Mutual Connectivity Analysis (MCA) Using Generalized Radial Basis Function Neural Networks for Nonlinear Functional Connectivity Network Recovery in Resting-State Functional MRI.

PubMed

DSouza, Adora M; Abidin, Anas Zainul; Nagarajan, Mahesh B; Wismüller, Axel

2016-03-29

We investigate the applicability of a computational framework, called mutual connectivity analysis (MCA), for directed functional connectivity analysis in both synthetic and resting-state functional MRI data. This framework comprises of first evaluating non-linear cross-predictability between every pair of time series prior to recovering the underlying network structure using community detection algorithms. We obtain the non-linear cross-prediction score between time series using Generalized Radial Basis Functions (GRBF) neural networks. These cross-prediction scores characterize the underlying functionally connected networks within the resting brain, which can be extracted using non-metric clustering approaches, such as the Louvain method. We first test our approach on synthetic models with known directional influence and network structure. Our method is able to capture the directional relationships between time series (with an area under the ROC curve = 0.92 ± 0.037) as well as the underlying network structure (Rand index = 0.87 ± 0.063) with high accuracy. Furthermore, we test this method for network recovery on resting-state fMRI data, where results are compared to the motor cortex network recovered from a motor stimulation sequence, resulting in a strong agreement between the two (Dice coefficient = 0.45). We conclude that our MCA approach is effective in analyzing non-linear directed functional connectivity and in revealing underlying functional network structure in complex systems.

Volterra-series-based nonlinear system modeling and its engineering applications: A state-of-the-art review

NASA Astrophysics Data System (ADS)

Cheng, C. M.; Peng, Z. K.; Zhang, W. M.; Meng, G.

2017-03-01

Nonlinear problems have drawn great interest and extensive attention from engineers, physicists and mathematicians and many other scientists because most real systems are inherently nonlinear in nature. To model and analyze nonlinear systems, many mathematical theories and methods have been developed, including Volterra series. In this paper, the basic definition of the Volterra series is recapitulated, together with some frequency domain concepts which are derived from the Volterra series, including the general frequency response function (GFRF), the nonlinear output frequency response function (NOFRF), output frequency response function (OFRF) and associated frequency response function (AFRF). The relationship between the Volterra series and other nonlinear system models and nonlinear problem solving methods are discussed, including the Taylor series, Wiener series, NARMAX model, Hammerstein model, Wiener model, Wiener-Hammerstein model, harmonic balance method, perturbation method and Adomian decomposition. The challenging problems and their state of arts in the series convergence study and the kernel identification study are comprehensively introduced. In addition, a detailed review is then given on the applications of Volterra series in mechanical engineering, aeroelasticity problem, control engineering, electronic and electrical engineering.

On a hierarchy of nonlinearly dispersive generalized Korteweg - de Vries evolution equations

DOE PAGES

Christov, Ivan C.

2015-08-20

We propose a hierarchy of nonlinearly dispersive generalized Korteweg–de Vries (KdV) evolution equations based on a modification of the Lagrangian density whose induced action functional the KdV equation extremizes. Two recent nonlinear evolution equations describing wave propagation in certain generalized continua with an inherent material length scale are members of the proposed hierarchy. Like KdV, the equations from the proposed hierarchy possess Hamiltonian structure. Unlike KdV, the solutions to these equations can be compact (i.e., they vanish outside of some open interval) and, in addition, peaked. Implicit solutions for these peaked, compact traveling waves (“peakompactons”) are presented.

Multilocality and fusion rules on the generalized structure functions in two-dimensional and three-dimensional Navier-Stokes turbulence.

PubMed

Gkioulekas, Eleftherios

2016-09-01

Using the fusion-rules hypothesis for three-dimensional and two-dimensional Navier-Stokes turbulence, we generalize a previous nonperturbative locality proof to multiple applications of the nonlinear interactions operator on generalized structure functions of velocity differences. We call this generalization of nonperturbative locality to multiple applications of the nonlinear interactions operator "multilocality." The resulting cross terms pose a new challenge requiring a new argument and the introduction of a new fusion rule that takes advantage of rotational symmetry. Our main result is that the fusion-rules hypothesis implies both locality and multilocality in both the IR and UV limits for the downscale energy cascade of three-dimensional Navier-Stokes turbulence and the downscale enstrophy cascade and inverse energy cascade of two-dimensional Navier-Stokes turbulence. We stress that these claims relate to nonperturbative locality of generalized structure functions on all orders and not the term-by-term perturbative locality of diagrammatic theories or closure models that involve only two-point correlation and response functions.

Stability of a general delayed virus dynamics model with humoral immunity and cellular infection

NASA Astrophysics Data System (ADS)

Elaiw, A. M.; Raezah, A. A.; Alofi, A. S.

2017-06-01

In this paper, we investigate the dynamical behavior of a general nonlinear model for virus dynamics with virus-target and infected-target incidences. The model incorporates humoral immune response and distributed time delays. The model is a four dimensional system of delay differential equations where the production and removal rates of the virus and cells are given by general nonlinear functions. We derive the basic reproduction parameter R˜0 G and the humoral immune response activation number R˜1 G and establish a set of conditions on the general functions which are sufficient to determine the global dynamics of the models. We use suitable Lyapunov functionals and apply LaSalle's invariance principle to prove the global asymptotic stability of the all equilibria of the model. We confirm the theoretical results by numerical simulations.

A concise introduction to Colombeau generalized functions and their applications in classical electrodynamics

NASA Astrophysics Data System (ADS)

Gsponer, Andre

2009-01-01

The objective of this introduction to Colombeau algebras of generalized functions (in which distributions can be freely multiplied) is to explain in elementary terms the essential concepts necessary for their application to basic nonlinear problems in classical physics. Examples are given in hydrodynamics and electrodynamics. The problem of the self-energy of a point electric charge is worked out in detail: the Coulomb potential and field are defined as Colombeau generalized functions, and integrals of nonlinear expressions corresponding to products of distributions (such as the square of the Coulomb field and the square of the delta function) are calculated. Finally, the methods introduced in Gsponer (2007 Eur. J. Phys. 28 267, 2007 Eur. J. Phys. 28 1021 and 2007 Eur. J. Phys. 28 1241), to deal with point-like singularities in classical electrodynamics are confirmed.

General Nonlinear Ferroelectric Model v. Beta

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dong, Wen; Robbins, Josh

2017-03-14

The purpose of this software is to function as a generalized ferroelectric material model. The material model is designed to work with existing finite element packages by providing updated information on material properties that are nonlinear and dependent on loading history. The two major nonlinear phenomena this model captures are domain-switching and phase transformation. The software itself does not contain potentially sensitive material information and instead provides a framework for different physical phenomena observed within ferroelectric materials. The model is calibrated to a specific ferroelectric material through input parameters provided by the user.

Detection of Differential Item Functioning with Nonlinear Regression: A Non-IRT Approach Accounting for Guessing

ERIC Educational Resources Information Center

Drabinová, Adéla; Martinková, Patrícia

2017-01-01

In this article we present a general approach not relying on item response theory models (non-IRT) to detect differential item functioning (DIF) in dichotomous items with presence of guessing. The proposed nonlinear regression (NLR) procedure for DIF detection is an extension of method based on logistic regression. As a non-IRT approach, NLR can…

Nonlinear Real-Time Optical Signal Processing

DTIC Science & Technology

1990-09-01

pattern recognition. Additional work concerns the relationship of parallel computation paradigms to optical computing and halftone screen techniques...paradigms to optical computing and halftone screen techniques for implementing general nonlinear functions. 3\\ 2 Research Progress This section...Vol. 23, No. 8, pp. 34-57, 1986. 2.4 Nonlinear Optical Processing with Halftones : Degradation and Compen- sation Models This paper is concerned with

A Nonlinear Transfer Operator Theorem

NASA Astrophysics Data System (ADS)

Pollicott, Mark

2017-02-01

In recent papers, Kenyon et al. (Ergod Theory Dyn Syst 32:1567-1584 2012), and Fan et al. (C R Math Acad Sci Paris 349:961-964 2011, Adv Math 295:271-333 2016) introduced a form of non-linear thermodynamic formalism based on solutions to a non-linear equation using matrices. In this note we consider the more general setting of Hölder continuous functions.

Nonlinear resonance scattering of femtosecond X-ray pulses on atoms in plasmas

NASA Astrophysics Data System (ADS)

Rosmej, F. B.; Astapenko, V. A.; Lisitsa, V. S.; Moroz, N. N.

2017-11-01

It is shown that for sufficiently short pulses the resonance scattering probability becomes a nonlinear function of the pulse duration. For fs X-ray pulses scattered on atoms in plasmas maxima and minima develop in the nonlinear regime whereas in the limit of long pulses the probability becomes linear and turns over into the standard description of the electromagnetic pulse scattering. Numerical calculations are carried out in terms of a generalized scattering probability for the total time of pulse duration including fine structure splitting and ion Doppler broadening in hot plasmas. For projected X-ray monocycles, the generalized nonlinear approach differs by 1-2 orders of magnitude from the standard theory.

Nonlinear normal vibration modes in the dynamics of nonlinear elastic systems

NASA Astrophysics Data System (ADS)

Mikhlin, Yu V.; Perepelkin, N. V.; Klimenko, A. A.; Harutyunyan, E.

2012-08-01

Nonlinear normal modes (NNMs) are a generalization of the linear normal vibrations. By the Kauderer-Rosenberg concept in the regime of the NNM all position coordinates are single-values functions of some selected position coordinate. By the Shaw-Pierre concept, the NNM is such a regime when all generalized coordinates and velocities are univalent functions of a couple of dominant (active) phase variables. The NNMs approach is used in some applied problems. In particular, the Kauderer-Rosenberg NNMs are analyzed in the dynamics of some pendulum systems. The NNMs of forced vibrations are investigated in a rotor system with an isotropic-elastic shaft. A combination of the Shaw-Pierre NNMs and the Rauscher method is used to construct the forced NNMs and the frequency responses in the rotor dynamics.

Electron acoustic nonlinear structures in planetary magnetospheres

NASA Astrophysics Data System (ADS)

Shah, K. H.; Qureshi, M. N. S.; Masood, W.; Shah, H. A.

2018-04-01

In this paper, we have studied linear and nonlinear propagation of electron acoustic waves (EAWs) comprising cold and hot populations in which the ions form the neutralizing background. The hot electrons have been assumed to follow the generalized ( r , q ) distribution which has the advantage that it mimics most of the distribution functions observed in space plasmas. Interestingly, it has been found that unlike Maxwellian and kappa distributions, the electron acoustic waves admit not only rarefactive structures but also allow the formation of compressive solitary structures for generalized ( r , q ) distribution. It has been found that the flatness parameter r , tail parameter q , and the nonlinear propagation velocity u affect the propagation characteristics of nonlinear EAWs. Using the plasmas parameters, typically found in Saturn's magnetosphere and the Earth's auroral region, where two populations of electrons and electron acoustic solitary waves (EASWs) have been observed, we have given an estimate of the scale lengths over which these nonlinear waves are expected to form and how the size of these structures would vary with the change in the shape of the distribution function and with the change of the plasma parameters.

A note on nonlinearity bias and dichotomous choice CVM: implications for aggregate benefits estimation

Treesearch

R.A. Souter; J. Michael Bowker

1996-01-01

It is a generally known statistical fact that the mean of a nonlinear function of a set of random variables is not equivalent to the function evaluated at the means of the variables. However, in dichotomous choice contingent valuation studies, a common practice is to calculate an overall mean (or median) by integrating over offer space (numerically or analytically) an...

Spectral analysis for nonstationary and nonlinear systems: a discrete-time-model-based approach.

PubMed

He, Fei; Billings, Stephen A; Wei, Hua-Liang; Sarrigiannis, Ptolemaios G; Zhao, Yifan

2013-08-01

A new frequency-domain analysis framework for nonlinear time-varying systems is introduced based on parametric time-varying nonlinear autoregressive with exogenous input models. It is shown how the time-varying effects can be mapped to the generalized frequency response functions (FRFs) to track nonlinear features in frequency, such as intermodulation and energy transfer effects. A new mapping to the nonlinear output FRF is also introduced. A simulated example and the application to intracranial electroencephalogram data are used to illustrate the theoretical results.

Lump solutions to nonlinear partial differential equations via Hirota bilinear forms

NASA Astrophysics Data System (ADS)

Ma, Wen-Xiu; Zhou, Yuan

2018-02-01

Lump solutions are analytical rational function solutions localized in all directions in space. We analyze a class of lump solutions, generated from quadratic functions, to nonlinear partial differential equations. The basis of success is the Hirota bilinear formulation and the primary object is the class of positive multivariate quadratic functions. A complete determination of quadratic functions positive in space and time is given, and positive quadratic functions are characterized as sums of squares of linear functions. Necessary and sufficient conditions for positive quadratic functions to solve Hirota bilinear equations are presented, and such polynomial solutions yield lump solutions to nonlinear partial differential equations under the dependent variable transformations u = 2(ln ⁡ f) x and u = 2(ln ⁡ f) xx, where x is one spatial variable. Applications are made for a few generalized KP and BKP equations.

Via generalized function projective synchronization in nonlinear Schrödinger equation for secure communication

NASA Astrophysics Data System (ADS)

Zhao, L. W.; Du, J. G.; Yin, J. L.

2018-05-01

This paper proposes a novel secured communication scheme in a chaotic system by applying generalized function projective synchronization of the nonlinear Schrödinger equation. This phenomenal approach guarantees a secured and convenient communication. Our study applied the Melnikov theorem with an active control strategy to suppress chaos in the system. The transmitted information signal is modulated into the parameter of the nonlinear Schrödinger equation in the transmitter and it is assumed that the parameter of the receiver system is unknown. Based on the Lyapunov stability theory and the adaptive control technique, the controllers are designed to make two identical nonlinear Schrödinger equation with the unknown parameter asymptotically synchronized. The numerical simulation results of our study confirmed the validity, effectiveness and the feasibility of the proposed novel synchronization method and error estimate for a secure communication. The Chaos masking signals of the information communication scheme, further guaranteed a safer and secured information communicated via this approach.

System Identification for Nonlinear Control Using Neural Networks

NASA Technical Reports Server (NTRS)

Stengel, Robert F.; Linse, Dennis J.

1990-01-01

An approach to incorporating artificial neural networks in nonlinear, adaptive control systems is described. The controller contains three principal elements: a nonlinear inverse dynamic control law whose coefficients depend on a comprehensive model of the plant, a neural network that models system dynamics, and a state estimator whose outputs drive the control law and train the neural network. Attention is focused on the system identification task, which combines an extended Kalman filter with generalized spline function approximation. Continual learning is possible during normal operation, without taking the system off line for specialized training. Nonlinear inverse dynamic control requires smooth derivatives as well as function estimates, imposing stringent goals on the approximating technique.

Application of numerical optimization techniques to control system design for nonlinear dynamic models of aircraft

NASA Technical Reports Server (NTRS)

Lan, C. Edward; Ge, Fuying

1989-01-01

Control system design for general nonlinear flight dynamic models is considered through numerical simulation. The design is accomplished through a numerical optimizer coupled with analysis of flight dynamic equations. The general flight dynamic equations are numerically integrated and dynamic characteristics are then identified from the dynamic response. The design variables are determined iteratively by the optimizer to optimize a prescribed objective function which is related to desired dynamic characteristics. Generality of the method allows nonlinear effects to aerodynamics and dynamic coupling to be considered in the design process. To demonstrate the method, nonlinear simulation models for an F-5A and an F-16 configurations are used to design dampers to satisfy specifications on flying qualities and control systems to prevent departure. The results indicate that the present method is simple in formulation and effective in satisfying the design objectives.

Examining the influence of link function misspecification in conventional regression models for developing crash modification factors.

PubMed

Wu, Lingtao; Lord, Dominique

2017-05-01

This study further examined the use of regression models for developing crash modification factors (CMFs), specifically focusing on the misspecification in the link function. The primary objectives were to validate the accuracy of CMFs derived from the commonly used regression models (i.e., generalized linear models or GLMs with additive linear link functions) when some of the variables have nonlinear relationships and quantify the amount of bias as a function of the nonlinearity. Using the concept of artificial realistic data, various linear and nonlinear crash modification functions (CM-Functions) were assumed for three variables. Crash counts were randomly generated based on these CM-Functions. CMFs were then derived from regression models for three different scenarios. The results were compared with the assumed true values. The main findings are summarized as follows: (1) when some variables have nonlinear relationships with crash risk, the CMFs for these variables derived from the commonly used GLMs are all biased, especially around areas away from the baseline conditions (e.g., boundary areas); (2) with the increase in nonlinearity (i.e., nonlinear relationship becomes stronger), the bias becomes more significant; (3) the quality of CMFs for other variables having linear relationships can be influenced when mixed with those having nonlinear relationships, but the accuracy may still be acceptable; and (4) the misuse of the link function for one or more variables can also lead to biased estimates for other parameters. This study raised the importance of the link function when using regression models for developing CMFs. Copyright © 2017 Elsevier Ltd. All rights reserved.

Reconstructing the primordial spectrum of fluctuations of the universe from the observed nonlinear clustering of galaxies

NASA Technical Reports Server (NTRS)

Hamilton, A. J. S.; Matthews, Alex; Kumar, P.; Lu, Edward

1991-01-01

It was discovered that the nonlinear evolution of the two point correlation function in N-body experiments of galaxy clustering with Omega = 1 appears to be described to good approximation by a simple general formula. The underlying form of the formula is physically motivated, but its detailed representation is obtained empirically by fitting to N-body experiments. In this paper, the formula is presented along with an inverse formula which converts a final, nonlinear correlation function into the initial linear correlation function. The inverse formula is applied to observational data from the CfA, IRAs, and APM galaxy surveys, and the initial spectrum of fluctuations of the universe, if Omega = 1.

A numerical method to solve the 1D and the 2D reaction diffusion equation based on Bessel functions and Jacobian free Newton-Krylov subspace methods

NASA Astrophysics Data System (ADS)

Parand, K.; Nikarya, M.

2017-11-01

In this paper a novel method will be introduced to solve a nonlinear partial differential equation (PDE). In the proposed method, we use the spectral collocation method based on Bessel functions of the first kind and the Jacobian free Newton-generalized minimum residual (JFNGMRes) method with adaptive preconditioner. In this work a nonlinear PDE has been converted to a nonlinear system of algebraic equations using the collocation method based on Bessel functions without any linearization, discretization or getting the help of any other methods. Finally, by using JFNGMRes, the solution of the nonlinear algebraic system is achieved. To illustrate the reliability and efficiency of the proposed method, we solve some examples of the famous Fisher equation. We compare our results with other methods.

Generalized Convexity and Concavity Properties of the Optimal Value Function in Parametric Nonlinear Programming.

DTIC Science & Technology

1983-04-11

existing ones. * -37- !I T-472 REFERENCES [1] Avriel, M., W. E. Diewert, S. Schaible and W. T. Ziemba (1981). Introduction to concave and generalized concave...functions. In Generalized Concavity in Optimization and Economics (S. Schaible and W. T. Ziemba , eds.), Academic Press, New York, pp. 21-50. (21 Bank...Optimality conditions involving generalized convex mappings. In Generalized Concavity in Optimization and Economics (S. Schaible and W. T. Ziemba

Quantum corrections to the generalized Proca theory via a matter field

NASA Astrophysics Data System (ADS)

Amado, André; Haghani, Zahra; Mohammadi, Azadeh; Shahidi, Shahab

2017-09-01

We study the quantum corrections to the generalized Proca theory via matter loops. We consider two types of interactions, linear and nonlinear in the vector field. Calculating the one-loop correction to the vector field propagator, three- and four-point functions, we show that the non-linear interactions are harmless, although they renormalize the theory. The linear matter-vector field interactions introduce ghost degrees of freedom to the generalized Proca theory. Treating the theory as an effective theory, we calculate the energy scale up to which the theory remains healthy.

Identification of aerodynamic models for maneuvering aircraft

NASA Technical Reports Server (NTRS)

Chin, Suei; Lan, C. Edward

1990-01-01

Due to the requirement of increased performance and maneuverability, the flight envelope of a modern fighter is frequently extended to the high angle-of-attack regime. Vehicles maneuvering in this regime are subjected to nonlinear aerodynamic loads. The nonlinearities are due mainly to three-dimensional separated flow and concentrated vortex flow that occur at large angles of attack. Accurate prediction of these nonlinear airloads is of great importance in the analysis of a vehicle's flight motion and in the design of its flight control system. A satisfactory evaluation of the performance envelope of the aircraft may require a large number of coupled computations, one for each change in initial conditions. To avoid the disadvantage of solving the coupled flow-field equations and aircraft's motion equations, an alternate approach is to use a mathematical modeling to describe the steady and unsteady aerodynamics for the aircraft equations of motion. Aerodynamic forces and moments acting on a rapidly maneuvering aircraft are, in general, nonlinear functions of motion variables, their time rate of change, and the history of maneuvering. A numerical method was developed to analyze the nonlinear and time-dependent aerodynamic response to establish the generalized indicial function in terms of motion variables and their time rates of change.

A modified variational method for nonlinear vibration analysis of rotating beams including Coriolis effects

NASA Astrophysics Data System (ADS)

Tian, Jiajin; Su, Jinpeng; Zhou, Kai; Hua, Hongxing

2018-07-01

This paper presents a general formulation for nonlinear vibration analysis of rotating beams. A modified variational method combined with a multi-segment partitioning technique is employed to derive the free and transient vibration behaviors of the rotating beams. The strain energy and kinetic energy functional are formulated based on the order truncation principle of the fully geometrically nonlinear beam theory. The Coriolis effects as well as nonlinear effects due to the coupling of bending-stretching, bending-twist and twist-stretching are taken into account. The present method relaxes the need to explicitly meet the requirements of the boundary conditions for the admissible functions, and allows the use of any linearly independent, complete basis functions as admissible functions for rotating beams. Moreover, the method is readily used to deal with the nonlinear transient vibration problems for rotating beams subjected to dynamic loads. The accuracy, convergence and efficiency of the proposed method are examined by numerical examples. The influences of Coriolis and centrifugal forces on the vibration behaviors of the beams with various hub radiuses and slenderness ratios and rotating at different angular velocities are also investigated.

An Efficient Numerical Approach for Nonlinear Fokker-Planck equations

NASA Astrophysics Data System (ADS)

Otten, Dustin; Vedula, Prakash

2009-03-01

Fokker-Planck equations which are nonlinear with respect to their probability densities that occur in many nonequilibrium systems relevant to mean field interaction models, plasmas, classical fermions and bosons can be challenging to solve numerically. To address some underlying challenges in obtaining numerical solutions, we propose a quadrature based moment method for efficient and accurate determination of transient (and stationary) solutions of nonlinear Fokker-Planck equations. In this approach the distribution function is represented as a collection of Dirac delta functions with corresponding quadrature weights and locations, that are in turn determined from constraints based on evolution of generalized moments. Properties of the distribution function can be obtained by solution of transport equations for quadrature weights and locations. We will apply this computational approach to study a wide range of problems, including the Desai-Zwanzig Model (for nonlinear muscular contraction) and multivariate nonlinear Fokker-Planck equations describing classical fermions and bosons, and will also demonstrate good agreement with results obtained from Monte Carlo and other standard numerical methods.

Jump resonant frequency islands in nonlinear feedback control systems

NASA Technical Reports Server (NTRS)

Koenigsberg, W. D.; Dunn, J. C.

1975-01-01

A new type of jump resonance is predicted and observed in certain nonlinear feedback control systems. The new jump resonance characteristic is described as a 'frequency island' due to the fact that a portion of the input-output transfer characteristic is disjoint from the main body. The presence of such frequency islands was predicted by using a sinusoidal describing function characterization of the dynamics of an inertial gyro employing nonlinear ternary rebalance logic. While the general conditions under which such islands are possible has not been examined, a numerical approach is presented which can aid in establishing their presence. The existence of the frequency islands predicted for the ternary rebalanced gyro was confirmed by simulating the nonlinear system and measuring the transfer function.

Gain optimization with non-linear controls

NASA Technical Reports Server (NTRS)

Slater, G. L.; Kandadai, R. D.

1984-01-01

An algorithm has been developed for the analysis and design of controls for non-linear systems. The technical approach is to use statistical linearization to model the non-linear dynamics of a system by a quasi-Gaussian model. A covariance analysis is performed to determine the behavior of the dynamical system and a quadratic cost function. Expressions for the cost function and its derivatives are determined so that numerical optimization techniques can be applied to determine optimal feedback laws. The primary application for this paper is centered about the design of controls for nominally linear systems but where the controls are saturated or limited by fixed constraints. The analysis is general, however, and numerical computation requires only that the specific non-linearity be considered in the analysis.

General methodology for simultaneous representation and discrimination of multiple object classes

NASA Astrophysics Data System (ADS)

Talukder, Ashit; Casasent, David P.

1998-03-01

We address a new general method for linear and nonlinear feature extraction for simultaneous representation and classification. We call this approach the maximum representation and discrimination feature (MRDF) method. We develop a novel nonlinear eigenfeature extraction technique to represent data with closed-form solutions and use it to derive a nonlinear MRDF algorithm. Results of the MRDF method on synthetic databases are shown and compared with results from standard Fukunaga-Koontz transform and Fisher discriminant function methods. The method is also applied to an automated product inspection problem and for classification and pose estimation of two similar objects under 3D aspect angle variations.

Evaluation of confidence intervals for a steady-state leaky aquifer model

USGS Publications Warehouse

Christensen, S.; Cooley, R.L.

1999-01-01

The fact that dependent variables of groundwater models are generally nonlinear functions of model parameters is shown to be a potentially significant factor in calculating accurate confidence intervals for both model parameters and functions of the parameters, such as the values of dependent variables calculated by the model. The Lagrangian method of Vecchia and Cooley [Vecchia, A.V. and Cooley, R.L., Water Resources Research, 1987, 23(7), 1237-1250] was used to calculate nonlinear Scheffe-type confidence intervals for the parameters and the simulated heads of a steady-state groundwater flow model covering 450 km2 of a leaky aquifer. The nonlinear confidence intervals are compared to corresponding linear intervals. As suggested by the significant nonlinearity of the regression model, linear confidence intervals are often not accurate. The commonly made assumption that widths of linear confidence intervals always underestimate the actual (nonlinear) widths was not correct. Results show that nonlinear effects can cause the nonlinear intervals to be asymmetric and either larger or smaller than the linear approximations. Prior information on transmissivities helps reduce the size of the confidence intervals, with the most notable effects occurring for the parameters on which there is prior information and for head values in parameter zones for which there is prior information on the parameters.The fact that dependent variables of groundwater models are generally nonlinear functions of model parameters is shown to be a potentially significant factor in calculating accurate confidence intervals for both model parameters and functions of the parameters, such as the values of dependent variables calculated by the model. The Lagrangian method of Vecchia and Cooley was used to calculate nonlinear Scheffe-type confidence intervals for the parameters and the simulated heads of a steady-state groundwater flow model covering 450 km2 of a leaky aquifer. The nonlinear confidence intervals are compared to corresponding linear intervals. As suggested by the significant nonlinearity of the regression model, linear confidence intervals are often not accurate. The commonly made assumption that widths of linear confidence intervals always underestimate the actual (nonlinear) widths was not correct. Results show that nonlinear effects can cause the nonlinear intervals to be asymmetric and either larger or smaller than the linear approximations. Prior information on transmissivities helps reduce the size of the confidence intervals, with the most notable effects occurring for the parameters on which there is prior information and for head values in parameter zones for which there is prior information on the parameters.

A Concise Introduction to Colombeau Generalized Functions and Their Applications in Classical Electrodynamics

ERIC Educational Resources Information Center

Gsponer, Andre

2009-01-01

The objective of this introduction to Colombeau algebras of generalized functions (in which distributions can be freely multiplied) is to explain in elementary terms the essential concepts necessary for their application to basic nonlinear problems in classical physics. Examples are given in hydrodynamics and electrodynamics. The problem of the…

Probabilistic DHP adaptive critic for nonlinear stochastic control systems.

PubMed

Herzallah, Randa

2013-06-01

Following the recently developed algorithms for fully probabilistic control design for general dynamic stochastic systems (Herzallah & Káarnáy, 2011; Kárný, 1996), this paper presents the solution to the probabilistic dual heuristic programming (DHP) adaptive critic method (Herzallah & Káarnáy, 2011) and randomized control algorithm for stochastic nonlinear dynamical systems. The purpose of the randomized control input design is to make the joint probability density function of the closed loop system as close as possible to a predetermined ideal joint probability density function. This paper completes the previous work (Herzallah & Káarnáy, 2011; Kárný, 1996) by formulating and solving the fully probabilistic control design problem on the more general case of nonlinear stochastic discrete time systems. A simulated example is used to demonstrate the use of the algorithm and encouraging results have been obtained. Copyright © 2013 Elsevier Ltd. All rights reserved.

Nonlinear refraction at the absorption edge in InAs.

PubMed

Poole, C D; Garmire, E

1984-08-01

The results of measurements of nonlinear refraction at the absorption edge in InAs between 68 and 90 K taken with an HF laser are compared with those of a band-gap resonant model in which the contribution of the light-hole band is included and found to account for more than 40% of the observed nonlinear refraction. A generalized expression for the nonlinear index is derived by using the complete Fermi-Dirac distribution function. Good agreement between theory and experiment is obtained, with no free parameters.

Numerical solution to generalized Burgers'-Fisher equation using Exp-function method hybridized with heuristic computation.

PubMed

Malik, Suheel Abdullah; Qureshi, Ijaz Mansoor; Amir, Muhammad; Malik, Aqdas Naveed; Haq, Ihsanul

2015-01-01

In this paper, a new heuristic scheme for the approximate solution of the generalized Burgers'-Fisher equation is proposed. The scheme is based on the hybridization of Exp-function method with nature inspired algorithm. The given nonlinear partial differential equation (NPDE) through substitution is converted into a nonlinear ordinary differential equation (NODE). The travelling wave solution is approximated by the Exp-function method with unknown parameters. The unknown parameters are estimated by transforming the NODE into an equivalent global error minimization problem by using a fitness function. The popular genetic algorithm (GA) is used to solve the minimization problem, and to achieve the unknown parameters. The proposed scheme is successfully implemented to solve the generalized Burgers'-Fisher equation. The comparison of numerical results with the exact solutions, and the solutions obtained using some traditional methods, including adomian decomposition method (ADM), homotopy perturbation method (HPM), and optimal homotopy asymptotic method (OHAM), show that the suggested scheme is fairly accurate and viable for solving such problems.

Numerical Solution to Generalized Burgers'-Fisher Equation Using Exp-Function Method Hybridized with Heuristic Computation

PubMed Central

Malik, Suheel Abdullah; Qureshi, Ijaz Mansoor; Amir, Muhammad; Malik, Aqdas Naveed; Haq, Ihsanul

2015-01-01

In this paper, a new heuristic scheme for the approximate solution of the generalized Burgers'-Fisher equation is proposed. The scheme is based on the hybridization of Exp-function method with nature inspired algorithm. The given nonlinear partial differential equation (NPDE) through substitution is converted into a nonlinear ordinary differential equation (NODE). The travelling wave solution is approximated by the Exp-function method with unknown parameters. The unknown parameters are estimated by transforming the NODE into an equivalent global error minimization problem by using a fitness function. The popular genetic algorithm (GA) is used to solve the minimization problem, and to achieve the unknown parameters. The proposed scheme is successfully implemented to solve the generalized Burgers'-Fisher equation. The comparison of numerical results with the exact solutions, and the solutions obtained using some traditional methods, including adomian decomposition method (ADM), homotopy perturbation method (HPM), and optimal homotopy asymptotic method (OHAM), show that the suggested scheme is fairly accurate and viable for solving such problems. PMID:25811858

Propagation of uncertainty by Monte Carlo simulations in case of basic geodetic computations

NASA Astrophysics Data System (ADS)

Wyszkowska, Patrycja

2017-12-01

The determination of the accuracy of functions of measured or adjusted values may be a problem in geodetic computations. The general law of covariance propagation or in case of the uncorrelated observations the propagation of variance (or the Gaussian formula) are commonly used for that purpose. That approach is theoretically justified for the linear functions. In case of the non-linear functions, the first-order Taylor series expansion is usually used but that solution is affected by the expansion error. The aim of the study is to determine the applicability of the general variance propagation law in case of the non-linear functions used in basic geodetic computations. The paper presents errors which are a result of negligence of the higher-order expressions and it determines the range of such simplification. The basis of that analysis is the comparison of the results obtained by the law of propagation of variance and the probabilistic approach, namely Monte Carlo simulations. Both methods are used to determine the accuracy of the following geodetic computations: the Cartesian coordinates of unknown point in the three-point resection problem, azimuths and distances of the Cartesian coordinates, height differences in the trigonometric and the geometric levelling. These simulations and the analysis of the results confirm the possibility of applying the general law of variance propagation in basic geodetic computations even if the functions are non-linear. The only condition is the accuracy of observations, which cannot be too low. Generally, this is not a problem with using present geodetic instruments.

A Thermodynamic Theory of Solid Viscoelasticity. Part 3: Nonlinear Glassy Viscoelasticity, Stability Constraints, Specifications

NASA Technical Reports Server (NTRS)

Freed, Alan; Leonov, Arkady I.

2002-01-01

This paper, the last in the series, continues developing the nonlinear constitutive relations for non-isothermal, compressible, solid viscoelasticity. We initially discuss a single integral approach, more suitable for the glassy state of rubber-like materials, with basic functionals involved in the thermodynamic description for this type of viscoelasticity. Then we switch our attention to analyzing stability constraints, imposed on the general formulation of the nonlinear theory of solid viscoelasticity. Finally, we discuss specific (known from the literature or new) expressions for material functions that are involved in the constitutive formulations of both the rubber-like and glassy-like, complementary parts of the theory.

The Prabhakar or three parameter Mittag-Leffler function: Theory and application

NASA Astrophysics Data System (ADS)

Garra, Roberto; Garrappa, Roberto

2018-03-01

The Prabhakar function (namely, a three parameter Mittag-Leffler function) is investigated. This function plays a fundamental role in the description of the anomalous dielectric properties in disordered materials and heterogeneous systems manifesting simultaneous nonlocality and nonlinearity and, more generally, in models of Havriliak-Negami type. After reviewing some of the main properties of the function, the asymptotic expansion for large arguments is investigated in the whole complex plane and, with major emphasis, along the negative semi-axis. Fractional integral and derivative operators of Prabhakar type are hence considered and some nonlinear heat conduction equations with memory involving Prabhakar derivatives are studied.

Hilbert complexes of nonlinear elasticity

NASA Astrophysics Data System (ADS)

Angoshtari, Arzhang; Yavari, Arash

2016-12-01

We introduce some Hilbert complexes involving second-order tensors on flat compact manifolds with boundary that describe the kinematics and the kinetics of motion in nonlinear elasticity. We then use the general framework of Hilbert complexes to write Hodge-type and Helmholtz-type orthogonal decompositions for second-order tensors. As some applications of these decompositions in nonlinear elasticity, we study the strain compatibility equations of linear and nonlinear elasticity in the presence of Dirichlet boundary conditions and the existence of stress functions on non-contractible bodies. As an application of these Hilbert complexes in computational mechanics, we briefly discuss the derivation of a new class of mixed finite element methods for nonlinear elasticity.

Nonlinear programming extensions to rational function approximation methods for unsteady aerodynamic forces

NASA Technical Reports Server (NTRS)

Tiffany, Sherwood H.; Adams, William M., Jr.

1988-01-01

The approximation of unsteady generalized aerodynamic forces in the equations of motion of a flexible aircraft are discussed. Two methods of formulating these approximations are extended to include the same flexibility in constraining the approximations and the same methodology in optimizing nonlinear parameters as another currently used extended least-squares method. Optimal selection of nonlinear parameters is made in each of the three methods by use of the same nonlinear, nongradient optimizer. The objective of the nonlinear optimization is to obtain rational approximations to the unsteady aerodynamics whose state-space realization is lower order than that required when no optimization of the nonlinear terms is performed. The free linear parameters are determined using the least-squares matrix techniques of a Lagrange multiplier formulation of an objective function which incorporates selected linear equality constraints. State-space mathematical models resulting from different approaches are described and results are presented that show comparative evaluations from application of each of the extended methods to a numerical example.

Unimodal dynamical systems: Comparison principles, spreading speeds and travelling waves

NASA Astrophysics Data System (ADS)

Yi, Taishan; Chen, Yuming; Wu, Jianhong

Reaction diffusion equations with delayed nonlinear reaction terms are used as prototypes to motivate an appropriate abstract formulation of dynamical systems with unimodal nonlinearity. For such non-monotone dynamical systems, we develop a general comparison principle and show how this general comparison principle, coupled with some existing results for monotone dynamical systems, can be used to establish results on the asymptotic speeds of spread and travelling waves. We illustrate our main results by an integral equation which includes a nonlocal delayed reaction diffusion equation and a nonlocal delayed lattice differential system in an unbounded domain, with the non-monotone nonlinearities including the Ricker birth function and the Mackey-Glass hematopoiesis feedback.

Structural stability of nonlinear population dynamics.

PubMed

Cenci, Simone; Saavedra, Serguei

2018-01-01

In population dynamics, the concept of structural stability has been used to quantify the tolerance of a system to environmental perturbations. Yet, measuring the structural stability of nonlinear dynamical systems remains a challenging task. Focusing on the classic Lotka-Volterra dynamics, because of the linearity of the functional response, it has been possible to measure the conditions compatible with a structurally stable system. However, the functional response of biological communities is not always well approximated by deterministic linear functions. Thus, it is unclear the extent to which this linear approach can be generalized to other population dynamics models. Here, we show that the same approach used to investigate the classic Lotka-Volterra dynamics, which is called the structural approach, can be applied to a much larger class of nonlinear models. This class covers a large number of nonlinear functional responses that have been intensively investigated both theoretically and experimentally. We also investigate the applicability of the structural approach to stochastic dynamical systems and we provide a measure of structural stability for finite populations. Overall, we show that the structural approach can provide reliable and tractable information about the qualitative behavior of many nonlinear dynamical systems.

Structural stability of nonlinear population dynamics

NASA Astrophysics Data System (ADS)

Cenci, Simone; Saavedra, Serguei

2018-01-01

In population dynamics, the concept of structural stability has been used to quantify the tolerance of a system to environmental perturbations. Yet, measuring the structural stability of nonlinear dynamical systems remains a challenging task. Focusing on the classic Lotka-Volterra dynamics, because of the linearity of the functional response, it has been possible to measure the conditions compatible with a structurally stable system. However, the functional response of biological communities is not always well approximated by deterministic linear functions. Thus, it is unclear the extent to which this linear approach can be generalized to other population dynamics models. Here, we show that the same approach used to investigate the classic Lotka-Volterra dynamics, which is called the structural approach, can be applied to a much larger class of nonlinear models. This class covers a large number of nonlinear functional responses that have been intensively investigated both theoretically and experimentally. We also investigate the applicability of the structural approach to stochastic dynamical systems and we provide a measure of structural stability for finite populations. Overall, we show that the structural approach can provide reliable and tractable information about the qualitative behavior of many nonlinear dynamical systems.

How to characterize a nonlinear elastic material? A review on nonlinear constitutive parameters in isotropic finite elasticity

PubMed Central

2017-01-01

The mechanical response of a homogeneous isotropic linearly elastic material can be fully characterized by two physical constants, the Young’s modulus and the Poisson’s ratio, which can be derived by simple tensile experiments. Any other linear elastic parameter can be obtained from these two constants. By contrast, the physical responses of nonlinear elastic materials are generally described by parameters which are scalar functions of the deformation, and their particular choice is not always clear. Here, we review in a unified theoretical framework several nonlinear constitutive parameters, including the stretch modulus, the shear modulus and the Poisson function, that are defined for homogeneous isotropic hyperelastic materials and are measurable under axial or shear experimental tests. These parameters represent changes in the material properties as the deformation progresses, and can be identified with their linear equivalent when the deformations are small. Universal relations between certain of these parameters are further established, and then used to quantify nonlinear elastic responses in several hyperelastic models for rubber, soft tissue and foams. The general parameters identified here can also be viewed as a flexible basis for coupling elastic responses in multi-scale processes, where an open challenge is the transfer of meaningful information between scales. PMID:29225507

Application of Contraction Mappings to the Control of Nonlinear Systems. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Killingsworth, W. R., Jr.

1972-01-01

The theoretical and applied aspects of successive approximation techniques are considered for the determination of controls for nonlinear dynamical systems. Particular emphasis is placed upon the methods of contraction mappings and modified contraction mappings. It is shown that application of the Pontryagin principle to the optimal nonlinear regulator problem results in necessary conditions for optimality in the form of a two point boundary value problem (TPBVP). The TPBVP is represented by an operator equation and functional analytic results on the iterative solution of operator equations are applied. The general convergence theorems are translated and applied to those operators arising from the optimal regulation of nonlinear systems. It is shown that simply structured matrices and similarity transformations may be used to facilitate the calculation of the matrix Green functions and the evaluation of the convergence criteria. A controllability theory based on the integral representation of TPBVP's, the implicit function theorem, and contraction mappings is developed for nonlinear dynamical systems. Contraction mappings are theoretically and practically applied to a nonlinear control problem with bounded input control and the Lipschitz norm is used to prove convergence for the nondifferentiable operator. A dynamic model representing community drug usage is developed and the contraction mappings method is used to study the optimal regulation of the nonlinear system.

Entire solutions of nonlinear differential-difference equations.

PubMed

Li, Cuiping; Lü, Feng; Xu, Junfeng

2016-01-01

In this paper, we describe the properties of entire solutions of a nonlinear differential-difference equation and a Fermat type equation, and improve several previous theorems greatly. In addition, we also deduce a uniqueness result for an entire function f(z) that shares a set with its shift [Formula: see text], which is a generalization of a result of Liu.

New evidence and impact of electron transport non-linearities based on new perturbative inter-modulation analysis

NASA Astrophysics Data System (ADS)

van Berkel, M.; Kobayashi, T.; Igami, H.; Vandersteen, G.; Hogeweij, G. M. D.; Tanaka, K.; Tamura, N.; Zwart, H. J.; Kubo, S.; Ito, S.; Tsuchiya, H.; de Baar, M. R.; LHD Experiment Group

2017-12-01

A new methodology to analyze non-linear components in perturbative transport experiments is introduced. The methodology has been experimentally validated in the Large Helical Device for the electron heat transport channel. Electron cyclotron resonance heating with different modulation frequencies by two gyrotrons has been used to directly quantify the amplitude of the non-linear component at the inter-modulation frequencies. The measurements show significant quadratic non-linear contributions and also the absence of cubic and higher order components. The non-linear component is analyzed using the Volterra series, which is the non-linear generalization of transfer functions. This allows us to study the radial distribution of the non-linearity of the plasma and to reconstruct linear profiles where the measurements were not distorted by non-linearities. The reconstructed linear profiles are significantly different from the measured profiles, demonstrating the significant impact that non-linearity can have.

