include load step between nominal...
Introduction to nonlinear science
Nicolis, G
1995-01-01
One of the most unexpected results in science in recent years is that quite ordinary systems obeying simple laws can give rise to complex, nonlinear or chaotic, behavior. In this book, the author presents a unified treatment of the concepts and tools needed to analyze nonlinear phenomena and to outline some representative applications drawn from the physical, engineering, and biological sciences. Some of the interesting topics covered include: dynamical systems with a finite number of degrees of freedom, linear stability analysis of fixed points, nonlinear behavior of fixed points, bifurcation analysis, spatially distributed systems, broken symmetries, pattern formation, and chaotic dynamics. The author makes a special effort to provide a logical connection between ordinary dynamical systems and spatially extended systems, and to balance the emphasis on chaotic behavior and more classical nonlinear behavior. He also develops a statistical approach to complex systems and compares it to traditional deterministi...
Nonlinear magnetoinductive transmission lines
Lazarides, Nikos; Tsironis, G P
2011-01-01
Power transmission in one-dimensional nonlinear magnetic metamaterials driven at one end is investigated numerically and analytically in a wide frequency range. The nonlinear magnetic metamaterials are composed of varactor-loaded split-ring resonators which are coupled magnetically through their mutual inductances, forming thus a magnetoiductive transmission line. In the linear limit, significant power transmission along the array only appears for frequencies inside the linear magnetoinductive wave band. We present analytical, closed form solutions for the magnetoinductive waves transmitting the power in this regime, and their discrete frequency dispersion. When nonlinearity is important, more frequency bands with significant power transmission along the array may appear. In the equivalent circuit picture, the nonlinear magnetoiductive transmission line driven at one end by a relatively weak electromotive force, can be modeled by coupled resistive-inductive-capacitive (RLC) circuits with voltage-dependent cap...
Optimization under Nonlinear Constraints
1982-01-01
In this paper a timesaving method is proposed for maximizing likelihood functions when the parameter space is subject to nonlinear constraints, expressible as second order polynomials. The suggested approach is especially attractive when dealing with systems with many parameters.
Nonlinearity in nanomechanical cantilevers
DEFF Research Database (Denmark)
Villanueva Torrijo, Luis Guillermo; Karabalin, R. B.; Matheny, M. H.
2013-01-01
Euler-Bernoulli beam theory is widely used to successfully predict the linear dynamics of micro-and nanocantilever beams. However, its capacity to characterize the nonlinear dynamics of these devices has not yet been rigorously assessed, despite its use in nanoelectromechanical systems development....... These findings underscore the delicate balance between inertial and geometric nonlinear effects in the fundamental mode, and strongly motivate further work to develop theories beyond the Euler-Bernoulli approximation. DOI: 10.1103/PhysRevB.87.024304....... In this article, we report the first highly controlled measurements of the nonlinear response of nanomechanical cantilevers using an ultralinear detection system. This is performed for an extensive range of devices to probe the validity of Euler-Bernoulli theory in the nonlinear regime. We find that its...
Vass, József
2016-01-01
A discretization scheme is introduced for a set of convection-diffusion equations with a non-linear reaction term, where the convection velocity is constant for each reactant. This constancy allows a transformation to new spatial variables, which ensures the global stability of discretization. Convection-diffusion equations are notorious for their lack of stability, arising from the algebraic interaction of the convection and diffusion terms. Unexpectedly, our implemented numerical algorithm proves to be faster than computing exact solutions derived for a special case, while remaining reasonably accurate, as demonstrated in our runtime and error analysis.
State-variable analysis of non-linear circuits with a desk computer
Cohen, E.
1981-01-01
State variable analysis was used to analyze the transient performance of non-linear circuits on a desk top computer. The non-linearities considered were not restricted to any circuit element. All that is required for analysis is the relationship defining each non-linearity be known in terms of points on a curve.
On Power Factor Improvement by Lossless Linear Filters in the Nonlinear Nonsinusoidal Case
Puerto-Flores, Dunstano del; Scherpen, Jacquelien M.A.; Ortega, Romeo
2010-01-01
Recently, it has been established that the problem of power factor compensation (PFC) for nonlinear loads with non-sinusoidal source voltage can be recast in terms of the property of cyclodissipativity. Using this framework we study the PFC for nonlinear loads containing a memoryless nonlinearity. W
On Power Factor Improvement by Lossless Linear Filters in the Nonlinear Nonsinusoidal Case
Puerto-Flores, Dunstano del; Scherpen, Jacquelien M.A.; Ortega, Romeo
2010-01-01
Recently, it has been established that the problem of power factor compensation (PFC) for nonlinear loads with non-sinusoidal source voltage can be recast in terms of the property of cyclodissipativity. Using this framework we study the PFC for nonlinear loads containing a memoryless nonlinearity.