Stability analysis of piecewise non-linear systems and its application to chaotic synchronisation with intermittent control

NASA Astrophysics Data System (ADS)

Wang, Qingzhi; Tan, Guanzheng; He, Yong; Wu, Min

2017-10-01

This paper considers a stability analysis issue of piecewise non-linear systems and applies it to intermittent synchronisation of chaotic systems. First, based on piecewise Lyapunov function methods, more general and less conservative stability criteria of piecewise non-linear systems in periodic and aperiodic cases are presented, respectively. Next, intermittent synchronisation conditions of chaotic systems are derived which extend existing results. Finally, Chua's circuit is taken as an example to verify the validity of our methods.

(2 + 1)-dimensional dynamical black holes in Einstein-nonlinear Maxwell theory

NASA Astrophysics Data System (ADS)

Gurtug, O.; Mazharimousavi, S. Habib; Halilsoy, M.

2018-02-01

Radiative extensions of BTZ metric in 2 + 1 dimensions are found which are sourced by nonlinear Maxwell fields and a null current. This may be considered as generalization of the problem formulated long go by Vaidya and Bonnor. The mass and charge are functions of retarded/advanced null coordinate apt for decay/inflation. The new solutions are constructed through a Theorem that works remarkably well for any nonlinear electrodynamic model. Hawking temperature is analyzed for the case of the Born-Infeld electrodynamics.

A novel method to produce nonlinear empirical physical formulas for experimental nonlinear electro-optical responses of doped nematic liquid crystals: Feedforward neural network approach

NASA Astrophysics Data System (ADS)

Yildiz, Nihat; San, Sait Eren; Okutan, Mustafa; Kaya, Hüseyin

2010-04-01

Among other significant obstacles, inherent nonlinearity in experimental physical response data poses severe difficulty in empirical physical formula (EPF) construction. In this paper, we applied a novel method (namely layered feedforward neural network (LFNN) approach) to produce explicit nonlinear EPFs for experimental nonlinear electro-optical responses of doped nematic liquid crystals (NLCs). Our motivation was that, as we showed in a previous theoretical work, an appropriate LFNN, due to its exceptional nonlinear function approximation capabilities, is highly relevant to EPF construction. Therefore, in this paper, we obtained excellently produced LFNN approximation functions as our desired EPFs for above-mentioned highly nonlinear response data of NLCs. In other words, by using suitable LFNNs, we successfully fitted the experimentally measured response and predicted the new (yet-to-be measured) response data. The experimental data (response versus input) were diffraction and dielectric properties versus bias voltage; and they were all taken from our previous experimental work. We conclude that in general, LFNN can be applied to construct various types of EPFs for the corresponding various nonlinear physical perturbation (thermal, electronic, molecular, electric, optical, etc.) data of doped NLCs.

Describing the Elephant: Structure and Function in Multivariate Data.

ERIC Educational Resources Information Center

McDonald, Roderick P.

1986-01-01

There is a unity underlying the diversity of models for the analysis of multivariate data. Essentially, they constitute a family of models, most generally nonlinear, for structural/functional relations between variables drawn from a behavior domain. (Author)

Electronic transport in disordered chains with saturable nonlinearity

NASA Astrophysics Data System (ADS)

dos Santos, J. L. L.; Nguyen, Ba Phi; de Moura, F. A. B. F.

2015-10-01

In this work we study numerically the dynamics of an initially localized wave packet in one-dimensional disordered chains with saturable nonlinearity. By using the generalized discrete nonlinear Schrödinger equation, we calculate two different physical quantities as a function of time, which are the participation number and the mean square displacement from the excitation site. From detailed numerical analysis, we find that the saturable nonlinearity can promote a sub-diffusive spreading of the wave packet even in the presence of diagonal disorder for a long time. In addition, we also investigate the effect of the saturated nonlinearity for initial times of the electronic evolution thus showing the possibility of mobile breather-like modes.

Nonlinear Wavefront Control with All-Dielectric Metasurfaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Lei; Kruk, Sergey; Koshelev, Kirill

Metasurfaces, two-dimensional lattices of nanoscale resonators, offer unique opportunities for functional flat optics and allow the control of the transmission, reflection, and polarization of a wavefront of light. Recently, all-dielectric metasurfaces reached remarkable efficiencies, often matching or out-performing conventional optical elements. The exploitation of the nonlinear optical response of metasurfaces offers a paradigm shift in nonlinear optics, and dielectric nonlinear metasurfaces are expected to enrich subwavelength photonics by enhancing substantially nonlinear response of natural materials combined with the efficient control of the phase of nonlinear waves. Here, we suggest a novel and rather general approach for engineering the wavefront ofmore » parametric waves of arbitrary complexity generated by a nonlinear metasurface. We design all-dielectric nonlinear metasurfaces, achieve a highly efficient wavefront control of a third-harmonic field, and demonstrate the generation of nonlinear beams at a designed angle and the generation of nonlinear focusing vortex beams. Lastly, our nonlinear metasurfaces produce phase gradients over a full 0–2π phase range with a 92% diffraction efficiency.« less

Nonlinear Wavefront Control with All-Dielectric Metasurfaces.

PubMed

Wang, Lei; Kruk, Sergey; Koshelev, Kirill; Kravchenko, Ivan; Luther-Davies, Barry; Kivshar, Yuri

2018-06-13

Metasurfaces, two-dimensional lattices of nanoscale resonators, offer unique opportunities for functional flat optics and allow the control of the transmission, reflection, and polarization of a wavefront of light. Recently, all-dielectric metasurfaces reached remarkable efficiencies, often matching or out-performing conventional optical elements. The exploitation of the nonlinear optical response of metasurfaces offers a paradigm shift in nonlinear optics, and dielectric nonlinear metasurfaces are expected to enrich subwavelength photonics by enhancing substantially nonlinear response of natural materials combined with the efficient control of the phase of nonlinear waves. Here, we suggest a novel and rather general approach for engineering the wavefront of parametric waves of arbitrary complexity generated by a nonlinear metasurface. We design all-dielectric nonlinear metasurfaces, achieve a highly efficient wavefront control of a third-harmonic field, and demonstrate the generation of nonlinear beams at a designed angle and the generation of nonlinear focusing vortex beams. Our nonlinear metasurfaces produce phase gradients over a full 0-2π phase range with a 92% diffraction efficiency.

Nonlinear Wavefront Control with All-Dielectric Metasurfaces

DOE PAGES

Wang, Lei; Kruk, Sergey; Koshelev, Kirill; ...

2018-05-11

Metasurfaces, two-dimensional lattices of nanoscale resonators, offer unique opportunities for functional flat optics and allow the control of the transmission, reflection, and polarization of a wavefront of light. Recently, all-dielectric metasurfaces reached remarkable efficiencies, often matching or out-performing conventional optical elements. The exploitation of the nonlinear optical response of metasurfaces offers a paradigm shift in nonlinear optics, and dielectric nonlinear metasurfaces are expected to enrich subwavelength photonics by enhancing substantially nonlinear response of natural materials combined with the efficient control of the phase of nonlinear waves. Here, we suggest a novel and rather general approach for engineering the wavefront ofmore » parametric waves of arbitrary complexity generated by a nonlinear metasurface. We design all-dielectric nonlinear metasurfaces, achieve a highly efficient wavefront control of a third-harmonic field, and demonstrate the generation of nonlinear beams at a designed angle and the generation of nonlinear focusing vortex beams. Lastly, our nonlinear metasurfaces produce phase gradients over a full 0–2π phase range with a 92% diffraction efficiency.« less

Aerodynamic mathematical modeling - basic concepts

NASA Technical Reports Server (NTRS)

Tobak, M.; Schiff, L. B.

1981-01-01

The mathematical modeling of the aerodynamic response of an aircraft to arbitrary maneuvers is reviewed. Bryan's original formulation, linear aerodynamic indicial functions, and superposition are considered. These concepts are extended into the nonlinear regime. The nonlinear generalization yields a form for the aerodynamic response that can be built up from the responses to a limited number of well defined characteristic motions, reproducible in principle either in wind tunnel experiments or flow field computations. A further generalization leads to a form accommodating the discontinuous and double valued behavior characteristics of hysteresis in the steady state aerodynamic response.

Self-consistency in the phonon space of the particle-phonon coupling model

NASA Astrophysics Data System (ADS)

Tselyaev, V.; Lyutorovich, N.; Speth, J.; Reinhard, P.-G.

2018-04-01

In the paper the nonlinear generalization of the time blocking approximation (TBA) is presented. The TBA is one of the versions of the extended random-phase approximation (RPA) developed within the Green-function method and the particle-phonon coupling model. In the generalized version of the TBA the self-consistency principle is extended onto the phonon space of the model. The numerical examples show that this nonlinear version of the TBA leads to the convergence of results with respect to enlarging the phonon space of the model.

Spectral decomposition of nonlinear systems with memory

NASA Astrophysics Data System (ADS)

Svenkeson, Adam; Glaz, Bryan; Stanton, Samuel; West, Bruce J.

2016-02-01

We present an alternative approach to the analysis of nonlinear systems with long-term memory that is based on the Koopman operator and a Lévy transformation in time. Memory effects are considered to be the result of interactions between a system and its surrounding environment. The analysis leads to the decomposition of a nonlinear system with memory into modes whose temporal behavior is anomalous and lacks a characteristic scale. On average, the time evolution of a mode follows a Mittag-Leffler function, and the system can be described using the fractional calculus. The general theory is demonstrated on the fractional linear harmonic oscillator and the fractional nonlinear logistic equation. When analyzing data from an ill-defined (black-box) system, the spectral decomposition in terms of Mittag-Leffler functions that we propose may uncover inherent memory effects through identification of a small set of dynamically relevant structures that would otherwise be obscured by conventional spectral methods. Consequently, the theoretical concepts we present may be useful for developing more general methods for numerical modeling that are able to determine whether observables of a dynamical system are better represented by memoryless operators, or operators with long-term memory in time, when model details are unknown.

Generalized Courant-Snyder Theory and Kapchinskij-Vladimirskij Distribution For High-intensity Beams In A Coupled Transverse Focusing Lattice

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hong QIn, Ronald Davidson

2011-07-18

The Courant-Snyder (CS) theory and the Kapchinskij-Vladimirskij (KV) distribution for high-intensity beams in a uncoupled focusing lattice are generalized to the case of coupled transverse dynamics. The envelope function is generalized to an envelope matrix, and the envelope equation becomes a matrix envelope equation with matrix operations that are non-commutative. In an uncoupled lattice, the KV distribution function, first analyzed in 1959, is the only known exact solution of the nonlinear Vlasov-Maxwell equations for high-intensity beams including self-fields in a self-consistent manner. The KV solution is generalized to high-intensity beams in a coupled transverse lattice using the generalized CS invariant.more » This solution projects to a rotating, pulsating elliptical beam in transverse configuration space. The fully self-consistent solution reduces the nonlinear Vlasov-Maxwell equations to a nonlinear matrix ordinary differential equation for the envelope matrix, which determines the geometry of the pulsating and rotating beam ellipse. These results provide us with a new theoretical tool to investigate the dynamics of high-intensity beams in a coupled transverse lattice. A strongly coupled lattice, a so-called N-rolling lattice, is studied as an example. It is found that strong coupling does not deteriorate the beam quality. Instead, the coupling induces beam rotation, and reduces beam pulsation.« less

Generalized Courant-Snyder theory and Kapchinskij-Vladimirskij distribution for high-intensity beams in a coupled transverse focusing lattice

DOE Office of Scientific and Technical Information (OSTI.GOV)

Qin Hong; Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026; Davidson, Ronald C.

2011-05-15

The Courant-Snyder (CS) theory and the Kapchinskij-Vladimirskij (KV) distribution for high-intensity beams in an uncoupled focusing lattice are generalized to the case of coupled transverse dynamics. The envelope function is generalized to an envelope matrix, and the envelope equation becomes a matrix envelope equation with matrix operations that are noncommutative. In an uncoupled lattice, the KV distribution function, first analyzed in 1959, is the only known exact solution of the nonlinear Vlasov-Maxwell equations for high-intensity beams including self-fields in a self-consistent manner. The KV solution is generalized to high-intensity beams in a coupled transverse lattice using the generalized CS invariant.more » This solution projects to a rotating, pulsating elliptical beam in transverse configuration space. The fully self-consistent solution reduces the nonlinear Vlasov-Maxwell equations to a nonlinear matrix ordinary differential equation for the envelope matrix, which determines the geometry of the pulsating and rotating beam ellipse. These results provide us with a new theoretical tool to investigate the dynamics of high-intensity beams in a coupled transverse lattice. A strongly coupled lattice, a so-called N-rolling lattice, is studied as an example. It is found that strong coupling does not deteriorate the beam quality. Instead, the coupling induces beam rotation and reduces beam pulsation.« less

Theoretical foundations for traditional and generalized sensitivity functions for nonlinear delay differential equations.

PubMed

Banks, H Thomas; Robbins, Danielle; Sutton, Karyn L

2013-01-01

In this paper we present new results for differentiability of delay systems with respect to initial conditions and delays. After motivating our results with a wide range of delay examples arising in biology applications, we further note the need for sensitivity functions (both traditional and generalized sensitivity functions), especially in control and estimation problems. We summarize general existence and uniqueness results before turning to our main results on differentiation with respect to delays, etc. Finally we discuss use of our results in the context of estimation problems.

An efficient computational method for solving nonlinear stochastic Itô integral equations: Application for stochastic problems in physics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Heydari, M.H., E-mail: heydari@stu.yazd.ac.ir; The Laboratory of Quantum Information Processing, Yazd University, Yazd; Hooshmandasl, M.R., E-mail: hooshmandasl@yazd.ac.ir

Because of the nonlinearity, closed-form solutions of many important stochastic functional equations are virtually impossible to obtain. Thus, numerical solutions are a viable alternative. In this paper, a new computational method based on the generalized hat basis functions together with their stochastic operational matrix of Itô-integration is proposed for solving nonlinear stochastic Itô integral equations in large intervals. In the proposed method, a new technique for computing nonlinear terms in such problems is presented. The main advantage of the proposed method is that it transforms problems under consideration into nonlinear systems of algebraic equations which can be simply solved. Errormore » analysis of the proposed method is investigated and also the efficiency of this method is shown on some concrete examples. The obtained results reveal that the proposed method is very accurate and efficient. As two useful applications, the proposed method is applied to obtain approximate solutions of the stochastic population growth models and stochastic pendulum problem.« less

Homogenized description and retrieval method of nonlinear metasurfaces

NASA Astrophysics Data System (ADS)

Liu, Xiaojun; Larouche, Stéphane; Smith, David R.

2018-03-01

A patterned, plasmonic metasurface can strongly scatter incident light, functioning as an extremely low-profile lens, filter, reflector or other optical device. When the metasurface is patterned uniformly, its linear optical properties can be expressed using effective surface electric and magnetic polarizabilities obtained through a homogenization procedure. The homogenized description of a nonlinear metasurface, however, presents challenges both because of the inherent anisotropy of the medium as well as the much larger set of potential wave interactions available, making it challenging to assign effective nonlinear parameters to the otherwise inhomogeneous layer of metamaterial elements. Here we show that a homogenization procedure can be developed to describe nonlinear metasurfaces, which derive their nonlinear response from the enhanced local fields arising within the structured plasmonic elements. With the proposed homogenization procedure, we are able to assign effective nonlinear surface polarization densities to a nonlinear metasurface, and link these densities to the effective nonlinear surface susceptibilities and averaged macroscopic pumping fields across the metasurface. These effective nonlinear surface polarization densities are further linked to macroscopic nonlinear fields through the generalized sheet transition conditions (GSTCs). By inverting the GSTCs, the effective nonlinear surface susceptibilities of the metasurfaces can be solved for, leading to a generalized retrieval method for nonlinear metasurfaces. The application of the homogenization procedure and the GSTCs are demonstrated by retrieving the nonlinear susceptibilities of a SiO2 nonlinear slab. As an example, we investigate a nonlinear metasurface which presents nonlinear magnetoelectric coupling in near infrared regime. The method is expected to apply to any patterned metasurface whose thickness is much smaller than the wavelengths of operation, with inclusions of arbitrary geometry and material composition, across the electromagnetic spectrum.

Theory of plasmonic effects in nonlinear optics: the case of graphene

NASA Astrophysics Data System (ADS)

Rostami, Habib; Katsnelson, Mikhail I.; Polini, Marco; Mikhail I. Katsnelson Collaboration; Habib Rostami; Marco Polini Collaboration

The nonlinear optical properties of two-dimensional electronic systems are beginning to attract considerable interest both in the theoretical and experimental sectors. Recent experiments on the nonlinear optical properties of graphene reveal considerably strong third harmonic generation and four-wave mixing of this single-atomic-layer electronic system. We develop a large-N theory of electron-electron interaction corrections to multi-legged Feynman diagrams describing second- and third-order nonlinear response functions. Our theory is completely general and is useful to understand all second- and third-order nonlinear effects, including harmonic generation, wave mixing, and photon drag. We apply our theoretical framework to the case of graphene, by carrying out microscopic calculations of the second- and third-order nonlinear response functions of an interacting two-dimensional gas of massless Dirac fermions. We compare our results with recent measurements, where all-optical launching of graphene plasmons has been achieved. This work was supported by Fondazione Istituto Italiano di Tecnologia, the European Union's Horizon 2020 research and innovation programme under Grant agreement No. 696656 GrapheneCore, and the ERC Advanced Grant 338957 FEMTO/NANO (M.I.K.).

Structural optimization of framed structures using generalized optimality criteria

NASA Technical Reports Server (NTRS)

Kolonay, R. M.; Venkayya, Vipperla B.; Tischler, V. A.; Canfield, R. A.

1989-01-01

The application of a generalized optimality criteria to framed structures is presented. The optimality conditions, Lagrangian multipliers, resizing algorithm, and scaling procedures are all represented as a function of the objective and constraint functions along with their respective gradients. The optimization of two plane frames under multiple loading conditions subject to stress, displacement, generalized stiffness, and side constraints is presented. These results are compared to those found by optimizing the frames using a nonlinear mathematical programming technique.

Decision making generalized by a cumulative probability weighting function

NASA Astrophysics Data System (ADS)

dos Santos, Lindomar Soares; Destefano, Natália; Martinez, Alexandre Souto

2018-01-01

Typical examples of intertemporal decision making involve situations in which individuals must choose between a smaller reward, but more immediate, and a larger one, delivered later. Analogously, probabilistic decision making involves choices between options whose consequences differ in relation to their probability of receiving. In Economics, the expected utility theory (EUT) and the discounted utility theory (DUT) are traditionally accepted normative models for describing, respectively, probabilistic and intertemporal decision making. A large number of experiments confirmed that the linearity assumed by the EUT does not explain some observed behaviors, as nonlinear preference, risk-seeking and loss aversion. That observation led to the development of new theoretical models, called non-expected utility theories (NEUT), which include a nonlinear transformation of the probability scale. An essential feature of the so-called preference function of these theories is that the probabilities are transformed by decision weights by means of a (cumulative) probability weighting function, w(p) . We obtain in this article a generalized function for the probabilistic discount process. This function has as particular cases mathematical forms already consecrated in the literature, including discount models that consider effects of psychophysical perception. We also propose a new generalized function for the functional form of w. The limiting cases of this function encompass some parametric forms already proposed in the literature. Far beyond a mere generalization, our function allows the interpretation of probabilistic decision making theories based on the assumption that individuals behave similarly in the face of probabilities and delays and is supported by phenomenological models.

Identification of Linear and Nonlinear Aerodynamic Impulse Responses Using Digital Filter Techniques

NASA Technical Reports Server (NTRS)

Silva, Walter A.

1997-01-01

This paper discusses the mathematical existence and the numerically-correct identification of linear and nonlinear aerodynamic impulse response functions. Differences between continuous-time and discrete-time system theories, which permit the identification and efficient use of these functions, will be detailed. Important input/output definitions and the concept of linear and nonlinear systems with memory will also be discussed. It will be shown that indicial (step or steady) responses (such as Wagner's function), forced harmonic responses (such as Theodorsen's function or those from doublet lattice theory), and responses to random inputs (such as gusts) can all be obtained from an aerodynamic impulse response function. This paper establishes the aerodynamic impulse response function as the most fundamental, and, therefore, the most computationally efficient, aerodynamic function that can be extracted from any given discrete-time, aerodynamic system. The results presented in this paper help to unify the understanding of classical two-dimensional continuous-time theories with modern three-dimensional, discrete-time theories. First, the method is applied to the nonlinear viscous Burger's equation as an example. Next the method is applied to a three-dimensional aeroelastic model using the CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) code and then to a two-dimensional model using the CFL3D Navier-Stokes code. Comparisons of accuracy and computational cost savings are presented. Because of its mathematical generality, an important attribute of this methodology is that it is applicable to a wide range of nonlinear, discrete-time problems.

Identification of Linear and Nonlinear Aerodynamic Impulse Responses Using Digital Filter Techniques

NASA Technical Reports Server (NTRS)

Silva, Walter A.

1997-01-01

This paper discusses the mathematical existence and the numerically-correct identification of linear and nonlinear aerodynamic impulse response functions. Differences between continuous-time and discrete-time system theories, which permit the identification and efficient use of these functions, will be detailed. Important input/output definitions and the concept of linear and nonlinear systems with memory will also be discussed. It will be shown that indicial (step or steady) responses (such as Wagner's function), forced harmonic responses (such as Tbeodorsen's function or those from doublet lattice theory), and responses to random inputs (such as gusts) can all be obtained from an aerodynamic impulse response function. This paper establishes the aerodynamic impulse response function as the most fundamental, and, therefore, the most computationally efficient, aerodynamic function that can be extracted from any given discrete-time, aerodynamic system. The results presented in this paper help to unify the understanding of classical two-dimensional continuous-time theories with modem three-dimensional, discrete-time theories. First, the method is applied to the nonlinear viscous Burger's equation as an example. Next the method is applied to a three-dimensional aeroelastic model using the CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) code and then to a two-dimensional model using the CFL3D Navier-Stokes code. Comparisons of accuracy and computational cost savings are presented. Because of its mathematical generality, an important attribute of this methodology is that it is applicable to a wide range of nonlinear, discrete-time problems.

Reconstruction of Complex Directional Networks with Group Lasso Nonlinear Conditional Granger Causality.

PubMed

Yang, Guanxue; Wang, Lin; Wang, Xiaofan

2017-06-07

Reconstruction of networks underlying complex systems is one of the most crucial problems in many areas of engineering and science. In this paper, rather than identifying parameters of complex systems governed by pre-defined models or taking some polynomial and rational functions as a prior information for subsequent model selection, we put forward a general framework for nonlinear causal network reconstruction from time-series with limited observations. With obtaining multi-source datasets based on the data-fusion strategy, we propose a novel method to handle nonlinearity and directionality of complex networked systems, namely group lasso nonlinear conditional granger causality. Specially, our method can exploit different sets of radial basis functions to approximate the nonlinear interactions between each pair of nodes and integrate sparsity into grouped variables selection. The performance characteristic of our approach is firstly assessed with two types of simulated datasets from nonlinear vector autoregressive model and nonlinear dynamic models, and then verified based on the benchmark datasets from DREAM3 Challenge4. Effects of data size and noise intensity are also discussed. All of the results demonstrate that the proposed method performs better in terms of higher area under precision-recall curve.

Solving nonlinear evolution equation system using two different methods

NASA Astrophysics Data System (ADS)

Kaplan, Melike; Bekir, Ahmet; Ozer, Mehmet N.

2015-12-01

This paper deals with constructing more general exact solutions of the coupled Higgs equation by using the (G0/G, 1/G)-expansion and (1/G0)-expansion methods. The obtained solutions are expressed by three types of functions: hyperbolic, trigonometric and rational functions with free parameters. It has been shown that the suggested methods are productive and will be used to solve nonlinear partial differential equations in applied mathematics and engineering. Throughout the paper, all the calculations are made with the aid of the Maple software.

Prolongation structures of nonlinear evolution equations

NASA Technical Reports Server (NTRS)

Wahlquist, H. D.; Estabrook, F. B.

1975-01-01

A technique is developed for systematically deriving a 'prolongation structure' - a set of interrelated potentials and pseudopotentials - for nonlinear partial differential equations in two independent variables. When this is applied to the Korteweg-de Vries equation, a new infinite set of conserved quantities is obtained. Known solution techniques are shown to result from the discovery of such a structure: related partial differential equations for the potential functions, linear 'inverse scattering' equations for auxiliary functions, Backlund transformations. Generalizations of these techniques will result from the use of irreducible matrix representations of the prolongation structure.

On new classes of solutions of nonlinear partial differential equations in the form of convergent special series

NASA Astrophysics Data System (ADS)

Filimonov, M. Yu.

2017-12-01

The method of special series with recursively calculated coefficients is used to solve nonlinear partial differential equations. The recurrence of finding the coefficients of the series is achieved due to a special choice of functions, in powers of which the solution is expanded in a series. We obtain a sequence of linear partial differential equations to find the coefficients of the series constructed. In many cases, one can deal with a sequence of linear ordinary differential equations. We construct classes of solutions in the form of convergent series for a certain class of nonlinear evolution equations. A new class of solutions of generalized Boussinesque equation with an arbitrary function in the form of a convergent series is constructed.

Extending nonlinear analysis to short ecological time series.

PubMed

Hsieh, Chih-hao; Anderson, Christian; Sugihara, George

2008-01-01

Nonlinearity is important and ubiquitous in ecology. Though detectable in principle, nonlinear behavior is often difficult to characterize, analyze, and incorporate mechanistically into models of ecosystem function. One obvious reason is that quantitative nonlinear analysis tools are data intensive (require long time series), and time series in ecology are generally short. Here we demonstrate a useful method that circumvents data limitation and reduces sampling error by combining ecologically similar multispecies time series into one long time series. With this technique, individual ecological time series containing as few as 20 data points can be mined for such important information as (1) significantly improved forecast ability, (2) the presence and location of nonlinearity, and (3) the effective dimensionality (the number of relevant variables) of an ecological system.

Global stability of plane Couette flow beyond the energy stability limit

NASA Astrophysics Data System (ADS)

Fuentes, Federico; Goluskin, David

2017-11-01

This talk will present computations verifying that the laminar state of plane Couette flow is nonlinearly stable to all perturbations. The Reynolds numbers up to which this globally stability is verified are larger than those at which stability can be proven by the energy method, which is the typical method for demonstrating nonlinear stability of a fluid flow. This improvement is achieved by constructing Lyapunov functions that are more general than the energy. These functions are not restricted to being quadratic, and they are allowed to depend explicitly on the spectrum of the velocity field in the eigenbasis of the energy stability operator. The optimal choice of such a Lyapunov function is a convex optimization problem, and it can be constructed with computer assistance by solving a semidefinite program. This general method will be described in a companion talk by David Goluskin; the present talk focuses on its application to plane Couette flow.

Energy Criterion for the Spectral Stability of Discrete Breathers.

PubMed

Kevrekidis, Panayotis G; Cuevas-Maraver, Jesús; Pelinovsky, Dmitry E

2016-08-26

Discrete breathers are ubiquitous structures in nonlinear anharmonic models ranging from the prototypical example of the Fermi-Pasta-Ulam model to Klein-Gordon nonlinear lattices, among many others. We propose a general criterion for the emergence of instabilities of discrete breathers analogous to the well-established Vakhitov-Kolokolov criterion for solitary waves. The criterion involves the change of monotonicity of the discrete breather's energy as a function of the breather frequency. Our analysis suggests and numerical results corroborate that breathers with increasing (decreasing) energy-frequency dependence are generically unstable in soft (hard) nonlinear potentials.

Falling head ponded infiltration in the nonlinear limit

NASA Astrophysics Data System (ADS)

Triadis, D.

2014-12-01

The Green and Ampt infiltration solution represents only an extreme example of behavior within a larger class of very nonlinear, delta function diffusivity soils. The mathematical analysis of these soils is greatly simplified by the existence of a sharp wetting front below the soil surface. Solutions for more realistic delta function soil models have recently been presented for infiltration under surface saturation without ponding. After general formulation of the problem, solutions for a full suite of delta function soils are derived for ponded surface water depleted by infiltration. Exact expressions for the cumulative infiltration as a function of time, or the drainage time as a function of the initial ponded depth may take implicit or parametric forms, and are supplemented by simple asymptotic expressions valid for small times, and small and large initial ponded depths. As with surface saturation without ponding, the Green-Ampt model overestimates the effect of the soil hydraulic conductivity. At the opposing extreme, a low-conductivity model is identified that also takes a very simple mathematical form and appears to be more accurate than the Green-Ampt model for larger ponded depths. Between these two, the nonlinear limit of Gardner's soil is recommended as a physically valid first approximation. Relative discrepancies between different soil models are observed to reach a maximum for intermediate values of the dimensionless initial ponded depth, and in general are smaller than for surface saturation without ponding.

Neural networks: further insights into error function, generalized weights and others

PubMed Central

2016-01-01

The article is a continuum of a previous one providing further insights into the structure of neural network (NN). Key concepts of NN including activation function, error function, learning rate and generalized weights are introduced. NN topology can be visualized with generic plot() function by passing a “nn” class object. Generalized weights assist interpretation of NN model with respect to the independent effect of individual input variables. A large variance of generalized weights for a covariate indicates non-linearity of its independent effect. If generalized weights of a covariate are approximately zero, the covariate is considered to have no effect on outcome. Finally, prediction of new observations can be performed using compute() function. Make sure that the feature variables passed to the compute() function are in the same order to that in the training NN. PMID:27668220

Robust Nonlinear Neural Codes

NASA Astrophysics Data System (ADS)

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.

Infinite hierarchy of nonlinear Schrödinger equations and their solutions.

PubMed

Ankiewicz, A; Kedziora, D J; Chowdury, A; Bandelow, U; Akhmediev, N

2016-01-01

We study the infinite integrable nonlinear Schrödinger equation hierarchy beyond the Lakshmanan-Porsezian-Daniel equation which is a particular (fourth-order) case of the hierarchy. In particular, we present the generalized Lax pair and generalized soliton solutions, plane wave solutions, Akhmediev breathers, Kuznetsov-Ma breathers, periodic solutions, and rogue wave solutions for this infinite-order hierarchy. We find that "even- order" equations in the set affect phase and "stretching factors" in the solutions, while "odd-order" equations affect the velocities. Hence odd-order equation solutions can be real functions, while even-order equation solutions are always complex.

Ascent guidance algorithm using lidar wind measurements

NASA Technical Reports Server (NTRS)

Cramer, Evin J.; Bradt, Jerre E.; Hardtla, John W.

1990-01-01

The formulation of a general nonlinear programming guidance algorithm that incorporates wind measurements in the computation of ascent guidance steering commands is discussed. A nonlinear programming (NLP) algorithm that is designed to solve a very general problem has the potential to address the diversity demanded by future launch systems. Using B-splines for the command functional form allows the NLP algorithm to adjust the shape of the command profile to achieve optimal performance. The algorithm flexibility is demonstrated by simulation of ascent with dynamic loading constraints through a set of random wind profiles with and without wind sensing capability.

Traveling waves and conservation laws for highly nonlinear wave equations modeling Hertz chains

NASA Astrophysics Data System (ADS)

Przedborski, Michelle; Anco, Stephen C.

2017-09-01

A highly nonlinear, fourth-order wave equation that models the continuum theory of long wavelength pulses in weakly compressed, homogeneous, discrete chains with a general power-law contact interaction is studied. For this wave equation, all solitary wave solutions and all nonlinear periodic wave solutions, along with all conservation laws, are derived. The solutions are explicitly parameterized in terms of the asymptotic value of the wave amplitude in the case of solitary waves and the peak of the wave amplitude in the case of nonlinear periodic waves. All cases in which the solution expressions can be stated in an explicit analytic form using elementary functions are worked out. In these cases, explicit expressions for the total energy and total momentum for all solutions are obtained as well. The derivation of the solutions uses the conservation laws combined with an energy analysis argument to reduce the wave equation directly to a separable first-order differential equation that determines the wave amplitude in terms of the traveling wave variable. This method can be applied more generally to other highly nonlinear wave equations.

Inverting Monotonic Nonlinearities by Entropy Maximization

PubMed Central

López-de-Ipiña Pena, Karmele; Caiafa, Cesar F.

2016-01-01

This paper proposes a new method for blind inversion of a monotonic nonlinear map applied to a sum of random variables. Such kinds of mixtures of random variables are found in source separation and Wiener system inversion problems, for example. The importance of our proposed method is based on the fact that it permits to decouple the estimation of the nonlinear part (nonlinear compensation) from the estimation of the linear one (source separation matrix or deconvolution filter), which can be solved by applying any convenient linear algorithm. Our new nonlinear compensation algorithm, the MaxEnt algorithm, generalizes the idea of Gaussianization of the observation by maximizing its entropy instead. We developed two versions of our algorithm based either in a polynomial or a neural network parameterization of the nonlinear function. We provide a sufficient condition on the nonlinear function and the probability distribution that gives a guarantee for the MaxEnt method to succeed compensating the distortion. Through an extensive set of simulations, MaxEnt is compared with existing algorithms for blind approximation of nonlinear maps. Experiments show that MaxEnt is able to successfully compensate monotonic distortions outperforming other methods in terms of the obtained Signal to Noise Ratio in many important cases, for example when the number of variables in a mixture is small. Besides its ability for compensating nonlinearities, MaxEnt is very robust, i.e. showing small variability in the results. PMID:27780261

Inverting Monotonic Nonlinearities by Entropy Maximization.

PubMed

Solé-Casals, Jordi; López-de-Ipiña Pena, Karmele; Caiafa, Cesar F

2016-01-01

This paper proposes a new method for blind inversion of a monotonic nonlinear map applied to a sum of random variables. Such kinds of mixtures of random variables are found in source separation and Wiener system inversion problems, for example. The importance of our proposed method is based on the fact that it permits to decouple the estimation of the nonlinear part (nonlinear compensation) from the estimation of the linear one (source separation matrix or deconvolution filter), which can be solved by applying any convenient linear algorithm. Our new nonlinear compensation algorithm, the MaxEnt algorithm, generalizes the idea of Gaussianization of the observation by maximizing its entropy instead. We developed two versions of our algorithm based either in a polynomial or a neural network parameterization of the nonlinear function. We provide a sufficient condition on the nonlinear function and the probability distribution that gives a guarantee for the MaxEnt method to succeed compensating the distortion. Through an extensive set of simulations, MaxEnt is compared with existing algorithms for blind approximation of nonlinear maps. Experiments show that MaxEnt is able to successfully compensate monotonic distortions outperforming other methods in terms of the obtained Signal to Noise Ratio in many important cases, for example when the number of variables in a mixture is small. Besides its ability for compensating nonlinearities, MaxEnt is very robust, i.e. showing small variability in the results.

A measurement fusion method for nonlinear system identification using a cooperative learning algorithm.

PubMed

Xia, Youshen; Kamel, Mohamed S

2007-06-01

Identification of a general nonlinear noisy system viewed as an estimation of a predictor function is studied in this article. A measurement fusion method for the predictor function estimate is proposed. In the proposed scheme, observed data are first fused by using an optimal fusion technique, and then the optimal fused data are incorporated in a nonlinear function estimator based on a robust least squares support vector machine (LS-SVM). A cooperative learning algorithm is proposed to implement the proposed measurement fusion method. Compared with related identification methods, the proposed method can minimize both the approximation error and the noise error. The performance analysis shows that the proposed optimal measurement fusion function estimate has a smaller mean square error than the LS-SVM function estimate. Moreover, the proposed cooperative learning algorithm can converge globally to the optimal measurement fusion function estimate. Finally, the proposed measurement fusion method is applied to ARMA signal and spatial temporal signal modeling. Experimental results show that the proposed measurement fusion method can provide a more accurate model.

Information processing in dendrites I. Input pattern generalisation.

PubMed

Gurney, K N

2001-10-01

In this paper and its companion, we address the question as to whether there are any general principles underlying information processing in the dendritic trees of biological neurons. In order to address this question, we make two assumptions. First, the key architectural feature of dendrites responsible for many of their information processing abilities is the existence of independent sub-units performing local non-linear processing. Second, any general functional principles operate at a level of abstraction in which neurons are modelled by Boolean functions. To accommodate these assumptions, we therefore define a Boolean model neuron-the multi-cube unit (MCU)-which instantiates the notion of the discrete functional sub-unit. We then use this model unit to explore two aspects of neural functionality: generalisation (in this paper) and processing complexity (in its companion). Generalisation is dealt with from a geometric viewpoint and is quantified using a new metric-the set of order parameters. These parameters are computed for threshold logic units (TLUs), a class of random Boolean functions, and MCUs. Our interpretation of the order parameters is consistent with our knowledge of generalisation in TLUs and with the lack of generalisation in randomly chosen functions. Crucially, the order parameters for MCUs imply that these functions possess a range of generalisation behaviour. We argue that this supports the general thesis that dendrites facilitate input pattern generalisation despite any local non-linear processing within functionally isolated sub-units.

Modeling non-linear growth responses to temperature and hydrology in wetland trees

NASA Astrophysics Data System (ADS)

Keim, R.; Allen, S. T.

2016-12-01

Growth responses of wetland trees to flooding and climate variations are difficult to model because they depend on multiple, apparently interacting factors, but are a critical link in hydrological control of wetland carbon budgets. To more generally understand tree growth to hydrological forcing, we modeled non-linear responses of tree ring growth to flooding and climate at sub-annual time steps, using Vaganov-Shashkin response functions. We calibrated the model to six baldcypress tree-ring chronologies from two hydrologically distinct sites in southern Louisiana, and tested several hypotheses of plasticity in wetlands tree responses to interacting environmental variables. The model outperformed traditional multiple linear regression. More importantly, optimized response parameters were generally similar among sites with varying hydrological conditions, suggesting generality to the functions. Model forms that included interacting responses to multiple forcing factors were more effective than were single response functions, indicating the principle of a single limiting factor is not correct in wetlands and both climatic and hydrological variables must be considered in predicting responses to hydrological or climate change.

Global gradient estimates for divergence-type elliptic problems involving general nonlinear operators

NASA Astrophysics Data System (ADS)

Cho, Yumi

2018-05-01

We study nonlinear elliptic problems with nonstandard growth and ellipticity related to an N-function. We establish global Calderón-Zygmund estimates of the weak solutions in the framework of Orlicz spaces over bounded non-smooth domains. Moreover, we prove a global regularity result for asymptotically regular problems which are getting close to the regular problems considered, when the gradient variable goes to infinity.

Nonlinear viscoelasticity and generalized failure criterion for biopolymer gels

NASA Astrophysics Data System (ADS)

Divoux, Thibaut; Keshavarz, Bavand; Manneville, Sébastien; McKinley, Gareth

2016-11-01

Biopolymer gels display a multiscale microstructure that is responsible for their solid-like properties. Upon external deformation, these soft viscoelastic solids exhibit a generic nonlinear mechanical response characterized by pronounced stress- or strain-stiffening prior to irreversible damage and failure, most often through macroscopic fractures. Here we show on a model acid-induced protein gel that the nonlinear viscoelastic properties of the gel can be described in terms of a 'damping function' which predicts the gel mechanical response quantitatively up to the onset of macroscopic failure. Using a nonlinear integral constitutive equation built upon the experimentally-measured damping function in conjunction with power-law linear viscoelastic response, we derive the form of the stress growth in the gel following the start up of steady shear. We also couple the shear stress response with Bailey's durability criteria for brittle solids in order to predict the critical values of the stress σc and strain γc for failure of the gel, and how they scale with the applied shear rate. This provides a generalized failure criterion for biopolymer gels in a range of different deformation histories. This work was funded by the MIT-France seed fund and by the CNRS PICS-USA scheme (#36939). BK acknowledges financial support from Axalta Coating Systems.

Excitation power quantities in phase resonance testing of nonlinear systems with phase-locked-loop excitation

NASA Astrophysics Data System (ADS)

Peter, Simon; Leine, Remco I.

2017-11-01

Phase resonance testing is one method for the experimental extraction of nonlinear normal modes. This paper proposes a novel method for nonlinear phase resonance testing. Firstly, the issue of appropriate excitation is approached on the basis of excitation power considerations. Therefore, power quantities known from nonlinear systems theory in electrical engineering are transferred to nonlinear structural dynamics applications. A new power-based nonlinear mode indicator function is derived, which is generally applicable, reliable and easy to implement in experiments. Secondly, the tuning of the excitation phase is automated by the use of a Phase-Locked-Loop controller. This method provides a very user-friendly and fast way for obtaining the backbone curve. Furthermore, the method allows to exploit specific advantages of phase control such as the robustness for lightly damped systems and the stabilization of unstable branches of the frequency response. The reduced tuning time for the excitation makes the commonly used free-decay measurements for the extraction of backbone curves unnecessary. Instead, steady-state measurements for every point of the curve are obtained. In conjunction with the new mode indicator function, the correlation of every measured point with the associated nonlinear normal mode of the underlying conservative system can be evaluated. Moreover, it is shown that the analysis of the excitation power helps to locate sources of inaccuracies in the force appropriation process. The method is illustrated by a numerical example and its functionality in experiments is demonstrated on a benchmark beam structure.

Nonlinear storage models of unconfined flow through a shallow aquifer on an inclined base and their quasi-steady flow application

NASA Astrophysics Data System (ADS)

Varvaris, Ioannis; Gravanis, Elias; Koussis, Antonis; Akylas, Evangelos

2013-04-01

Hillslope processes involving flow through an inclined shallow aquifer range from subsurface stormflow to stream base flow (drought flow, or groundwater recession flow). In the case of recharge, the infiltrating water moves vertically as unsaturated flow until it reaches the saturated groundwater, where the flow is approximately parallel to the base of the aquifer. Boussinesq used the Dupuit-Forchheimer (D-F) hydraulic theory to formulate unconfined groundwater flow through a soil layer resting on an impervious inclined bed, deriving a nonlinear equation for the flow rate that consists of a linear gravity-driven component and a quadratic pressure-gradient component. Inserting that flow rate equation into the differential storage balance equation (volume conservation) Boussinesq obtained a nonlinear second-order partial differential equation for the depth. So far however, only few special solutions have been advanced for that governing equation. The nonlinearity of the equation of Boussinesq is the major obstacle to deriving a general analytical solution for the depth profile of unconfined flow on a sloping base with recharge (from which the discharges could be then determined). Henderson and Wooding (1964) were able to obtain an exact analytical solution for steady unconfined flow on a sloping base, with recharge, and their work deserves special note in the realm of solutions of the nonlinear equation of Boussinesq. However, the absence of a general solution for the transient case, which is of practical interest to hydrologists, has been the motivation for developing approximate solutions of the non-linear equation of Boussinesq. In this work, we derive the aquifer storage function by integrating analytically over the aquifer base the depth profiles resulting from the complete nonlinear Boussinesq equation for steady flow. This storage function consists of a linear and a nonlinear outflow-dependent term. Then, we use this physics-based storage function in the transient storage balance over the hillslope, obtaining analytical solutions of the outflow and the storage, for recharge and drainage, via a quasi-steady flow calculation. The hydraulically derived storage model is thus embedded in a quasi-steady approximation of transient unconfined flow in sloping aquifers. We generalise this hydrologic model of groundwater flow by modifying the storage function to be the weighted sum of the linear and the nonlinear storage terms, determining the weighting factor objectively from a known integral quantity of the flow (either an initial volume of water stored in the aquifer or a drained water volume). We demonstrate the validity of this model through comparisons with experimental data and simulation results.

Generalized image contrast enhancement technique based on the Heinemann contrast discrimination model

NASA Astrophysics Data System (ADS)

Liu, Hong; Nodine, Calvin F.

1996-07-01

This paper presents a generalized image contrast enhancement technique, which equalizes the perceived brightness distribution based on the Heinemann contrast discrimination model. It is based on the mathematically proven existence of a unique solution to a nonlinear equation, and is formulated with easily tunable parameters. The model uses a two-step log-log representation of luminance contrast between targets and surround in a luminous background setting. The algorithm consists of two nonlinear gray scale mapping functions that have seven parameters, two of which are adjustable Heinemann constants. Another parameter is the background gray level. The remaining four parameters are nonlinear functions of the gray-level distribution of the given image, and can be uniquely determined once the previous three are set. Tests have been carried out to demonstrate the effectiveness of the algorithm for increasing the overall contrast of radiology images. The traditional histogram equalization can be reinterpreted as an image enhancement technique based on the knowledge of human contrast perception. In fact, it is a special case of the proposed algorithm.

The non-Gaussian joint probability density function of slope and elevation for a nonlinear gravity wave field. [in ocean surface

NASA Technical Reports Server (NTRS)

Huang, N. E.; Long, S. R.; Bliven, L. F.; Tung, C.-C.

1984-01-01

On the basis of the mapping method developed by Huang et al. (1983), an analytic expression for the non-Gaussian joint probability density function of slope and elevation for nonlinear gravity waves is derived. Various conditional and marginal density functions are also obtained through the joint density function. The analytic results are compared with a series of carefully controlled laboratory observations, and good agreement is noted. Furthermore, the laboratory wind wave field observations indicate that the capillary or capillary-gravity waves may not be the dominant components in determining the total roughness of the wave field. Thus, the analytic results, though derived specifically for the gravity waves, may have more general applications.

Nonlinear programming extensions to rational function approximations of unsteady aerodynamics

NASA Technical Reports Server (NTRS)

Tiffany, Sherwood H.; Adams, William M., Jr.

1987-01-01

This paper deals with approximating unsteady generalized aerodynamic forces in the equations of motion of a flexible aircraft. Two methods of formulating these approximations are extended to include both the same flexibility in constraining them and the same methodology in optimizing nonlinear parameters as another currently used 'extended least-squares' method. Optimal selection of 'nonlinear' parameters is made in each of the three methods by use of the same nonlinear (nongradient) optimizer. The objective of the nonlinear optimization is to obtain rational approximations to the unsteady aerodynamics whose state-space realization is of lower order than that required when no optimization of the nonlinear terms is performed. The free 'linear' parameters are determined using least-squares matrix techniques on a Lagrange multiplier formulation of an objective function which incorporates selected linear equality constraints. State-space mathematical models resulting from the different approaches are described, and results are presented which show comparative evaluations from application of each of the extended methods to a numerical example. The results obtained for the example problem show a significant (up to 63 percent) reduction in the number of differential equations used to represent the unsteady aerodynamic forces in linear time-invariant equations of motion as compared to a conventional method in which nonlinear terms are not optimized.

Ward Identity and Scattering Amplitudes for Nonlinear Sigma Models

NASA Astrophysics Data System (ADS)

Low, Ian; Yin, Zhewei

2018-02-01

We present a Ward identity for nonlinear sigma models using generalized nonlinear shift symmetries, without introducing current algebra or coset space. The Ward identity constrains correlation functions of the sigma model such that the Adler's zero is guaranteed for S -matrix elements, and gives rise to a subleading single soft theorem that is valid at the quantum level and to all orders in the Goldstone decay constant. For tree amplitudes, the Ward identity leads to a novel Berends-Giele recursion relation as well as an explicit form of the subleading single soft factor. Furthermore, interactions of the cubic biadjoint scalar theory associated with the single soft limit, which was previously discovered using the Cachazo-He-Yuan representation of tree amplitudes, can be seen to emerge from matrix elements of conserved currents corresponding to the generalized shift symmetry.

Order Selection for General Expression of Nonlinear Autoregressive Model Based on Multivariate Stepwise Regression

NASA Astrophysics Data System (ADS)

Shi, Jinfei; Zhu, Songqing; Chen, Ruwen

2017-12-01

An order selection method based on multiple stepwise regressions is proposed for General Expression of Nonlinear Autoregressive model which converts the model order problem into the variable selection of multiple linear regression equation. The partial autocorrelation function is adopted to define the linear term in GNAR model. The result is set as the initial model, and then the nonlinear terms are introduced gradually. Statistics are chosen to study the improvements of both the new introduced and originally existed variables for the model characteristics, which are adopted to determine the model variables to retain or eliminate. So the optimal model is obtained through data fitting effect measurement or significance test. The simulation and classic time-series data experiment results show that the method proposed is simple, reliable and can be applied to practical engineering.

Large amplitude flexural vibration of thin elastic flat plates and shells

NASA Technical Reports Server (NTRS)

Pandalia, K. A. V.

1972-01-01

The general equations governing the large amplitude flexural vibration of any thin elastic shell using curvilinear orthogonal coordinates are derived and consist of two coupled, nonlinear, partial differential equations in the normal displacement w and the stress function F. From these equations, the governing equations for the case of shells of revolution or flat plates can be readily obtained as special cases. The material of the shell or plate is isotropic and homogeneous and Hooke's law for the two-dimensional case is valid. It is suggested that the difference between the hardening type of nonlinearity in the case of flat plates and straight beams and the softening type of nonlinearity in the case of shells and rings can, in general, be traced to the amount of curvature present in the underformed median surface of the structure concerned.

Traveling wave solutions of the Boussinesq equation via the new approach of generalized (G'/G)-expansion method.

PubMed

Alam, Md Nur; Akbar, M Ali; Roshid, Harun-Or-

2014-01-01

Exact solutions of nonlinear evolution equations (NLEEs) play a vital role to reveal the internal mechanism of complex physical phenomena. In this work, the exact traveling wave solutions of the Boussinesq equation is studied by using the new generalized (G'/G)-expansion method. Abundant traveling wave solutions with arbitrary parameters are successfully obtained by this method and the wave solutions are expressed in terms of the hyperbolic, trigonometric, and rational functions. It is shown that the new approach of generalized (G'/G)-expansion method is a powerful and concise mathematical tool for solving nonlinear partial differential equations in mathematical physics and engineering. 05.45.Yv, 02.30.Jr, 02.30.Ik.

Characteristics of solitary waves, quasiperiodic solutions, homoclinic breather solutions and rogue waves in the generalized variable-coefficient forced Kadomtsev-Petviashvili equation

NASA Astrophysics Data System (ADS)

Yan, Xue-Wei; Tian, Shou-Fu; Dong, Min-Jie; Zou, Li

2017-12-01

In this paper, the generalized variable-coefficient forced Kadomtsev-Petviashvili (gvcfKP) equation is investigated, which can be used to characterize the water waves of long wavelength relating to nonlinear restoring forces. Using a dependent variable transformation and combining the Bell’s polynomials, we accurately derive the bilinear expression for the gvcfKP equation. By virtue of bilinear expression, its solitary waves are computed in a very direct method. By using the Riemann theta function, we derive the quasiperiodic solutions for the equation under some limitation factors. Besides, an effective way can be used to calculate its homoclinic breather waves and rogue waves, respectively, by using an extended homoclinic test function. We hope that our results can help enrich the dynamical behavior of the nonlinear wave equations with variable-coefficient.

A quadrature based method of moments for nonlinear Fokker-Planck equations

NASA Astrophysics Data System (ADS)

Otten, Dustin L.; Vedula, Prakash

2011-09-01

Fokker-Planck equations which are nonlinear with respect to their probability densities and occur in many nonequilibrium systems relevant to mean field interaction models, plasmas, fermions and bosons can be challenging to solve numerically. To address some underlying challenges, we propose the application of the direct quadrature based method of moments (DQMOM) for efficient and accurate determination of transient (and stationary) solutions of nonlinear Fokker-Planck equations (NLFPEs). In DQMOM, probability density (or other distribution) functions are represented using a finite collection of Dirac delta functions, characterized by quadrature weights and locations (or abscissas) that are determined based on constraints due to evolution of generalized moments. Three particular examples of nonlinear Fokker-Planck equations considered in this paper include descriptions of: (i) the Shimizu-Yamada model, (ii) the Desai-Zwanzig model (both of which have been developed as models of muscular contraction) and (iii) fermions and bosons. Results based on DQMOM, for the transient and stationary solutions of the nonlinear Fokker-Planck equations, have been found to be in good agreement with other available analytical and numerical approaches. It is also shown that approximate reconstruction of the underlying probability density function from moments obtained from DQMOM can be satisfactorily achieved using a maximum entropy method.

Generalized image contrast enhancement technique based on Heinemann contrast discrimination model

NASA Astrophysics Data System (ADS)

Liu, Hong; Nodine, Calvin F.

1994-03-01

This paper presents a generalized image contrast enhancement technique which equalizes perceived brightness based on the Heinemann contrast discrimination model. This is a modified algorithm which presents an improvement over the previous study by Mokrane in its mathematically proven existence of a unique solution and in its easily tunable parameterization. The model uses a log-log representation of contrast luminosity between targets and the surround in a fixed luminosity background setting. The algorithm consists of two nonlinear gray-scale mapping functions which have seven parameters, two of which are adjustable Heinemann constants. Another parameter is the background gray level. The remaining four parameters are nonlinear functions of gray scale distribution of the image, and can be uniquely determined once the previous three are given. Tests have been carried out to examine the effectiveness of the algorithm for increasing the overall contrast of images. It can be demonstrated that the generalized algorithm provides better contrast enhancement than histogram equalization. In fact, the histogram equalization technique is a special case of the proposed mapping.

Modulation stability analysis of exact multidimensional solutions to the generalized nonlinear Schrödinger equation and the Gross-Pitaevskii equation using a variational approach.

PubMed

Petrović, Nikola Z; Aleksić, Najdan B; Belić, Milivoj

2015-04-20

We analyze the modulation stability of spatiotemporal solitary and traveling wave solutions to the multidimensional nonlinear Schrödinger equation and the Gross-Pitaevskii equation with variable coefficients that were obtained using Jacobi elliptic functions. For all the solutions we obtain either unconditional stability, or a conditional stability that can be furnished through the use of dispersion management.

High-accuracy power series solutions with arbitrarily large radius of convergence for the fractional nonlinear Schrödinger-type equations

NASA Astrophysics Data System (ADS)

Khawaja, U. Al; Al-Refai, M.; Shchedrin, Gavriil; Carr, Lincoln D.

2018-06-01

Fractional nonlinear differential equations present an interplay between two common and important effective descriptions used to simplify high dimensional or more complicated theories: nonlinearity and fractional derivatives. These effective descriptions thus appear commonly in physical and mathematical modeling. We present a new series method providing systematic controlled accuracy for solutions of fractional nonlinear differential equations, including the fractional nonlinear Schrödinger equation and the fractional nonlinear diffusion equation. The method relies on spatially iterative use of power series expansions. Our approach permits an arbitrarily large radius of convergence and thus solves the typical divergence problem endemic to power series approaches. In the specific case of the fractional nonlinear Schrödinger equation we find fractional generalizations of cnoidal waves of Jacobi elliptic functions as well as a fractional bright soliton. For the fractional nonlinear diffusion equation we find the combination of fractional and nonlinear effects results in a more strongly localized solution which nevertheless still exhibits power law tails, albeit at a much lower density.

Exact solutions to the time-fractional differential equations via local fractional derivatives

NASA Astrophysics Data System (ADS)

Guner, Ozkan; Bekir, Ahmet

2018-01-01

This article utilizes the local fractional derivative and the exp-function method to construct the exact solutions of nonlinear time-fractional differential equations (FDEs). For illustrating the validity of the method, it is applied to the time-fractional Camassa-Holm equation and the time-fractional-generalized fifth-order KdV equation. Moreover, the exact solutions are obtained for the equations which are formed by different parameter values related to the time-fractional-generalized fifth-order KdV equation. This method is an reliable and efficient mathematical tool for solving FDEs and it can be applied to other non-linear FDEs.

PRESS-based EFOR algorithm for the dynamic parametrical modeling of nonlinear MDOF systems

NASA Astrophysics Data System (ADS)

Liu, Haopeng; Zhu, Yunpeng; Luo, Zhong; Han, Qingkai

2017-09-01

In response to the identification problem concerning multi-degree of freedom (MDOF) nonlinear systems, this study presents the extended forward orthogonal regression (EFOR) based on predicted residual sums of squares (PRESS) to construct a nonlinear dynamic parametrical model. The proposed parametrical model is based on the non-linear autoregressive with exogenous inputs (NARX) model and aims to explicitly reveal the physical design parameters of the system. The PRESS-based EFOR algorithm is proposed to identify such a model for MDOF systems. By using the algorithm, we built a common-structured model based on the fundamental concept of evaluating its generalization capability through cross-validation. The resulting model aims to prevent over-fitting with poor generalization performance caused by the average error reduction ratio (AERR)-based EFOR algorithm. Then, a functional relationship is established between the coefficients of the terms and the design parameters of the unified model. Moreover, a 5-DOF nonlinear system is taken as a case to illustrate the modeling of the proposed algorithm. Finally, a dynamic parametrical model of a cantilever beam is constructed from experimental data. Results indicate that the dynamic parametrical model of nonlinear systems, which depends on the PRESS-based EFOR, can accurately predict the output response, thus providing a theoretical basis for the optimal design of modeling methods for MDOF nonlinear systems.

Residual mode correction in calibrating nonlinear damper for vibration control of flexible structures

NASA Astrophysics Data System (ADS)

Sun, Limin; Chen, Lin

2017-10-01

Residual mode correction is found crucial in calibrating linear resonant absorbers for flexible structures. The classic modal representation augmented with stiffness and inertia correction terms accounting for non-resonant modes improves the calibration accuracy and meanwhile avoids complex modal analysis of the full system. This paper explores the augmented modal representation in calibrating control devices with nonlinearity, by studying a taut cable attached with a general viscous damper and its Equivalent Dynamic Systems (EDSs), i.e. the augmented modal representations connected to the same damper. As nonlinearity is concerned, Frequency Response Functions (FRFs) of the EDSs are investigated in detail for parameter calibration, using the harmonic balance method in combination with numerical continuation. The FRFs of the EDSs and corresponding calibration results are then compared with those of the full system documented in the literature for varied structural modes, damper locations and nonlinearity. General agreement is found and in particular the EDS with both stiffness and inertia corrections (quasi-dynamic correction) performs best among available approximate methods. This indicates that the augmented modal representation although derived from linear cases is applicable to a relatively wide range of damper nonlinearity. Calibration of nonlinear devices by this means still requires numerical analysis while the efficiency is largely improved owing to the system order reduction.

Exact and Approximate Statistical Inference for Nonlinear Regression and the Estimating Equation Approach.

PubMed

Demidenko, Eugene

2017-09-01

The exact density distribution of the nonlinear least squares estimator in the one-parameter regression model is derived in closed form and expressed through the cumulative distribution function of the standard normal variable. Several proposals to generalize this result are discussed. The exact density is extended to the estimating equation (EE) approach and the nonlinear regression with an arbitrary number of linear parameters and one intrinsically nonlinear parameter. For a very special nonlinear regression model, the derived density coincides with the distribution of the ratio of two normally distributed random variables previously obtained by Fieller (1932), unlike other approximations previously suggested by other authors. Approximations to the density of the EE estimators are discussed in the multivariate case. Numerical complications associated with the nonlinear least squares are illustrated, such as nonexistence and/or multiple solutions, as major factors contributing to poor density approximation. The nonlinear Markov-Gauss theorem is formulated based on the near exact EE density approximation.

New class of generalized photon-added coherent states and some of their non-classical properties

NASA Astrophysics Data System (ADS)

Mojaveri, B.; Dehghani, A.; Mahmoodi, S.

2014-08-01

In this paper, we construct a new class of generalized photon added coherent states (GPACSs), |z,m{{\\rangle }_{r}} by excitations on a newly introduced family of generalized coherent states (GCSs) |z{{\\rangle }_{r}} (A Dehghani and B Mojaveri 2012 J. Phys. A: Math. Theor. 45 095304), obtained via generalized hypergeometric type displacement operators acting on the vacuum state of the simple harmonic oscillator. We show that these states realize resolution of the identity property through positive definite measures on the complex plane. Meanwhile, we demonstrate that the introduced states can also be interpreted as nonlinear coherent states (NLCSs), with a spacial nonlinearity function. Finally, some of their non-classical features as well as their quantum statistical properties are compared with Agarwal's photon-added coherent states (PACSs), \\left| z,m \\right\\rangle .

Boltzmann sampling from the Ising model using quantum heating of coupled nonlinear oscillators.

PubMed

Goto, Hayato; Lin, Zhirong; Nakamura, Yasunobu

2018-05-08

A network of Kerr-nonlinear parametric oscillators without dissipation has recently been proposed for solving combinatorial optimization problems via quantum adiabatic evolution through its bifurcation point. Here we investigate the behavior of the quantum bifurcation machine (QbM) in the presence of dissipation. Our numerical study suggests that the output probability distribution of the dissipative QbM is Boltzmann-like, where the energy in the Boltzmann distribution corresponds to the cost function of the optimization problem. We explain the Boltzmann distribution by generalizing the concept of quantum heating in a single nonlinear oscillator to the case of multiple coupled nonlinear oscillators. The present result also suggests that such driven dissipative nonlinear oscillator networks can be applied to Boltzmann sampling, which is used, e.g., for Boltzmann machine learning in the field of artificial intelligence.

Joint recognition and discrimination in nonlinear feature space

NASA Astrophysics Data System (ADS)

Talukder, Ashit; Casasent, David P.

1997-09-01

A new general method for linear and nonlinear feature extraction is presented. It is novel since it provides both representation and discrimination while most other methods are concerned with only one of these issues. We call this approach the maximum representation and discrimination feature (MRDF) method and show that the Bayes classifier and the Karhunen- Loeve transform are special cases of it. We refer to our nonlinear feature extraction technique as nonlinear eigen- feature extraction. It is new since it has a closed-form solution and produces nonlinear decision surfaces with higher rank than do iterative methods. Results on synthetic databases are shown and compared with results from standard Fukunaga- Koontz transform and Fisher discriminant function methods. The method is also applied to an automated product inspection problem (discrimination) and to the classification and pose estimation of two similar objects (representation and discrimination).

Exact traveling wave solutions of the KP-BBM equation by using the new approach of generalized (G'/G)-expansion method.

PubMed

Alam, Md Nur; Akbar, M Ali

2013-01-01

The new approach of the generalized (G'/G)-expansion method is an effective and powerful mathematical tool in finding exact traveling wave solutions of nonlinear evolution equations (NLEEs) in science, engineering and mathematical physics. In this article, the new approach of the generalized (G'/G)-expansion method is applied to construct traveling wave solutions of the Kadomtsev-Petviashvili-Benjamin-Bona-Mahony (KP-BBM) equation. The solutions are expressed in terms of the hyperbolic functions, the trigonometric functions and the rational functions. By means of this scheme, we found some new traveling wave solutions of the above mentioned equation.

Generalized decompositions of dynamic systems and vector Lyapunov functions

NASA Astrophysics Data System (ADS)

Ikeda, M.; Siljak, D. D.

1981-10-01

The notion of decomposition is generalized to provide more freedom in constructing vector Lyapunov functions for stability analysis of nonlinear dynamic systems. A generalized decomposition is defined as a disjoint decomposition of a system which is obtained by expanding the state-space of a given system. An inclusion principle is formulated for the solutions of the expansion to include the solutions of the original system, so that stability of the expansion implies stability of the original system. Stability of the expansion can then be established by standard disjoint decompositions and vector Lyapunov functions. The applicability of the new approach is demonstrated using the Lotka-Volterra equations.

Nonlinear Scattering of Acoustic Waves by Vibrating Obstacles.

DTIC Science & Technology

1983-06-01

2xB’(x) - 2(v+l)B(x). (A40) As a first example of this general form, we let f(x) e-X 2 . [This is the usual weighting function used in the orthogonality ... Some examples involving Laguerre functions. We nov consider integrals of the general forim where L,(x) is the Laguerre function of order v, and f(x...phenomena Integrals 20. ABSTRACT (ContiIne an reverse sle if 009000MY and Ideitfy 67 6l4k rom’ ") The problem of the generation of sum- and difference

Computations involving differential operators and their actions on functions

NASA Technical Reports Server (NTRS)

Crouch, Peter E.; Grossman, Robert; Larson, Richard

1991-01-01

The algorithms derived by Grossmann and Larson (1989) are further developed for rewriting expressions involving differential operators. The differential operators involved arise in the local analysis of nonlinear dynamical systems. These algorithms are extended in two different directions: the algorithms are generalized so that they apply to differential operators on groups and the data structures and algorithms are developed to compute symbolically the action of differential operators on functions. Both of these generalizations are needed for applications.

A study on nonlinear estimation of submaximal effort tolerance based on the generalized MET concept and the 6MWT in pulmonary rehabilitation

PubMed Central

Szczegielniak, Jan; Łuniewski, Jacek; Stanisławski, Rafał; Bogacz, Katarzyna; Krajczy, Marcin; Rydel, Marek

2018-01-01

Background The six-minute walk test (6MWT) is considered to be a simple and inexpensive tool for the assessment of functional tolerance of submaximal effort. The aim of this work was 1) to background the nonlinear nature of the energy expenditure process due to physical activity, 2) to compare the results/scores of the submaximal treadmill exercise test and those of 6MWT in pulmonary patients and 3) to develop nonlinear mathematical models relating the two. Methods The study group included patients with the COPD. All patients were subjected to a submaximal exercise test and a 6MWT. To develop an optimal mathematical solution and compare the results of the exercise test and the 6MWT, the least squares and genetic algorithms were employed to estimate parameters of polynomial expansion and piecewise linear models. Results Mathematical analysis enabled to construct nonlinear models for estimating the MET result of submaximal exercise test based on average walk velocity (or distance) in the 6MWT. Conclusions Submaximal effort tolerance in COPD patients can be effectively estimated from new, rehabilitation-oriented, nonlinear models based on the generalized MET concept and the 6MWT. PMID:29425213

A general one-dimension nonlinear magneto-elastic coupled constitutive model for magnetostrictive materials

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Da-Guang; Li, Meng-Han; Zhou, Hao-Miao, E-mail: zhouhm@cjlu.edu.cn

2015-10-15

For magnetostrictive rods under combined axial pre-stress and magnetic field, a general one-dimension nonlinear magneto-elastic coupled constitutive model was built in this paper. First, the elastic Gibbs free energy was expanded into polynomial, and the relationship between stress and strain and the relationship between magnetization and magnetic field with the polynomial form were obtained with the help of thermodynamic relations. Then according to microscopic magneto-elastic coupling mechanism and some physical facts of magnetostrictive materials, a nonlinear magneto-elastic constitutive with concise form was obtained when the relations of nonlinear strain and magnetization in the polynomial constitutive were instead with transcendental functions.more » The comparisons between the prediction and the experimental data of different magnetostrictive materials, such as Terfenol-D, Metglas and Ni showed that the predicted magnetostrictive strain and magnetization curves were consistent with experimental results under different pre-stresses whether in the region of low and moderate field or high field. Moreover, the model can fully reflect the nonlinear magneto-mechanical coupling characteristics between magnetic, magnetostriction and elasticity, and it can effectively predict the changes of material parameters with pre-stress and bias field, which is useful in practical applications.« less

A flexible model for the mean and variance functions, with application to medical cost data.

PubMed

Chen, Jinsong; Liu, Lei; Zhang, Daowen; Shih, Ya-Chen T

2013-10-30

Medical cost data are often skewed to the right and heteroscedastic, having a nonlinear relation with covariates. To tackle these issues, we consider an extension to generalized linear models by assuming nonlinear associations of covariates in the mean function and allowing the variance to be an unknown but smooth function of the mean. We make no further assumption on the distributional form. The unknown functions are described by penalized splines, and the estimation is carried out using nonparametric quasi-likelihood. Simulation studies show the flexibility and advantages of our approach. We apply the model to the annual medical costs of heart failure patients in the clinical data repository at the University of Virginia Hospital System. Copyright © 2013 John Wiley & Sons, Ltd.

Convexity and Concavity Properties of the Optimal Value Function in Parametric Nonlinear Programming.

DTIC Science & Technology

1982-12-21

and W. T. ZIEMBA (1981). Intro- duction to concave and generalized concave functions. In Gener- alized Concavity in Optimization and Economics (S...Schaible and W. T. Ziemba , eds.), pp. 21-50. Academic Press, New York. BANK, B., J. GUDDAT, D. KLATTE, B. KUMMER, and K. TAMMER (1982). Non- Linear

Nonlinearly driven harmonics of Alfvén modes

NASA Astrophysics Data System (ADS)

Zhang, B.; Breizman, B. N.; Zheng, L. J.; Berk, H. L.

2014-01-01

In order to study the leading order nonlinear magneto-hydrodynamic (MHD) harmonic response of a plasma in realistic geometry, the AEGIS code has been generalized to account for inhomogeneous source terms. These source terms are expressed in terms of the quadratic corrections that depend on the functional form of a linear MHD eigenmode, such as the Toroidal Alfvén Eigenmode. The solution of the resultant equation gives the second order harmonic response. Preliminary results are presented here.

Global attractivity of an almost periodic N-species nonlinear ecological competitive model

NASA Astrophysics Data System (ADS)

Xia, Yonghui; Han, Maoan; Huang, Zhenkun

2008-01-01

By using comparison theorem and constructing suitable Lyapunov functional, we study the following almost periodic nonlinear N-species competitive Lotka-Volterra model: A set of sufficient conditions is obtained for the existence and global attractivity of a unique positive almost periodic solution of the above model. As applications, some special competition models are studied again, our new results improve and generalize former results. Examples and their simulations show the feasibility of our main results.

The "killing zone" revisited: serial nonlinearities predict general aviation accident rates from pilot total flight hours.

PubMed

Knecht, William R

2013-11-01

Is there a "killing zone" (Craig, 2001)-a range of pilot flight time over which general aviation (GA) pilots are at greatest risk? More broadly, can we predict accident rates, given a pilot's total flight hours (TFH)? These questions interest pilots, aviation policy makers, insurance underwriters, and researchers alike. Most GA research studies implicitly assume that accident rates are linearly related to TFH, but that relation may actually be multiply nonlinear. This work explores the ability of serial nonlinear modeling functions to predict GA accident rates from noisy rate data binned by TFH. Two sets of National Transportation Safety Board (NTSB)/Federal Aviation Administration (FAA) data were log-transformed, then curve-fit to a gamma-pdf-based function. Despite high rate-noise, this produced weighted goodness-of-fit (Rw(2)) estimates of .654 and .775 for non-instrument-rated (non-IR) and instrument-rated pilots (IR) respectively. Serial-nonlinear models could be useful to directly predict GA accident rates from TFH, and as an independent variable or covariate to control for flight risk during data analysis. Applied to FAA data, these models imply that the "killing zone" may be broader than imagined. Relatively high risk for an individual pilot may extend well beyond the 2000-h mark before leveling off to a baseline rate. Published by Elsevier Ltd.

Non-linear corrections to the time-covariance function derived from a multi-state chemical master equation.

PubMed

Scott, M

2012-08-01

The time-covariance function captures the dynamics of biochemical fluctuations and contains important information about the underlying kinetic rate parameters. Intrinsic fluctuations in biochemical reaction networks are typically modelled using a master equation formalism. In general, the equation cannot be solved exactly and approximation methods are required. For small fluctuations close to equilibrium, a linearisation of the dynamics provides a very good description of the relaxation of the time-covariance function. As the number of molecules in the system decrease, deviations from the linear theory appear. Carrying out a systematic perturbation expansion of the master equation to capture these effects results in formidable algebra; however, symbolic mathematics packages considerably expedite the computation. The authors demonstrate that non-linear effects can reveal features of the underlying dynamics, such as reaction stoichiometry, not available in linearised theory. Furthermore, in models that exhibit noise-induced oscillations, non-linear corrections result in a shift in the base frequency along with the appearance of a secondary harmonic.

A Case Study on the Application of a Structured Experimental Method for Optimal Parameter Design of a Complex Control System

NASA Technical Reports Server (NTRS)

Torres-Pomales, Wilfredo

2015-01-01

This report documents a case study on the application of Reliability Engineering techniques to achieve an optimal balance between performance and robustness by tuning the functional parameters of a complex non-linear control system. For complex systems with intricate and non-linear patterns of interaction between system components, analytical derivation of a mathematical model of system performance and robustness in terms of functional parameters may not be feasible or cost-effective. The demonstrated approach is simple, structured, effective, repeatable, and cost and time efficient. This general approach is suitable for a wide range of systems.

A new polytopic approach for the unknown input functional observer design

NASA Astrophysics Data System (ADS)

Bezzaoucha, Souad; Voos, Holger; Darouach, Mohamed

2018-03-01

In this paper, a constructive procedure to design Functional Unknown Input Observers for nonlinear continuous time systems is proposed under the Polytopic Takagi-Sugeno framework. An equivalent representation for the nonlinear model is achieved using the sector nonlinearity transformation. Applying the Lyapunov theory and the ? attenuation, linear matrix inequalities conditions are deduced which are solved for feasibility to obtain the observer design matrices. To cope with the effect of unknown inputs, classical approach of decoupling the unknown input for the linear case is used. Both algebraic and solver-based solutions are proposed (relaxed conditions). Necessary and sufficient conditions for the existence of the functional polytopic observer are given. For both approaches, the general and particular cases (measurable premise variables, full state estimation with full and reduced order cases) are considered and it is shown that the proposed conditions correspond to the one presented for standard linear case. To illustrate the proposed theoretical results, detailed numerical simulations are presented for a Quadrotor Aerial Robots Landing and a Waste Water Treatment Plant. Both systems are highly nonlinear and represented in a T-S polytopic form with unmeasurable premise variables and unknown inputs.

Constructing general partial differential equations using polynomial and neural networks.

PubMed

Zjavka, Ladislav; Pedrycz, Witold

2016-01-01

Sum fraction terms can approximate multi-variable functions on the basis of discrete observations, replacing a partial differential equation definition with polynomial elementary data relation descriptions. Artificial neural networks commonly transform the weighted sum of inputs to describe overall similarity relationships of trained and new testing input patterns. Differential polynomial neural networks form a new class of neural networks, which construct and solve an unknown general partial differential equation of a function of interest with selected substitution relative terms using non-linear multi-variable composite polynomials. The layers of the network generate simple and composite relative substitution terms whose convergent series combinations can describe partial dependent derivative changes of the input variables. This regression is based on trained generalized partial derivative data relations, decomposed into a multi-layer polynomial network structure. The sigmoidal function, commonly used as a nonlinear activation of artificial neurons, may transform some polynomial items together with the parameters with the aim to improve the polynomial derivative term series ability to approximate complicated periodic functions, as simple low order polynomials are not able to fully make up for the complete cycles. The similarity analysis facilitates substitutions for differential equations or can form dimensional units from data samples to describe real-world problems. Copyright © 2015 Elsevier Ltd. All rights reserved.

Observability of nonlinear dynamics: normalized results and a time-series approach.

PubMed

Aguirre, Luis A; Bastos, Saulo B; Alves, Marcela A; Letellier, Christophe

2008-03-01

This paper investigates the observability of nonlinear dynamical systems. Two difficulties associated with previous studies are dealt with. First, a normalized degree observability is defined. This permits the comparison of different systems, which was not generally possible before. Second, a time-series approach is proposed based on omnidirectional nonlinear correlation functions to rank a set of time series of a system in terms of their potential use to reconstruct the original dynamics without requiring the knowledge of the system equations. The two approaches proposed in this paper and a former method were applied to five benchmark systems and an overall agreement of over 92% was found.

Stochastic response and bifurcation of periodically driven nonlinear oscillators by the generalized cell mapping method

NASA Astrophysics Data System (ADS)

Han, Qun; Xu, Wei; Sun, Jian-Qiao

2016-09-01

The stochastic response of nonlinear oscillators under periodic and Gaussian white noise excitations is studied with the generalized cell mapping based on short-time Gaussian approximation (GCM/STGA) method. The solutions of the transition probability density functions over a small fraction of the period are constructed by the STGA scheme in order to construct the GCM over one complete period. Both the transient and steady-state probability density functions (PDFs) of a smooth and discontinuous (SD) oscillator are computed to illustrate the application of the method. The accuracy of the results is verified by direct Monte Carlo simulations. The transient responses show the evolution of the PDFs from being Gaussian to non-Gaussian. The effect of a chaotic saddle on the stochastic response is also studied. The stochastic P-bifurcation in terms of the steady-state PDFs occurs with the decrease of the smoothness parameter, which corresponds to the deterministic pitchfork bifurcation.

Unified theory of nonlinear electrodynamics and gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Torres-Gomez, Alexander; Krasnov, Kirill; Scarinci, Carlos

2011-01-15

We describe a class of unified theories of electromagnetism and gravity. The Lagrangian is of the BF type, with a potential for the B field, the gauge group is U(2) (complexified). Given a choice of the potential function the theory is a deformation of (complex) general relativity and electromagnetism, and describes just two propagating polarizations of the graviton and two of the photon. When gravity is switched off the theory becomes the usual nonlinear electrodynamics with a general structure function. The Einstein-Maxwell theory can be recovered by sending some of the parameters of the defining potential to zero, but formore » any generic choice of the potential the theory is indistinguishable from Einstein-Maxwell at low energies. A real theory is obtained by imposing suitable reality conditions. We also study the spherically-symmetric solution and show how the usual Reissner-Nordstrom solution is recovered.« less

Synchronization of a Class of Switched Neural Networks with Time-Varying Delays via Nonlinear Feedback Control.

PubMed

Wang, Leimin; Shen, Yi; Zhang, Guodong

2016-10-01

This paper is concerned with the synchronization problem for a class of switched neural networks (SNNs) with time-varying delays. First, a new crucial lemma which includes and extends the classical exponential stability theorem is constructed. Then by using the lemma, new algebraic criteria of ψ -type synchronization (synchronization with general decay rate) for SNNs are established via the designed nonlinear feedback control. The ψ -type synchronization which is in a general framework is obtained by introducing a ψ -type function. It contains exponential synchronization, polynomial synchronization, and other synchronization as its special cases. The results of this paper are general, and they also complement and extend some previous results. Finally, numerical simulations are carried out to demonstrate the effectiveness of the obtained results.

Nonlinear Thermoelastic Effects in Surface Mechanics.

DTIC Science & Technology

1980-01-01

remaining quartic polynomial generated by det(A) .0 is presumed to not yield real roots (real characteristics) associated with elastic waves because...0253 UNCLASSIFIED NL NONINEAR THEMLOEIASTIC EFF’ECTS IN SUFC MECHANICS D T ICX2 ) J.1. PFirin General Electric Company. JUN 1 8 8 Schenectady, New York...f - Generalized analytic functions Ei Lagrangian strain components lk - Generalized Cauchy kernels, Eq. (1I) E - Young’s modulus, Pa ulk

Further Results on Constructions of Generalized Bent Boolean Functions

DTIC Science & Technology

2016-03-01

China; 2Naval Postgraduate School, Applied Mathematics Department, Monterey, CA 93943, USA; 3Science and Technology on Communication Security...in 1976 as an interesting combinatorial object with the important property of having op- timal nonlinearity [1]. Since bent functions have many...77–94 10 Zhao Y, Li H L. On bent functions with some symmet- ric properties. Discret Appl Math, 2006, 154: 2537– 2543

Optical solitons, nonlinear self-adjointness and conservation laws for the cubic nonlinear Shrödinger's equation with repulsive delta potential

NASA Astrophysics Data System (ADS)

Baleanu, Dumitru; Inc, Mustafa; Aliyu, Aliyu Isa; Yusuf, Abdullahi

2017-11-01

In this paper, the complex envelope function ansatz method is used to acquire the optical solitons to the cubic nonlinear Shrödinger's equation with repulsive delta potential (δ-NLSE). The method reveals dark and bright optical solitons. The necessary constraint conditions which guarantee the existence of the solitons are also presented. We studied the δ-NLSE by analyzing a system of partial differential equations (PDEs) obtained by decomposing the equation into real and imaginary components. We derive the Lie point symmetry generators of the system and prove that the system is nonlinearly self-adjoint with an explicit form of a differential substitution satisfying the nonlinear self-adjoint condition. Then we use these facts to establish a set of conserved vectors for the system using the general Cls theorem presented by Ibragimov. Some interesting figures for the acquired solutions are also presented.

Spatiotemporal polarization modulation microscopy with a microretarder array

NASA Astrophysics Data System (ADS)

Ding, Changqin; Ulcickas, James R. W.; Simpson, Garth J.

2018-02-01

A patterned microretarder array positioned in the rear conjugate plane of a microscope enables rapid polarizationdependent nonlinear optical microscopy. The pattern introduced to the array results in periodic modulation of the polarization-state of the incident light as a function of position within the field of view with no moving parts or active control. Introduction of a single stationary optical element and a fixed polarizer into the beam of a nonlinear optical microscope enabled nonlinear optical tensor recovery, which informs on local structure and orientation. Excellent agreement was observed between the measured and predicted second harmonic generation (SHG) of z-cut quartz, selected as a test system with well-established nonlinear optical properties. Subsequent studies of spatially varying samples further support the general applicability of this relatively simple strategy for detailed polarization analysis in both conventional and nonlinear optical imaging of structurally diverse samples.

Nonlinear Acoustical Assessment of Precipitate Nucleation

NASA Technical Reports Server (NTRS)

Cantrell, John H.; Yost, William T.

2004-01-01

The purpose of the present work is to show that measurements of the acoustic nonlinearity parameter in heat treatable alloys as a function of heat treatment time can provide quantitative information about the kinetics of precipitate nucleation and growth in such alloys. Generally, information on the kinetics of phase transformations is obtained from time-sequenced electron microscopical examination and differential scanning microcalorimetry. The present nonlinear acoustical assessment of precipitation kinetics is based on the development of a multiparameter analytical model of the effects on the nonlinearity parameter of precipitate nucleation and growth in the alloy system. A nonlinear curve fit of the model equation to the experimental data is then used to extract the kinetic parameters related to the nucleation and growth of the targeted precipitate. The analytical model and curve fit is applied to the assessment of S' precipitation in aluminum alloy 2024 during artificial aging from the T4 to the T6 temper.

Dispersive optical soliton solutions for higher order nonlinear Sasa-Satsuma equation in mono mode fibers via new auxiliary equation method

NASA Astrophysics Data System (ADS)

Khater, Mostafa M. A.; Seadawy, Aly R.; Lu, Dianchen

2018-01-01

In this research, we apply new technique for higher order nonlinear Schrödinger equation which is representing the propagation of short light pulses in the monomode optical fibers and the evolution of slowly varying packets of quasi-monochromatic waves in weakly nonlinear media that have dispersion. Nonlinear Schrödinger equation is one of the basic model in fiber optics. We apply new auxiliary equation method for nonlinear Sasa-Satsuma equation to obtain a new optical forms of solitary traveling wave solutions. Exact and solitary traveling wave solutions are obtained in different kinds like trigonometric, hyperbolic, exponential, rational functions, …, etc. These forms of solutions that we represent in this research prove the superiority of our new technique on almost thirteen powerful methods. The main merits of this method over the other methods are that it gives more general solutions with some free parameters.

New Operational Matrices for Solving Fractional Differential Equations on the Half-Line

PubMed Central

2015-01-01

In this paper, the fractional-order generalized Laguerre operational matrices (FGLOM) of fractional derivatives and fractional integration are derived. These operational matrices are used together with spectral tau method for solving linear fractional differential equations (FDEs) of order ν (0 < ν < 1) on the half line. An upper bound of the absolute errors is obtained for the approximate and exact solutions. Fractional-order generalized Laguerre pseudo-spectral approximation is investigated for solving nonlinear initial value problem of fractional order ν. The extension of the fractional-order generalized Laguerre pseudo-spectral method is given to solve systems of FDEs. We present the advantages of using the spectral schemes based on fractional-order generalized Laguerre functions and compare them with other methods. Several numerical examples are implemented for FDEs and systems of FDEs including linear and nonlinear terms. We demonstrate the high accuracy and the efficiency of the proposed techniques. PMID:25996369

New operational matrices for solving fractional differential equations on the half-line.

PubMed

Bhrawy, Ali H; Taha, Taha M; Alzahrani, Ebraheem O; Alzahrani, Ebrahim O; Baleanu, Dumitru; Alzahrani, Abdulrahim A

2015-01-01

In this paper, the fractional-order generalized Laguerre operational matrices (FGLOM) of fractional derivatives and fractional integration are derived. These operational matrices are used together with spectral tau method for solving linear fractional differential equations (FDEs) of order ν (0 < ν < 1) on the half line. An upper bound of the absolute errors is obtained for the approximate and exact solutions. Fractional-order generalized Laguerre pseudo-spectral approximation is investigated for solving nonlinear initial value problem of fractional order ν. The extension of the fractional-order generalized Laguerre pseudo-spectral method is given to solve systems of FDEs. We present the advantages of using the spectral schemes based on fractional-order generalized Laguerre functions and compare them with other methods. Several numerical examples are implemented for FDEs and systems of FDEs including linear and nonlinear terms. We demonstrate the high accuracy and the efficiency of the proposed techniques.

A non-linear regression analysis program for describing electrophysiological data with multiple functions using Microsoft Excel.

PubMed

Brown, Angus M

2006-04-01

The objective of this present study was to demonstrate a method for fitting complex electrophysiological data with multiple functions using the SOLVER add-in of the ubiquitous spreadsheet Microsoft Excel. SOLVER minimizes the difference between the sum of the squares of the data to be fit and the function(s) describing the data using an iterative generalized reduced gradient method. While it is a straightforward procedure to fit data with linear functions, and we have previously demonstrated a method of non-linear regression analysis of experimental data based upon a single function, it is more complex to fit data with multiple functions, usually requiring specialized expensive computer software. In this paper we describe an easily understood program for fitting experimentally acquired data, in this case the stimulus-evoked compound action potential from the mouse optic nerve, with multiple Gaussian functions. The program is flexible and can be applied to describe data with a wide variety of user-input functions.