Nonlinear physics of shear Alfvén waves
Energy Technology Data Exchange (ETDEWEB)
Zonca, Fulvio [Associazione EURATOM-ENEA sulla Fusione, C.P. 65-00044 Frascati, Italy and Institute for Fusion Theory and Simulation, Zhejiang University, Hangzhou 31007 (China); Chen, Liu [Institute for Fusion Theory and Simulation, Zhejiang University, Hangzhou 31007, P.R.C. and Department of Physics and Astronomy, University of California, Irvine, CA 92697 (United States)
2014-02-12
Shear Alfvén waves (SAW) play fundamental roles in thermonuclear plasmas of fusion interest, since they are readily excited by energetic particles in the MeV range as well as by the thermal plasma components. Thus, understanding fluctuation induced transport in burning plasmas requires understanding nonlinear SAW physics. There exist two possible routes to nonlinear SAW physics: (i) wave-wave interactions and the resultant spectral energy transfer; (ii) nonlinear wave-particle interactions of SAW instabilities with energetic particles. Within the first route, it is advantageous to understand and describe nonlinear processes in term of proximity of the system to the Alfvénic state, where wave-wave interactions are minimized due to the cancellation of Reynolds and Maxwell stresses. Here, various wave-wave nonlinear dynamics are elucidated in terms of how they break the Alfvénic state. In particular, we discuss the qualitative and quantitative modification of the SAW parametric decay process due to finite ion compressibility and finite ion Larmor radius. We also show that toroidal geometry plays a crucial role in the nonlinear excitation of zonal structures by Alfvén eigenmodes. Within the second route, the coherent nonlinear dynamics of structures in the energetic particle phase space, by which secular resonant particle transport can occur on meso- and macro-scales, must be addressed and understood. These 'nonlinear equilibria' or 'phase-space zonal structures' dynamically evolve on characteristic (fluctuation induced) turbulent transport time scales, which are generally of the same order of the nonlinear time scale of the underlying fluctuations. In this work, we introduce the general structure of nonlinear Schrödinger equations with complex integro-differential nonlinear terms, which govern these physical processes. To elucidate all these aspects, theoretical analyses are presented together with numerical simulation results.
Effect of gain nonlinearity in semiconductor lasers
DEFF Research Database (Denmark)
Jensen, Niels H.; Christiansen, Peter Leth; Skovgaard, Ove
1988-01-01
Semiconductor lasers are modeled by single-mode rate equations with Langevin noise terms and the influence of nonlinear gain is investigated. For cw operation the probability distribution for the carrier number and the photon number in the laser cavity is obtained. The corresponding (2......+1)-dimensional Fokker-Planck equation is derived and integrated on an Amdahl VP1100 vector processor. Above threshold the resulting probability density agrees with the rate-equation predictions. The case of high-speed modulation is also considered. The nonlinear gain is found to stabilize the laser....
Explicit solutions of nonlinear wave equation systems
Institute of Scientific and Technical Information of China (English)
Ahmet Bekir; Burcu Ayhan; M.Naci (O)zer
2013-01-01
We apply the (G'/G)-expansion method to solve two systems of nonlinear differential equations and construct traveling wave solutions expressed in terms of hyperbolic functions,trigonometric functions,and rational functions with arbitrary parameters.We highlight the power of the (G'/G)-expansion method in providing generalized solitary wave solutions of different physical structures.It is shown that the (G'/G)-expansion method is very effective and provides a powerful mathematical tool to solve nonlinear differential equation systems in mathematical physics.
Adaptive and Nonlinear Control
1992-02-29
in [22], we also applied the concept of zero dynamics to the problem of exact linearization of a nonlinear control system by dynamic feedback. Exact ...nonlinear systems, although it was well-known that the conditions for exact linearization are very stringent and consequently do not apply to a broad...29th IEEE Conference n Decision and Control, Invited Paper delivered by Dr. Gilliam. Exact Linearization of Zero Dynamics, 29th IEEE Conference on
Nonlinear Optics and Turbulence
1992-10-01
currently at Queen Mary College, London Patrick Dunne, (Ph.D., 1987, M.I.T., Hydrodynamic Stability, Nonlinear Waves), 1987-1988. Alecsander Dyachenko...U I I I U I I 3 9 3 V. BIOGRAPHIES A. FACULTY BRUCE BAYLY, 31, Ph.D. 1986, Princeton University. Postdoctoral visiting member 1986-88 at Courant...Caputo, A. C. Newell, and M. Shelley , "Nonlinear Wave Propagation Through a Random Medium and Soliton Tunneling", Integrable Systems and
Low power continuous wave laser induced optical nonlinearities in saffron ( Crocus Sativus L.)
Nasibov, H.; Mamedbeili, I.