The pointwise estimates of diffusion wave of the compressible micropolar fluids

NASA Astrophysics Data System (ADS)

Wu, Zhigang; Wang, Weike

2018-09-01

The pointwise estimates for the compressible micropolar fluids in dimension three are given, which exhibit generalized Huygens' principle for the fluid density and fluid momentum as the compressible Navier-Stokes equation, while the micro-rational momentum behaves like the fluid momentum of the Euler equation with damping. To circumvent the complexity from 7 × 7 Green's matrix, we use the decomposition of fluid part and electromagnetic part for the momentums to study three smaller Green's matrices. The following from this decomposition is that we have to deal with the new problem that the nonlinear terms contain nonlocal operators. We solve it by using the natural match of these new Green's functions and the nonlinear terms. Moreover, to derive the different pointwise estimates for different unknown variables such that the estimate of each unknown variable is in agreement with its Green's function, we develop some new estimates on the nonlinear interplay between different waves.

Adaptive Neural Control of Uncertain MIMO Nonlinear Systems With State and Input Constraints.

PubMed

Chen, Ziting; Li, Zhijun; Chen, C L Philip

2017-06-01

An adaptive neural control strategy for multiple input multiple output nonlinear systems with various constraints is presented in this paper. To deal with the nonsymmetric input nonlinearity and the constrained states, the proposed adaptive neural control is combined with the backstepping method, radial basis function neural network, barrier Lyapunov function (BLF), and disturbance observer. By ensuring the boundedness of the BLF of the closed-loop system, it is demonstrated that the output tracking is achieved with all states remaining in the constraint sets and the general assumption on nonsingularity of unknown control coefficient matrices has been eliminated. The constructed adaptive neural control has been rigorously proved that it can guarantee the semiglobally uniformly ultimate boundedness of all signals in the closed-loop system. Finally, the simulation studies on a 2-DOF robotic manipulator system indicate that the designed adaptive control is effective.

Privacy-preserving outlier detection through random nonlinear data distortion.

PubMed

Bhaduri, Kanishka; Stefanski, Mark D; Srivastava, Ashok N

2011-02-01

Consider a scenario in which the data owner has some private or sensitive data and wants a data miner to access them for studying important patterns without revealing the sensitive information. Privacy-preserving data mining aims to solve this problem by randomly transforming the data prior to their release to the data miners. Previous works only considered the case of linear data perturbations--additive, multiplicative, or a combination of both--for studying the usefulness of the perturbed output. In this paper, we discuss nonlinear data distortion using potentially nonlinear random data transformation and show how it can be useful for privacy-preserving anomaly detection from sensitive data sets. We develop bounds on the expected accuracy of the nonlinear distortion and also quantify privacy by using standard definitions. The highlight of this approach is to allow a user to control the amount of privacy by varying the degree of nonlinearity. We show how our general transformation can be used for anomaly detection in practice for two specific problem instances: a linear model and a popular nonlinear model using the sigmoid function. We also analyze the proposed nonlinear transformation in full generality and then show that, for specific cases, it is distance preserving. A main contribution of this paper is the discussion between the invertibility of a transformation and privacy preservation and the application of these techniques to outlier detection. The experiments conducted on real-life data sets demonstrate the effectiveness of the approach.

Boundedness and global stability of the two-predator and one-prey models with nonlinear prey-taxis

NASA Astrophysics Data System (ADS)

Wang, Jianping; Wang, Mingxin

2018-06-01

This paper concerns the reaction-diffusion systems modeling the population dynamics of two predators and one prey with nonlinear prey-taxis. We first investigate the global existence and boundedness of the unique classical solution for the general model. Then, we study the global stabilities of nonnegative spatially homogeneous equilibria for an explicit system with type I functional responses and density-dependent death rates for the predators and logistic growth for the prey. Moreover, the convergence rates are also established.

Estimation on nonlinear damping in second order distributed parameter systems

NASA Technical Reports Server (NTRS)

Banks, H. T.; Reich, Simeon; Rosen, I. G.

1989-01-01

An approximation and convergence theory for the identification of nonlinear damping in abstract wave equations is developed. It is assumed that the unknown dissipation mechanism to be identified can be described by a maximal monotone operator acting on the generalized velocity. The stiffness is assumed to be linear and symmetric. Functional analytic techniques are used to establish that solutions to a sequence of finite dimensional (Galerkin) approximating identification problems in some sense approximate a solution to the original infinite dimensional inverse problem.

Reservoir Computing Beyond Memory-Nonlinearity Trade-off.

PubMed

Inubushi, Masanobu; Yoshimura, Kazuyuki

2017-08-31

Reservoir computing is a brain-inspired machine learning framework that employs a signal-driven dynamical system, in particular harnessing common-signal-induced synchronization which is a widely observed nonlinear phenomenon. Basic understanding of a working principle in reservoir computing can be expected to shed light on how information is stored and processed in nonlinear dynamical systems, potentially leading to progress in a broad range of nonlinear sciences. As a first step toward this goal, from the viewpoint of nonlinear physics and information theory, we study the memory-nonlinearity trade-off uncovered by Dambre et al. (2012). Focusing on a variational equation, we clarify a dynamical mechanism behind the trade-off, which illustrates why nonlinear dynamics degrades memory stored in dynamical system in general. Moreover, based on the trade-off, we propose a mixture reservoir endowed with both linear and nonlinear dynamics and show that it improves the performance of information processing. Interestingly, for some tasks, significant improvements are observed by adding a few linear dynamics to the nonlinear dynamical system. By employing the echo state network model, the effect of the mixture reservoir is numerically verified for a simple function approximation task and for more complex tasks.

Traveling wave solutions of the nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Akbari-Moghanjoughi, M.

2017-10-01

In this paper, we investigate the traveling soliton and the periodic wave solutions of the nonlinear Schrödinger equation (NLSE) with generalized nonlinear functionality. We also explore the underlying close connection between the well-known KdV equation and the NLSE. It is remarked that both one-dimensional KdV and NLSE models share the same pseudoenergy spectrum. We also derive the traveling wave solutions for two cases of weakly nonlinear mathematical models, namely, the Helmholtz and the Duffing oscillators' potentials. It is found that these models only allow gray-type NLSE solitary propagations. It is also found that the pseudofrequency ratio for the Helmholtz potential between the nonlinear periodic carrier and the modulated sinusoidal waves is always in the range 0.5 ≤ Ω/ω ≤ 0.537285 regardless of the potential parameter values. The values of Ω/ω = {0.5, 0.537285} correspond to the cnoidal waves modulus of m = {0, 1} for soliton and sinusoidal limits and m = 0.5, respectively. Moreover, the current NLSE model is extended to fully NLSE (FNLSE) situation for Sagdeev oscillator pseudopotential which can be derived using a closed set of hydrodynamic fluid equations with a fully integrable Hamiltonian system. The generalized quasi-three-dimensional traveling wave solution is also derived. The current simple hydrodynamic plasma model may also be generalized to two dimensions and other complex situations including different charged species and cases with magnetic or gravitational field effects.

Generalized Weierstrass-Mandelbrot Function Model for Actual Stocks Markets Indexes with Nonlinear Characteristics

NASA Astrophysics Data System (ADS)

Zhang, L.; Yu, C.; Sun, J. Q.

2015-03-01

It is difficult to simulate the dynamical behavior of actual financial markets indexes effectively, especially when they have nonlinear characteristics. So it is significant to propose a mathematical model with these characteristics. In this paper, we investigate a generalized Weierstrass-Mandelbrot function (WMF) model with two nonlinear characteristics: fractal dimension D where 2 > D > 1.5 and Hurst exponent (H) where 1 > H > 0.5 firstly. And then we study the dynamical behavior of H for WMF as D and the spectrum of the time series γ change in three-dimensional space, respectively. Because WMF and the actual stock market indexes have two common features: fractal behavior using fractal dimension and long memory effect by Hurst exponent, we study the relationship between WMF and the actual stock market indexes. We choose a random value of γ and fixed value of D for WMF to simulate the S&P 500 indexes at different time ranges. As shown in the simulation results of three-dimensional space, we find that γ is important in WMF model and different γ may have the same effect for the nonlinearity of WMF. Then we calculate the skewness and kurtosis of actual Daily S&P 500 index in different time ranges which can be used to choose the value of γ. Based on these results, we choose appropriate γ, D and initial value into WMF to simulate Daily S&P 500 indexes. Using the fit line method in two-dimensional space for the simulated values, we find that the generalized WMF model is effective for simulating different actual stock market indexes in different time ranges. It may be useful for understanding the dynamical behavior of many different financial markets.

Nonlinear Network Description for Many-Body Quantum Systems in Continuous Space

NASA Astrophysics Data System (ADS)

Ruggeri, Michele; Moroni, Saverio; Holzmann, Markus

2018-05-01

We show that the recently introduced iterative backflow wave function can be interpreted as a general neural network in continuum space with nonlinear functions in the hidden units. Using this wave function in variational Monte Carlo simulations of liquid 4He in two and three dimensions, we typically find a tenfold increase in accuracy over currently used wave functions. Furthermore, subsequent stages of the iteration procedure define a set of increasingly good wave functions, each with its own variational energy and variance of the local energy: extrapolation to zero variance gives energies in close agreement with the exact values. For two dimensional 4He, we also show that the iterative backflow wave function can describe both the liquid and the solid phase with the same functional form—a feature shared with the shadow wave function, but now joined by much higher accuracy. We also achieve significant progress for liquid 3He in three dimensions, improving previous variational and fixed-node energies.

Fast Nonlinear Generalized Inversion of Gravity Data with Application to the Three-Dimensional Crustal Density Structure of Sichuan Basin, Southwest China

NASA Astrophysics Data System (ADS)

Wang, Jun; Meng, Xiaohong; Li, Fang

2017-11-01

Generalized inversion is one of the important steps in the quantitative interpretation of gravity data. With appropriate algorithm and parameters, it gives a view of the subsurface which characterizes different geological bodies. However, generalized inversion of gravity data is time consuming due to the large amount of data points and model cells adopted. Incorporating of various prior information as constraints deteriorates the above situation. In the work discussed in this paper, a method for fast nonlinear generalized inversion of gravity data is proposed. The fast multipole method is employed for forward modelling. The inversion objective function is established with weighted data misfit function along with model objective function. The total objective function is solved by a dataspace algorithm. Moreover, depth weighing factor is used to improve depth resolution of the result, and bound constraint is incorporated by a transfer function to limit the model parameters in a reliable range. The matrix inversion is accomplished by a preconditioned conjugate gradient method. With the above algorithm, equivalent density vectors can be obtained, and interpolation is performed to get the finally density model on the fine mesh in the model domain. Testing on synthetic gravity data demonstrated that the proposed method is faster than conventional generalized inversion algorithm to produce an acceptable solution for gravity inversion problem. The new developed inversion method was also applied for inversion of the gravity data collected over Sichuan basin, southwest China. The established density structure in this study helps understanding the crustal structure of Sichuan basin and provides reference for further oil and gas exploration in this area.

Optimal control of dissipative nonlinear dynamical systems with triggers of coupled singularities

NASA Astrophysics Data System (ADS)

Stevanović Hedrih, K.

2008-02-01

This paper analyses the controllability of motion of nonconservative nonlinear dynamical systems in which triggers of coupled singularities exist or appear. It is shown that the phase plane method is useful for the analysis of nonlinear dynamics of nonconservative systems with one degree of freedom of control strategies and also shows the way it can be used for controlling the relative motion in rheonomic systems having equivalent scleronomic conservative or nonconservative system For the system with one generalized coordinate described by nonlinear differential equation of nonlinear dynamics with trigger of coupled singularities, the functions of system potential energy and conservative force must satisfy some conditions defined by a Theorem on the existence of a trigger of coupled singularities and the separatrix in the form of "an open a spiral form" of number eight. Task of the defined dynamical nonconservative system optimal control is: by using controlling force acting to the system, transfer initial state of the nonlinear dynamics of the system into the final state of the nonlinear dynamics in the minimal time for that optimal control task

Adaptive Neural Output-Feedback Control for a Class of Nonlower Triangular Nonlinear Systems With Unmodeled Dynamics.

PubMed

Wang, Huanqing; Liu, Peter Xiaoping; Li, Shuai; Wang, Ding

2017-08-29

This paper presents the development of an adaptive neural controller for a class of nonlinear systems with unmodeled dynamics and immeasurable states. An observer is designed to estimate system states. The structure consistency of virtual control signals and the variable partition technique are combined to overcome the difficulties appearing in a nonlower triangular form. An adaptive neural output-feedback controller is developed based on the backstepping technique and the universal approximation property of the radial basis function (RBF) neural networks. By using the Lyapunov stability analysis, the semiglobally and uniformly ultimate boundedness of all signals within the closed-loop system is guaranteed. The simulation results show that the controlled system converges quickly, and all the signals are bounded. This paper is novel at least in the two aspects: 1) an output-feedback control strategy is developed for a class of nonlower triangular nonlinear systems with unmodeled dynamics and 2) the nonlinear disturbances and their bounds are the functions of all states, which is in a more general form than existing results.

Nonlinear Transfer of Signal and Noise Correlations in Cortical Networks

PubMed Central

Lyamzin, Dmitry R.; Barnes, Samuel J.; Donato, Roberta; Garcia-Lazaro, Jose A.; Keck, Tara

2015-01-01

Signal and noise correlations, a prominent feature of cortical activity, reflect the structure and function of networks during sensory processing. However, in addition to reflecting network properties, correlations are also shaped by intrinsic neuronal mechanisms. Here we show that spike threshold transforms correlations by creating nonlinear interactions between signal and noise inputs; even when input noise correlation is constant, spiking noise correlation varies with both the strength and correlation of signal inputs. We characterize these effects systematically in vitro in mice and demonstrate their impact on sensory processing in vivo in gerbils. We also find that the effects of nonlinear correlation transfer on cortical responses are stronger in the synchronized state than in the desynchronized state, and show that they can be reproduced and understood in a model with a simple threshold nonlinearity. Since these effects arise from an intrinsic neuronal property, they are likely to be present across sensory systems and, thus, our results are a critical step toward a general understanding of how correlated spiking relates to the structure and function of cortical networks. PMID:26019325

Semiclassical Path Integral Calculation of Nonlinear Optical Spectroscopy.

PubMed

Provazza, Justin; Segatta, Francesco; Garavelli, Marco; Coker, David F

2018-02-13

Computation of nonlinear optical response functions allows for an in-depth connection between theory and experiment. Experimentally recorded spectra provide a high density of information, but to objectively disentangle overlapping signals and to reach a detailed and reliable understanding of the system dynamics, measurements must be integrated with theoretical approaches. Here, we present a new, highly accurate and efficient trajectory-based semiclassical path integral method for computing higher order nonlinear optical response functions for non-Markovian open quantum systems. The approach is, in principle, applicable to general Hamiltonians and does not require any restrictions on the form of the intrasystem or system-bath couplings. This method is systematically improvable and is shown to be valid in parameter regimes where perturbation theory-based methods qualitatively breakdown. As a test of the methodology presented here, we study a system-bath model for a coupled dimer for which we compare against numerically exact results and standard approximate perturbation theory-based calculations. Additionally, we study a monomer with discrete vibronic states that serves as the starting point for future investigation of vibronic signatures in nonlinear electronic spectroscopy.

Employing general fit-bases for construction of potential energy surfaces with an adaptive density-guided approach

NASA Astrophysics Data System (ADS)

Klinting, Emil Lund; Thomsen, Bo; Godtliebsen, Ian Heide; Christiansen, Ove

2018-02-01

We present an approach to treat sets of general fit-basis functions in a single uniform framework, where the functional form is supplied on input, i.e., the use of different functions does not require new code to be written. The fit-basis functions can be used to carry out linear fits to the grid of single points, which are generated with an adaptive density-guided approach (ADGA). A non-linear conjugate gradient method is used to optimize non-linear parameters if such are present in the fit-basis functions. This means that a set of fit-basis functions with the same inherent shape as the potential cuts can be requested and no other choices with regards to the fit-basis functions need to be taken. The general fit-basis framework is explored in relation to anharmonic potentials for model systems, diatomic molecules, water, and imidazole. The behaviour and performance of Morse and double-well fit-basis functions are compared to that of polynomial fit-basis functions for unsymmetrical single-minimum and symmetrical double-well potentials. Furthermore, calculations for water and imidazole were carried out using both normal coordinates and hybrid optimized and localized coordinates (HOLCs). Our results suggest that choosing a suitable set of fit-basis functions can improve the stability of the fitting routine and the overall efficiency of potential construction by lowering the number of single point calculations required for the ADGA. It is possible to reduce the number of terms in the potential by choosing the Morse and double-well fit-basis functions. These effects are substantial for normal coordinates but become even more pronounced if HOLCs are used.

Smooth function approximation using neural networks.

PubMed

Ferrari, Silvia; Stengel, Robert F

2005-01-01

An algebraic approach for representing multidimensional nonlinear functions by feedforward neural networks is presented. In this paper, the approach is implemented for the approximation of smooth batch data containing the function's input, output, and possibly, gradient information. The training set is associated to the network adjustable parameters by nonlinear weight equations. The cascade structure of these equations reveals that they can be treated as sets of linear systems. Hence, the training process and the network approximation properties can be investigated via linear algebra. Four algorithms are developed to achieve exact or approximate matching of input-output and/or gradient-based training sets. Their application to the design of forward and feedback neurocontrollers shows that algebraic training is characterized by faster execution speeds and better generalization properties than contemporary optimization techniques.

Thermospheric dynamics - A system theory approach

NASA Technical Reports Server (NTRS)

Codrescu, M.; Forbes, J. M.; Roble, R. G.

1990-01-01

A system theory approach to thermospheric modeling is developed, based upon a linearization method which is capable of preserving nonlinear features of a dynamical system. The method is tested using a large, nonlinear, time-varying system, namely the thermospheric general circulation model (TGCM) of the National Center for Atmospheric Research. In the linearized version an equivalent system, defined for one of the desired TGCM output variables, is characterized by a set of response functions that is constructed from corresponding quasi-steady state and unit sample response functions. The linearized version of the system runs on a personal computer and produces an approximation of the desired TGCM output field height profile at a given geographic location.

Non-linear eigensolver-based alternative to traditional SCF methods

NASA Astrophysics Data System (ADS)

Gavin, B.; Polizzi, E.

2013-05-01

The self-consistent procedure in electronic structure calculations is revisited using a highly efficient and robust algorithm for solving the non-linear eigenvector problem, i.e., H({ψ})ψ = Eψ. This new scheme is derived from a generalization of the FEAST eigenvalue algorithm to account for the non-linearity of the Hamiltonian with the occupied eigenvectors. Using a series of numerical examples and the density functional theory-Kohn/Sham model, it will be shown that our approach can outperform the traditional SCF mixing-scheme techniques by providing a higher converge rate, convergence to the correct solution regardless of the choice of the initial guess, and a significant reduction of the eigenvalue solve time in simulations.

Plant functional trait diversity regulates the nonlinear response of productivity to regional climate change in Tibetan alpine grasslands.

PubMed

Wu, Jianshuang; Wurst, Susanne; Zhang, Xianzhou

2016-10-19

The biodiversity-productivity relationship is still under debate for alpine grasslands on the Tibetan Plateau. We know little about direct and indirect effects of biotic and abiotic drivers on this relationship, especially in regard to plant functional trait diversity. Here, we examine how aboveground net primary productivity (ANPP) and precipitation use efficiency (PUE) respond to climate, soil and community structure across alpine grasslands on the Northern Tibetan Plateau. We found that both ANPP and PUE showed nonlinear patterns along water availability and site altitude variation, which together accounted for 80.3% and 68.8% of variation in ANPP and PUE, respectively, by optimal generalized additive models. Functional trait divergence (FTD) and community weighted mean (CWM) of plant functional traits were as important as plant species diversity (PSD) for explaining the nonlinear productivity-climate relationship. These findings were confirmed by results from principal component analyses and structural equation models. We also found that FTD was negatively correlated with PSD across different alpine grasslands. Our results implicate: first, the combinatorial influences of temperature and precipitation gradients are important for predicting alpine grassland dynamics; second, the convergence and divergence of plant functional traits may have the potential to elucidate the effect of plant diversity on ecosystem functionality.

Plant functional trait diversity regulates the nonlinear response of productivity to regional climate change in Tibetan alpine grasslands

PubMed Central

Wu, Jianshuang; Wurst, Susanne; Zhang, Xianzhou

2016-01-01

The biodiversity-productivity relationship is still under debate for alpine grasslands on the Tibetan Plateau. We know little about direct and indirect effects of biotic and abiotic drivers on this relationship, especially in regard to plant functional trait diversity. Here, we examine how aboveground net primary productivity (ANPP) and precipitation use efficiency (PUE) respond to climate, soil and community structure across alpine grasslands on the Northern Tibetan Plateau. We found that both ANPP and PUE showed nonlinear patterns along water availability and site altitude variation, which together accounted for 80.3% and 68.8% of variation in ANPP and PUE, respectively, by optimal generalized additive models. Functional trait divergence (FTD) and community weighted mean (CWM) of plant functional traits were as important as plant species diversity (PSD) for explaining the nonlinear productivity-climate relationship. These findings were confirmed by results from principal component analyses and structural equation models. We also found that FTD was negatively correlated with PSD across different alpine grasslands. Our results implicate: first, the combinatorial influences of temperature and precipitation gradients are important for predicting alpine grassland dynamics; second, the convergence and divergence of plant functional traits may have the potential to elucidate the effect of plant diversity on ecosystem functionality. PMID:27759112

Cumulant generating function formula of heat transfer in ballistic systems with lead-lead coupling and general nonlinear systems

NASA Astrophysics Data System (ADS)

Li, Huanan

2013-03-01

Based on a two-time observation protocol, we consider heat transfer in a given time interval tM in a lead-junction-lead system taking coupling between the leads into account. In view of the two-time observation, consistency conditions are carefully verified in our specific family of quantum histories. Furthermore, its implication is briefly explored. Then using the nonequilibrium Green's function method, we obtain an exact formula for the cumulant generating function for heat transfer between the two leads, valid in both transient and steady-state regimes. Also, a compact formula for the cumulant generating function in the long-time limit is derived, for which the Gallavotti-Cohen fluctuation symmetry is explicitly verified. In addition, we briefly discuss Di Ventra's repartitioning trick regarding whether the repartitioning procedure of the total Hamiltonian affects the nonequilibrium steady-state current fluctuation. All kinds of properties of nonequilibrium current fluctuations, such as the fluctuation theorem in different time regimes, could be readily given according to these exact formulas. Finally a practical formalism dealing with cumulants of heat transfer across general nonlinear quantum systems is established based on field theoretical/algebraic method.

A general decay result of a viscoelastic equation with past history and boundary feedback

NASA Astrophysics Data System (ADS)

Messaoudi, Salim A.; Al-Gharabli, Mohammad M.

2015-08-01

In this paper, we consider a viscoelastic equation with a nonlinear feedback localized on a part of the boundary and in the presence of infinite memory term. In the domain as well as on a part of the boundary, we use the multiplier method and some properties of the convex functions to prove an explicit and general decay result.

Improved modeling of turbulent forced convection heat transfer in straight ducts

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rokni, M.; Sunden, B.

1999-08-01

This investigation concerns numerical calculation of turbulent forced convective heat transfer and fluid flow in their fully developed state at low Reynolds number. The authors have developed a low Reynolds number version of the nonlinear {kappa}-{epsilon} model combined with the heat flux models of simple eddy diffusivity (SED), low Reynolds number version of generalized gradient diffusion hypothesis (GGDH), and wealth {proportional_to} earning {times} time (WET) in general three-dimensional geometries. The numerical approach is based on the finite volume technique with a nonstaggered grid arrangement and the SIMPLEC algorithm. Results have been obtained with the nonlinear {kappa}-{epsilon} model, combined with themore » Lam-Bremhorst and the Abe-Kondoh-Nagano damping functions for low Reynolds numbers.« less

Brain-Inspired Constructive Learning Algorithms with Evolutionally Additive Nonlinear Neurons

NASA Astrophysics Data System (ADS)

Fang, Le-Heng; Lin, Wei; Luo, Qiang

In this article, inspired partially by the physiological evidence of brain’s growth and development, we developed a new type of constructive learning algorithm with evolutionally additive nonlinear neurons. The new algorithms have remarkable ability in effective regression and accurate classification. In particular, the algorithms are able to sustain a certain reduction of the loss function when the dynamics of the trained network are bogged down in the vicinity of the local minima. The algorithm augments the neural network by adding only a few connections as well as neurons whose activation functions are nonlinear, nonmonotonic, and self-adapted to the dynamics of the loss functions. Indeed, we analytically demonstrate the reduction dynamics of the algorithm for different problems, and further modify the algorithms so as to obtain an improved generalization capability for the augmented neural networks. Finally, through comparing with the classical algorithm and architecture for neural network construction, we show that our constructive learning algorithms as well as their modified versions have better performances, such as faster training speed and smaller network size, on several representative benchmark datasets including the MNIST dataset for handwriting digits.

Pseudo almost periodic solutions to some systems of nonlinear hyperbolic second-order partial differential equations

NASA Astrophysics Data System (ADS)

Al-Islam, Najja Shakir

In this Dissertation, the existence of pseudo almost periodic solutions to some systems of nonlinear hyperbolic second-order partial differential equations is established. For that, (Al-Islam [4]) is first studied and then obtained under some suitable assumptions. That is, the existence of pseudo almost periodic solutions to a hyperbolic second-order partial differential equation with delay. The second-order partial differential equation (1) represents a mathematical model for the dynamics of gas absorption, given by uxt+a x,tux=Cx,t,u x,t , u0,t=4 t, 1 where a : [0, L] x RR , C : [0, L] x R x RR , and ϕ : RR are (jointly) continuous functions ( t being the greatest integer function) and L > 0. The results in this Dissertation generalize those of Poorkarimi and Wiener [22]. Secondly, a generalization of the above-mentioned system consisting of the non-linear hyperbolic second-order partial differential equation uxt+a x,tux+bx,t ut+cx,tu=f x,t,u, x∈ 0,L,t∈ R, 2 equipped with the boundary conditions ux,0 =40x, u0,t=u 0t, uxx,0=y 0x, x∈0,L, t∈R, 3 where a, b, c : [0, L ] x RR and f : [0, L] x R x RR are (jointly) continuous functions is studied. Under some suitable assumptions, the existence and uniqueness of pseudo almost periodic solutions to particular cases, as well as the general case of the second-order hyperbolic partial differential equation (2) are studied. The results of all studies contained within this text extend those obtained by Aziz and Meyers [6] in the periodic setting.

On the formulation of the aerodynamic characteristics in aircraft dynamics

NASA Technical Reports Server (NTRS)

Tobak, M.; Schiff, L. B.

1976-01-01

The theory of functionals is used to reformulate the notions of aerodynamic indicial functions and superposition. Integral forms for the aerodynamic response to arbitrary motions are derived that are free of dependence on a linearity assumption. Simplifications of the integral forms lead to practicable nonlinear generalizations of the linear superpositions and stability derivative formulations. Applied to arbitrary nonplanar motions, the generalization yields a form for the aerodynamic response that can be compounded of the contributions from a limited number of well-defined characteristic motions, in principle reproducible in the wind tunnel. Further generalizations that would enable the consideration of random fluctuations and multivalued aerodynamic responses are indicated.

Nonlinear and non-Hermitian optical systems applied to the development of filters and optical sensors

NASA Astrophysics Data System (ADS)

Amaro de Faria Júnior, A. C.

2015-09-01

In this work we present a method of investigation of nonlinear optical beams generated from non-Hermitian optical systems1 . This method can be applied in the development of optical filters and optical sensors to process, analyze and choose the passband of the propagation modes of an optical pulse from an non-Hermitian optical system. Non-Hermitian optical systems can be used to develop optical fiber sensors that suppress certain propagation modes of optical pulses that eventually behave as quantum noise. Such systems are described by the Nonlinear Schrödinger-like Equation with Parity-Time (PT) Symmetric Optical Potentials. There are optical fiber sensors that due to high laser intensity and frequency can produce quantum noise, such as Raman and Brillouin scattering. However, the optical fiber, for example, can be designed so that its geometry suppress certain propagation modes of the beam. We apply some results of non- Hermitian optical systems with PT symmetry to simulate optical lattice by a appropriate potential function, which among other applications, can naturally suppress certain propagation modes of an optical beam propagating through a waveguide. In other words, the optical system is modeled by a potential function in the Nonlinear Schrödinger-like Equation that one relates with the geometric aspects of the wave guides and with the optical beam interacting with the waveguide material. The paper is organized as follows: sections 1 and 2 present a brief description about nonlinear optical systems and non-Hermitian optical systems with PT symmetry. Section 3 presents a description of the dynamics of nonlinear optical pulses propagating through optical networks described by a optical potential non-Hermitian. Sections 4 and 5 present a general description of this non-Hermitian optical systems and how to get them from a more general model. Section 6 presents some conclusions and comment and the final section presents the references. Begin the abstract two lines below author names and addresses.

Analytic study of solutions for a (3 + 1) -dimensional generalized KP equation

NASA Astrophysics Data System (ADS)

Gao, Hui; Cheng, Wenguang; Xu, Tianzhou; Wang, Gangwei

2018-03-01

The (3 + 1) -dimensional generalized KP (gKP) equation is an important nonlinear partial differential equation in theoretical and mathematical physics which can be used to describe nonlinear wave motion. Through the Hirota bilinear method, one-solition, two-solition and N-solition solutions are derived via symbolic computation. Two classes of lump solutions, rationally localized in all directions in space, to the dimensionally reduced cases in (2 + 1)-dimensions, are constructed by using a direct method based on the Hirota bilinear form of the equation. It implies that we can derive the lump solutions of the reduced gKP equation from positive quadratic function solutions to the aforementioned bilinear equation. Meanwhile, we get interaction solutions between a lump and a kink of the gKP equation. The lump appears from a kink and is swallowed by it with the change of time. This work offers a possibility which can enrich the variety of the dynamical features of solutions for higher-dimensional nonlinear evolution equations.

Design of asymptotic estimators: an approach based on neural networks and nonlinear programming.

PubMed

Alessandri, Angelo; Cervellera, Cristiano; Sanguineti, Marcello

2007-01-01

A methodology to design state estimators for a class of nonlinear continuous-time dynamic systems that is based on neural networks and nonlinear programming is proposed. The estimator has the structure of a Luenberger observer with a linear gain and a parameterized (in general, nonlinear) function, whose argument is an innovation term representing the difference between the current measurement and its prediction. The problem of the estimator design consists in finding the values of the gain and of the parameters that guarantee the asymptotic stability of the estimation error. Toward this end, if a neural network is used to take on this function, the parameters (i.e., the neural weights) are chosen, together with the gain, by constraining the derivative of a quadratic Lyapunov function for the estimation error to be negative definite on a given compact set. It is proved that it is sufficient to impose the negative definiteness of such a derivative only on a suitably dense grid of sampling points. The gain is determined by solving a Lyapunov equation. The neural weights are searched for via nonlinear programming by minimizing a cost penalizing grid-point constraints that are not satisfied. Techniques based on low-discrepancy sequences are applied to deal with a small number of sampling points, and, hence, to reduce the computational burden required to optimize the parameters. Numerical results are reported and comparisons with those obtained by the extended Kalman filter are made.

Composite Beam Theory with Material Nonlinearities and Progressive Damage

NASA Astrophysics Data System (ADS)

Jiang, Fang

Beam has historically found its broad applications. Nowadays, many engineering constructions still rely on this type of structure which could be made of anisotropic and heterogeneous materials. These applications motivate the development of beam theory in which the impact of material nonlinearities and damage on the global constitutive behavior has been a focus in recent years. Reliable predictions of these nonlinear beam responses depend on not only the quality of the material description but also a comprehensively generalized multiscale methodology which fills the theoretical gaps between the scales in an efficient yet high-fidelity manner. The conventional beam modeling methodologies which are built upon ad hoc assumptions are in lack of such reliability in need. Therefore, the focus of this dissertation is to create a reliable yet efficient method and the corresponding tool for composite beam modeling. A nonlinear beam theory is developed based on the Mechanics of Structure Genome (MSG) using the variational asymptotic method (VAM). The three-dimensional (3D) nonlinear continuum problem is rigorously reduced to a one-dimensional (1D) beam model and a two-dimensional (2D) cross-sectional analysis featuring both geometric and material nonlinearities by exploiting the small geometric parameter which is an inherent geometric characteristic of the beam. The 2D nonlinear cross-sectional analysis utilizes the 3D material models to homogenize the beam cross-sectional constitutive responses considering the nonlinear elasticity and progressive damage. The results from such a homogenization are inputs as constitutive laws into the global nonlinear 1D beam analysis. The theoretical foundation is formulated without unnecessary kinematic assumptions. Curvilinear coordinates and vector calculus are utilized to build the 3D deformation gradient tensor, of which the components are formulated in terms of cross-sectional coordinates, generalized beam strains, unknown warping functions, and the 3D spatial gradients of these warping functions. Asymptotic analysis of the extended Hamiltonian's principle suggests dropping the terms of axial gradients of the warping functions. As a result, the solid mechanics problem resolved into a 3D continuum is dimensionally reduced to a problem of solving the warping functions on a 2D cross-sectional field by minimizing the information loss. The present theory is implemented using the finite element method (FEM) in Variational Asymptotic Beam Sectional Analysis (VABS), a general-purpose cross-sectional analysis tool. An iterative method is applied to solve the finite warping field for the classical-type model in the form of the Euler-Bernoulli beam theory. The deformation gradient tensor is directly used to enable the capability of dealing with finite deformation, various strain definitions, and several types of material constitutive laws regarding the nonlinear elasticity and progressive damage. Analytical and numerical examples are given for various problems including the trapeze effect, Poynting effect, Brazier effect, extension-bending coupling effect, and free edge damage. By comparison with the predictions from 3D finite element analyses (FEA), 2D FEA based on plane stress assumptions, and experimental data, the structural and material responses are proven to be rigorously captured by the present theory and the computational cost is significantly reduced. Due to the semi-analytical feature of the code developed, the unrealistic numerical issues widely seen in the conventional FEA with strain softening material behaviors are prevented by VABS. In light of these intrinsic features, the nonlinear elastic and inelastic 3D material models can be economically calibrated by data-matching the VABS predictions directly with the experimental measurements from slender coupons. Furthermore, the global behavior of slender composite structures in meters can also be effectively characterized by VABS without unnecessary loss of important information of its local laminae in micrometers.

A Comparison of Two-Stage Approaches for Fitting Nonlinear Ordinary Differential Equation (ODE) Models with Mixed Effects

PubMed Central

Chow, Sy-Miin; Bendezú, Jason J.; Cole, Pamela M.; Ram, Nilam

2016-01-01

Several approaches currently exist for estimating the derivatives of observed data for model exploration purposes, including functional data analysis (FDA), generalized local linear approximation (GLLA), and generalized orthogonal local derivative approximation (GOLD). These derivative estimation procedures can be used in a two-stage process to fit mixed effects ordinary differential equation (ODE) models. While the performance and utility of these routines for estimating linear ODEs have been established, they have not yet been evaluated in the context of nonlinear ODEs with mixed effects. We compared properties of the GLLA and GOLD to an FDA-based two-stage approach denoted herein as functional ordinary differential equation with mixed effects (FODEmixed) in a Monte Carlo study using a nonlinear coupled oscillators model with mixed effects. Simulation results showed that overall, the FODEmixed outperformed both the GLLA and GOLD across all the embedding dimensions considered, but a novel use of a fourth-order GLLA approach combined with very high embedding dimensions yielded estimation results that almost paralleled those from the FODEmixed. We discuss the strengths and limitations of each approach and demonstrate how output from each stage of FODEmixed may be used to inform empirical modeling of young children’s self-regulation. PMID:27391255

A Comparison of Two-Stage Approaches for Fitting Nonlinear Ordinary Differential Equation Models with Mixed Effects.

PubMed

Chow, Sy-Miin; Bendezú, Jason J; Cole, Pamela M; Ram, Nilam

2016-01-01

Several approaches exist for estimating the derivatives of observed data for model exploration purposes, including functional data analysis (FDA; Ramsay & Silverman, 2005 ), generalized local linear approximation (GLLA; Boker, Deboeck, Edler, & Peel, 2010 ), and generalized orthogonal local derivative approximation (GOLD; Deboeck, 2010 ). These derivative estimation procedures can be used in a two-stage process to fit mixed effects ordinary differential equation (ODE) models. While the performance and utility of these routines for estimating linear ODEs have been established, they have not yet been evaluated in the context of nonlinear ODEs with mixed effects. We compared properties of the GLLA and GOLD to an FDA-based two-stage approach denoted herein as functional ordinary differential equation with mixed effects (FODEmixed) in a Monte Carlo (MC) study using a nonlinear coupled oscillators model with mixed effects. Simulation results showed that overall, the FODEmixed outperformed both the GLLA and GOLD across all the embedding dimensions considered, but a novel use of a fourth-order GLLA approach combined with very high embedding dimensions yielded estimation results that almost paralleled those from the FODEmixed. We discuss the strengths and limitations of each approach and demonstrate how output from each stage of FODEmixed may be used to inform empirical modeling of young children's self-regulation.

Enhanced Third-Order Optical Nonlinearity Driven by Surface-Plasmon Field Gradients.

PubMed

Kravtsov, Vasily; AlMutairi, Sultan; Ulbricht, Ronald; Kutayiah, A Ryan; Belyanin, Alexey; Raschke, Markus B

2018-05-18

Efficient nonlinear optical frequency mixing in small volumes is key for future on-chip photonic devices. However, the generally low conversion efficiency severely limits miniaturization to nanoscale dimensions. Here we demonstrate that gradient-field effects can provide for an efficient, conventionally dipole-forbidden nonlinear response. We show that a longitudinal nonlinear source current can dominate the third-order optical nonlinearity of the free electron response in gold in the technologically important near-IR frequency range where the nonlinearities due to other mechanisms are particularly small. Using adiabatic nanofocusing to spatially confine the excitation fields, from measurements of the 2ω_{1}-ω_{2} four-wave mixing response as a function of detuning ω_{1}-ω_{2}, we find up to 10^{-5} conversion efficiency with a gradient-field contribution to χ_{Au}^{(3)} of up to 10^{-19}  m^{2}/V^{2}. The results are in good agreement with the theory based on plasma hydrodynamics and underlying electron dynamics. The associated increase in the nonlinear conversion efficiency with a decreasing sample size, which can even overcompensate the volume decrease, offers a new approach for enhanced nonlinear nano-optics. This will enable more efficient nonlinear optical devices and the extension of coherent multidimensional spectroscopies to the nanoscale.

Enhanced Third-Order Optical Nonlinearity Driven by Surface-Plasmon Field Gradients

NASA Astrophysics Data System (ADS)

Kravtsov, Vasily; AlMutairi, Sultan; Ulbricht, Ronald; Kutayiah, A. Ryan; Belyanin, Alexey; Raschke, Markus B.

2018-05-01

Efficient nonlinear optical frequency mixing in small volumes is key for future on-chip photonic devices. However, the generally low conversion efficiency severely limits miniaturization to nanoscale dimensions. Here we demonstrate that gradient-field effects can provide for an efficient, conventionally dipole-forbidden nonlinear response. We show that a longitudinal nonlinear source current can dominate the third-order optical nonlinearity of the free electron response in gold in the technologically important near-IR frequency range where the nonlinearities due to other mechanisms are particularly small. Using adiabatic nanofocusing to spatially confine the excitation fields, from measurements of the 2 ω1-ω2 four-wave mixing response as a function of detuning ω1-ω2, we find up to 10-5 conversion efficiency with a gradient-field contribution to χAu(3 ) of up to 10-19 m2/V2 . The results are in good agreement with the theory based on plasma hydrodynamics and underlying electron dynamics. The associated increase in the nonlinear conversion efficiency with a decreasing sample size, which can even overcompensate the volume decrease, offers a new approach for enhanced nonlinear nano-optics. This will enable more efficient nonlinear optical devices and the extension of coherent multidimensional spectroscopies to the nanoscale.

A non-symmetric Yang-Baxter algebra for the quantum nonlinear Schrödinger model

NASA Astrophysics Data System (ADS)

Vlaar, Bart

2013-06-01

We study certain non-symmetric wavefunctions associated with the quantum nonlinear Schrödinger model, introduced by Komori and Hikami using Gutkin’s propagation operator, which involves representations of the degenerate affine Hecke algebra. We highlight how these functions can be generated using a vertex-type operator formalism similar to the recursion defining the symmetric (Bethe) wavefunction in the quantum inverse scattering method. Furthermore, some of the commutation relations encoded in the Yang-Baxter equation for the relevant monodromy matrix are generalized to the non-symmetric case.

General relativity as the effective theory of GL(4,R) spontaneous symmetry breaking

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tomboulis, E. T.

2011-10-15

We assume a GL(4,R) space-time symmetry which is spontaneously broken to SO(3,1). We carry out the coset construction of the effective theory for the nonlinearly realized broken symmetry in terms of the Goldstone fields and matter fields transforming linearly under the unbroken Lorentz subgroup. We then identify functions of the Goldstone and matter fields that transform linearly also under the broken symmetry. Expressed in terms of these quantities the effective theory reproduces the vierbein formalism of general relativity with general coordinate invariance being automatically realized nonlinearly over GL(4,R). The coset construction makes no assumptions about any underlying theory that mightmore » be responsible for the assumed symmetry breaking. We give a brief discussion of the possibility of field theories with GL(4,R) rather than Lorentz space-time symmetry providing the underlying dynamics.« less

A phenomenological approach to modeling chemical dynamics in nonlinear and two-dimensional spectroscopy.

PubMed

Ramasesha, Krupa; De Marco, Luigi; Horning, Andrew D; Mandal, Aritra; Tokmakoff, Andrei

2012-04-07

We present an approach for calculating nonlinear spectroscopic observables, which overcomes the approximations inherent to current phenomenological models without requiring the computational cost of performing molecular dynamics simulations. The trajectory mapping method uses the semi-classical approximation to linear and nonlinear response functions, and calculates spectra from trajectories of the system's transition frequencies and transition dipole moments. It rests on identifying dynamical variables important to the problem, treating the dynamics of these variables stochastically, and then generating correlated trajectories of spectroscopic quantities by mapping from the dynamical variables. This approach allows one to describe non-Gaussian dynamics, correlated dynamics between variables of the system, and nonlinear relationships between spectroscopic variables of the system and the bath such as non-Condon effects. We illustrate the approach by applying it to three examples that are often not adequately treated by existing analytical models--the non-Condon effect in the nonlinear infrared spectra of water, non-Gaussian dynamics inherent to strongly hydrogen bonded systems, and chemical exchange processes in barrier crossing reactions. The methods described are generally applicable to nonlinear spectroscopy throughout the optical, infrared and terahertz regions.

Nonlinear Dust Acoustic Waves in a Magnetized Dusty Plasma with Trapped and Superthermal Electrons

NASA Astrophysics Data System (ADS)

Ahmadi, Abrishami S.; Nouri, Kadijani M.

2014-06-01

In this work, the effects of superthermal and trapped electrons on the oblique propagation of nonlinear dust-acoustic waves in a magnetized dusty (complex) plasma are investigated. The dynamic of electrons is simulated by the generalized Lorentzian (κ) distribution function (DF). The dust grains are cold and their dynamics are simulated by hydrodynamic equations. Using the standard reductive perturbation technique (RPT) a nonlinear modified Korteweg-de Vries (mKdV) equation is derived. Two types of solitary waves; fast and slow dust acoustic solitons, exist in this plasma. Calculations reveal that compressive solitary structures are likely to propagate in this plasma where dust grains are negatively (or positively) charged. The properties of dust acoustic solitons (DASs) are also investigated numerically.

Rational solitons in deep nonlinear optical Bragg grating.

PubMed

Alatas, H; Iskandar, A A; Tjia, M O; Valkering, T P

2006-06-01

We have examined the rational solitons in the Generalized Coupled Mode model for a deep nonlinear Bragg grating. These solitons are the degenerate forms of the ordinary solitons and appear at the transition lines in the parameter plane. A simple formulation is presented for the investigation of the bifurcations induced by detuning the carrier wave frequency. The analysis yields among others the appearance of in-gap dark and antidark rational solitons unknown in the nonlinear shallow grating. The exact expressions for the corresponding rational solitons are also derived in the process, which are characterized by rational algebraic functions. It is further demonstrated that certain effects in the soliton energy variations are to be expected when the frequency is varied across the values where the rational solitons appear.

Complexiton and solitary wave solutions of the coupled nonlinear Maccari’s system using two integration schemes

NASA Astrophysics Data System (ADS)

Inc, Mustafa; Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru; Nuray, Elif

2018-01-01

In this paper, we consider a coupled nonlinear Maccari’s system (CNMS) which describes the motion of isolated waves localized in a small part of space. There are some integration tools that are adopted to retrieve the solitary wave solutions. They are the modified F-Expansion and the generalized projective Riccati equation methods. Topological, non-topological, complexiton, singular and trigonometric function solutions are derived. A comparison between the results in this paper and the well-known results in the literature is also given. The derived structures of the obtained solutions offer a rich platform to study the nonlinear CNMS. Numerical simulation of the obtained solutions are presented with interesting figures showing the physical meaning of the solutions.

Rogue periodic waves of the focusing nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Chen, Jinbing; Pelinovsky, Dmitry E.

2018-02-01

Rogue periodic waves stand for rogue waves on a periodic background. The nonlinear Schrödinger equation in the focusing case admits two families of periodic wave solutions expressed by the Jacobian elliptic functions dn and cn. Both periodic waves are modulationally unstable with respect to long-wave perturbations. Exact solutions for the rogue periodic waves are constructed by using the explicit expressions for the periodic eigenfunctions of the Zakharov-Shabat spectral problem and the Darboux transformations. These exact solutions generalize the classical rogue wave (the so-called Peregrine's breather). The magnification factor of the rogue periodic waves is computed as a function of the elliptic modulus. Rogue periodic waves constructed here are compared with the rogue wave patterns obtained numerically in recent publications.

Rogue periodic waves of the focusing nonlinear Schrödinger equation.

PubMed

Chen, Jinbing; Pelinovsky, Dmitry E

2018-02-01

Rogue periodic waves stand for rogue waves on a periodic background. The nonlinear Schrödinger equation in the focusing case admits two families of periodic wave solutions expressed by the Jacobian elliptic functions dn and cn . Both periodic waves are modulationally unstable with respect to long-wave perturbations. Exact solutions for the rogue periodic waves are constructed by using the explicit expressions for the periodic eigenfunctions of the Zakharov-Shabat spectral problem and the Darboux transformations. These exact solutions generalize the classical rogue wave (the so-called Peregrine's breather). The magnification factor of the rogue periodic waves is computed as a function of the elliptic modulus. Rogue periodic waves constructed here are compared with the rogue wave patterns obtained numerically in recent publications.

Adaptive variable structure hierarchical fuzzy control for a class of high-order nonlinear dynamic systems.

PubMed

Mansouri, Mohammad; Teshnehlab, Mohammad; Aliyari Shoorehdeli, Mahdi

2015-05-01

In this paper, a novel adaptive hierarchical fuzzy control system based on the variable structure control is developed for a class of SISO canonical nonlinear systems in the presence of bounded disturbances. It is assumed that nonlinear functions of the systems be completely unknown. Switching surfaces are incorporated into the hierarchical fuzzy control scheme to ensure the system stability. A fuzzy soft switching system decides the operation area of the hierarchical fuzzy control and variable structure control systems. All the nonlinearly appeared parameters of conclusion parts of fuzzy blocks located in different layers of the hierarchical fuzzy control system are adjusted through adaptation laws deduced from the defined Lyapunov function. The proposed hierarchical fuzzy control system reduces the number of rules and consequently the number of tunable parameters with respect to the ordinary fuzzy control system. Global boundedness of the overall adaptive system and the desired precision are achieved using the proposed adaptive control system. In this study, an adaptive hierarchical fuzzy system is used for two objectives; it can be as a function approximator or a control system based on an intelligent-classic approach. Three theorems are proven to investigate the stability of the nonlinear dynamic systems. The important point about the proposed theorems is that they can be applied not only to hierarchical fuzzy controllers with different structures of hierarchical fuzzy controller, but also to ordinary fuzzy controllers. Therefore, the proposed algorithm is more general. To show the effectiveness of the proposed method four systems (two mechanical, one mathematical and one chaotic) are considered in simulations. Simulation results demonstrate the validity, efficiency and feasibility of the proposed approach to control of nonlinear dynamic systems. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Fitting aerodynamic forces in the Laplace domain: An application of a nonlinear nongradient technique to multilevel constrained optimization

NASA Technical Reports Server (NTRS)

Tiffany, S. H.; Adams, W. M., Jr.

1984-01-01

A technique which employs both linear and nonlinear methods in a multilevel optimization structure to best approximate generalized unsteady aerodynamic forces for arbitrary motion is described. Optimum selection of free parameters is made in a rational function approximation of the aerodynamic forces in the Laplace domain such that a best fit is obtained, in a least squares sense, to tabular data for purely oscillatory motion. The multilevel structure and the corresponding formulation of the objective models are presented which separate the reduction of the fit error into linear and nonlinear problems, thus enabling the use of linear methods where practical. Certain equality and inequality constraints that may be imposed are identified; a brief description of the nongradient, nonlinear optimizer which is used is given; and results which illustrate application of the method are presented.

Enhanced nonlinear interactions in quantum optomechanics via mechanical amplification

PubMed Central

Lemonde, Marc-Antoine; Didier, Nicolas; Clerk, Aashish A.

2016-01-01

The quantum nonlinear regime of optomechanics is reached when nonlinear effects of the radiation pressure interaction are observed at the single-photon level. This requires couplings larger than the mechanical frequency and cavity-damping rate, and is difficult to achieve experimentally. Here we show how to exponentially enhance the single-photon optomechanical coupling strength using only additional linear resources. Our method is based on using a large-amplitude, strongly detuned mechanical parametric drive to amplify mechanical zero-point fluctuations and hence enhance the radiation pressure interaction. It has the further benefit of allowing time-dependent control, enabling pulsed schemes. For a two-cavity optomechanical set-up, we show that our scheme generates photon blockade for experimentally accessible parameters, and even makes the production of photonic states with negative Wigner functions possible. We discuss how our method is an example of a more general strategy for enhancing boson-mediated two-particle interactions and nonlinearities. PMID:27108814

Extrinsic Contribution and Instability Properties in Lead-Based and Lead-Free Piezoceramics

PubMed Central

García, José Eduardo

2015-01-01

Piezoceramic materials generally exhibit a notable instability of their functional properties when they work under real external conditions. This undesirable effect, known as nonlinear behavior, is mostly associated with the extrinsic contribution to material response. In this article, the role of the ferroelectric domain walls’ motion in the nonlinear response in the most workable lead-based and lead-free piezoceramics is reviewed. Initially, the extrinsic origin of the nonlinear response is discussed in terms of the temperature dependence of material response. The influence of the crystallographic phase and of the phase boundaries on the material response are then reviewed. Subsequently, the impact of the defects created by doping in order to control the extrinsic contribution is discussed as a way of tuning material properties. Finally, some aspects related to the grain-size effect on the nonlinear response of piezoceramics are surveyed. PMID:28793681

Thermal conductance of suspended nanoribbons: interplay between strain and interatomic potential nonlinearity

NASA Astrophysics Data System (ADS)

Barreto, Roberto; Florencia Carusela, M.; Monastra, Alejandro G.

2017-10-01

We investigate the role that nonlinearity in the interatomic potential has on the thermal conductance of a suspended nanoribbon when it is subjected to a longitudinal strain. To focus on the first cubic and quartic nonlinear terms of a general potential, we propose an atomic system based on an α-β Fermi-Pasta-Ulam nearest neighbor interaction. We perform classical molecular dynamics simulations to investigate the contribution of longitudinal, transversal and flexural modes to the thermal conductance as a function of the α-β parameters and the applied strain. We compare the cases where atoms are allowed to vibrate only in plane (2D) with the case of vibrations in and out of plane (3D). We find that the dependence of conductance on α and β relies on a crossover phenomenon between linear/nonlinear delocalized/localized flexural and transversal modes, driven by an on/off switch of the strain.

Effect of initial strain and material nonlinearity on the nonlinear static and dynamic response of graphene sheets

NASA Astrophysics Data System (ADS)

Singh, Sandeep; Patel, B. P.

2018-06-01

Computationally efficient multiscale modelling based on Cauchy-Born rule in conjunction with finite element method is employed to study static and dynamic characteristics of graphene sheets, with/without considering initial strain, involving Green-Lagrange geometric and material nonlinearities. The strain energy density function at continuum level is established by coupling the deformation at continuum level to that at atomic level through Cauchy-Born rule. The atomic interactions between carbon atoms are modelled through Tersoff-Brenner potential. The governing equation of motion obtained using Hamilton's principle is solved through standard Newton-Raphson method for nonlinear static response and Newmark's time integration technique to obtain nonlinear transient response characteristics. Effect of initial strain on the linear free vibration frequencies, nonlinear static and dynamic response characteristics is investigated in detail. The present multiscale modelling based results are found to be in good agreement with those obtained through molecular mechanics simulation. Two different types of boundary constraints generally used in MM simulation are explored in detail and few interesting findings are brought out. The effect of initial strain is found to be greater in linear response when compared to that in nonlinear response.

Electron Interactions with Non-Linear Polyatomic Molecules and Their Radicals

DTIC Science & Technology

1993-12-01

developed which generates SCE quantities from molecular wave functions. This progress was realized in terms of some actual calculations on some molecules...section 4.A describes the basics of the Partial Differential Equation Theory; section 4.B describes the generalization to a finite element...Information Service (NTIS). At NTIS, it will be available to the general public, including foreign nations. This technical report has been reviewed and

Convolutionless Nakajima-Zwanzig equations for stochastic analysis in nonlinear dynamical systems.

PubMed

Venturi, D; Karniadakis, G E

2014-06-08

Determining the statistical properties of stochastic nonlinear systems is of major interest across many disciplines. Currently, there are no general efficient methods to deal with this challenging problem that involves high dimensionality, low regularity and random frequencies. We propose a framework for stochastic analysis in nonlinear dynamical systems based on goal-oriented probability density function (PDF) methods. The key idea stems from techniques of irreversible statistical mechanics, and it relies on deriving evolution equations for the PDF of quantities of interest, e.g. functionals of the solution to systems of stochastic ordinary and partial differential equations. Such quantities could be low-dimensional objects in infinite dimensional phase spaces. We develop the goal-oriented PDF method in the context of the time-convolutionless Nakajima-Zwanzig-Mori formalism. We address the question of approximation of reduced-order density equations by multi-level coarse graining, perturbation series and operator cumulant resummation. Numerical examples are presented for stochastic resonance and stochastic advection-reaction problems.

Convolutionless Nakajima–Zwanzig equations for stochastic analysis in nonlinear dynamical systems

PubMed Central

Venturi, D.; Karniadakis, G. E.

2014-01-01

Determining the statistical properties of stochastic nonlinear systems is of major interest across many disciplines. Currently, there are no general efficient methods to deal with this challenging problem that involves high dimensionality, low regularity and random frequencies. We propose a framework for stochastic analysis in nonlinear dynamical systems based on goal-oriented probability density function (PDF) methods. The key idea stems from techniques of irreversible statistical mechanics, and it relies on deriving evolution equations for the PDF of quantities of interest, e.g. functionals of the solution to systems of stochastic ordinary and partial differential equations. Such quantities could be low-dimensional objects in infinite dimensional phase spaces. We develop the goal-oriented PDF method in the context of the time-convolutionless Nakajima–Zwanzig–Mori formalism. We address the question of approximation of reduced-order density equations by multi-level coarse graining, perturbation series and operator cumulant resummation. Numerical examples are presented for stochastic resonance and stochastic advection–reaction problems. PMID:24910519

Stable sequential Kuhn-Tucker theorem in iterative form or a regularized Uzawa algorithm in a regular nonlinear programming problem

NASA Astrophysics Data System (ADS)

Sumin, M. I.

2015-06-01

A parametric nonlinear programming problem in a metric space with an operator equality constraint in a Hilbert space is studied assuming that its lower semicontinuous value function at a chosen individual parameter value has certain subdifferentiability properties in the sense of nonlinear (nonsmooth) analysis. Such subdifferentiability can be understood as the existence of a proximal subgradient or a Fréchet subdifferential. In other words, an individual problem has a corresponding generalized Kuhn-Tucker vector. Under this assumption, a stable sequential Kuhn-Tucker theorem in nondifferential iterative form is proved and discussed in terms of minimizing sequences on the basis of the dual regularization method. This theorem provides necessary and sufficient conditions for the stable construction of a minimizing approximate solution in the sense of Warga in the considered problem, whose initial data can be approximately specified. A substantial difference of the proved theorem from its classical same-named analogue is that the former takes into account the possible instability of the problem in the case of perturbed initial data and, as a consequence, allows for the inherited instability of classical optimality conditions. This theorem can be treated as a regularized generalization of the classical Uzawa algorithm to nonlinear programming problems. Finally, the theorem is applied to the "simplest" nonlinear optimal control problem, namely, to a time-optimal control problem.

Designing Agent Collectives For Systems With Markovian Dynamics

NASA Technical Reports Server (NTRS)

Wolpert, David H.; Lawson, John W.

2004-01-01

The Collective Intelligence (COIN) framework concerns the design of collectives of agents so that as those agents strive to maximize their individual utility functions, their interaction causes a provided world utility function concerning the entire collective to be also maximized. Here we show how to extend that framework to scenarios having Markovian dynamics when no re-evolution of the system from counter-factual initial conditions (an often expensive calculation) is permitted. Our approach transforms the (time-extended) argument of each agent's utility function before evaluating that function. This transformation has benefits in scenarios not involving Markovian dynamics of an agent's utility function are observable. We investigate this transformation in simulations involving both hear and quadratic (nonlinear) dynamics. In addition, we find that a certain subset of these transformations, which result in utilities that have low opacity (analogous to having high signal to noise) but are not factored (analogous to not being incentive compatible), reliably improve performance over that arising with factored utilities. We also present a Taylor Series method for the fully general nonlinear case.

Multipoint propagators in cosmological gravitational instability

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bernardeau, Francis; Crocce, Martin; Scoccimarro, Roman

2008-11-15

We introduce the concept of multipoint propagators between linear cosmic fields and their nonlinear counterparts in the context of cosmological perturbation theory. Such functions express how a nonlinearly evolved Fourier mode depends on the full ensemble of modes in the initial density field. We identify and resum the dominant diagrams in the large-k limit, showing explicitly that multipoint propagators decay into the nonlinear regime at the same rate as the two-point propagator. These analytic results generalize the large-k limit behavior of the two-point propagator to arbitrary order. We measure the three-point propagator as a function of triangle shape in numericalmore » simulations and confirm the results of our high-k resummation. We show that any n-point spectrum can be reconstructed from multipoint propagators, which leads to a physical connection between nonlinear corrections to the power spectrum at small scales and higher-order correlations at large scales. As a first application of these results, we calculate the reduced bispectrum at one loop in renormalized perturbation theory and show that we can predict the decrease in its dependence on triangle shape at redshift zero, when standard perturbation theory is least successful.« less

Nonlinear transient analysis by energy minimization: A theoretical basis for the ACTION computer code. [predicting the response of a lightweight aircraft during a crash

NASA Technical Reports Server (NTRS)

Kamat, M. P.

1980-01-01

The formulation basis for establishing the static or dynamic equilibrium configurations of finite element models of structures which may behave in the nonlinear range are provided. With both geometric and time independent material nonlinearities included, the development is restricted to simple one and two dimensional finite elements which are regarded as being the basic elements for modeling full aircraft-like structures under crash conditions. Representations of a rigid link and an impenetrable contact plane are added to the deformation model so that any number of nodes of the finite element model may be connected by a rigid link or may contact the plane. Equilibrium configurations are derived as the stationary conditions of a potential function of the generalized nodal variables of the model. Minimization of the nonlinear potential function is achieved by using the best current variable metric update formula for use in unconstrained minimization. Powell's conjugate gradient algorithm, which offers very low storage requirements at some slight increase in the total number of calculations, is the other alternative algorithm to be used for extremely large scale problems.

The Swift-Hohenberg equation with a nonlocal nonlinearity

NASA Astrophysics Data System (ADS)

Morgan, David; Dawes, Jonathan H. P.

2014-03-01

It is well known that aspects of the formation of localised states in a one-dimensional Swift-Hohenberg equation can be described by Ginzburg-Landau-type envelope equations. This paper extends these multiple scales analyses to cases where an additional nonlinear integral term, in the form of a convolution, is present. The presence of a kernel function introduces a new lengthscale into the problem, and this results in additional complexity in both the derivation of envelope equations and in the bifurcation structure. When the kernel is short-range, weakly nonlinear analysis results in envelope equations of standard type but whose coefficients are modified in complicated ways by the nonlinear nonlocal term. Nevertheless, these computations can be formulated quite generally in terms of properties of the Fourier transform of the kernel function. When the lengthscale associated with the kernel is longer, our method leads naturally to the derivation of two different, novel, envelope equations that describe aspects of the dynamics in these new regimes. The first of these contains additional bifurcations, and unexpected loops in the bifurcation diagram. The second of these captures the stretched-out nature of the homoclinic snaking curves that arises due to the nonlocal term.

A generalization of the power law distribution with nonlinear exponent

NASA Astrophysics Data System (ADS)

Prieto, Faustino; Sarabia, José María

2017-01-01

The power law distribution is usually used to fit data in the upper tail of the distribution. However, commonly it is not valid to model data in all the range. In this paper, we present a new family of distributions, the so-called Generalized Power Law (GPL), which can be useful for modeling data in all the range and possess power law tails. To do that, we model the exponent of the power law using a non-linear function which depends on data and two parameters. Then, we provide some basic properties and some specific models of that new family of distributions. After that, we study a relevant model of the family, with special emphasis on the quantile and hazard functions, and the corresponding estimation and testing methods. Finally, as an empirical evidence, we study how the debt is distributed across municipalities in Spain. We check that power law model is only valid in the upper tail; we show analytically and graphically the competence of the new model with municipal debt data in the whole range; and we compare the new distribution with other well-known distributions including the Lognormal, the Generalized Pareto, the Fisk, the Burr type XII and the Dagum models.

Structure of multiphoton quantum optics. II. Bipartite systems, physical processes, and heterodyne squeezed states

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dell'Anno, Fabio; De Siena, Silvio; Illuminati, Fabrizio

2004-03-01

Extending the scheme developed for a single mode of the electromagnetic field in the preceding paper [F. Dell'Anno, S. De Siena, and F. Illuminati, Phys. Rev. A 69, 033812 (2004)], we introduce two-mode nonlinear canonical transformations depending on two heterodyne mixing angles. They are defined in terms of Hermitian nonlinear functions that realize heterodyne superpositions of conjugate quadratures of bipartite systems. The canonical transformations diagonalize a class of Hamiltonians describing nondegenerate and degenerate multiphoton processes. We determine the coherent states associated with the canonical transformations, which generalize the nondegenerate two-photon squeezed states. Such heterodyne multiphoton squeezed states are defined asmore » the simultaneous eigenstates of the transformed, coupled annihilation operators. They are generated by nonlinear unitary evolutions acting on two-mode squeezed states. They are non-Gaussian, highly nonclassical, entangled states. For a quadratic nonlinearity the heterodyne multiphoton squeezed states define two-mode cubic phase states. The statistical properties of these states can be widely adjusted by tuning the heterodyne mixing angles, the phases of the nonlinear couplings, as well as the strength of the nonlinearity. For quadratic nonlinearity, we study the higher-order contributions to the susceptibility in nonlinear media and we suggest possible experimental realizations of multiphoton conversion processes generating the cubic-phase heterodyne squeezed states.« less

Structure of multiphoton quantum optics. II. Bipartite systems, physical processes, and heterodyne squeezed states

NASA Astrophysics Data System (ADS)

dell'Anno, Fabio; de Siena, Silvio; Illuminati, Fabrizio

2004-03-01

Extending the scheme developed for a single mode of the electromagnetic field in the preceding paper [

Valuing the visual impact of wind farms: A calculus method for synthesizing choice experiments studies.

PubMed

Wen, Cheng; Dallimer, Martin; Carver, Steve; Ziv, Guy

2018-05-06

Despite the great potential of mitigating carbon emission, development of wind farms is often opposed by local communities due to the visual impact on landscape. A growing number of studies have applied nonmarket valuation methods like Choice Experiments (CE) to value the visual impact by eliciting respondents' willingness to pay (WTP) or willingness to accept (WTA) for hypothetical wind farms through survey questions. Several meta-analyses have been found in the literature to synthesize results from different valuation studies, but they have various limitations related to the use of the prevailing multivariate meta-regression analysis. In this paper, we propose a new meta-analysis method to establish general functions for the relationships between the estimated WTP or WTA and three wind farm attributes, namely the distance to residential/coastal areas, the number of turbines and turbine height. This method involves establishing WTA or WTP functions for individual studies, fitting the average derivative functions and deriving the general integral functions of WTP or WTA against wind farm attributes. Results indicate that respondents in different studies consistently showed increasing WTP for moving wind farms to greater distances, which can be fitted by non-linear (natural logarithm) functions. However, divergent preferences for the number of turbines and turbine height were found in different studies. We argue that the new analysis method proposed in this paper is an alternative to the mainstream multivariate meta-regression analysis for synthesizing CE studies and the general integral functions of WTP or WTA against wind farm attributes are useful for future spatial modelling and benefit transfer studies. We also suggest that future multivariate meta-analyses should include non-linear components in the regression functions. Copyright © 2018. Published by Elsevier B.V.

Variable-Metric Algorithm For Constrained Optimization

NASA Technical Reports Server (NTRS)

Frick, James D.

1989-01-01

Variable Metric Algorithm for Constrained Optimization (VMACO) is nonlinear computer program developed to calculate least value of function of n variables subject to general constraints, both equality and inequality. First set of constraints equality and remaining constraints inequalities. Program utilizes iterative method in seeking optimal solution. Written in ANSI Standard FORTRAN 77.

Geometrically nonlinear resonance of higher-order shear deformable functionally graded carbon-nanotube-reinforced composite annular sector plates excited by harmonic transverse loading

NASA Astrophysics Data System (ADS)

Gholami, Raheb; Ansari, Reza

2018-02-01

This article presents an attempt to study the nonlinear resonance of functionally graded carbon-nanotube-reinforced composite (FG-CNTRC) annular sector plates excited by a uniformly distributed harmonic transverse load. To this purpose, first, the extended rule of mixture including the efficiency parameters is employed to approximately obtain the effective material properties of FG-CNTRC annular sector plates. Then, the focus is on presenting the weak form of discretized mathematical formulation of governing equations based on the variational differential quadrature (VDQ) method and Hamilton's principle. The geometric nonlinearity and shear deformation effects are considered based on the von Kármán assumptions and Reddy's third-order shear deformation plate theory, respectively. The discretization process is performed via the generalized differential quadrature (GDQ) method together with numerical differential and integral operators. Then, an efficient multi-step numerical scheme is used to obtain the nonlinear dynamic behavior of the FG-CNTRC annular sector plates near their primary resonance as the frequency-response curve. The accuracy of the present results is first verified and then a parametric study is presented to show the impacts of CNT volume fraction, CNT distribution pattern, geometry of annular sector plate and sector angle on the nonlinear frequency-response curve of FG-CNTRC annular sector plates with different edge supports.

Skeletal muscle tensile strain dependence: hyperviscoelastic nonlinearity

PubMed Central

Wheatley, Benjamin B; Morrow, Duane A; Odegard, Gregory M; Kaufman, Kenton R; Donahue, Tammy L Haut

2015-01-01

Introduction Computational modeling of skeletal muscle requires characterization at the tissue level. While most skeletal muscle studies focus on hyperelasticity, the goal of this study was to examine and model the nonlinear behavior of both time-independent and time-dependent properties of skeletal muscle as a function of strain. Materials and Methods Nine tibialis anterior muscles from New Zealand White rabbits were subject to five consecutive stress relaxation cycles of roughly 3% strain. Individual relaxation steps were fit with a three-term linear Prony series. Prony series coefficients and relaxation ratio were assessed for strain dependence using a general linear statistical model. A fully nonlinear constitutive model was employed to capture the strain dependence of both the viscoelastic and instantaneous components. Results Instantaneous modulus (p<0.0005) and mid-range relaxation (p<0.0005) increased significantly with strain level, while relaxation at longer time periods decreased with strain (p<0.0005). Time constants and overall relaxation ratio did not change with strain level (p>0.1). Additionally, the fully nonlinear hyperviscoelastic constitutive model provided an excellent fit to experimental data, while other models which included linear components failed to capture muscle function as accurately. Conclusions Material properties of skeletal muscle are strain-dependent at the tissue level. This strain dependence can be included in computational models of skeletal muscle performance with a fully nonlinear hyperviscoelastic model. PMID:26409235

Continuous functional magnetic resonance imaging reveals dynamic nonlinearities of "dose-response" curves for finger opposition.

PubMed

Berns, G S; Song, A W; Mao, H

1999-07-15

Linear experimental designs have dominated the field of functional neuroimaging, but although successful at mapping regions of relative brain activation, the technique assumes that both cognition and brain activation are linear processes. To test these assumptions, we performed a continuous functional magnetic resonance imaging (MRI) experiment of finger opposition. Subjects performed a visually paced bimanual finger-tapping task. The frequency of finger tapping was continuously varied between 1 and 5 Hz, without any rest blocks. After continuous acquisition of fMRI images, the task-related brain regions were identified with independent components analysis (ICA). When the time courses of the task-related components were plotted against tapping frequency, nonlinear "dose- response" curves were obtained for most subjects. Nonlinearities appeared in both the static and dynamic sense, with hysteresis being prominent in several subjects. The ICA decomposition also demonstrated the spatial dynamics with different components active at different times. These results suggest that the brain response to tapping frequency does not scale linearly, and that it is history-dependent even after accounting for the hemodynamic response function. This implies that finger tapping, as measured with fMRI, is a nonstationary process. When analyzed with a conventional general linear model, a strong correlation to tapping frequency was identified, but the spatiotemporal dynamics were not apparent.

Simple robust control laws for robot manipulators. Part 1: Non-adaptive case

NASA Technical Reports Server (NTRS)

Wen, J. T.; Bayard, D. S.

1987-01-01

A new class of exponentially stabilizing control laws for joint level control of robot arms is introduced. It has been recently recognized that the nonlinear dynamics associated with robotic manipulators have certain inherent passivity properties. More specifically, the derivation of the robotic dynamic equations from the Hamilton's principle gives rise to natural Lyapunov functions for control design based on total energy considerations. Through a slight modification of the energy Lyapunov function and the use of a convenient lemma to handle third order terms in the Lyapunov function derivatives, closed loop exponential stability for both the set point and tracking control problem is demonstrated. The exponential convergence property also leads to robustness with respect to frictions, bounded modeling errors and instrument noise. In one new design, the nonlinear terms are decoupled from real-time measurements which completely removes the requirement for on-line computation of nonlinear terms in the controller implementation. In general, the new class of control laws offers alternatives to the more conventional computed torque method, providing tradeoffs between robustness, computation and convergence properties. Furthermore, these control laws have the unique feature that they can be adapted in a very simple fashion to achieve asymptotically stable adaptive control.

Plasticity Tool for Predicting Shear Nonlinearity of Unidirectional Laminates Under Multiaxial Loading

NASA Technical Reports Server (NTRS)

Wang, John T.; Bomarito, Geoffrey F.

2016-01-01

This study implements a plasticity tool to predict the nonlinear shear behavior of unidirectional composite laminates under multiaxial loadings, with an intent to further develop the tool for use in composite progressive damage analysis. The steps for developing the plasticity tool include establishing a general quadratic yield function, deriving the incremental elasto-plastic stress-strain relations using the yield function with associated flow rule, and integrating the elasto-plastic stress-strain relations with a modified Euler method and a substepping scheme. Micromechanics analyses are performed to obtain normal and shear stress-strain curves that are used in determining the plasticity parameters of the yield function. By analyzing a micromechanics model, a virtual testing approach is used to replace costly experimental tests for obtaining stress-strain responses of composites under various loadings. The predicted elastic moduli and Poisson's ratios are in good agreement with experimental data. The substepping scheme for integrating the elasto-plastic stress-strain relations is suitable for working with displacement-based finite element codes. An illustration problem is solved to show that the plasticity tool can predict the nonlinear shear behavior for a unidirectional laminate subjected to multiaxial loadings.

Nonlinear dynamics, fractals, cardiac physiology and sudden death

NASA Technical Reports Server (NTRS)

Goldberger, Ary L.

1987-01-01

The authors propose a diametrically opposite viewpoint to the generally accepted tendency of equating healthy function with order and disease with chaos. With regard to the question of sudden cardiac death and chaos, it is suggested that certain features of dynamical chaos related to fractal structure and fractal dynamics may be important organizing principles in normal physiology and that certain pathologies, including ventricular fibrillation, represent a class of 'pathological periodicities'. Some laboratory work bearing on the relation of nonlinear analysis to physiological and pathophysiological data is briefly reviewed, with tentative theories and models described in reference to the mechanism of ventricular fibrillation.

Exact travelling wave solutions for a diffusion-convection equation in two and three spatial dimensions

NASA Astrophysics Data System (ADS)

Elwakil, S. A.; El-Labany, S. K.; Zahran, M. A.; Sabry, R.

2004-04-01

The modified extended tanh-function method were applied to the general class of nonlinear diffusion-convection equations where the concentration-dependent diffusivity, D( u), was taken to be a constant while the concentration-dependent hydraulic conductivity, K( u) were taken to be in a power law. The obtained solutions include rational-type, triangular-type, singular-type, and solitary wave solutions. In fact, the profile of the obtained solitary wave solutions resemble the characteristics of a shock-wave like structure for an arbitrary m (where m>1 is the power of the nonlinear convection term).

Nonlinear constitutive theory for turbine engine structural analysis

NASA Technical Reports Server (NTRS)

Thompson, R. L.

1982-01-01

A number of viscoplastic constitutive theories and a conventional constitutive theory are evaluated and compared in their ability to predict nonlinear stress-strain behavior in gas turbine engine components at elevated temperatures. Specific application of these theories is directed towards the structural analysis of combustor liners undergoing transient, cyclic, thermomechanical load histories. The combustor liner material considered in this study is Hastelloy X. The material constants for each of the theories (as a function of temperature) are obtained from existing, published experimental data. The viscoplastic theories and a conventional theory are incorporated into a general purpose, nonlinear, finite element computer program. Several numerical examples of combustor liner structural analysis using these theories are given to demonstrate their capabilities. Based on the numerical stress-strain results, the theories are evaluated and compared.

Nondimensional Parameters and Equations for Nonlinear and Bifurcation Analyses of Thin Anisotropic Quasi-Shallow Shells

NASA Technical Reports Server (NTRS)

Nemeth, Michael P.

2010-01-01

A comprehensive development of nondimensional parameters and equations for nonlinear and bifurcations analyses of quasi-shallow shells, based on the Donnell-Mushtari-Vlasov theory for thin anisotropic shells, is presented. A complete set of field equations for geometrically imperfect shells is presented in terms general of lines-of-curvature coordinates. A systematic nondimensionalization of these equations is developed, several new nondimensional parameters are defined, and a comprehensive stress-function formulation is presented that includes variational principles for equilibrium and compatibility. Bifurcation analysis is applied to the nondimensional nonlinear field equations and a comprehensive set of bifurcation equations are presented. An extensive collection of tables and figures are presented that show the effects of lamina material properties and stacking sequence on the nondimensional parameters.

Control of propagation of spatially localized polariton wave packets in a Bragg mirror with embedded quantum wells

NASA Astrophysics Data System (ADS)

Sedova, I. E.; Chestnov, I. Yu.; Arakelian, S. M.; Kavokin, A. V.; Sedov, E. S.

2018-01-01

We considered the nonlinear dynamics of Bragg polaritons in a specially designed stratified semiconductor structure with embedded quantum wells, which possesses a convex dispersion. The model for the ensemble of single periodically arranged quantum wells coupled with the Bragg photon fields has been developed. In particular, the generalized Gross-Pitaevskii equation with the non-parabolic dispersion has been obtained for the Bragg polariton wave function. We revealed a number of dynamical regimes for polariton wave packets resulting from competition of the convex dispersion and the repulsive nonlinearity effects. Among the regimes are spreading, breathing and soliton propagation. When the control parameters including the exciton-photon detuning, the matter-field coupling and the nonlinearity are manipulated, the dynamical regimes switch between themselves.

Closed form solutions of two time fractional nonlinear wave equations

NASA Astrophysics Data System (ADS)

Akbar, M. Ali; Ali, Norhashidah Hj. Mohd.; Roy, Ripan

2018-06-01

In this article, we investigate the exact traveling wave solutions of two nonlinear time fractional wave equations. The fractional derivatives are described in the sense of conformable fractional derivatives. In addition, the traveling wave solutions are accomplished in the form of hyperbolic, trigonometric, and rational functions involving free parameters. To investigate such types of solutions, we implement the new generalized (G‧ / G) -expansion method. The extracted solutions are reliable, useful and suitable to comprehend the optimal control problems, chaotic vibrations, global and local bifurcations and resonances, furthermore, fission and fusion phenomena occur in solitons, the relativistic energy-momentum relation, scalar electrodynamics, quantum relativistic one-particle theory, electromagnetic interactions etc. The results reveal that the method is very fruitful and convenient for exploring nonlinear differential equations of fractional order treated in theoretical physics.

Bright solitons for a generalized nonautonomous nonlinear equation in a nonlinear inhomogeneous fiber

NASA Astrophysics Data System (ADS)

Xie, Xi-Yang; Tian, Bo; Liu, Lei; Guan, Yue-Yang; Jiang, Yan

2017-06-01

In this paper, we investigate a generalized nonautonomous nonlinear equation, which describes the ultrashort optical pulse propagating in a nonlinear inhomogeneous fiber. Under certain integrable constraints, bilinear forms, bright one- and two-soliton solutions are obtained. Via certain transformation, we investigate the properties of the solitons with the first-order dispersion parameter σ1(x, t), second-order dispersion parameter σ2(x, t), third-order dispersion parameter σ3(x, t), phase modulation and gain (loss) v(x, t). Soliton propagation and collision are graphically presented and analyzed: One soliton is shown to maintain its amplitude and width during the propagation. When we choose σ1(x, t), σ2(x, t) and σ3(x, t) differently, travelling direction of the soliton is found to alter. v(x, t) is observed to affect the amplitude of the soliton. Head-on collision between the two solitons is presented with σ1(x, t), σ2(x, t), σ3(x, t) and v(x, t) as the constants, and solitons' amplitudes are the same before and after the collision. When σ1(x, t), σ2(x, t) and σ3(x, t) are chosen as certain functions, the solitons' traveling directions change during the collision. v(x, t) can influence the amplitudes of the two solitons.

The Fourier decomposition method for nonlinear and non-stationary time series analysis.

PubMed

Singh, Pushpendra; Joshi, Shiv Dutt; Patney, Rakesh Kumar; Saha, Kaushik

2017-03-01

for many decades, there has been a general perception in the literature that Fourier methods are not suitable for the analysis of nonlinear and non-stationary data. In this paper, we propose a novel and adaptive Fourier decomposition method (FDM), based on the Fourier theory, and demonstrate its efficacy for the analysis of nonlinear and non-stationary time series. The proposed FDM decomposes any data into a small number of 'Fourier intrinsic band functions' (FIBFs). The FDM presents a generalized Fourier expansion with variable amplitudes and variable frequencies of a time series by the Fourier method itself. We propose an idea of zero-phase filter bank-based multivariate FDM (MFDM), for the analysis of multivariate nonlinear and non-stationary time series, using the FDM. We also present an algorithm to obtain cut-off frequencies for MFDM. The proposed MFDM generates a finite number of band-limited multivariate FIBFs (MFIBFs). The MFDM preserves some intrinsic physical properties of the multivariate data, such as scale alignment, trend and instantaneous frequency. The proposed methods provide a time-frequency-energy (TFE) distribution that reveals the intrinsic structure of a data. Numerical computations and simulations have been carried out and comparison is made with the empirical mode decomposition algorithms.

Development of orientation tuning in simple cells of primary visual cortex

PubMed Central

Moore, Bartlett D.

2012-01-01

Orientation selectivity and its development are basic features of visual cortex. The original model of orientation selectivity proposes that elongated simple cell receptive fields are constructed from convergent input of an array of lateral geniculate nucleus neurons. However, orientation selectivity of simple cells in the visual cortex is generally greater than the linear contributions based on projections from spatial receptive field profiles. This implies that additional selectivity may arise from intracortical mechanisms. The hierarchical processing idea implies mainly linear connections, whereas cortical contributions are generally considered to be nonlinear. We have explored development of orientation selectivity in visual cortex with a focus on linear and nonlinear factors in a population of anesthetized 4-wk postnatal kittens and adult cats. Linear contributions are estimated from receptive field maps by which orientation tuning curves are generated and bandwidth is quantified. Nonlinear components are estimated as the magnitude of the power function relationship between responses measured from drifting sinusoidal gratings and those predicted from the spatial receptive field. Measured bandwidths for kittens are slightly larger than those in adults, whereas predicted bandwidths are substantially broader. These results suggest that relatively strong nonlinearities in early postnatal stages are substantially involved in the development of orientation tuning in visual cortex. PMID:22323631

Predicting adsorptive removal of chlorophenol from aqueous solution using artificial intelligence based modeling approaches.

PubMed

Singh, Kunwar P; Gupta, Shikha; Ojha, Priyanka; Rai, Premanjali

2013-04-01

The research aims to develop artificial intelligence (AI)-based model to predict the adsorptive removal of 2-chlorophenol (CP) in aqueous solution by coconut shell carbon (CSC) using four operational variables (pH of solution, adsorbate concentration, temperature, and contact time), and to investigate their effects on the adsorption process. Accordingly, based on a factorial design, 640 batch experiments were conducted. Nonlinearities in experimental data were checked using Brock-Dechert-Scheimkman (BDS) statistics. Five nonlinear models were constructed to predict the adsorptive removal of CP in aqueous solution by CSC using four variables as input. Performances of the constructed models were evaluated and compared using statistical criteria. BDS statistics revealed strong nonlinearity in experimental data. Performance of all the models constructed here was satisfactory. Radial basis function network (RBFN) and multilayer perceptron network (MLPN) models performed better than generalized regression neural network, support vector machines, and gene expression programming models. Sensitivity analysis revealed that the contact time had highest effect on adsorption followed by the solution pH, temperature, and CP concentration. The study concluded that all the models constructed here were capable of capturing the nonlinearity in data. A better generalization and predictive performance of RBFN and MLPN models suggested that these can be used to predict the adsorption of CP in aqueous solution using CSC.

Global stability and exact solution of an arbitrary-solute nonlinear cellular mass transport system.

PubMed

Benson, James D

2014-12-01

The prediction of the cellular state as a function of extracellular concentrations and temperatures has been of interest to physiologists for nearly a century. One of the most widely used models in the field is one where mass flux is linearly proportional to the concentration difference across the membrane. These fluxes define a nonlinear differential equation system for the intracellular state, which when coupled with appropriate initial conditions, define the intracellular state as a function of the extracellular concentrations of both permeating and nonpermeating solutes. Here we take advantage of a reparametrization scheme to extend existing stability results to a more general setting and to a develop analytical solutions to this model for an arbitrary number of extracellular solutes. Copyright © 2014 Elsevier Inc. All rights reserved.

Structural Properties and Estimation of Delay Systems. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Kwong, R. H. S.

1975-01-01

Two areas in the theory of delay systems were studied: structural properties and their applications to feedback control, and optimal linear and nonlinear estimation. The concepts of controllability, stabilizability, observability, and detectability were investigated. The property of pointwise degeneracy of linear time-invariant delay systems is considered. Necessary and sufficient conditions for three dimensional linear systems to be made pointwise degenerate by delay feedback were obtained, while sufficient conditions for this to be possible are given for higher dimensional linear systems. These results were applied to obtain solvability conditions for the minimum time output zeroing control problem by delay feedback. A representation theorem is given for conditional moment functionals of general nonlinear stochastic delay systems, and stochastic differential equations are derived for conditional moment functionals satisfying certain smoothness properties.

Generalized Wideband Harmonic Imaging of Nonlinearly Loaded Scatterers: Theory, Analysis, and Application for Forward-Looking Radar Target Detection

DTIC Science & Technology

2014-09-01

signal) operations; it is general enough so that it can accommodate high - power (large-signal) sensing as well—which may be needed to detect targets... Generalized Wideband Harmonic Imaging of Nonlinearly Loaded Scatterers: Theory, Analysis, and Application for Forward-Looking Radar Target...Research Laboratory Adelphi, MD 20783-1138 ARL-TR-7121 September 2014 Generalized Wideband Harmonic Imaging of Nonlinearly Loaded

General purpose nonlinear system solver based on Newton-Krylov method.

DOE Office of Scientific and Technical Information (OSTI.GOV)

2013-12-01

KINSOL is part of a software family called SUNDIALS: SUite of Nonlinear and Differential/Algebraic equation Solvers [1]. KINSOL is a general-purpose nonlinear system solver based on Newton-Krylov and fixed-point solver technologies [2].

Finsler geometry of nonlinear elastic solids with internal structure

NASA Astrophysics Data System (ADS)

Clayton, J. D.