2010-12-01
We report on the low power CW laser induced nonlinear optical responses of Saffron (stigmata of Crocus Savitus L.) ethanol and methanol extracts. The optical nonlinearities were investigated by performing Z-scan measurements at 470 and 535 nm wavelengths. At both wavelengths the material has a strong nonlinear refraction, mainly of thermal origin. However, only at 470 nm wavelength the material exhibit pronounced saturable nonlinear absorption. Long-term (70 days) stability measurements indicated that the nonlinearities in the Saffron extracts are due to their nonvolatile components. This study shows that there is great potential for Saffron extracts to be used in nonlinear photonic applications.
Yang, Qianli; Pitkow, Xaq
2015-03-01
Most interesting natural sensory stimuli are encoded in the brain in a form that can only be decoded nonlinearly. But despite being a core function of the brain, nonlinear population codes are rarely studied and poorly understood. Interestingly, the few existing models of nonlinear codes are inconsistent with known architectural features of the brain. In particular, these codes have information content that scales with the size of the cortical population, even if that violates the data processing inequality by exceeding the amount of information entering the sensory system. Here we provide a valid theory of nonlinear population codes by generalizing recent work on information-limiting correlations in linear population codes. Although these generalized, nonlinear information-limiting correlations bound the performance of any decoder, they also make decoding more robust to suboptimal computation, allowing many suboptimal decoders to achieve nearly the same efficiency as an optimal decoder. Although these correlations are extremely difficult to measure directly, particularly for nonlinear codes, we provide a simple, practical test by which one can use choice-related activity in small populations of neurons to determine whether decoding is suboptimal or optimal and limited by correlated noise. We conclude by describing an example computation in the vestibular system where this theory applies. QY and XP was supported by a grant from the McNair foundation.
Nonlinear systems in medicine.
Higgins, John P
2002-01-01
Many achievements in medicine have come from applying linear theory to problems. Most current methods of data analysis use linear models, which are based on proportionality between two variables and/or relationships described by linear differential equations. However, nonlinear behavior commonly occurs within human systems due to their complex dynamic nature; this cannot be described adequately by linear models. Nonlinear thinking has grown among physiologists and physicians over the past century, and non-linear system theories are beginning to be applied to assist in interpreting, explaining, and predicting biological phenomena. Chaos theory describes elements manifesting behavior that is extremely sensitive to initial conditions, does not repeat itself and yet is deterministic. Complexity theory goes one step beyond chaos and is attempting to explain complex behavior that emerges within dynamic nonlinear systems. Nonlinear modeling still has not been able to explain all of the complexity present in human systems, and further models still need to be refined and developed. However, nonlinear modeling is helping to explain some system behaviors that linear systems cannot and thus will augment our understanding of the nature of complex dynamic systems within the human body in health and in disease states.
COMPARISON OF NONLINEAR DYNAMICS OPTIMIZATION METHODS FOR APS-U
Energy Technology Data Exchange (ETDEWEB)
Sun, Y.; Borland, Michael
2017-06-25
Many different objectives and genetic algorithms have been proposed for storage ring nonlinear dynamics performance optimization. These optimization objectives include nonlinear chromaticities and driving/detuning terms, on-momentum and off-momentum dynamic acceptance, chromatic detuning, local momentum acceptance, variation of transverse invariant, Touschek lifetime, etc. In this paper, the effectiveness of several different optimization methods and objectives are compared for the nonlinear beam dynamics optimization of the Advanced Photon Source upgrade (APS-U) lattice. The optimized solutions from these different methods are preliminarily compared in terms of the dynamic acceptance, local momentum acceptance, chromatic detuning, and other performance measures.
Nonlinear Time Series Forecast Using Radial Basis Function Neural Networks
Institute of Scientific and Technical Information of China (English)
ZHENGXin; CHENTian-Lun
2003-01-01
In the research of using Radial Basis Function Neural Network (RBF NN) forecasting nonlinear time series, we investigate how the different clusterings affect the process of learning and forecasting. We find that k-means clustering is very suitable. In order to increase the precision we introduce a nonlinear feedback term to escape from the local minima of energy, then we use the model to forecast the nonlinear time series which are produced by Mackey-Glass equation and stocks. By selecting the k-means clustering and the suitable feedback term, much better forecasting results are obtained.
Nonlinear Time Series Forecast Using Radial Basis Function Neural Networks
Institute of Scientific and Technical Information of China (English)
ZHENG Xin; CHEN Tian-Lun
2003-01-01
In the research of using Radial Basis Function Neural Network (RBF NN) forecasting nonlinear timeseries, we investigate how the different clusterings affect the process of learning and forecasting. We find that k-meansclustering is very suitable. In order to increase the precision we introduce a nonlinear feedback term to escape from thelocal minima of energy, then we use the model to forecast the nonlinear time series which are produced by Mackey-Glassequation and stocks. By selecting the k-means clustering and the suitable feedback term, much better forecasting resultsare obtained.