2017-02-01

Concepts from Finsler differential geometry are applied towards a theory of deformable continua with internal structure. The general theory accounts for finite deformation, nonlinear elasticity, and various kinds of structural features in a solid body. The general kinematic structure of the theory includes macroscopic and microscopic displacement fields-i.e., a multiscale representation-whereby the latter are represented mathematically by the director vector of pseudo-Finsler space, not necessarily of unit magnitude. A physically appropriate fundamental (metric) tensor is introduced, leading to affine and nonlinear connections. A deformation gradient tensor is defined via differentiation of the macroscopic motion field, and another metric indicative of strain in the body is a function of this gradient. A total energy functional of strain, referential microscopic coordinates, and horizontal covariant derivatives of the latter is introduced. Variational methods are applied to derive Euler-Lagrange equations and Neumann boundary conditions. The theory is shown to encompass existing continuum physics models such as micromorphic, micropolar, strain gradient, phase field, and conventional nonlinear elasticity models, and it can reduce to such models when certain assumptions on geometry, kinematics, and energy functionals are imposed. The theory is applied to analyze two physical problems in crystalline solids: shear localization/fracture in a two-dimensional body and cavitation in a spherical body. In these examples, a conformal or Weyl-type transformation of the fundamental tensor enables a description of dilatation associated, respectively, with cleavage surface roughness and nucleation of voids or vacancies. For the shear localization problem, the Finsler theory is able to accurately reproduce the surface energy of Griffith's fracture mechanics, and it predicts dilatation-induced toughening as observed in experiments on brittle crystals. For the cavitation problem, the Finsler theory is able to accurately reproduce the vacancy formation energy at a nanoscale resolution, and various solutions describe localized cavitation at the core of the body and/or distributed dilatation and softening associated with amorphization as observed in atomic simulations, with relative stability of solutions depending on the regularization length.

Estimating PM2.5 Concentrations in Xi'an City Using a Generalized Additive Model with Multi-Source Monitoring Data

PubMed Central

Song, Yong-Ze; Yang, Hong-Lei; Peng, Jun-Huan; Song, Yi-Rong; Sun, Qian; Li, Yuan

2015-01-01

Particulate matter with an aerodynamic diameter <2.5 μm (PM2.5) represents a severe environmental problem and is of negative impact on human health. Xi'an City, with a population of 6.5 million, is among the highest concentrations of PM2.5 in China. In 2013, in total, there were 191 days in Xi’an City on which PM2.5 concentrations were greater than 100 μg/m3. Recently, a few studies have explored the potential causes of high PM2.5 concentration using remote sensing data such as the MODIS aerosol optical thickness (AOT) product. Linear regression is a commonly used method to find statistical relationships among PM2.5 concentrations and other pollutants, including CO, NO2, SO2, and O3, which can be indicative of emission sources. The relationships of these variables, however, are usually complicated and non-linear. Therefore, a generalized additive model (GAM) is used to estimate the statistical relationships between potential variables and PM2.5 concentrations. This model contains linear functions of SO2 and CO, univariate smoothing non-linear functions of NO2, O3, AOT and temperature, and bivariate smoothing non-linear functions of location and wind variables. The model can explain 69.50% of PM2.5 concentrations, with R2 = 0.691, which improves the result of a stepwise linear regression (R2 = 0.582) by 18.73%. The two most significant variables, CO concentration and AOT, represent 20.65% and 19.54% of the deviance, respectively, while the three other gas-phase concentrations, SO2, NO2, and O3 account for 10.88% of the total deviance. These results show that in Xi'an City, the traffic and other industrial emissions are the primary source of PM2.5. Temperature, location, and wind variables also non-linearly related with PM2.5. PMID:26540446

Nonlinear electrodynamics of high-temperature superconductors

NASA Astrophysics Data System (ADS)

Zutic, Igor

We investigate the effects of nonlinear electrodynamics in unconventional superconductors. These effects can serve as fingerprints to identify the symmetry of the superconducting pairing state and to provide information about the unknown pairing mechanism in High Temperature Superconductors (HTSC). In the Meissner regime, at low temperatures, a nonlinear magnetic response arises from the presence of lines on the Fermi surface where the superconducting energy gap is very small or zero. This can be used to perform "node spectroscopy", that is, as a sensitive bulk probe to locate the angular position of those lines. We first compute the nonlinear magnetic moment as a function of applied field and geometry, assuming d-wave pairing and anisotropic penetration depth, for realistic finite sample. Our novel, numerically implemented, perturbative procedure exploits the small ratio of the penetration depths to the sample size and substantially reduces the computational work required. We next generalize these considerations to other candidates for the energy gap and to perform node spectroscopy. In calculating the nonlinear supercurrent response, we include the effects of orthorhombic distortion and a-b plane anisotropy. Analytic results presented demonstrate a systematic way to experimentally distinguish order parameters of different symmetries, including cases with mixed symmetry (for example, d+s and s+id). We finally extend our findings to the case of low frequency harmonic magnetic field. The nonlinear magnetic response for various physical quantities generates higher harmonics of the frequency of the applied field. We discuss how examination of the field and angular dependences of these harmonics allows determination of the structure of the energy gap. We show how to distinguish nodes from small minima ("quasinodes"). Gaps with nodal lines give rise to universal power law field dependences for the nonlinear magnetic moment and torque. They both have separable temporal and angular dependences. In contrast, with gap functions which only have quasinodes, these quantities do not display power laws in the applied field, and their temporal and angular dependences are not separable. We discuss how to perform measurements so as to maximize the nonlinear signal, and how to determine the gap function symmetry.

Systematic derivation of reaction-diffusion equations with distributed delays and relations to fractional reaction-diffusion equations and hyperbolic transport equations: application to the theory of Neolithic transition.

PubMed

Vlad, Marcel Ovidiu; Ross, John

2002-12-01

We introduce a general method for the systematic derivation of nonlinear reaction-diffusion equations with distributed delays. We study the interactions among different types of moving individuals (atoms, molecules, quasiparticles, biological organisms, etc). The motion of each species is described by the continuous time random walk theory, analyzed in the literature for transport problems, whereas the interactions among the species are described by a set of transformation rates, which are nonlinear functions of the local concentrations of the different types of individuals. We use the time interval between two jumps (the transition time) as an additional state variable and obtain a set of evolution equations, which are local in time. In order to make a connection with the transport models used in the literature, we make transformations which eliminate the transition time and derive a set of nonlocal equations which are nonlinear generalizations of the so-called generalized master equations. The method leads under different specified conditions to various types of nonlocal transport equations including a nonlinear generalization of fractional diffusion equations, hyperbolic reaction-diffusion equations, and delay-differential reaction-diffusion equations. Thus in the analysis of a given problem we can fit to the data the type of reaction-diffusion equation and the corresponding physical and kinetic parameters. The method is illustrated, as a test case, by the study of the neolithic transition. We introduce a set of assumptions which makes it possible to describe the transition from hunting and gathering to agriculture economics by a differential delay reaction-diffusion equation for the population density. We derive a delay evolution equation for the rate of advance of agriculture, which illustrates an application of our analysis.

Stochastic wave-function unravelling of the generalized Lindblad equation

NASA Astrophysics Data System (ADS)

Semin, V.; Semina, I.; Petruccione, F.

2017-12-01

We investigate generalized non-Markovian stochastic Schrödinger equations (SSEs), driven by a multidimensional counting process and multidimensional Brownian motion introduced by A. Barchielli and C. Pellegrini [J. Math. Phys. 51, 112104 (2010), 10.1063/1.3514539]. We show that these SSEs can be translated in a nonlinear form, which can be efficiently simulated. The simulation is illustrated by the model of a two-level system in a structured bath, and the results of the simulations are compared with the exact solution of the generalized master equation.

Margin-maximizing feature elimination methods for linear and nonlinear kernel-based discriminant functions.

PubMed

Aksu, Yaman; Miller, David J; Kesidis, George; Yang, Qing X

2010-05-01

Feature selection for classification in high-dimensional spaces can improve generalization, reduce classifier complexity, and identify important, discriminating feature "markers." For support vector machine (SVM) classification, a widely used technique is recursive feature elimination (RFE). We demonstrate that RFE is not consistent with margin maximization, central to the SVM learning approach. We thus propose explicit margin-based feature elimination (MFE) for SVMs and demonstrate both improved margin and improved generalization, compared with RFE. Moreover, for the case of a nonlinear kernel, we show that RFE assumes that the squared weight vector 2-norm is strictly decreasing as features are eliminated. We demonstrate this is not true for the Gaussian kernel and, consequently, RFE may give poor results in this case. MFE for nonlinear kernels gives better margin and generalization. We also present an extension which achieves further margin gains, by optimizing only two degrees of freedom--the hyperplane's intercept and its squared 2-norm--with the weight vector orientation fixed. We finally introduce an extension that allows margin slackness. We compare against several alternatives, including RFE and a linear programming method that embeds feature selection within the classifier design. On high-dimensional gene microarray data sets, University of California at Irvine (UCI) repository data sets, and Alzheimer's disease brain image data, MFE methods give promising results.

Global identifiability of linear compartmental models--a computer algebra algorithm.

PubMed

Audoly, S; D'Angiò, L; Saccomani, M P; Cobelli, C

1998-01-01

A priori global identifiability deals with the uniqueness of the solution for the unknown parameters of a model and is, thus, a prerequisite for parameter estimation of biological dynamic models. Global identifiability is however difficult to test, since it requires solving a system of algebraic nonlinear equations which increases both in nonlinearity degree and number of terms and unknowns with increasing model order. In this paper, a computer algebra tool, GLOBI (GLOBal Identifiability) is presented, which combines the topological transfer function method with the Buchberger algorithm, to test global identifiability of linear compartmental models. GLOBI allows for the automatic testing of a priori global identifiability of general structure compartmental models from general multi input-multi output experiments. Examples of usage of GLOBI to analyze a priori global identifiability of some complex biological compartmental models are provided.

Symbolic computation of equivalence transformations and parameter reduction for nonlinear physical models

NASA Astrophysics Data System (ADS)

Cheviakov, Alexei F.

2017-11-01

An efficient systematic procedure is provided for symbolic computation of Lie groups of equivalence transformations and generalized equivalence transformations of systems of differential equations that contain arbitrary elements (arbitrary functions and/or arbitrary constant parameters), using the software package GeM for Maple. Application of equivalence transformations to the reduction of the number of arbitrary elements in a given system of equations is discussed, and several examples are considered. The first computational example of generalized equivalence transformations where the transformation of the dependent variable involves an arbitrary constitutive function is presented. As a detailed physical example, a three-parameter family of nonlinear wave equations describing finite anti-plane shear displacements of an incompressible hyperelastic fiber-reinforced medium is considered. Equivalence transformations are computed and employed to radically simplify the model for an arbitrary fiber direction, invertibly reducing the model to a simple form that corresponds to a special fiber direction, and involves no arbitrary elements. The presented computation algorithm is applicable to wide classes of systems of differential equations containing arbitrary elements.

The Association of Health and Income in the Elderly: Experience from a Southern State of Brazil

PubMed Central

Fillenbaum, Gerda G.; Blay, Sergio L.; Pieper, Carl F.; King, Katherine E.; Andreoli, Sergio B.; Gastal, Fábio L.

2013-01-01

Objectives In high income, developed countries, health status tends to improve as income increases, but primarily through the 50th-66th percentile of income. It is unclear whether the same limitation holds in middle income countries, and for both general assessments of health and specific conditions. Methods Data were obtained from Brazil, a middle income country. In-person interviews with a representative sample of community residents age ≥60 (N=6963), in the southern state of Rio Grande do Sul, obtained information on demographic characteristics including household income and number of persons supported, general health status (self-rated health, functional status), depression, and seven physician-diagnosed, self-reported health conditions. Analyses used household income (adjusted for number supported and economies of scale) together with higher order income terms, and controlled for demographics and comorbidities, to ascertain nonlinearity between income and general and specific health measures. Results In fully controlled analyses income was associated with general measures of health (linearly with self-rated health, nonlinearly with functional status). For specific health measures there was a consistent linear association with depression, pulmonary disorders, renal disorders, and sensory impairment. For musculoskeletal, cardiovascular (negative association), and gastrointestinal disorders this association no longer held when comorbidities were controlled. There was no association with diabetes. Conclusion Contrary to findings in high income countries, the association of household-size-adjusted income with health was generally linear, sometimes negative, and sometimes absent when comorbidities were controlled. PMID:24058505

Data-based virtual unmodeled dynamics driven multivariable nonlinear adaptive switching control.

PubMed

Chai, Tianyou; Zhang, Yajun; Wang, Hong; Su, Chun-Yi; Sun, Jing

2011-12-01

For a complex industrial system, its multivariable and nonlinear nature generally make it very difficult, if not impossible, to obtain an accurate model, especially when the model structure is unknown. The control of this class of complex systems is difficult to handle by the traditional controller designs around their operating points. This paper, however, explores the concepts of controller-driven model and virtual unmodeled dynamics to propose a new design framework. The design consists of two controllers with distinct functions. First, using input and output data, a self-tuning controller is constructed based on a linear controller-driven model. Then the output signals of the controller-driven model are compared with the true outputs of the system to produce so-called virtual unmodeled dynamics. Based on the compensator of the virtual unmodeled dynamics, the second controller based on a nonlinear controller-driven model is proposed. Those two controllers are integrated by an adaptive switching control algorithm to take advantage of their complementary features: one offers stabilization function and another provides improved performance. The conditions on the stability and convergence of the closed-loop system are analyzed. Both simulation and experimental tests on a heavily coupled nonlinear twin-tank system are carried out to confirm the effectiveness of the proposed method.

Aquifer Reclamation Design: The Use of Contaminant Transport Simulation Combined With Nonlinear Programing

NASA Astrophysics Data System (ADS)

Gorelick, Steven M.; Voss, Clifford I.; Gill, Philip E.; Murray, Walter; Saunders, Michael A.; Wright, Margaret H.

1984-04-01

A simulation-management methodology is demonstrated for the rehabilitation of aquifers that have been subjected to chemical contamination. Finite element groundwater flow and contaminant transport simulation are combined with nonlinear optimization. The model is capable of determining well locations plus pumping and injection rates for groundwater quality control. Examples demonstrate linear or nonlinear objective functions subject to linear and nonlinear simulation and water management constraints. Restrictions can be placed on hydraulic heads, stresses, and gradients, in addition to contaminant concentrations and fluxes. These restrictions can be distributed over space and time. Three design strategies are demonstrated for an aquifer that is polluted by a constant contaminant source: they are pumping for contaminant removal, water injection for in-ground dilution, and a pumping, treatment, and injection cycle. A transient model designs either contaminant plume interception or in-ground dilution so that water quality standards are met. The method is not limited to these cases. It is generally applicable to the optimization of many types of distributed parameter systems.

A new smooth robust control design for uncertain nonlinear systems with non-vanishing disturbances

NASA Astrophysics Data System (ADS)

Xian, Bin; Zhang, Yao

2016-06-01

In this paper, we consider the control problem for a general class of nonlinear system subjected to uncertain dynamics and non-varnishing disturbances. A smooth nonlinear control algorithm is presented to tackle these uncertainties and disturbances. The proposed control design employs the integral of a nonlinear sigmoid function to compensate the uncertain dynamics, and achieve a uniformly semi-global practical asymptotic stable tracking control of the system outputs. A novel Lyapunov-based stability analysis is employed to prove the convergence of the tracking errors and the stability of the closed-loop system. Numerical simulation results on a two-link robot manipulator are presented to illustrate the performance of the proposed control algorithm comparing with the layer-boundary sliding mode controller and the robust of integration of sign of error control design. Furthermore, real-time experiment results for the attitude control of a quadrotor helicopter are also included to confirm the effectiveness of the proposed algorithm.

Cluster Synchronization of Diffusively Coupled Nonlinear Systems: A Contraction-Based Approach

NASA Astrophysics Data System (ADS)

Aminzare, Zahra; Dey, Biswadip; Davison, Elizabeth N.; Leonard, Naomi Ehrich

2018-04-01

Finding the conditions that foster synchronization in networked nonlinear systems is critical to understanding a wide range of biological and mechanical systems. However, the conditions proved in the literature for synchronization in nonlinear systems with linear coupling, such as has been used to model neuronal networks, are in general not strict enough to accurately determine the system behavior. We leverage contraction theory to derive new sufficient conditions for cluster synchronization in terms of the network structure, for a network where the intrinsic nonlinear dynamics of each node may differ. Our result requires that network connections satisfy a cluster-input-equivalence condition, and we explore the influence of this requirement on network dynamics. For application to networks of nodes with FitzHugh-Nagumo dynamics, we show that our new sufficient condition is tighter than those found in previous analyses that used smooth or nonsmooth Lyapunov functions. Improving the analytical conditions for when cluster synchronization will occur based on network configuration is a significant step toward facilitating understanding and control of complex networked systems.

Trajectory planning of mobile robots using indirect solution of optimal control method in generalized point-to-point task

NASA Astrophysics Data System (ADS)

Nazemizadeh, M.; Rahimi, H. N.; Amini Khoiy, K.

2012-03-01

This paper presents an optimal control strategy for optimal trajectory planning of mobile robots by considering nonlinear dynamic model and nonholonomic constraints of the system. The nonholonomic constraints of the system are introduced by a nonintegrable set of differential equations which represent kinematic restriction on the motion. The Lagrange's principle is employed to derive the nonlinear equations of the system. Then, the optimal path planning of the mobile robot is formulated as an optimal control problem. To set up the problem, the nonlinear equations of the system are assumed as constraints, and a minimum energy objective function is defined. To solve the problem, an indirect solution of the optimal control method is employed, and conditions of the optimality derived as a set of coupled nonlinear differential equations. The optimality equations are solved numerically, and various simulations are performed for a nonholonomic mobile robot to illustrate effectiveness of the proposed method.

Speed selection for traveling-wave solutions to the diffusion-reaction equation with cubic reaction term and Burgers nonlinear convection.

PubMed

Sabelnikov, V A; Lipatnikov, A N

2014-09-01

The problem of traveling wave (TW) speed selection for solutions to a generalized Murray-Burgers-KPP-Fisher parabolic equation with a strictly positive cubic reaction term is considered theoretically and the initial boundary value problem is numerically solved in order to support obtained analytical results. Depending on the magnitude of a parameter inherent in the reaction term (i) the term is either a concave function or a function with the inflection point and (ii) transition from pulled to pushed TW solution occurs due to interplay of two nonlinear terms; the reaction term and the Burgers convection term. Explicit pushed TW solutions are derived. It is shown that physically observable TW solutions, i.e., solutions obtained by solving the initial boundary value problem with a sufficiently steep initial condition, can be determined by seeking the TW solution characterized by the maximum decay rate at its leading edge. In the Appendix, the developed approach is applied to a non-linear diffusion-reaction equation that is widely used to model premixed turbulent combustion.

A fast method to emulate an iterative POCS image reconstruction algorithm.

PubMed

Zeng, Gengsheng L

2017-10-01

Iterative image reconstruction algorithms are commonly used to optimize an objective function, especially when the objective function is nonquadratic. Generally speaking, the iterative algorithms are computationally inefficient. This paper presents a fast algorithm that has one backprojection and no forward projection. This paper derives a new method to solve an optimization problem. The nonquadratic constraint, for example, an edge-preserving denoising constraint is implemented as a nonlinear filter. The algorithm is derived based on the POCS (projections onto projections onto convex sets) approach. A windowed FBP (filtered backprojection) algorithm enforces the data fidelity. An iterative procedure, divided into segments, enforces edge-enhancement denoising. Each segment performs nonlinear filtering. The derived iterative algorithm is computationally efficient. It contains only one backprojection and no forward projection. Low-dose CT data are used for algorithm feasibility studies. The nonlinearity is implemented as an edge-enhancing noise-smoothing filter. The patient studies results demonstrate its effectiveness in processing low-dose x ray CT data. This fast algorithm can be used to replace many iterative algorithms. © 2017 American Association of Physicists in Medicine.

Designing Agent Collectives For Systems With Markovian Dynamics

NASA Technical Reports Server (NTRS)

Wolpert, David H.; Lawson, John W.; Clancy, Daniel (Technical Monitor)

2001-01-01

The "Collective Intelligence" (COIN) framework concerns the design of collectives of agents so that as those agents strive to maximize their individual utility functions, their interaction causes a provided "world" utility function concerning the entire collective to be also maximized. Here we show how to extend that framework to scenarios having Markovian dynamics when no re-evolution of the system from counter-factual initial conditions (an often expensive calculation) is permitted. Our approach transforms the (time-extended) argument of each agent's utility function before evaluating that function. This transformation has benefits in scenarios not involving Markovian dynamics, in particular scenarios where not all of the arguments of an agent's utility function are observable. We investigate this transformation in simulations involving both linear and quadratic (nonlinear) dynamics. In addition, we find that a certain subset of these transformations, which result in utilities that have low "opacity (analogous to having high signal to noise) but are not "factored" (analogous to not being incentive compatible), reliably improve performance over that arising with factored utilities. We also present a Taylor Series method for the fully general nonlinear case.

Self adaptive solution strategies: Locally bound constrained Newton Raphson solution algorithms

NASA Technical Reports Server (NTRS)

Padovan, Joe

1991-01-01

A summary is given of strategies which enable the automatic adjustment of the constraint surfaces recently used to extend the range and numerical stability/efficiency of nonlinear finite element equation solvers. In addition to handling kinematic and material induced nonlinearity, both pre-and postbuckling behavior can be treated. The scheme employs localized bounds on various hierarchical partitions of the field variables. These are used to resize, shape, and orient the global constraint surface, thereby enabling essentially automatic load/deflection incrementation. Due to the generality of the approach taken, it can be implemented in conjunction with the constraints of an arbitrary functional type. To benchmark the method, several numerical experiments are presented. These include problems involving kinematic and material nonlinearity, as well as pre- and postbuckling characteristics. Also included is a list of papers published in the course of the work.

A three-parameter two-state model of receptor function that incorporates affinity, efficacy, and signal amplification.

PubMed

Buchwald, Peter

2017-06-01

A generalized model of receptor function is proposed that relies on the essential assumptions of the minimal two-state receptor theory (i.e., ligand binding followed by receptor activation), but uses a different parametrization and allows nonlinear response (transduction) for possible signal amplification. For the most general case, three parameters are used: K d , the classic equilibrium dissociation constant to characterize binding affinity; ε , an intrinsic efficacy to characterize the ability of the bound ligand to activate the receptor (ranging from 0 for an antagonist to 1 for a full agonist); and γ , a gain (amplification) parameter to characterize the nonlinearity of postactivation signal transduction (ranging from 1 for no amplification to infinity). The obtained equation, E/Emax=εγLεγ+1-εL+Kd, resembles that of the operational (Black and Leff) or minimal two-state (del Castillo-Katz) models, E/Emax=τLτ+1L+Kd, with εγ playing a role somewhat similar to that of the τ efficacy parameter of those models, but has several advantages. Its parameters are more intuitive as they are conceptually clearly related to the different steps of binding, activation, and signal transduction (amplification), and they are also better suited for optimization by nonlinear regression. It allows fitting of complex data where receptor binding and response are measured separately and the fractional occupancy and response are mismatched. Unlike the previous models, it is a true generalized model as simplified forms can be reproduced with special cases of its parameters. Such simplified forms can be used on their own to characterize partial agonism, competing partial and full agonists, or signal amplification.

Lattice Boltzmann model for high-order nonlinear partial differential equations

NASA Astrophysics Data System (ADS)

Chai, Zhenhua; He, Nanzhong; Guo, Zhaoli; Shi, Baochang

2018-01-01

In this paper, a general lattice Boltzmann (LB) model is proposed for the high-order nonlinear partial differential equation with the form ∂tϕ +∑k=1mαk∂xkΠk(ϕ ) =0 (1 ≤k ≤m ≤6 ), αk are constant coefficients, Πk(ϕ ) are some known differential functions of ϕ . As some special cases of the high-order nonlinear partial differential equation, the classical (m)KdV equation, KdV-Burgers equation, K (n ,n ) -Burgers equation, Kuramoto-Sivashinsky equation, and Kawahara equation can be solved by the present LB model. Compared to the available LB models, the most distinct characteristic of the present model is to introduce some suitable auxiliary moments such that the correct moments of equilibrium distribution function can be achieved. In addition, we also conducted a detailed Chapman-Enskog analysis, and found that the high-order nonlinear partial differential equation can be correctly recovered from the proposed LB model. Finally, a large number of simulations are performed, and it is found that the numerical results agree with the analytical solutions, and usually the present model is also more accurate than the existing LB models [H. Lai and C. Ma, Sci. China Ser. G 52, 1053 (2009), 10.1007/s11433-009-0149-3; H. Lai and C. Ma, Phys. A (Amsterdam) 388, 1405 (2009), 10.1016/j.physa.2009.01.005] for high-order nonlinear partial differential equations.

A Geomorphologic Synthesis of Nonlinearity in Surface Runoff

NASA Astrophysics Data System (ADS)

Wang, C. T.; Gupta, Vijay K.; Waymire, Ed

1981-06-01

The geomorphic approach leading to a representation of an instantaneous unit hydrograph (iuh) which we developed earlier is generalized to incorporate nonlinear effects in the rainfall-runoff transformation. It is demonstrated that the nonlinearity in the transformation enters in part through the dependence of the mean holding time on the rainfall intensity. Under an assumed first approximation that this dependence is the sole source of nonlinearity an explicit quasi-linear representation results for the rainfall- runoff transformation. The kernel function of this transformation can be termed as the instantaneous response function (irf) in contradistinction to the notion of an iuh for the case of a linear rainfall-runoff transformation. The predictions from the quasi-linear theory agree very well with predictions from the kinematic wave approach for the one small basin that is analyzed. Also, for two large basins in Illinois having areas of about 1100 mi2 the predictions from the quasi-linear approach compare very well with the observed flows. A measure of nonlinearity, α naturally arises through the dependence of the mean holding time KB(i0) on the rainfall intensity i0via KB (i0) ˜ i0 -α. Computations of α for four basins show that α approaches ⅔ as basin size decreases and approaches zero as the basin size increases. A semilog plot of α versus the square root of the basin area gives a straight line. Confirmation of this relationship for other basins would be of basic importance in predicting flows from ungaged basins.

Lattice Boltzmann model for high-order nonlinear partial differential equations.

PubMed

Chai, Zhenhua; He, Nanzhong; Guo, Zhaoli; Shi, Baochang

2018-01-01

In this paper, a general lattice Boltzmann (LB) model is proposed for the high-order nonlinear partial differential equation with the form ∂_{t}ϕ+∑_{k=1}^{m}α_{k}∂_{x}^{k}Π_{k}(ϕ)=0 (1≤k≤m≤6), α_{k} are constant coefficients, Π_{k}(ϕ) are some known differential functions of ϕ. As some special cases of the high-order nonlinear partial differential equation, the classical (m)KdV equation, KdV-Burgers equation, K(n,n)-Burgers equation, Kuramoto-Sivashinsky equation, and Kawahara equation can be solved by the present LB model. Compared to the available LB models, the most distinct characteristic of the present model is to introduce some suitable auxiliary moments such that the correct moments of equilibrium distribution function can be achieved. In addition, we also conducted a detailed Chapman-Enskog analysis, and found that the high-order nonlinear partial differential equation can be correctly recovered from the proposed LB model. Finally, a large number of simulations are performed, and it is found that the numerical results agree with the analytical solutions, and usually the present model is also more accurate than the existing LB models [H. Lai and C. Ma, Sci. China Ser. G 52, 1053 (2009)1672-179910.1007/s11433-009-0149-3; H. Lai and C. Ma, Phys. A (Amsterdam) 388, 1405 (2009)PHYADX0378-437110.1016/j.physa.2009.01.005] for high-order nonlinear partial differential equations.

Spillover, nonlinearity, and flexible structures

NASA Technical Reports Server (NTRS)

Bass, Robert W.; Zes, Dean

1991-01-01

Many systems whose evolution in time is governed by Partial Differential Equations (PDEs) are linearized around a known equilibrium before Computer Aided Control Engineering (CACE) is considered. In this case, there are infinitely many independent vibrational modes, and it is intuitively evident on physical grounds that infinitely many actuators would be needed in order to control all modes. A more precise, general formulation of this grave difficulty (spillover problem) is due to A.V. Balakrishnan. A possible route to circumvention of this difficulty lies in leaving the PDE in its original nonlinear form, and adding the essentially finite dimensional control action prior to linearization. One possibly applicable technique is the Liapunov Schmidt rigorous reduction of singular infinite dimensional implicit function problems to finite dimensional implicit function problems. Omitting details of Banach space rigor, the formalities of this approach are given.

Stability of uncertain systems. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Blankenship, G. L.

1971-01-01

The asymptotic properties of feedback systems are discussed, containing uncertain parameters and subjected to stochastic perturbations. The approach is functional analytic in flavor and thereby avoids the use of Markov techniques and auxiliary Lyapunov functionals characteristic of the existing work in this area. The results are given for the probability distributions of the accessible signals in the system and are proved using the Prohorov theory of the convergence of measures. For general nonlinear systems, a result similar to the small loop-gain theorem of deterministic stability theory is given. Boundedness is a property of the induced distributions of the signals and not the usual notion of boundedness in norm. For the special class of feedback systems formed by the cascade of a white noise, a sector nonlinearity and convolution operator conditions are given to insure the total boundedness of the overall feedback system.

Generalized nonlinear Schrödinger equation and ultraslow optical solitons in a cold four-state atomic system.

PubMed

Hang, Chao; Huang, Guoxiang; Deng, L

2006-03-01

We investigate the influence of high-order dispersion and nonlinearity on the propagation of ultraslow optical solitons in a lifetime broadened four-state atomic system under a Raman excitation. Using a standard method of multiple-scales we derive a generalized nonlinear Schrödinger equation and show that for realistic physical parameters and at the pulse duration of 10(-6)s, the effects of third-order linear dispersion, nonlinear dispersion, and delay in nonlinear refractive index can be significant and may not be considered as perturbations. We provide exact soliton solutions for the generalized nonlinear Schrödinger equation and demonstrate that optical solitons obtained may still have ultraslow propagating velocity. Numerical simulations on the stability and interaction of these ultraslow optical solitons in the presence of linear and differential absorptions are also presented.

Regular black holes in f(T) Gravity through a nonlinear electrodynamics source

DOE Office of Scientific and Technical Information (OSTI.GOV)

Junior, Ednaldo L.B.; Rodrigues, Manuel E.; Houndjo, Mahouton J.S., E-mail: ednaldobarrosjr@gmail.com, E-mail: esialg@gmail.com, E-mail: sthoundjo@yahoo.fr

2015-10-01

We seek to obtain a new class of exact solutions of regular black holes in f(T) Gravity with non-linear electrodynamics material content, with spherical symmetry in 4D. The equations of motion provide the regaining of various solutions of General Relativity, as a particular case where the function f(T)=T. We developed a powerful method for finding exact solutions, where we get the first new class of regular black holes solutions in the f(T) Theory, where all the geometrics scalars disappear at the origin of the radial coordinate and are finite everywhere, as well as a new class of singular black holes.

Controllable parabolic-cylinder optical rogue wave.

PubMed

Zhong, Wei-Ping; Chen, Lang; Belić, Milivoj; Petrović, Nikola

2014-10-01

We demonstrate controllable parabolic-cylinder optical rogue waves in certain inhomogeneous media. An analytical rogue wave solution of the generalized nonlinear Schrödinger equation with spatially modulated coefficients and an external potential in the form of modulated quadratic potential is obtained by the similarity transformation. Numerical simulations are performed for comparison with the analytical solutions and to confirm the stability of the rogue wave solution obtained. These optical rogue waves are built by the products of parabolic-cylinder functions and the basic rogue wave solution of the standard nonlinear Schrödinger equation. Such rogue waves may appear in different forms, as the hump and paw profiles.

Detection of weak signals in memory thermal baths.

PubMed

Jiménez-Aquino, J I; Velasco, R M; Romero-Bastida, M

2014-11-01

The nonlinear relaxation time and the statistics of the first passage time distribution in connection with the quasideterministic approach are used to detect weak signals in the decay process of the unstable state of a Brownian particle embedded in memory thermal baths. The study is performed in the overdamped approximation of a generalized Langevin equation characterized by an exponential decay in the friction memory kernel. A detection criterion for each time scale is studied: The first one is referred to as the receiver output, which is given as a function of the nonlinear relaxation time, and the second one is related to the statistics of the first passage time distribution.

Hamilton's Equations with Euler Parameters for Rigid Body Dynamics Modeling. Chapter 3

NASA Technical Reports Server (NTRS)

Shivarama, Ravishankar; Fahrenthold, Eric P.

2004-01-01

A combination of Euler parameter kinematics and Hamiltonian mechanics provides a rigid body dynamics model well suited for use in strongly nonlinear problems involving arbitrarily large rotations. The model is unconstrained, free of singularities, includes a general potential energy function and a minimum set of momentum variables, and takes an explicit state space form convenient for numerical implementation. The general formulation may be specialized to address particular applications, as illustrated in several three dimensional example problems.

A general-purpose optimization program for engineering design

NASA Technical Reports Server (NTRS)

Vanderplaats, G. N.; Sugimoto, H.

1986-01-01

A new general-purpose optimization program for engineering design is described. ADS (Automated Design Synthesis) is a FORTRAN program for nonlinear constrained (or unconstrained) function minimization. The optimization process is segmented into three levels: Strategy, Optimizer, and One-dimensional search. At each level, several options are available so that a total of nearly 100 possible combinations can be created. An example of available combinations is the Augmented Lagrange Multiplier method, using the BFGS variable metric unconstrained minimization together with polynomial interpolation for the one-dimensional search.

Physics, Nonlinear Time Series Analysis, Data Assimilation and Hyperfast Modeling of Nonlinear Ocean Waves

DTIC Science & Technology

2010-09-30

Hyperfast Modeling of Nonlinear Ocean Waves A. R. Osborne Dipartimento di Fisica Generale, Università di Torino Via Pietro Giuria 1, 10125...PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) Universit?i Torino,Dipartimento di Fisica Generale,Via Pietro Giuria 1,10125 Torino, Italy, 8. PERFORMING

Elementary properties of triangle in normed spaces

NASA Astrophysics Data System (ADS)

Triana, Deri; Yunus, Mahmud

2018-03-01

Based on concepts of trigonometric on plane, In this paper we generalized those concept in normed spaces. About the orthogonality concept between two vectors already well known, we are interested to develop elementary properties of triangle, especially the properties of its angle. We propose a non-linear (Wilson) functional to define an angle and explore its properties.

Guided particle swarm optimization method to solve general nonlinear optimization problems

NASA Astrophysics Data System (ADS)

Abdelhalim, Alyaa; Nakata, Kazuhide; El-Alem, Mahmoud; Eltawil, Amr

2018-04-01

The development of hybrid algorithms is becoming an important topic in the global optimization research area. This article proposes a new technique in hybridizing the particle swarm optimization (PSO) algorithm and the Nelder-Mead (NM) simplex search algorithm to solve general nonlinear unconstrained optimization problems. Unlike traditional hybrid methods, the proposed method hybridizes the NM algorithm inside the PSO to improve the velocities and positions of the particles iteratively. The new hybridization considers the PSO algorithm and NM algorithm as one heuristic, not in a sequential or hierarchical manner. The NM algorithm is applied to improve the initial random solution of the PSO algorithm and iteratively in every step to improve the overall performance of the method. The performance of the proposed method was tested over 20 optimization test functions with varying dimensions. Comprehensive comparisons with other methods in the literature indicate that the proposed solution method is promising and competitive.

Parametric Studies of Square Solar Sails Using Finite Element Analysis

NASA Technical Reports Server (NTRS)

Sleight, David W.; Muheim, Danniella M.

2004-01-01

Parametric studies are performed on two generic square solar sail designs to identify parameters of interest. The studies are performed on systems-level models of full-scale solar sails, and include geometric nonlinearity and inertia relief, and use a Newton-Raphson scheme to apply sail pre-tensioning and solar pressure. Computational strategies and difficulties encountered during the analyses are also addressed. The purpose of this paper is not to compare the benefits of one sail design over the other. Instead, the results of the parametric studies may be used to identify general response trends, and areas of potential nonlinear structural interactions for future studies. The effects of sail size, sail membrane pre-stress, sail membrane thickness, and boom stiffness on the sail membrane and boom deformations, boom loads, and vibration frequencies are studied. Over the range of parameters studied, the maximum sail deflection and boom deformations are a nonlinear function of the sail properties. In general, the vibration frequencies and modes are closely spaced. For some vibration mode shapes, local deformation patterns that dominate the response are identified. These localized patterns are attributed to the presence of negative stresses in the sail membrane that are artifacts of the assumption of ignoring the effects of wrinkling in the modeling process, and are not believed to be physically meaningful. Over the range of parameters studied, several regions of potential nonlinear modal interaction are identified.

Phase Domain Walls in Weakly Nonlinear Deep Water Surface Gravity Waves.

PubMed

Tsitoura, F; Gietz, U; Chabchoub, A; Hoffmann, N

2018-06-01

We report a theoretical derivation, an experimental observation and a numerical validation of nonlinear phase domain walls in weakly nonlinear deep water surface gravity waves. The domain walls presented are connecting homogeneous zones of weakly nonlinear plane Stokes waves of identical amplitude and wave vector but differences in phase. By exploiting symmetry transformations within the framework of the nonlinear Schrödinger equation we demonstrate the existence of exact analytical solutions representing such domain walls in the weakly nonlinear limit. The walls are in general oblique to the direction of the wave vector and stationary in moving reference frames. Experimental and numerical studies confirm and visualize the findings. Our present results demonstrate that nonlinear domain walls do exist in the weakly nonlinear regime of general systems exhibiting dispersive waves.

Phase Domain Walls in Weakly Nonlinear Deep Water Surface Gravity Waves

NASA Astrophysics Data System (ADS)

Tsitoura, F.; Gietz, U.; Chabchoub, A.; Hoffmann, N.

2018-06-01

We report a theoretical derivation, an experimental observation and a numerical validation of nonlinear phase domain walls in weakly nonlinear deep water surface gravity waves. The domain walls presented are connecting homogeneous zones of weakly nonlinear plane Stokes waves of identical amplitude and wave vector but differences in phase. By exploiting symmetry transformations within the framework of the nonlinear Schrödinger equation we demonstrate the existence of exact analytical solutions representing such domain walls in the weakly nonlinear limit. The walls are in general oblique to the direction of the wave vector and stationary in moving reference frames. Experimental and numerical studies confirm and visualize the findings. Our present results demonstrate that nonlinear domain walls do exist in the weakly nonlinear regime of general systems exhibiting dispersive waves.

Adaptive Constrained Optimal Control Design for Data-Based Nonlinear Discrete-Time Systems With Critic-Only Structure.

PubMed

Luo, Biao; Liu, Derong; Wu, Huai-Ning

2018-06-01

Reinforcement learning has proved to be a powerful tool to solve optimal control problems over the past few years. However, the data-based constrained optimal control problem of nonaffine nonlinear discrete-time systems has rarely been studied yet. To solve this problem, an adaptive optimal control approach is developed by using the value iteration-based Q-learning (VIQL) with the critic-only structure. Most of the existing constrained control methods require the use of a certain performance index and only suit for linear or affine nonlinear systems, which is unreasonable in practice. To overcome this problem, the system transformation is first introduced with the general performance index. Then, the constrained optimal control problem is converted to an unconstrained optimal control problem. By introducing the action-state value function, i.e., Q-function, the VIQL algorithm is proposed to learn the optimal Q-function of the data-based unconstrained optimal control problem. The convergence results of the VIQL algorithm are established with an easy-to-realize initial condition . To implement the VIQL algorithm, the critic-only structure is developed, where only one neural network is required to approximate the Q-function. The converged Q-function obtained from the critic-only VIQL method is employed to design the adaptive constrained optimal controller based on the gradient descent scheme. Finally, the effectiveness of the developed adaptive control method is tested on three examples with computer simulation.

On a new class of completely integrable nonlinear wave equations. II. Multi-Hamiltonian structure

NASA Astrophysics Data System (ADS)

Nutku, Y.

1987-11-01

The multi-Hamiltonian structure of a class of nonlinear wave equations governing the propagation of finite amplitude waves is discussed. Infinitely many conservation laws had earlier been obtained for these equations. Starting from a (primary) Hamiltonian formulation of these equations the necessary and sufficient conditions for the existence of bi-Hamiltonian structure are obtained and it is shown that the second Hamiltonian operator can be constructed solely through a knowledge of the first Hamiltonian function. The recursion operator which first appears at the level of bi-Hamiltonian structure gives rise to an infinite sequence of conserved Hamiltonians. It is found that in general there exist two different infinite sequences of conserved quantities for these equations. The recursion relation defining higher Hamiltonian structures enables one to obtain the necessary and sufficient conditions for the existence of the (k+1)st Hamiltonian operator which depends on the kth Hamiltonian function. The infinite sequence of conserved Hamiltonians are common to all the higher Hamiltonian structures. The equations of gas dynamics are discussed as an illustration of this formalism and it is shown that in general they admit tri-Hamiltonian structure with two distinct infinite sets of conserved quantities. The isothermal case of γ=1 is an exceptional one that requires separate treatment. This corresponds to a specialization of the equations governing the expansion of plasma into vacuum which will be shown to be equivalent to Poisson's equation in nonlinear acoustics.

Magnetosonic solitons in space plasmas: dark or bright solitons?

NASA Astrophysics Data System (ADS)

Pokhotelov, O. A.; Onishchenko, O. G.; Balikhin, M. A.; Stenflo, L.; Shukla, P. K.

2007-12-01

The nonlinear theory of large-amplitude magnetosonic (MS) waves in highβ space plasmas is revisited. It is shown that solitary waves can exist in the form of `bright' or `dark' solitons in which the magnetic field is increased or decreased relative to the background magnetic field. This depends on the shape of the equilibrium ion distribution function. The basic parameter that controls the nonlinear structure is the wave dispersion, which can be either positive or negative. A general dispersion relation for MS waves propagating perpendicularly to the external magnetic field in a plasma with an arbitrary velocity distribution function is derived.It takes into account general plasma equilibria, such as the Dory-Guest-Harris (DGH) or Kennel-Ashour-Abdalla (KA) loss-cone equilibria, as well as distributions with a power-law velocity dependence that can be modelled by κdistributions. It is shown that in a bi-Maxwellian plasma the dispersion is negative, i.e. the phase velocity decreases with an increase of the wavenumber. This means that the solitary solution in this case has the form of a `bright' soliton with the magnetic field increased. On the contrary, in some non-Maxwellian plasmas, such as those with ring-type ion distributions or DGH plasmas, the solitary solution may have the form of a magnetic hole. The results of similar investigations based on nonlinear Hall-MHD equations are reviewed. The relevance of our theoretical results to existing satellite wave observations is outlined.

Magnetosonic Solitons in Non-Maxwellian Space Plasmas

NASA Astrophysics Data System (ADS)

Pokhotelov, O. A.; Balikhin, M.; Onishchenko, O. G.

2006-12-01

The nonlinear theory of large-amplitude magnetosonic (MS) waves in high-beta space plasmas is developed. It is shown that solitary waves can exist in the form of magnetic humps and holes in which the magnetic field is increased or decreased relative to the background magnetic field. This depends on the shape of the equilibrium ion velocity distribution function. The basic parameter that controls the nonlinear structure is the wave dispersion which can be either positive or negative. A general dispersion relation for MS waves propagating perpendicularly to the external magnetic field in a plasma with an arbitrary velocity distribution function is derived. It takes into account general plasma equilibria such as the Dory-Guest-Harris or Kennel- Ashour-Abdalla loss cone equilibria, as well as distributions with a power law velocity dependence that can be modelled by kappa-distributions. It is shown that in Maxwellian and bi-Maxwellian plasmas the dispersion is negative, i.e. the phase velocity decreases with an increase of the wave number. This means that the solitary solution in this case has the form of a magnetic hump with the magnetic field increased. On the contrary, in some non-Maxwellian plasmas such as those with ring-type ion distributions or DGH plasmas, the solitary solution may have the form of a magnetic hole. The results of similar investigations based on nonlinear Hall-MHD equations are reviewed. The relevance of our theoretical results to experimental observations is outlined

Complete super-sample lensing covariance in the response approach

NASA Astrophysics Data System (ADS)

Barreira, Alexandre; Krause, Elisabeth; Schmidt, Fabian

2018-06-01

We derive the complete super-sample covariance (SSC) of the matter and weak lensing convergence power spectra using the power spectrum response formalism to accurately describe the coupling of super- to sub-survey modes. The SSC term is completely characterized by the survey window function, the nonlinear matter power spectrum and the full first-order nonlinear power spectrum response function, which describes the response to super-survey density and tidal field perturbations. Generalized separate universe simulations can efficiently measure these responses in the nonlinear regime of structure formation, which is necessary for lensing applications. We derive the lensing SSC formulae for two cases: one under the Limber and flat-sky approximations, and a more general one that goes beyond the Limber approximation in the super-survey mode and is valid for curved sky applications. Quantitatively, we find that for sky fractions fsky ≈ 0.3 and a single source redshift at zS=1, the use of the flat-sky and Limber approximation underestimates the total SSC contribution by ≈ 10%. The contribution from super-survey tidal fields to the lensing SSC, which has not been included in cosmological analyses so far, is shown to represent about 5% of the total lensing covariance on multipoles l1,l2 gtrsim 300. The SSC is the dominant off-diagonal contribution to the total lensing covariance, making it appropriate to include these tidal terms and beyond flat-sky/Limber corrections in cosmic shear analyses.

Generalized neurofuzzy network modeling algorithms using Bézier-Bernstein polynomial functions and additive decomposition.

PubMed

Hong, X; Harris, C J

2000-01-01

This paper introduces a new neurofuzzy model construction algorithm for nonlinear dynamic systems based upon basis functions that are Bézier-Bernstein polynomial functions. This paper is generalized in that it copes with n-dimensional inputs by utilising an additive decomposition construction to overcome the curse of dimensionality associated with high n. This new construction algorithm also introduces univariate Bézier-Bernstein polynomial functions for the completeness of the generalized procedure. Like the B-spline expansion based neurofuzzy systems, Bézier-Bernstein polynomial function based neurofuzzy networks hold desirable properties such as nonnegativity of the basis functions, unity of support, and interpretability of basis function as fuzzy membership functions, moreover with the additional advantages of structural parsimony and Delaunay input space partition, essentially overcoming the curse of dimensionality associated with conventional fuzzy and RBF networks. This new modeling network is based on additive decomposition approach together with two separate basis function formation approaches for both univariate and bivariate Bézier-Bernstein polynomial functions used in model construction. The overall network weights are then learnt using conventional least squares methods. Numerical examples are included to demonstrate the effectiveness of this new data based modeling approach.

Quantum simulation from the bottom up: the case of rebits

NASA Astrophysics Data System (ADS)

Enshan Koh, Dax; Yuezhen Niu, Murphy; Yoder, Theodore J.

2018-05-01

Typically, quantum mechanics is thought of as a linear theory with unitary evolution governed by the Schrödinger equation. While this is technically true and useful for a physicist, with regards to computation it is an unfortunately narrow point of view. Just as a classical computer can simulate highly nonlinear functions of classical states, so too can the more general quantum computer simulate nonlinear evolutions of quantum states. We detail one particular simulation of nonlinearity on a quantum computer, showing how the entire class of -unitary evolutions (on n qubits) can be simulated using a unitary, real-amplitude quantum computer (consisting of n  +  1 qubits in total). These operators can be represented as the sum of a linear and antilinear operator, and add an intriguing new set of nonlinear quantum gates to the toolbox of the quantum algorithm designer. Furthermore, a subgroup of these nonlinear evolutions, called the -Cliffords, can be efficiently classically simulated, by making use of the fact that Clifford operators can simulate non-Clifford (in fact, non-linear) operators. This perspective of using the physical operators that we have to simulate non-physical ones that we do not is what we call bottom-up simulation, and we give some examples of its broader implications.

Nonlinear phenomena in the vocalizations of North Atlantic right whales (Eubalaena glacialis) and killer whales (Orcinus orca).

PubMed

Tyson, Reny B; Nowacek, Douglas P; Miller, Patrick J O

2007-09-01

Nonlinear phenomena or nonlinearities in animal vocalizations include features such as subharmonics, deterministic chaos, biphonation, and frequency jumps that until recently were generally ignored in acoustic analyses. Recent documentation of these phenomena in several species suggests that they may play a communicative role, though the exact function is still under investigation. Here, qualitative descriptions and quantitative analyses of nonlinearities in the vocalizations of killer whales (Orcinus orca) and North Atlantic right whales (Eubalaena glacialis) are provided. All four nonlinear features were present in both species, with at least one feature occurring in 92.4% of killer and 65.7% of right whale vocalizations analyzed. Occurrence of biphonation varied the most between species, being present in 89.0% of killer whale vocalizations and only 20.4% of right whale vocalizations. Because deterministic chaos is qualitatively and quantitatively different than random or Gaussian noise, a program (TISEAN) designed specifically to identify deterministic chaos to confirm the presence of this nonlinearity was used. All segments tested in this software indicate that both species do indeed exhibit deterministic chaos. The results of this study provide confirmation that such features are common in the vocalizations of cetacean species and lay the groundwork for future studies.

A new analytical method for characterizing nonlinear visual processes with stimuli of arbitrary distribution: Theory and applications.

PubMed

Hayashi, Ryusuke; Watanabe, Osamu; Yokoyama, Hiroki; Nishida, Shin'ya

2017-06-01

Characterization of the functional relationship between sensory inputs and neuronal or observers' perceptual responses is one of the fundamental goals of systems neuroscience and psychophysics. Conventional methods, such as reverse correlation and spike-triggered data analyses are limited in their ability to resolve complex and inherently nonlinear neuronal/perceptual processes because these methods require input stimuli to be Gaussian with a zero mean. Recent studies have shown that analyses based on a generalized linear model (GLM) do not require such specific input characteristics and have advantages over conventional methods. GLM, however, relies on iterative optimization algorithms and its calculation costs become very expensive when estimating the nonlinear parameters of a large-scale system using large volumes of data. In this paper, we introduce a new analytical method for identifying a nonlinear system without relying on iterative calculations and yet also not requiring any specific stimulus distribution. We demonstrate the results of numerical simulations, showing that our noniterative method is as accurate as GLM in estimating nonlinear parameters in many cases and outperforms conventional, spike-triggered data analyses. As an example of the application of our method to actual psychophysical data, we investigated how different spatiotemporal frequency channels interact in assessments of motion direction. The nonlinear interaction estimated by our method was consistent with findings from previous vision studies and supports the validity of our method for nonlinear system identification.

A novel technique to solve nonlinear higher-index Hessenberg differential-algebraic equations by Adomian decomposition method.

PubMed

Benhammouda, Brahim

2016-01-01

Since 1980, the Adomian decomposition method (ADM) has been extensively used as a simple powerful tool that applies directly to solve different kinds of nonlinear equations including functional, differential, integro-differential and algebraic equations. However, for differential-algebraic equations (DAEs) the ADM is applied only in four earlier works. There, the DAEs are first pre-processed by some transformations like index reductions before applying the ADM. The drawback of such transformations is that they can involve complex algorithms, can be computationally expensive and may lead to non-physical solutions. The purpose of this paper is to propose a novel technique that applies the ADM directly to solve a class of nonlinear higher-index Hessenberg DAEs systems efficiently. The main advantage of this technique is that; firstly it avoids complex transformations like index reductions and leads to a simple general algorithm. Secondly, it reduces the computational work by solving only linear algebraic systems with a constant coefficient matrix at each iteration, except for the first iteration where the algebraic system is nonlinear (if the DAE is nonlinear with respect to the algebraic variable). To demonstrate the effectiveness of the proposed technique, we apply it to a nonlinear index-three Hessenberg DAEs system with nonlinear algebraic constraints. This technique is straightforward and can be programmed in Maple or Mathematica to simulate real application problems.

A multiplicative process for generating a beta-like survival function with application to the UK 2016 EU referendum results

NASA Astrophysics Data System (ADS)

Fenner, Trevor; Kaufmann, Eric; Levene, Mark; Loizou, George

Human dynamics and sociophysics suggest statistical models that may explain and provide us with better insight into social phenomena. Contextual and selection effects tend to produce extreme values in the tails of rank-ordered distributions of both census data and district-level election outcomes. Models that account for this nonlinearity generally outperform linear models. Fitting nonlinear functions based on rank-ordering census and election data therefore improves the fit of aggregate voting models. This may help improve ecological inference, as well as election forecasting in majoritarian systems. We propose a generative multiplicative decrease model that gives rise to a rank-order distribution and facilitates the analysis of the recent UK EU referendum results. We supply empirical evidence that the beta-like survival function, which can be generated directly from our model, is a close fit to the referendum results, and also may have predictive value when covariate data are available.

Generalized Fractional Derivative Anisotropic Viscoelastic Characterization.

PubMed

Hilton, Harry H

2012-01-18

Isotropic linear and nonlinear fractional derivative constitutive relations are formulated and examined in terms of many parameter generalized Kelvin models and are analytically extended to cover general anisotropic homogeneous or non-homogeneous as well as functionally graded viscoelastic material behavior. Equivalent integral constitutive relations, which are computationally more powerful, are derived from fractional differential ones and the associated anisotropic temperature-moisture-degree-of-cure shift functions and reduced times are established. Approximate Fourier transform inversions for fractional derivative relations are formulated and their accuracy is evaluated. The efficacy of integer and fractional derivative constitutive relations is compared and the preferential use of either characterization in analyzing isotropic and anisotropic real materials must be examined on a case-by-case basis. Approximate protocols for curve fitting analytical fractional derivative results to experimental data are formulated and evaluated.

Multi-level adaptive finite element methods. 1: Variation problems

NASA Technical Reports Server (NTRS)

Brandt, A.

1979-01-01

A general numerical strategy for solving partial differential equations and other functional problems by cycling between coarser and finer levels of discretization is described. Optimal discretization schemes are provided together with very fast general solvers. It is described in terms of finite element discretizations of general nonlinear minimization problems. The basic processes (relaxation sweeps, fine-grid-to-coarse-grid transfers of residuals, coarse-to-fine interpolations of corrections) are directly and naturally determined by the objective functional and the sequence of approximation spaces. The natural processes, however, are not always optimal. Concrete examples are given and some new techniques are reviewed. Including the local truncation extrapolation and a multilevel procedure for inexpensively solving chains of many boundary value problems, such as those arising in the solution of time-dependent problems.

Optimal estimation for discrete time jump processes

NASA Technical Reports Server (NTRS)

Vaca, M. V.; Tretter, S. A.

1978-01-01

Optimum estimates of nonobservable random variables or random processes which influence the rate functions of a discrete time jump process (DTJP) are derived. The approach used is based on the a posteriori probability of a nonobservable event expressed in terms of the a priori probability of that event and of the sample function probability of the DTJP. Thus a general representation is obtained for optimum estimates, and recursive equations are derived for minimum mean-squared error (MMSE) estimates. In general, MMSE estimates are nonlinear functions of the observations. The problem is considered of estimating the rate of a DTJP when the rate is a random variable with a beta probability density function and the jump amplitudes are binomially distributed. It is shown that the MMSE estimates are linear. The class of beta density functions is rather rich and explains why there are insignificant differences between optimum unconstrained and linear MMSE estimates in a variety of problems.

Maximization of Learning Speed in the Motor Cortex Due to Neuronal Redundancy

PubMed Central

Takiyama, Ken; Okada, Masato

2012-01-01

Many redundancies play functional roles in motor control and motor learning. For example, kinematic and muscle redundancies contribute to stabilizing posture and impedance control, respectively. Another redundancy is the number of neurons themselves; there are overwhelmingly more neurons than muscles, and many combinations of neural activation can generate identical muscle activity. The functional roles of this neuronal redundancy remains unknown. Analysis of a redundant neural network model makes it possible to investigate these functional roles while varying the number of model neurons and holding constant the number of output units. Our analysis reveals that learning speed reaches its maximum value if and only if the model includes sufficient neuronal redundancy. This analytical result does not depend on whether the distribution of the preferred direction is uniform or a skewed bimodal, both of which have been reported in neurophysiological studies. Neuronal redundancy maximizes learning speed, even if the neural network model includes recurrent connections, a nonlinear activation function, or nonlinear muscle units. Furthermore, our results do not rely on the shape of the generalization function. The results of this study suggest that one of the functional roles of neuronal redundancy is to maximize learning speed. PMID:22253586

Exact multisoliton solutions of general nonlinear Schrödinger equation with derivative.

PubMed

Li, Qi; Duan, Qiu-yuan; Zhang, Jian-bing

2014-01-01

Multisoliton solutions are derived for a general nonlinear Schrödinger equation with derivative by using Hirota's approach. The dynamics of one-soliton solution and two-soliton interactions are also illustrated. The considered equation can reduce to nonlinear Schrödinger equation with derivative as well as the solutions.

An experimentally based nonlinear viscoelastic model of joint passive moment.

PubMed

Esteki, A; Mansour, J M

1996-04-01

Previous investigations have not converged on a generally accepted model of the dissipative part of joint passive moment. To provide a basis for developing a model, a series of measurements were performed to characterize the passive moment at the metacarpophalangeal joint of the index finger. Two measurement procedures were used, one in moment relaxation over a range of fixed joint angles and the other at a series of constant joint velocities. Fung's quasi-linear viscoelastic theory motivated the development of the passive moment model. Using this approach, it was not necessary to make restrictive assumptions regarding the viscoelastic behavior of the passive moment. The generality of the formulation allowed specific functions to be chosen based on experimental data rather than finding coefficients which attempted to fit a preselected model of the data. It was shown that a nonlinear viscoelastic model described the passive stiffness. No significant frictional effects were found. Of particular importance was the nonlinear behavior of the dissipative part of the passive moment which was modeled by joint speed raised to a power less than one. This result could explain the differing findings among previous investigations, and may have important implications for control of limb movement.

Modeling exposure–lag–response associations with distributed lag non-linear models

PubMed Central

Gasparrini, Antonio

2014-01-01

In biomedical research, a health effect is frequently associated with protracted exposures of varying intensity sustained in the past. The main complexity of modeling and interpreting such phenomena lies in the additional temporal dimension needed to express the association, as the risk depends on both intensity and timing of past exposures. This type of dependency is defined here as exposure–lag–response association. In this contribution, I illustrate a general statistical framework for such associations, established through the extension of distributed lag non-linear models, originally developed in time series analysis. This modeling class is based on the definition of a cross-basis, obtained by the combination of two functions to flexibly model linear or nonlinear exposure-responses and the lag structure of the relationship, respectively. The methodology is illustrated with an example application to cohort data and validated through a simulation study. This modeling framework generalizes to various study designs and regression models, and can be applied to study the health effects of protracted exposures to environmental factors, drugs or carcinogenic agents, among others. © 2013 The Authors. Statistics in Medicine published by John Wiley & Sons, Ltd. PMID:24027094

Stability properties of a general class of nonlinear dynamical systems

NASA Astrophysics Data System (ADS)

Gléria, I. M.; Figueiredo, A.; Rocha Filho, T. M.

2001-05-01

We establish sufficient conditions for the boundedness of the trajectories and the stability of the fixed points in a class of general nonlinear systems, the so-called quasi-polynomial vector fields, with the help of a natural embedding of such systems in a family of generalized Lotka-Volterra (LV) equations. A purely algebraic procedure is developed to determine such conditions. We apply our method to obtain new results for LV systems, by a reparametrization in time variable, and to study general nonlinear vector fields, originally far from the LV format.

Extended Kalman Filter for Estimation of Parameters in Nonlinear State-Space Models of Biochemical Networks

PubMed Central

Sun, Xiaodian; Jin, Li; Xiong, Momiao

2008-01-01

It is system dynamics that determines the function of cells, tissues and organisms. To develop mathematical models and estimate their parameters are an essential issue for studying dynamic behaviors of biological systems which include metabolic networks, genetic regulatory networks and signal transduction pathways, under perturbation of external stimuli. In general, biological dynamic systems are partially observed. Therefore, a natural way to model dynamic biological systems is to employ nonlinear state-space equations. Although statistical methods for parameter estimation of linear models in biological dynamic systems have been developed intensively in the recent years, the estimation of both states and parameters of nonlinear dynamic systems remains a challenging task. In this report, we apply extended Kalman Filter (EKF) to the estimation of both states and parameters of nonlinear state-space models. To evaluate the performance of the EKF for parameter estimation, we apply the EKF to a simulation dataset and two real datasets: JAK-STAT signal transduction pathway and Ras/Raf/MEK/ERK signaling transduction pathways datasets. The preliminary results show that EKF can accurately estimate the parameters and predict states in nonlinear state-space equations for modeling dynamic biochemical networks. PMID:19018286

Nonlinear Pattern Selection in Bi-Modal Interfacial Instabilities

NASA Astrophysics Data System (ADS)

Picardo, Jason; Narayanan, Ranga

2016-11-01

We study the evolution of two interacting unstable interfaces, with the aim of understanding the role of non-linearity in pattern selection. Specifically, we consider two superposed thin films on a heated surface, that are susceptible to thermocapillary and Rayleigh-Taylor instabilities. Due to the presence of two unstable interfaces, the dispersion curve (linear growth rate plotted as a function of the perturbation wavelength) exhibits two peaks. If these peaks have equal heights, then the two corresponding disturbance patterns will grow with the same linear growth rate. Therefore, any selection between the two must occur via nonlinear effects. The two-interface problem under consideration provides a variety of such bi-modal situations, in which the role of nonlinearity in pattern selection is unveiled. We use a combination of long wave asymptotics, numerical simulations and amplitude expansions to understand the subtle nonlinear interactions between the two peak modes. Our results offer a counter-example to Rayleigh's principle of pattern formation, that the fastest growing linear mode will dominate the final pattern. Far from being governed by any such general dogma, the final selected pattern varies considerably from case to case. The authors acknowledge funding from NSF (0968313) and the Fulbright-Nehru fellowship.

Soliton and periodic solutions for time-dependent coefficient non-linear equation

NASA Astrophysics Data System (ADS)

Guner, Ozkan

2016-01-01

In this article, we establish exact solutions for the generalized (3+1)-dimensional variable coefficient Kadomtsev-Petviashvili (GVCKP) equation. Using solitary wave ansatz in terms of ? functions and the modified sine-cosine method, we find exact analytical bright soliton solutions and exact periodic solutions for the considered model. The physical parameters in the soliton solutions are obtained as function of the dependent model coefficients. The effectiveness and reliability of the method are shown by its application to the GVCKP equation.

Convection Regularization of High Wavenumbers in Turbulence ANS Shocks

DTIC Science & Technology

2011-07-31

dynamics of particles that adhere to one another upon collision and has been studied as a simple cosmological model for describing the nonlinear formation of...solution we mean a solution to the Cauchy problem in the following sense. Definition 5.1. A function u : R × [0, T ] 7→ RN is a weak solution of the...step 2 the limit function in the α → 0 limit is shown to satisfy the definition of a weak solution for the Cauchy problem. Without loss of generality

Linear and nonlinear stiffness and friction in biological rhythmic movements.

PubMed

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.

Optimizing Synchronization Stability of the Kuramoto Model in Complex Networks and Power Grids

NASA Astrophysics Data System (ADS)

Li, Bo; Wong, K. Y. Michael

Maintaining the stability of synchronization state is crucial for the functioning of many natural and artificial systems. For the Kuramoto model on general weighted networks, the synchronization stability, measured by the dominant Lyapunov exponent at the steady state, is shown to have intricate and nonlinear dependence on the network topology and the dynamical parameters. Specifically, the dominant Lyapunov exponent corresponds to the algebraic connectivity of a meta-graph whose edge weight depends nonlinearly on the steady states. In this study, we utilize the cut-set space (DC) approximation to estimate the nonlinear steady state and simplify the calculation of the stability measure, based on which we further derive efficient algorithms to optimize the synchronization stability. The properties of the optimized networks and application in power grid stability are also discussed. This work is supported by a Grant from the Research Grant Council of Hong Kong (Grant Numbers 605813 and 16322616).

On the correct implementation of Fermi-Dirac statistics and electron trapping in nonlinear electrostatic plane wave propagation in collisionless plasmas

NASA Astrophysics Data System (ADS)

Schamel, Hans; Eliasson, Bengt

2016-05-01

Quantum statistics and electron trapping have a decisive influence on the propagation characteristics of coherent stationary electrostatic waves. The description of these strictly nonlinear structures, which are of electron hole type and violate linear Vlasov theory due to the particle trapping at any excitation amplitude, is obtained by a correct reduction of the three-dimensional Fermi-Dirac distribution function to one dimension and by a proper incorporation of trapping. For small but finite amplitudes, the holes become of cnoidal wave type and the electron density is shown to be described by a ϕ ( x ) 1 / 2 rather than a ϕ ( x ) expansion, where ϕ ( x ) is the electrostatic potential. The general coefficients are presented for a degenerate plasma as well as the quantum statistical analogue to these steady state coherent structures, including the shape of ϕ ( x ) and the nonlinear dispersion relation, which describes their phase velocity.

Nonlinear GARCH model and 1 / f noise

NASA Astrophysics Data System (ADS)

Kononovicius, A.; Ruseckas, J.

2015-06-01

Auto-regressive conditionally heteroskedastic (ARCH) family models are still used, by practitioners in business and economic policy making, as a conditional volatility forecasting models. Furthermore ARCH models still are attracting an interest of the researchers. In this contribution we consider the well known GARCH(1,1) process and its nonlinear modifications, reminiscent of NGARCH model. We investigate the possibility to reproduce power law statistics, probability density function and power spectral density, using ARCH family models. For this purpose we derive stochastic differential equations from the GARCH processes in consideration. We find the obtained equations to be similar to a general class of stochastic differential equations known to reproduce power law statistics. We show that linear GARCH(1,1) process has power law distribution, but its power spectral density is Brownian noise-like. However, the nonlinear modifications exhibit both power law distribution and power spectral density of the 1 /fβ form, including 1 / f noise.

Sum-Frequency Generation from a Thin Cylindrical Layer

NASA Astrophysics Data System (ADS)

Shamyna, A. A.; Kapshai, V. N.

2018-01-01

In the Rayleigh-Gans-Debye approximation, we have solved the problem of the sum-frequency generation by two plane elliptically polarized electromagnetic waves from the surface of a dielectric particle of a cylindrical shape that is coated by a thin layer possessing nonlinear optical properties. The formulas that describe the sum-frequency field have been presented in the tensor and vector forms for the second-order nonlinear dielectric susceptibility tensor, which was chosen in the general form, containing chiral components. Expressions describing the sum-frequency field from the cylindrical particle ends have been obtained for the case of a nonlinear layer possessing chiral properties. Three-dimensional directivity patterns of the sum-frequency radiation have been analyzed for different combinations of parameters (angles of incidence, degrees of ellipticity, orientations of polarization ellipses, cylindrical particle dimensions). The mathematical properties of the spatial distribution functions of the sum-frequency field, which characterize the symmetry of directivity patterns, have been revealed.

Improving stability and strength characteristics of framed structures with nonlinear behavior

NASA Technical Reports Server (NTRS)

Pezeshk, Shahram

1990-01-01

In this paper an optimal design procedure is introduced to improve the overall performance of nonlinear framed structures. The design methodology presented here is a multiple-objective optimization procedure whose objective functions involve the buckling eigenvalues and eigenvectors of the structure. A constant volume with bounds on the design variables is used in conjunction with an optimality criterion approach. The method provides a general tool for solving complex design problems and generally leads to structures with better limit strength and stability. Many algorithms have been developed to improve the limit strength of structures. In most applications geometrically linear analysis is employed with the consequence that overall strength of the design is overestimated. Directly optimizing the limit load of the structure would require a full nonlinear analysis at each iteration which would be prohibitively expensive. The objective of this paper is to develop an algorithm that can improve the limit-load of geometrically nonlinear framed structures while avoiding the nonlinear analysis. One of the novelties of the new design methodology is its ability to efficiently model and design structures under multiple loading conditions. These loading conditions can be different factored loads or any kind of loads that can be applied to the structure simultaneously or independently. Attention is focused on optimal design of space framed structures. Three-dimensional design problems are more complicated to carry out, but they yield insight into real behavior of the structure and can help avoiding some of the problems that might appear in planar design procedure such as the need for out-of-plane buckling constraint. Although researchers in the field of structural engineering generally agree that optimum design of three-dimension building frames especially in the seismic regions would be beneficial, methods have been slow to emerge. Most of the research in this area has dealt with the optimization of truss and plane frame structures.

Nonlinear integrable model of Frenkel-like excitations on a ribbon of triangular lattice

NASA Astrophysics Data System (ADS)

Vakhnenko, Oleksiy O.

2015-03-01

Following the considerable progress in nanoribbon technology, we propose to model the nonlinear Frenkel-like excitations on a triangular-lattice ribbon by the integrable nonlinear ladder system with the background-controlled intersite resonant coupling. The system of interest arises as a proper reduction of first general semidiscrete integrable system from an infinite hierarchy. The most significant local conservation laws related to the first general integrable system are found explicitly in the framework of generalized recursive approach. The obtained general local densities are equally applicable to any general semidiscrete integrable system from the respective infinite hierarchy. Using the recovered second densities, the Hamiltonian formulation of integrable nonlinear ladder system with background-controlled intersite resonant coupling is presented. In doing so, the relevant Poisson structure turns out to be essentially nontrivial. The Darboux transformation scheme as applied to the first general semidiscrete system is developed and the key role of Bäcklund transformation in justification of its self-consistency is pointed out. The spectral properties of Darboux matrix allow to restore the whole Darboux matrix thus ensuring generation one more soliton as compared with a priori known seed solution of integrable nonlinear system. The power of Darboux-dressing method is explicitly demonstrated in generating the multicomponent one-soliton solution to the integrable nonlinear ladder system with background-controlled intersite resonant coupling.

Quasi-static ensemble variational data assimilation: a theoretical and numerical study with the iterative ensemble Kalman smoother

NASA Astrophysics Data System (ADS)

Fillion, Anthony; Bocquet, Marc; Gratton, Serge

2018-04-01

The analysis in nonlinear variational data assimilation is the solution of a non-quadratic minimization. Thus, the analysis efficiency relies on its ability to locate a global minimum of the cost function. If this minimization uses a Gauss-Newton (GN) method, it is critical for the starting point to be in the attraction basin of a global minimum. Otherwise the method may converge to a local extremum, which degrades the analysis. With chaotic models, the number of local extrema often increases with the temporal extent of the data assimilation window, making the former condition harder to satisfy. This is unfortunate because the assimilation performance also increases with this temporal extent. However, a quasi-static (QS) minimization may overcome these local extrema. It accomplishes this by gradually injecting the observations in the cost function. This method was introduced by Pires et al. (1996) in a 4D-Var context. We generalize this approach to four-dimensional strong-constraint nonlinear ensemble variational (EnVar) methods, which are based on both a nonlinear variational analysis and the propagation of dynamical error statistics via an ensemble. This forces one to consider the cost function minimizations in the broader context of cycled data assimilation algorithms. We adapt this QS approach to the iterative ensemble Kalman smoother (IEnKS), an exemplar of nonlinear deterministic four-dimensional EnVar methods. Using low-order models, we quantify the positive impact of the QS approach on the IEnKS, especially for long data assimilation windows. We also examine the computational cost of QS implementations and suggest cheaper algorithms.

Investigation on nonautonomous soliton management in generalized external potentials via dispersion and nonlinearity

NASA Astrophysics Data System (ADS)

Vijayalekshmi, S.; Mani Rajan, M. S.; Mahalingam, A.; Uthayakumar, A.

2015-09-01

We investigate the controllable behavior of nonautonomous soliton in external potentials with variable dispersion and nonlinearity management functions, which describes the propagation of optical pulses in an inhomogeneous fiber system. We derive the Lax pair with a variable spectral parameter and the exact multi-soliton solution is generated via Darboux transformation. Based on these solutions, several novel optical solitons are constructed by selecting appropriate functions and the main evolution features of these waves are shown by some interesting figures with computer simulation. As few examples, breathers in periodic potential, soliton compression in an exponentially dispersion decreasing fiber and interaction of boomerang solitons are discussed. The presented results have applications in the study of nonautonomous soliton birefringence-managed switching architecture. These results are potentially useful in the management of nonautonomous soliton with external potentials in the optical soliton communications and long-haul telecommunication networks.

A Formally Verified Conflict Detection Algorithm for Polynomial Trajectories

NASA Technical Reports Server (NTRS)

Narkawicz, Anthony; Munoz, Cesar

2015-01-01

In air traffic management, conflict detection algorithms are used to determine whether or not aircraft are predicted to lose horizontal and vertical separation minima within a time interval assuming a trajectory model. In the case of linear trajectories, conflict detection algorithms have been proposed that are both sound, i.e., they detect all conflicts, and complete, i.e., they do not present false alarms. In general, for arbitrary nonlinear trajectory models, it is possible to define detection algorithms that are either sound or complete, but not both. This paper considers the case of nonlinear aircraft trajectory models based on polynomial functions. In particular, it proposes a conflict detection algorithm that precisely determines whether, given a lookahead time, two aircraft flying polynomial trajectories are in conflict. That is, it has been formally verified that, assuming that the aircraft trajectories are modeled as polynomial functions, the proposed algorithm is both sound and complete.

Nonlinear differential equations for the wavefront surface at arbitrary Hartmann-plane distances.

PubMed

Téllez-Quiñones, Alejandro; Malacara-Doblado, Daniel; Flores-Hernández, Ricardo; Gutiérrez-Hernández, David A; León-Rodríguez, Miguel

2016-03-20

In the Hartmann test, a wave aberration function W is estimated from the information of the spot diagram drawn in an observation plane. The distance from a reference plane to the observation plane, the Hartmann-plane distance, is typically chosen as z=f, where f is the radius of a reference sphere. The function W and the transversal aberrations {X,Y} calculated at the plane z=f are related by two well-known linear differential equations. Here, we propose two nonlinear differential equations to denote a more general relation between W and the transversal aberrations {U,V} calculated at any arbitrary Hartmann-plane distance z=r. We also show how to directly estimate the wavefront surface w from the information of {U,V}. The use of arbitrary r values could improve the reliability of the measurements of W, or w, when finding difficulties in adequate ray identification at z=f.

Probabilistic density function method for nonlinear dynamical systems driven by colored noise

DOE Office of Scientific and Technical Information (OSTI.GOV)

Barajas-Solano, David A.; Tartakovsky, Alexandre M.

2016-05-01

We present a probability density function (PDF) method for a system of nonlinear stochastic ordinary differential equations driven by colored noise. The method provides an integro-differential equation for the temporal evolution of the joint PDF of the system's state, which we close by means of a modified Large-Eddy-Diffusivity-type closure. Additionally, we introduce the generalized local linearization (LL) approximation for deriving a computable PDF equation in the form of the second-order partial differential equation (PDE). We demonstrate the proposed closure and localization accurately describe the dynamics of the PDF in phase space for systems driven by noise with arbitrary auto-correlation time.more » We apply the proposed PDF method to the analysis of a set of Kramers equations driven by exponentially auto-correlated Gaussian colored noise to study the dynamics and stability of a power grid.« less

A study of the nonlinear aerodynamics of bodies in nonplanar motion. Ph.D. Thesis - Stanford Univ., Calif.; [numerical analysis of aerodynamic force and moment systems during large amplitude, arbitrary motions

NASA Technical Reports Server (NTRS)

Schiff, L. B.

1974-01-01

Concepts from the theory of functionals are used to develop nonlinear formulations of the aerodynamic force and moment systems acting on bodies in large-amplitude, arbitrary motions. The analysis, which proceeds formally once the functional dependence of the aerodynamic reactions upon the motion variables is established, ensures the inclusion, within the resulting formulation, of pertinent aerodynamic terms that normally are excluded in the classical treatment. Applied to the large-amplitude, slowly varying, nonplanar motion of a body, the formulation suggests that the aerodynamic moment can be compounded of the moments acting on the body in four basic motions: steady angle of attack, pitch oscillations, either roll or yaw oscillations, and coning motion. Coning, where the nose of the body describes a circle around the velocity vector, characterizes the nonplanar nature of the general motion.

Time series trends of the safety effects of pavement resurfacing.

PubMed

Park, Juneyoung; Abdel-Aty, Mohamed; Wang, Jung-Han

2017-04-01

This study evaluated the safety performance of pavement resurfacing projects on urban arterials in Florida using the observational before and after approaches. The safety effects of pavement resurfacing were quantified in the crash modification factors (CMFs) and estimated based on different ranges of heavy vehicle traffic volume and time changes for different severity levels. In order to evaluate the variation of CMFs over time, crash modification functions (CMFunctions) were developed using nonlinear regression and time series models. The results showed that pavement resurfacing projects decrease crash frequency and are found to be more safety effective to reduce severe crashes in general. Moreover, the results of the general relationship between the safety effects and time changes indicated that the CMFs increase over time after the resurfacing treatment. It was also found that pavement resurfacing projects for the urban roadways with higher heavy vehicle volume rate are more safety effective than the roadways with lower heavy vehicle volume rate. Based on the exploration and comparison of the developed CMFucntions, the seasonal autoregressive integrated moving average (SARIMA) and exponential functional form of the nonlinear regression models can be utilized to identify the trend of CMFs over time. Copyright © 2017 Elsevier Ltd. All rights reserved.

Spectral stability of shifted states on star graphs

NASA Astrophysics Data System (ADS)

Kairzhan, Adilbek; Pelinovsky, Dmitry E.

2018-03-01

We consider the nonlinear Schrödinger (NLS) equation with the subcritical power nonlinearity on a star graph consisting of N edges and a single vertex under generalized Kirchhoff boundary conditions. The stationary NLS equation may admit a family of solitary waves parameterized by a translational parameter, which we call the shifted states. The two main examples include (i) the star graph with even N under the classical Kirchhoff boundary conditions and (ii) the star graph with one incoming edge and N  -  1 outgoing edges under a single constraint on coefficients of the generalized Kirchhoff boundary conditions. We obtain the general counting results on the Morse index of the shifted states and apply them to the two examples. In the case of (i), we prove that the shifted states with even N ≥slant 4 are saddle points of the action functional which are spectrally unstable under the NLS flow. In the case of (ii), we prove that the shifted states with the monotone profiles in the N  -  1 edges are spectrally stable, whereas the shifted states with non-monotone profiles in the N  -  1 edges are spectrally unstable, the two families intersect at the half-soliton states which are spectrally stable but nonlinearly unstable under the NLS flow. Since the NLS equation on a star graph with shifted states can be reduced to the homogeneous NLS equation on an infinite line, the spectral instability of shifted states is due to the perturbations breaking this reduction. We give a simple argument suggesting that the spectrally stable shifted states in the case of (ii) are nonlinearly unstable under the NLS flow due to the perturbations breaking the reduction to the homogeneous NLS equation.

Wave propagation in ordered, disordered, and nonlinear photonic band gap materials

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lidorikis, Elefterios

Photonic band gap materials are artificial dielectric structures that give the promise of molding and controlling the flow of optical light the same way semiconductors mold and control the electric current flow. In this dissertation the author studied two areas of photonic band gap materials. The first area is focused on the properties of one-dimensional PBG materials doped with Kerr-type nonlinear material, while, the second area is focused on the mechanisms responsible for the gap formation as well as other properties of two-dimensional PBG materials. He first studied, in Chapter 2, the general adequacy of an approximate structure model inmore » which the nonlinearity is assumed to be concentrated in equally-spaced very thin layers, or 6-functions, while the rest of the space is linear. This model had been used before, but its range of validity and the physical reasons for its limitations were not quite clear yet. He performed an extensive examination of many aspects of the model's nonlinear response and comparison against more realistic models with finite-width nonlinear layers, and found that the d-function model is quite adequate, capturing the essential features in the transmission characteristics. The author found one exception, coming from the deficiency of processing a rigid bottom band edge, i.e. the upper edge of the gaps is always independent of the refraction index contrast. This causes the model to miss-predict that there are no soliton solutions for a positive Kerr-coefficient, something known to be untrue.« less

Nonlinear Filtering Effects of Reservoirs on Flood Frequency Curves at the Regional Scale: RESERVOIRS FILTER FLOOD FREQUENCY CURVES

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Wei; Li, Hong-Yi; Leung, L. Ruby

Anthropogenic activities, e.g., reservoir operation, may alter the characteristics of Flood Frequency Curve (FFC) and challenge the basic assumption of stationarity used in flood frequency analysis. This paper presents a combined data-modeling analysis of the nonlinear filtering effects of reservoirs on the FFCs over the contiguous United States. A dimensionless Reservoir Impact Index (RII), defined as the total upstream reservoir storage capacity normalized by the annual streamflow volume, is used to quantify reservoir regulation effects. Analyses are performed for 388 river stations with an average record length of 50 years. The first two moments of the FFC, mean annual maximummore » flood (MAF) and coefficient of variations (CV), are calculated for the pre- and post-dam periods and compared to elucidate the reservoir regulation effects as a function of RII. It is found that MAF generally decreases with increasing RII but stabilizes when RII exceeds a threshold value, and CV increases with RII until a threshold value beyond which CV decreases with RII. The processes underlying the nonlinear threshold behavior of MAF and CV are investigated using three reservoir models with different levels of complexity. All models capture the non-linear relationships of MAF and CV with RII, suggesting that the basic flood control function of reservoirs is key to the non-linear relationships. The relative roles of reservoir storage capacity, operation objectives, available storage prior to a flood event, and reservoir inflow pattern are systematically investigated. Our findings may help improve flood-risk assessment and mitigation in regulated river systems at the regional scale.« less

Distributed robust finite-time nonlinear consensus protocols for multi-agent systems

NASA Astrophysics Data System (ADS)

Zuo, Zongyu; Tie, Lin

2016-04-01

This paper investigates the robust finite-time consensus problem of multi-agent systems in networks with undirected topology. Global nonlinear consensus protocols augmented with a variable structure are constructed with the aid of Lyapunov functions for each single-integrator agent dynamics in the presence of external disturbances. In particular, it is shown that the finite settling time of the proposed general framework for robust consensus design is upper bounded for any initial condition. This makes it possible for network consensus problems to design and estimate the convergence time offline for a multi-agent team with a given undirected information flow. Finally, simulation results are presented to demonstrate the performance and effectiveness of our finite-time protocols.

Soliton, rational, and periodic solutions for the infinite hierarchy of defocusing nonlinear Schrödinger equations.

PubMed

Ankiewicz, Adrian

2016-07-01

Analysis of short-pulse propagation in positive dispersion media, e.g., in optical fibers and in shallow water, requires assorted high-order derivative terms. We present an infinite-order "dark" hierarchy of equations, starting from the basic defocusing nonlinear Schrödinger equation. We present generalized soliton solutions, plane-wave solutions, and periodic solutions of all orders. We find that "even"-order equations in the set affect phase and "stretching factors" in the solutions, while "odd"-order equations affect the velocities. Hence odd-order equation solutions can be real functions, while even-order equation solutions are complex. There are various applications in optics and water waves.

Nonlinear optimization simplified by hypersurface deformation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stillinger, F.H.; Weber, T.A.

1988-09-01

A general strategy is advanced for simplifying nonlinear optimization problems, the ant-lion method. This approach exploits shape modifications of the cost-function hypersurface which distend basins surrounding low-lying minima (including global minima). By intertwining hypersurface deformations with steepest-descent displacements, the search is concentrated on a small relevant subset of all minima. Specific calculations demonstrating the value of this method are reported for the partitioning of two classes of irregular but nonrandom graphs, the prime-factor graphs and the pi graphs. We also indicate how this approach can be applied to the traveling salesman problem and to design layout optimization, and that itmore » may be useful in combination with simulated annealing strategies.« less

Mystic: Implementation of the Static Dynamic Optimal Control Algorithm for High-Fidelity, Low-Thrust Trajectory Design

NASA Technical Reports Server (NTRS)

Whiffen, Gregory J.

2006-01-01

Mystic software is designed to compute, analyze, and visualize optimal high-fidelity, low-thrust trajectories, The software can be used to analyze inter-planetary, planetocentric, and combination trajectories, Mystic also provides utilities to assist in the operation and navigation of low-thrust spacecraft. Mystic will be used to design and navigate the NASA's Dawn Discovery mission to orbit the two largest asteroids, The underlying optimization algorithm used in the Mystic software is called Static/Dynamic Optimal Control (SDC). SDC is a nonlinear optimal control method designed to optimize both 'static variables' (parameters) and dynamic variables (functions of time) simultaneously. SDC is a general nonlinear optimal control algorithm based on Bellman's principal.

Z-scan theory for nonlocal nonlinear media with simultaneous nonlinear refraction and nonlinear absorption.

PubMed

Rashidian Vaziri, Mohammad Reza

2013-07-10

In this paper, the Z-scan theory for nonlocal nonlinear media has been further developed when nonlinear absorption and nonlinear refraction appear simultaneously. To this end, the nonlinear photoinduced phase shift between the impinging and outgoing Gaussian beams from a nonlocal nonlinear sample has been generalized. It is shown that this kind of phase shift will reduce correctly to its known counterpart for the case of pure refractive nonlinearity. Using this generalized form of phase shift, the basic formulas for closed- and open-aperture beam transmittances in the far field have been provided, and a simple procedure for interpreting the Z-scan results has been proposed. In this procedure, by separately performing open- and closed-aperture Z-scan experiments and using the represented relations for the far-field transmittances, one can measure the nonlinear absorption coefficient and nonlinear index of refraction as well as the order of nonlocality. Theoretically, it is shown that when the absorptive nonlinearity is present in addition to the refractive nonlinearity, the sample nonlocal response can noticeably suppress the peak and enhance the valley of the Z-scan closed-aperture transmittance curves, which is due to the nonlocal action's ability to change the beam transverse dimensions.