Handbook of nonlinear optical crystals
Dmitriev, Valentin G; Nikogosyan, David N
1991-01-01
This Handbook of Nonlinear Optical Crystals provides a complete description of the properties and applications of nonlinear crystals In addition, it presents the most important equations for calculating the main parameters of nonlinear frequency converters This comprehensive reference work will be of great value to all scientists and engineers working in nonlinear optics, quantum electronics and laser physics
Indian Academy of Sciences (India)
Arun K Jain; B N Joshi
2014-04-01
Cluster knockout reactions are expected to reveal the amount of clustering (such as that of , d and even of heavier clusters such as 12C, 16O etc.) in the target nucleus. In simple terms, incident medium high-energy nuclear projectile interacts strongly with the cluster (present in the target nucleus) as if it were existing as a free entity. Theoretically, the relatively softer interactions of the two outgoing particles with the residual nucleus lead to optical distortions and are treated in terms of distorted wave (DW) formalism. The long-range projectile–cluster interaction is accounted for, in terms of the finite range (FR) direct reaction formalism, as against the more commonly adopted zero-range (ZR) distorted wave impulse approximation (DWIA) formalism. Comparison of the DWIA calculations with the observed data provide information about the momentum distribution and the clustering spectroscopic factor of the target nucleus. Interesting results and some recent advancements in the area of (, 2) reactions and heavy cluster knockout reactions are discussed. Importance of the finite-range vertex and the final-state interactions are brought out.
Nonlinear Approaches in Engineering Applications
Jazar, Reza
2012-01-01
Nonlinear Approaches in Engineering Applications focuses on nonlinear phenomena that are common in the engineering field. The nonlinear approaches described in this book provide a sound theoretical base and practical tools to design and analyze engineering systems with high efficiency and accuracy and with less energy and downtime. Presented here are nonlinear approaches in areas such as dynamic systems, optimal control and approaches in nonlinear dynamics and acoustics. Coverage encompasses a wide range of applications and fields including mathematical modeling and nonlinear behavior as applied to microresonators, nanotechnologies, nonlinear behavior in soil erosion,nonlinear population dynamics, and optimization in reducing vibration and noise as well as vibration in triple-walled carbon nanotubes. This book also: Provides a complete introduction to nonlinear behavior of systems and the advantages of nonlinearity as a tool for solving engineering problems Includes applications and examples drawn from the el...
Modeling of the vibrating beam accelerometer nonlinearities
Romanowski, P. A.; Knop, R. C.
Successful modeling and processing of the output of a quartz Vibrating Beam Accelerometer (VBA), whose errors are inherently nonlinear with respect to input acceleration, are reported. The VBA output, with two signals that are frequencies of vibrating quartz beams, has inherent higher-order terms. In order to avoid vibration rectification errors, the signal output must be sampled at a rapid rate and the output must be reduced using a nonlinear model. The present model, with acceleration as a function of frequency, is derived by a least-squares process where the covariance matrix is obtained from simulated data. The system performance is found to be acceptable to strategic levels, and it is shown that a vibration rectification error of 400 micrograms/sq g can be reduced to 4 micrograms/sq g by using the processor electronics and a nonlinear model.
Periodic solutions of nonlinear vibrating beams
Directory of Open Access Journals (Sweden)
J. Berkovits
2003-01-01
Full Text Available The aim of this paper is to prove new existence and multiplicity results for periodic semilinear beam equation with a nonlinear time-independent perturbation in case the period is not prescribed. Since the spectrum of the linear part varies with the period, the solvability of the equation depends crucially on the period which can be chosen as a free parameter. Since the period of the external forcing is generally unknown a priori, we consider the following natural problem. For a given time-independent nonlinearity, find periods T for which the equation is solvable for any T-periodic forcing. We will also deal with the existence of multiple solutions when the nonlinearity interacts with the spectrum of the linear part. We show that under certain conditions multiple solutions do exist for any small forcing term with suitable period T. The results are obtained via generalized Leray-Schauder degree and reductions to invariant subspaces.
Correlations and Non-Linear Probability Models
DEFF Research Database (Denmark)
Breen, Richard; Holm, Anders; Karlson, Kristian Bernt
2014-01-01
the dependent variable of the latent variable model and its predictor variables. We show how this correlation can be derived from the parameters of non-linear probability models, develop tests for the statistical significance of the derived correlation, and illustrate its usefulness in two applications. Under......Although the parameters of logit and probit and other non-linear probability models are often explained and interpreted in relation to the regression coefficients of an underlying linear latent variable model, we argue that they may also be usefully interpreted in terms of the correlations between...... certain circumstances, which we explain, the derived correlation provides a way of overcoming the problems inherent in cross-sample comparisons of the parameters of non-linear probability models....