Real-Time Fault Detection Approach for Nonlinear Systems and its Asynchronous T-S Fuzzy Observer-Based Implementation.

PubMed

Li, Linlin; Ding, Steven X; Qiu, Jianbin; Yang, Ying

2017-02-01

This paper is concerned with a real-time observer-based fault detection (FD) approach for a general type of nonlinear systems in the presence of external disturbances. To this end, in the first part of this paper, we deal with the definition and the design condition for an L ∞ / L 2 type of nonlinear observer-based FD systems. This analytical framework is fundamental for the development of real-time nonlinear FD systems with the aid of some well-established techniques. In the second part, we address the integrated design of the L ∞ / L 2 observer-based FD systems by applying Takagi-Sugeno (T-S) fuzzy dynamic modeling technique as the solution tool. This fuzzy observer-based FD approach is developed via piecewise Lyapunov functions, and can be applied to the case that the premise variables of the FD system is nonsynchronous with the premise variables of the fuzzy model of the plant. In the end, a case study on the laboratory setup of three-tank system is given to show the efficiency of the proposed results.

Nonlinear bending models for beams and plates

PubMed Central

Antipov, Y. A.

2014-01-01

A new nonlinear model for large deflections of a beam is proposed. It comprises the Euler–Bernoulli boundary value problem for the deflection and a nonlinear integral condition. When bending does not alter the beam length, this condition guarantees that the deflected beam has the original length and fixes the horizontal displacement of the free end. The numerical results are in good agreement with the ones provided by the elastica model. Dynamic and two-dimensional generalizations of this nonlinear one-dimensional static model are also discussed. The model problem for an inextensible rectangular Kirchhoff plate, when one side is clamped, the opposite one is subjected to a shear force, and the others are free of moments and forces, is reduced to a singular integral equation with two fixed singularities. The singularities of the unknown function are examined, and a series-form solution is derived by the collocation method in terms of the associated Jacobi polynomials. The procedure requires solving an infinite system of linear algebraic equations for the expansion coefficients subject to the inextensibility condition. PMID:25294960

A Leonard-Sanders-Budiansky-Koiter-Type Nonlinear Shell Theory with a Hierarchy of Transverse-Shearing Deformations

NASA Technical Reports Server (NTRS)

Nemeth, Michael P.

2013-01-01

A detailed exposition on a refined nonlinear shell theory suitable for nonlinear buckling analyses of laminated-composite shell structures is presented. This shell theory includes the classical nonlinear shell theory attributed to Leonard, Sanders, Koiter, and Budiansky as an explicit proper subset. This approach is used in order to leverage the exisiting experience base and to make the theory attractive to industry. In addition, the formalism of general tensors is avoided in order to expose the details needed to fully understand and use the theory. The shell theory is based on "small" strains and "moderate" rotations, and no shell-thinness approximations are used. As a result, the strain-displacement relations are exact within the presumptions of "small" strains and "moderate" rotations. The effects of transverse-shearing deformations are included in the theory by using analyst-defined functions to describe the through-the-thickness distributions of transverse-shearing strains. Constitutive equations for laminated-composite shells are derived without using any shell-thinness approximations, and simplified forms and special cases are presented.

A heuristic neural network initialization scheme for modeling nonlinear functions in engineering mechanics: continuous development

NASA Astrophysics Data System (ADS)

Pei, Jin-Song; Mai, Eric C.

2007-04-01

This paper introduces a continuous effort towards the development of a heuristic initialization methodology for constructing multilayer feedforward neural networks to model nonlinear functions. In this and previous studies that this work is built upon, including the one presented at SPIE 2006, the authors do not presume to provide a universal method to approximate arbitrary functions, rather the focus is given to the development of a rational and unambiguous initialization procedure that applies to the approximation of nonlinear functions in the specific domain of engineering mechanics. The applications of this exploratory work can be numerous including those associated with potential correlation and interpretation of the inner workings of neural networks, such as damage detection. The goal of this study is fulfilled by utilizing the governing physics and mathematics of nonlinear functions and the strength of the sigmoidal basis function. A step-by-step graphical procedure utilizing a few neural network prototypes as "templates" to approximate commonly seen memoryless nonlinear functions of one or two variables is further developed in this study. Decomposition of complex nonlinear functions into a summation of some simpler nonlinear functions is utilized to exploit this prototype-based initialization methodology. Training examples are presented to demonstrate the rationality and effciency of the proposed methodology when compared with the popular Nguyen-Widrow initialization algorithm. Future work is also identfied.

Utility of coupling nonlinear optimization methods with numerical modeling software

DOE Office of Scientific and Technical Information (OSTI.GOV)

Murphy, M.J.

1996-08-05

Results of using GLO (Global Local Optimizer), a general purpose nonlinear optimization software package for investigating multi-parameter problems in science and engineering is discussed. The package consists of the modular optimization control system (GLO), a graphical user interface (GLO-GUI), a pre-processor (GLO-PUT), a post-processor (GLO-GET), and nonlinear optimization software modules, GLOBAL & LOCAL. GLO is designed for controlling and easy coupling to any scientific software application. GLO runs the optimization module and scientific software application in an iterative loop. At each iteration, the optimization module defines new values for the set of parameters being optimized. GLO-PUT inserts the new parametermore » values into the input file of the scientific application. GLO runs the application with the new parameter values. GLO-GET determines the value of the objective function by extracting the results of the analysis and comparing to the desired result. GLO continues to run the scientific application over and over until it finds the ``best`` set of parameters by minimizing (or maximizing) the objective function. An example problem showing the optimization of material model is presented (Taylor cylinder impact test).« less

Comparison of dynamical approximation schemes for non-linear gravitational clustering

NASA Technical Reports Server (NTRS)

Melott, Adrian L.

1994-01-01

We have recently conducted a controlled comparison of a number of approximations for gravitational clustering against the same n-body simulations. These include ordinary linear perturbation theory (Eulerian), the adhesion approximation, the frozen-flow approximation, the Zel'dovich approximation (describable as first-order Lagrangian perturbation theory), and its second-order generalization. In the last two cases we also created new versions of approximation by truncation, i.e., smoothing the initial conditions by various smoothing window shapes and varying their sizes. The primary tool for comparing simulations to approximation schemes was crosscorrelation of the evolved mass density fields, testing the extent to which mass was moved to the right place. The Zel'dovich approximation, with initial convolution with a Gaussian e(exp -k(exp 2)/k(exp 2, sub G)) where k(sub G) is adjusted to be just into the nonlinear regime of the evolved model (details in text) worked extremely well. Its second-order generalization worked slightly better. All other schemes, including those proposed as generalizations of the Zel'dovich approximation created by adding forces, were in fact generally worse by this measure. By explicitly checking, we verified that the success of our best-choice was a result of the best treatment of the phases of nonlinear Fourier components. Of all schemes tested, the adhesion approximation produced the most accurate nonlinear power spectrum and density distribution, but its phase errors suggest mass condensations were moved to slightly the wrong location. Due to its better reproduction of the mass density distribution function and power spectrum, it might be preferred for some uses. We recommend either n-body simulations or our modified versions of the Zel'dovich approximation, depending upon the purpose. The theoretical implication is that pancaking is implicit in all cosmological gravitational clustering, at least from Gaussian initial conditions, even when subcondensations are present.

Out-of-time-order fluctuation-dissipation theorem

NASA Astrophysics Data System (ADS)

Tsuji, Naoto; Shitara, Tomohiro; Ueda, Masahito

2018-01-01

We prove a generalized fluctuation-dissipation theorem for a certain class of out-of-time-ordered correlators (OTOCs) with a modified statistical average, which we call bipartite OTOCs, for general quantum systems in thermal equilibrium. The difference between the bipartite and physical OTOCs defined by the usual statistical average is quantified by a measure of quantum fluctuations known as the Wigner-Yanase skew information. Within this difference, the theorem describes a universal relation between chaotic behavior in quantum systems and a nonlinear-response function that involves a time-reversed process. We show that the theorem can be generalized to higher-order n -partite OTOCs as well as in the form of generalized covariance.

Study report on guidelines and test procedures for investigating stability of nonlinear cardiovascular control system models

NASA Technical Reports Server (NTRS)

Fitzjerrell, D. G.

1974-01-01

A general study of the stability of nonlinear as compared to linear control systems is presented. The analysis is general and, therefore, applies to other types of nonlinear biological control systems as well as the cardiovascular control system models. Both inherent and numerical stability are discussed for corresponding analytical and graphic methods and numerical methods.

Inexact nonlinear improved fuzzy chance-constrained programming model for irrigation water management under uncertainty

NASA Astrophysics Data System (ADS)

Zhang, Chenglong; Zhang, Fan; Guo, Shanshan; Liu, Xiao; Guo, Ping

2018-01-01

An inexact nonlinear mλ-measure fuzzy chance-constrained programming (INMFCCP) model is developed for irrigation water allocation under uncertainty. Techniques of inexact quadratic programming (IQP), mλ-measure, and fuzzy chance-constrained programming (FCCP) are integrated into a general optimization framework. The INMFCCP model can deal with not only nonlinearities in the objective function, but also uncertainties presented as discrete intervals in the objective function, variables and left-hand side constraints and fuzziness in the right-hand side constraints. Moreover, this model improves upon the conventional fuzzy chance-constrained programming by introducing a linear combination of possibility measure and necessity measure with varying preference parameters. To demonstrate its applicability, the model is then applied to a case study in the middle reaches of Heihe River Basin, northwest China. An interval regression analysis method is used to obtain interval crop water production functions in the whole growth period under uncertainty. Therefore, more flexible solutions can be generated for optimal irrigation water allocation. The variation of results can be examined by giving different confidence levels and preference parameters. Besides, it can reflect interrelationships among system benefits, preference parameters, confidence levels and the corresponding risk levels. Comparison between interval crop water production functions and deterministic ones based on the developed INMFCCP model indicates that the former is capable of reflecting more complexities and uncertainties in practical application. These results can provide more reliable scientific basis for supporting irrigation water management in arid areas.

Gradient optimization and nonlinear control

NASA Technical Reports Server (NTRS)

Hasdorff, L.

1976-01-01

The book represents an introduction to computation in control by an iterative, gradient, numerical method, where linearity is not assumed. The general language and approach used are those of elementary functional analysis. The particular gradient method that is emphasized and used is conjugate gradient descent, a well known method exhibiting quadratic convergence while requiring very little more computation than simple steepest descent. Constraints are not dealt with directly, but rather the approach is to introduce them as penalty terms in the criterion. General conjugate gradient descent methods are developed and applied to problems in control.

Modelling nonlinear viscoelastic behaviours of loudspeaker suspensions-like structures

NASA Astrophysics Data System (ADS)

Maillou, Balbine; Lotton, Pierrick; Novak, Antonin; Simon, Laurent

2018-03-01

Mechanical properties of an electrodynamic loudspeaker are mainly determined by its suspensions (surround and spider) that behave nonlinearly and typically exhibit frequency dependent viscoelastic properties such as creep effect. The paper aims at characterizing the mechanical behaviour of electrodynamic loudspeaker suspensions at low frequencies using nonlinear identification techniques developed in recent years. A Generalized Hammerstein based model can take into account both frequency dependency and nonlinear properties. As shown in the paper, the model generalizes existing nonlinear or viscoelastic models commonly used for loudspeaker modelling. It is further experimentally shown that a possible input-dependent law may play a key role in suspension characterization.

General implementation of arbitrary nonlinear quadrature phase gates

NASA Astrophysics Data System (ADS)

Marek, Petr; Filip, Radim; Ogawa, Hisashi; Sakaguchi, Atsushi; Takeda, Shuntaro; Yoshikawa, Jun-ichi; Furusawa, Akira

2018-02-01

We propose general methodology of deterministic single-mode quantum interaction nonlinearly modifying single quadrature variable of a continuous-variable system. The methodology is based on linear coupling of the system to ancillary systems subsequently measured by quadrature detectors. The nonlinear interaction is obtained by using the data from the quadrature detection for dynamical manipulation of the coupling parameters. This measurement-induced methodology enables direct realization of arbitrary nonlinear quadrature interactions without the need to construct them from the lowest-order gates. Such nonlinear interactions are crucial for more practical and efficient manipulation of continuous quadrature variables as well as qubits encoded in continuous-variable systems.

Nonlinear analysis of a rotor-bearing system using describing functions

NASA Astrophysics Data System (ADS)

Maraini, Daniel; Nataraj, C.

2018-04-01

This paper presents a technique for modelling the nonlinear behavior of a rotor-bearing system with Hertzian contact, clearance, and rotating unbalance. The rotor-bearing system is separated into linear and nonlinear components, and the nonlinear bearing force is replaced with an equivalent describing function gain. The describing function captures the relationship between the amplitude of the fundamental input to the nonlinearity and the fundamental output. The frequency response is constructed for various values of the clearance parameter, and the results show the presence of a jump resonance in bearings with both clearance and preload. Nonlinear hardening type behavior is observed in the case with clearance and softening behavior is observed for the case with preload. Numerical integration is also carried out on the nonlinear equations of motion showing strong agreement with the approximate solution. This work could easily be extended to include additional nonlinearities that arise from defects, providing a powerful diagnostic tool.

Flow assignment model for quantitative analysis of diverting bulk freight from road to railway

PubMed Central

Liu, Chang; Wang, Jiaxi; Xiao, Jie; Liu, Siqi; Wu, Jianping; Li, Jian

2017-01-01

Since railway transport possesses the advantage of high volume and low carbon emissions, diverting some freight from road to railway will help reduce the negative environmental impacts associated with transport. This paper develops a flow assignment model for quantitative analysis of diverting truck freight to railway. First, a general network which considers road transportation, railway transportation, handling and transferring is established according to all the steps in the whole transportation process. Then general functions which embody the factors which the shippers will pay attention to when choosing mode and path are formulated. The general functions contain the congestion cost on road, the capacity constraints of railways and freight stations. Based on the general network and general cost function, a user equilibrium flow assignment model is developed to simulate the flow distribution on the general network under the condition that all shippers choose transportation mode and path independently. Since the model is nonlinear and challenging, we adopt a method that uses tangent lines to constitute envelope curve to linearize it. Finally, a numerical example is presented to test the model and show the method of making quantitative analysis of bulk freight modal shift between road and railway. PMID:28771536

A third-order class-D amplifier with and without ripple compensation

NASA Astrophysics Data System (ADS)

Cox, Stephen M.; du Toit Mouton, H.

2018-06-01

We analyse the nonlinear behaviour of a third-order class-D amplifier, and demonstrate the remarkable effectiveness of the recently introduced ripple compensation (RC) technique in reducing the audio distortion of the device. The amplifier converts an input audio signal to a high-frequency train of rectangular pulses, whose widths are modulated according to the input signal (pulse-width modulation) and employs negative feedback. After determining the steady-state operating point for constant input and calculating its stability, we derive a small-signal model (SSM), which yields in closed form the transfer function relating (infinitesimal) input and output disturbances. This SSM shows how the RC technique is able to linearise the small-signal response of the device. We extend this SSM through a fully nonlinear perturbation calculation of the dynamics of the amplifier, based on the disparity in time scales between the pulse train and the audio signal. We obtain the nonlinear response of the amplifier to a general audio signal, avoiding the linearisation inherent in the SSM; we thereby more precisely quantify the reduction in distortion achieved through RC. Finally, simulations corroborate our theoretical predictions and illustrate the dramatic deterioration in performance that occurs when the amplifier is operated in an unstable regime. The perturbation calculation is rather general, and may be adapted to quantify the way in which other nonlinear negative-feedback pulse-modulated devices track a time-varying input signal that slowly modulates the system parameters.

Soliton solutions of the quantum Zakharov-Kuznetsov equation which arises in quantum magneto-plasmas

NASA Astrophysics Data System (ADS)

Sindi, Cevat Teymuri; Manafian, Jalil

2017-02-01

In this paper, we extended the improved tan(φ/2)-expansion method (ITEM) and the generalized G'/G-expansion method (GGEM) proposed by Manafian and Fazli (Opt. Quantum Electron. 48, 413 (2016)) to construct new types of soliton wave solutions of nonlinear partial differential equations (NPDEs). Moreover, we use of the improvement of the Exp-function method (IEFM) proposed by Jahani and Manafian (Eur. Phys. J. Plus 131, 54 (2016)) for obtaining solutions of NPDEs. The merit of the presented three methods is they can find further solutions to the considered problems, including soliton, periodic, kink, kink-singular wave solutions. This paper studies the quantum Zakharov-Kuznetsov (QZK) equation by the aid of the improved tan(φ/2)-expansion method, the generalized G'/G-expansion method and the improvement of the Exp-function method. Moreover, the 1-soliton solution of the modified QZK equation with power law nonlinearity is obtained by the aid of traveling wave hypothesis with the necessary constraints in place for the existence of the soliton. Comparing our new results with Ebadi et al. results (Astrophys. Space Sci. 341, 507 (2012)), namely, G'/G-expansion method, exp-function method, modified F-expansion method, shows that our results give further solutions. Finally, these solutions might play an important role in engineering, physics and applied mathematics fields.

Proposed method to construct Boolean functions with maximum possible annihilator immunity

NASA Astrophysics Data System (ADS)

Goyal, Rajni; Panigrahi, Anupama; Bansal, Rohit

2017-07-01

Nonlinearity and Algebraic(annihilator) immunity are two core properties of a Boolean function because optimum values of Annihilator Immunity and nonlinearity are required to resist fast algebraic attack and differential cryptanalysis respectively. For a secure cypher system, Boolean function(S-Boxes) should resist maximum number of attacks. It is possible if a Boolean function has optimal trade-off among its properties. Before constructing Boolean functions, we fixed the criteria of our constructions based on its properties. In present work, our construction is based on annihilator immunity and nonlinearity. While keeping above facts in mind,, we have developed a multi-objective evolutionary approach based on NSGA-II and got the optimum value of annihilator immunity with good bound of nonlinearity. We have constructed balanced Boolean functions having the best trade-off among balancedness, Annihilator immunity and nonlinearity for 5, 6 and 7 variables by the proposed method.

Transverse effects in nonlinear optics: Toward the photon superfluid

NASA Astrophysics Data System (ADS)

McCormick, Colin Fraser

Nonlinear optics displays a wealth of transverse effects. These effects are particularly rich in the presence of an optical cavity. Many considerations suggest that in a Kerr nonlinear cavity a new state of light known as a "photon superfluid" can form, with strong analogies to atomic superfluids. The conditions for the formation of the photon superfluid include requirements on the cavity, input light fields and the nonlinear medium as well as various timescales. The most favorable candidate nonlinear medium for observing the photon super-fluid is an atomic vapor. With a strong and fast Kerr effect, atomic vapors also have the advantage of a Kerr coefficient that is tunable in both magnitude and sign. A series of z-scan experiments in far-detuned atomic rubidium vapor is reported, measuring the Kerr coefficient and determining its functional dependence on detuning to be that of a Doppler-broadened two-level model with adiabatic following of the electric field by the atom pseudomoment. Saturation effects are found to be important. Z-scan measurements for detunings within the Doppler profile are shown to agree well with numerical simulations based on the Doppler-broadened model. Agreement between absorptive and refractive non-linear coefficients is evidence of the Kramers-Kronig relations at work, even in this nonlinear system. The formation of the photon superfluid is discussed and the calculation of a new process, nearly collinear four-wave mixing, is presented. This process is essentially an inverse beam filamentation that is likely to be the underlying physical mechanism for transverse cooling and condensation of photons in a nonlinear optical cavity. Nearly collinear four-wave mixing may also be related to phenomena in general nonlinear physics, including modulation instability and Fermi-Pasta-Ulam recurrence.

Synaptic control of the shape of the motoneuron pool input-output function

PubMed Central

Heckman, Charles J.

2017-01-01

Although motoneurons have often been considered to be fairly linear transducers of synaptic input, recent evidence suggests that strong persistent inward currents (PICs) in motoneurons allow neuromodulatory and inhibitory synaptic inputs to induce large nonlinearities in the relation between the level of excitatory input and motor output. To try to estimate the possible extent of this nonlinearity, we developed a pool of model motoneurons designed to replicate the characteristics of motoneuron input-output properties measured in medial gastrocnemius motoneurons in the decerebrate cat with voltage-clamp and current-clamp techniques. We drove the model pool with a range of synaptic inputs consisting of various mixtures of excitation, inhibition, and neuromodulation. We then looked at the relation between excitatory drive and total pool output. Our results revealed that the PICs not only enhance gain but also induce a strong nonlinearity in the relation between the average firing rate of the motoneuron pool and the level of excitatory input. The relation between the total simulated force output and input was somewhat more linear because of higher force outputs in later-recruited units. We also found that the nonlinearity can be increased by increasing neuromodulatory input and/or balanced inhibitory input and minimized by a reciprocal, push-pull pattern of inhibition. We consider the possibility that a flexible input-output function may allow motor output to be tuned to match the widely varying demands of the normal motor repertoire. NEW & NOTEWORTHY Motoneuron activity is generally considered to reflect the level of excitatory drive. However, the activation of voltage-dependent intrinsic conductances can distort the relation between excitatory drive and the total output of a pool of motoneurons. Using a pool of realistic motoneuron models, we show that pool output can be a highly nonlinear function of synaptic input but linearity can be achieved through adjusting the time course of excitatory and inhibitory synaptic inputs. PMID:28053245

Conditional nonlinear optimal perturbations based on the particle swarm optimization and their applications to the predictability problems

NASA Astrophysics Data System (ADS)

Zheng, Qin; Yang, Zubin; Sha, Jianxin; Yan, Jun

2017-02-01

In predictability problem research, the conditional nonlinear optimal perturbation (CNOP) describes the initial perturbation that satisfies a certain constraint condition and causes the largest prediction error at the prediction time. The CNOP has been successfully applied in estimation of the lower bound of maximum predictable time (LBMPT). Generally, CNOPs are calculated by a gradient descent algorithm based on the adjoint model, which is called ADJ-CNOP. This study, through the two-dimensional Ikeda model, investigates the impacts of the nonlinearity on ADJ-CNOP and the corresponding precision problems when using ADJ-CNOP to estimate the LBMPT. Our conclusions are that (1) when the initial perturbation is large or the prediction time is long, the strong nonlinearity of the dynamical model in the prediction variable will lead to failure of the ADJ-CNOP method, and (2) when the objective function has multiple extreme values, ADJ-CNOP has a large probability of producing local CNOPs, hence making a false estimation of the LBMPT. Furthermore, the particle swarm optimization (PSO) algorithm, one kind of intelligent algorithm, is introduced to solve this problem. The method using PSO to compute CNOP is called PSO-CNOP. The results of numerical experiments show that even with a large initial perturbation and long prediction time, or when the objective function has multiple extreme values, PSO-CNOP can always obtain the global CNOP. Since the PSO algorithm is a heuristic search algorithm based on the population, it can overcome the impact of nonlinearity and the disturbance from multiple extremes of the objective function. In addition, to check the estimation accuracy of the LBMPT presented by PSO-CNOP and ADJ-CNOP, we partition the constraint domain of initial perturbations into sufficiently fine grid meshes and take the LBMPT obtained by the filtering method as a benchmark. The result shows that the estimation presented by PSO-CNOP is closer to the true value than the one by ADJ-CNOP with the forecast time increasing.

The Poisson-Boltzmann theory for the two-plates problem: some exact results.

PubMed

Xing, Xiang-Jun

2011-12-01

The general solution to the nonlinear Poisson-Boltzmann equation for two parallel charged plates, either inside a symmetric electrolyte, or inside a 2q:-q asymmetric electrolyte, is found in terms of Weierstrass elliptic functions. From this we derive some exact asymptotic results for the interaction between charged plates, as well as the exact form of the renormalized surface charge density.

General existence principles for Stieltjes differential equations with applications to mathematical biology

NASA Astrophysics Data System (ADS)

López Pouso, Rodrigo; Márquez Albés, Ignacio

2018-04-01

Stieltjes differential equations, which contain equations with impulses and equations on time scales as particular cases, simply consist on replacing usual derivatives by derivatives with respect to a nondecreasing function. In this paper we prove new existence results for functional and discontinuous Stieltjes differential equations and we show that such general results have real world applications. Specifically, we show that Stieltjes differential equations are specially suitable to study populations which exhibit dormant states and/or very short (impulsive) periods of reproduction. In particular, we construct two mathematical models for the evolution of a silkworm population. Our first model can be explicitly solved, as it consists on a linear Stieltjes equation. Our second model, more realistic, is nonlinear, discontinuous and functional, and we deduce the existence of solutions by means of a result proven in this paper.

A class of non-linear exposure-response models suitable for health impact assessment applicable to large cohort studies of ambient air pollution.

PubMed

Nasari, Masoud M; Szyszkowicz, Mieczysław; Chen, Hong; Crouse, Daniel; Turner, Michelle C; Jerrett, Michael; Pope, C Arden; Hubbell, Bryan; Fann, Neal; Cohen, Aaron; Gapstur, Susan M; Diver, W Ryan; Stieb, David; Forouzanfar, Mohammad H; Kim, Sun-Young; Olives, Casey; Krewski, Daniel; Burnett, Richard T

2016-01-01

The effectiveness of regulatory actions designed to improve air quality is often assessed by predicting changes in public health resulting from their implementation. Risk of premature mortality from long-term exposure to ambient air pollution is the single most important contributor to such assessments and is estimated from observational studies generally assuming a log-linear, no-threshold association between ambient concentrations and death. There has been only limited assessment of this assumption in part because of a lack of methods to estimate the shape of the exposure-response function in very large study populations. In this paper, we propose a new class of variable coefficient risk functions capable of capturing a variety of potentially non-linear associations which are suitable for health impact assessment. We construct the class by defining transformations of concentration as the product of either a linear or log-linear function of concentration multiplied by a logistic weighting function. These risk functions can be estimated using hazard regression survival models with currently available computer software and can accommodate large population-based cohorts which are increasingly being used for this purpose. We illustrate our modeling approach with two large cohort studies of long-term concentrations of ambient air pollution and mortality: the American Cancer Society Cancer Prevention Study II (CPS II) cohort and the Canadian Census Health and Environment Cohort (CanCHEC). We then estimate the number of deaths attributable to changes in fine particulate matter concentrations over the 2000 to 2010 time period in both Canada and the USA using both linear and non-linear hazard function models.

Display nonlinearity in digital image processing for visual communications

NASA Astrophysics Data System (ADS)

Peli, Eli

1992-11-01

The luminance emitted from a cathode ray tube (CRT) display is a nonlinear function (the gamma function) of the input video signal voltage. In most analog video systems, compensation for this nonlinear transfer function is implemented in the camera amplifiers. When CRT displays are used to present psychophysical stimuli in vision research, the specific display nonlinearity usually is measured and accounted for to ensure that the luminance of each pixel in the synthetic image property represents the intended value. However, when using digital image processing, the linear analog-to-digital converters store a digital image that is nonlinearly related to the displayed or recorded image. The effect of this nonlinear transformation on a variety of image-processing applications used in visual communications is described.

Display nonlinearity in digital image processing for visual communications

NASA Astrophysics Data System (ADS)

Peli, Eli

1991-11-01

The luminance emitted from a cathode ray tube, (CRT) display is a nonlinear function (the gamma function) of the input video signal voltage. In most analog video systems, compensation for this nonlinear transfer function is implemented in the camera amplifiers. When CRT displays are used to present psychophysical stimuli in vision research, the specific display nonlinearity usually is measured and accounted for to ensure that the luminance of each pixel in the synthetic image properly represents the intended value. However, when using digital image processing, the linear analog-to-digital converters store a digital image that is nonlinearly related to the displayed or recorded image. This paper describes the effect of this nonlinear transformation on a variety of image-processing applications used in visual communications.

Development of a winter wheat adjustable crop calendar model. [Colorado, Idaho, Oklahoma, Montana, Kansas, Missouri, North Dakota and Texas

NASA Technical Reports Server (NTRS)

Baker, J. R. (Principal Investigator)

1979-01-01

The author has identified the following significant results. Least squares techniques were applied for parameter estimation of functions to predict winter wheat phenological stage with daily maximum temperature, minimum temperature, daylength, and precipitation as independent variables. After parameter estimation, tests were conducted using independent data. It may generally be concluded that exponential functions have little advantage over polynomials. Precipitation was not found to significantly affect the fits. The Robertson triquadratic form, in general use for spring wheat, yielded good results, but special techniques and care are required. In most instances, equations with nonlinear effects were found to yield erratic results when utilized with averaged daily environmental values as independent variables.

Linear stability and nonlinear analyses of traffic waves for the general nonlinear car-following model with multi-time delays

NASA Astrophysics Data System (ADS)

Sun, Dihua; Chen, Dong; Zhao, Min; Liu, Weining; Zheng, Linjiang

2018-07-01

In this paper, the general nonlinear car-following model with multi-time delays is investigated in order to describe the reactions of vehicle to driving behavior. Platoon stability and string stability criteria are obtained for the general nonlinear car-following model. Burgers equation and Korteweg de Vries (KdV) equation and their solitary wave solutions are derived adopting the reductive perturbation method. We investigate the properties of typical optimal velocity model using both analytic and numerical methods, which estimates the impact of delays about the evolution of traffic congestion. The numerical results show that time delays in sensing relative movement is more sensitive to the stability of traffic flow than time delays in sensing host motion.

A survey of the core-congruential formulation for geometrically nonlinear TL finite elements

NASA Technical Reports Server (NTRS)

Felippa, Carlos A.; Crivelli, Luis A.; Haugen, Bjorn

1994-01-01

This article presents a survey of the core-congruential formulation (CCF) for geometrically nonlinear mechanical finite elements based on the total Lagrangian (TL) kinematic description. Although the key ideas behind the CCF can be traced back to Rajasekaran and Murray in 1973, it has not subsequently received serious attention. The CCF is distinguished by a two-phase development of the finite element stiffness equations. The initial phase developed equations for individual particles. These equations are expressed in terms of displacement gradients as degrees of freedom. The second phase involves congruential-type transformations that eventually binds the element particles of an individual element in terms of its node-displacement degrees of freedom. Two versions of the CCF, labeled direct and generalized, are distinguished. The direct CCF (DCCF) is first described in general form and then applied to the derivation of geometrically nonlinear bar, and plane stress elements using the Green-Lagrange strain measure. The more complex generalized CCF (GCCF) is described and applied to the derivation of 2D and 3D Timoshenko beam elements. Several advantages of the CCF, notably the physically clean separation of material and geometric stiffnesses, and its independence with respect to the ultimate choice of shape functions and element degrees of freedom, are noted. Application examples involving very large motions solved with the 3D beam element display the range of applicability of this formulation, which transcends the kinematic limitations commonly attributed to the TL description.

Solution of monotone complementarity and general convex programming problems using a modified potential reduction interior point method

DOE PAGES

Huang, Kuo -Ling; Mehrotra, Sanjay

2016-11-08

We present a homogeneous algorithm equipped with a modified potential function for the monotone complementarity problem. We show that this potential function is reduced by at least a constant amount if a scaled Lipschitz condition (SLC) is satisfied. A practical algorithm based on this potential function is implemented in a software package named iOptimize. The implementation in iOptimize maintains global linear and polynomial time convergence properties, while achieving practical performance. It either successfully solves the problem, or concludes that the SLC is not satisfied. When compared with the mature software package MOSEK (barrier solver version 6.0.0.106), iOptimize solves convex quadraticmore » programming problems, convex quadratically constrained quadratic programming problems, and general convex programming problems in fewer iterations. Moreover, several problems for which MOSEK fails are solved to optimality. In addition, we also find that iOptimize detects infeasibility more reliably than the general nonlinear solvers Ipopt (version 3.9.2) and Knitro (version 8.0).« less

Long-term evolution of electron distribution function due to nonlinear resonant interaction with whistler mode waves

NASA Astrophysics Data System (ADS)

Artemyev, Anton V.; Neishtadt, Anatoly I.; Vasiliev, Alexei A.

2018-04-01

Accurately modelling and forecasting of the dynamics of the Earth's radiation belts with the available computer resources represents an important challenge that still requires significant advances in the theoretical plasma physics field of wave-particle resonant interaction. Energetic electron acceleration or scattering into the Earth's atmosphere are essentially controlled by their resonances with electromagnetic whistler mode waves. The quasi-linear diffusion equation describes well this resonant interaction for low intensity waves. During the last decade, however, spacecraft observations in the radiation belts have revealed a large number of whistler mode waves with sufficiently high intensity to interact with electrons in the nonlinear regime. A kinetic equation including such nonlinear wave-particle interactions and describing the long-term evolution of the electron distribution is the focus of the present paper. Using the Hamiltonian theory of resonant phenomena, we describe individual electron resonance with an intense coherent whistler mode wave. The derived characteristics of such a resonance are incorporated into a generalized kinetic equation which includes non-local transport in energy space. This transport is produced by resonant electron trapping and nonlinear acceleration. We describe the methods allowing the construction of nonlinear resonant terms in the kinetic equation and discuss possible applications of this equation.

Supervised nonlinear spectral unmixing using a postnonlinear mixing model for hyperspectral imagery.

PubMed

Altmann, Yoann; Halimi, Abderrahim; Dobigeon, Nicolas; Tourneret, Jean-Yves

2012-06-01

This paper presents a nonlinear mixing model for hyperspectral image unmixing. The proposed model assumes that the pixel reflectances are nonlinear functions of pure spectral components contaminated by an additive white Gaussian noise. These nonlinear functions are approximated using polynomial functions leading to a polynomial postnonlinear mixing model. A Bayesian algorithm and optimization methods are proposed to estimate the parameters involved in the model. The performance of the unmixing strategies is evaluated by simulations conducted on synthetic and real data.

A Pair of Resonance Stripe Solitons and Lump Solutions to a Reduced (3+1)-Dimensional Nonlinear Evolution Equation

NASA Astrophysics Data System (ADS)

Chen, Mei-Dan; Li, Xian; Wang, Yao; Li, Biao

2017-06-01

With symbolic computation, some lump solutions are presented to a (3+1)-dimensional nonlinear evolution equation by searching the positive quadratic function from the Hirota bilinear form of equation. The quadratic function contains six free parameters, four of which satisfy two determinant conditions guaranteeing analyticity and rational localization of the solutions, while the others are free. Then, by combining positive quadratic function with exponential function, the interaction solutions between lump solutions and the stripe solitons are presented on the basis of some conditions. Furthermore, we extend this method to obtain more general solutions by combining of positive quadratic function and hyperbolic cosine function. Thus the interaction solutions between lump solutions and a pair of resonance stripe solitons are derived and asymptotic property of the interaction solutions are analyzed under some specific conditions. Finally, the dynamic properties of these solutions are shown in figures by choosing the values of the parameters. Supported by National Natural Science Foundation of China under Grant Nos. 11271211, 11275072, and 11435005, Ningbo Natural Science Foundation under Grant No. 2015A610159 and the Opening Project of Zhejiang Provincial Top Key Discipline of Physics Sciences in Ningbo University under Grant No. xkzw11502 and K.C. Wong Magna Fund in Ningbo University

An assembly of steadily translating bubbles in a Hele-Shaw channel

NASA Astrophysics Data System (ADS)

Crowdy, Darren

2009-01-01

This paper presents new solutions for any finite number of bubbles steadily translating along a Hele-Shaw channel. This constitutes a nonlinear free boundary problem. The solutions can be written down explicitly in terms of a special transcendental function called the Schottky-Klein prime function. This work generalizes the exact solutions for a single bubble in a channel found by Tanveer (1987 Phys. Fluids 30 651-8) as well as the solutions for streams of bubbles aligned along the channel centreline due to Vasconcelos (1994 Phys. Rev. E 50 R3306-9).

Optimal trajectory generation for mechanical arms. M.S. Thesis

NASA Technical Reports Server (NTRS)

Iemenschot, J. A.

1972-01-01

A general method of generating optimal trajectories between an initial and a final position of an n degree of freedom manipulator arm with nonlinear equations of motion is proposed. The method is based on the assumption that the time history of each of the coordinates can be expanded in a series of simple time functions. By searching over the coefficients of the terms in the expansion, trajectories which minimize the value of a given cost function can be obtained. The method has been applied to a planar three degree of freedom arm.

An inverse problem strategy based on forward model evaluations: Gradient-based optimization without adjoint solves

DOE Office of Scientific and Technical Information (OSTI.GOV)

Aguilo Valentin, Miguel Alejandro

2016-07-01

This study presents a new nonlinear programming formulation for the solution of inverse problems. First, a general inverse problem formulation based on the compliance error functional is presented. The proposed error functional enables the computation of the Lagrange multipliers, and thus the first order derivative information, at the expense of just one model evaluation. Therefore, the calculation of the Lagrange multipliers does not require the solution of the computationally intensive adjoint problem. This leads to significant speedups for large-scale, gradient-based inverse problems.

Exact traveling wave solutions for system of nonlinear evolution equations.

PubMed

Khan, Kamruzzaman; Akbar, M Ali; Arnous, Ahmed H

2016-01-01

In this work, recently deduced generalized Kudryashov method is applied to the variant Boussinesq equations, and the (2 + 1)-dimensional breaking soliton equations. As a result a range of qualitative explicit exact traveling wave solutions are deduced for these equations, which motivates us to develop, in the near future, a new approach to obtain unsteady solutions of autonomous nonlinear evolution equations those arise in mathematical physics and engineering fields. It is uncomplicated to extend this method to higher-order nonlinear evolution equations in mathematical physics. And it should be possible to apply the same method to nonlinear evolution equations having more general forms of nonlinearities by utilizing the traveling wave hypothesis.

Plasticity - Theory and finite element applications.

NASA Technical Reports Server (NTRS)

Armen, H., Jr.; Levine, H. S.

1972-01-01

A unified presentation is given of the development and distinctions associated with various incremental solution procedures used to solve the equations governing the nonlinear behavior of structures, and this is discussed within the framework of the finite-element method. Although the primary emphasis here is on material nonlinearities, consideration is also given to geometric nonlinearities acting separately or in combination with nonlinear material behavior. The methods discussed here are applicable to a broad spectrum of structures, ranging from simple beams to general three-dimensional bodies. The finite-element analysis methods for material nonlinearity are general in the sense that any of the available plasticity theories can be incorporated to treat strain hardening or ideally plastic behavior.

Physical uniqueness of higher-order Korteweg-de Vries theory for continuously stratified fluids without background shear

NASA Astrophysics Data System (ADS)

Shimizu, Kenji

2017-10-01

The 2nd-order Korteweg-de Vries (KdV) equation and the Gardner (or extended KdV) equation are often used to investigate internal solitary waves, commonly observed in oceans and lakes. However, application of these KdV-type equations for continuously stratified fluids to geophysical problems is hindered by nonuniqueness of the higher-order coefficients and the associated correction functions to the wave fields. This study proposes to reduce arbitrariness of the higher-order KdV theory by considering its uniqueness in the following three physical senses: (i) consistency of the nonlinear higher-order coefficients and correction functions with the corresponding phase speeds, (ii) wavenumber-independence of the vertically integrated available potential energy, and (iii) its positive definiteness. The spectral (or generalized Fourier) approach based on vertical modes in the isopycnal coordinate is shown to enable an alternative derivation of the 2nd-order KdV equation, without encountering nonuniqueness. Comparison with previous theories shows that Parseval's theorem naturally yields a unique set of special conditions for (ii) and (iii). Hydrostatic fully nonlinear solutions, derived by combining the spectral approach and simple-wave analysis, reveal that both proposed and previous 2nd-order theories satisfy (i), provided that consistent definitions are used for the wave amplitude and the nonlinear correction. This condition reduces the arbitrariness when higher-order KdV-type theories are compared with observations or numerical simulations. The coefficients and correction functions that satisfy (i)-(iii) are given by explicit formulae to 2nd order and by algebraic recurrence relationships to arbitrary order for hydrostatic fully nonlinear and linear fully nonhydrostatic effects.

General displaced SU(1, 1) number states: Revisited

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dehghani, A., E-mail: alireza.dehghani@gmail.com, E-mail: a-dehghani@tabrizu.ac.ir

2014-04-15

The most general displaced number states, based on the bosonic and an irreducible representation of the Lie algebra symmetry of su(1, 1) and associated with the Calogero-Sutherland model are introduced. Here, we utilize the Barut-Girardello displacement operator instead of the Klauder-Perelomov counterpart, to construct new kind of the displaced number states which can be classified in nonlinear coherent states regime, too, with special nonlinearity functions. They depend on two parameters, and can be converted into the well-known Barut-Girardello coherent and number states, respectively, depending on which of the parameters equal to zero. A discussion of the statistical properties of thesemore » states is included. Significant are their squeezing properties and anti-bunching effects which can be raised by increasing the energy quantum number. Depending on the particular choice of the parameters of the above scenario, we are able to determine the status of compliance with flexible statistics. Major parts of the issue is spent on something that these states, in fact, should be considered as new kind of photon-added coherent states, too. Which can be reproduced through an iterated action of a creation operator on new nonlinear Barut-Girardello coherent states. Where the latter carry, also, outstanding statistical features.« less

Correlations of RMT characteristic polynomials and integrability: Hermitean matrices

DOE Office of Scientific and Technical Information (OSTI.GOV)

Osipov, Vladimir Al., E-mail: Vladimir.Osipov@uni-due.d; Kanzieper, Eugene, E-mail: Eugene.Kanzieper@hit.ac.i; Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100

Integrable theory is formulated for correlation functions of characteristic polynomials associated with invariant non-Gaussian ensembles of Hermitean random matrices. By embedding the correlation functions of interest into a more general theory of {tau} functions, we (i) identify a zoo of hierarchical relations satisfied by {tau} functions in an abstract infinite-dimensional space and (ii) present a technology to translate these relations into hierarchically structured nonlinear differential equations describing the correlation functions of characteristic polynomials in the physical, spectral space. Implications of this formalism for fermionic, bosonic, and supersymmetric variations of zero-dimensional replica field theories are discussed at length. A particular emphasismore » is placed on the phenomenon of fermionic-bosonic factorisation of random-matrix-theory correlation functions.« less

First-principles study of structural, electronic, linear and nonlinear optical properties of Ga{2}PSb ternary chalcopyrite

NASA Astrophysics Data System (ADS)

Ouahrani, T.; Reshak, A. H.; de La Roza, A. Otero; Mebrouki, M.; Luaña, V.; Khenata, R.; Amrani, B.

2009-12-01

We report results from first-principles density functional calculations using the full-potential linear augmented plane wave (FP-LAPW) method. The generalized gradient approximation (GGA) and the Engel-Vosko-generalized gradient approximation (EV-GGA) were used for the exchange-correlation energy of the structural, electronic, linear and nonlinear optical properties of the chalcopyrite Ga2PSb compound. The valence band maximum (VBM) is located at the Γv point, and the conduction band minimum (CBM) is located at the Γc point, resulting in a direct band gap of about 0.365 eV for GGA and 0.83 eV for EV-GGA. In comparison with the experimental one (1.2 eV) we found that EV-GGA calculation gives energy gap in reasonable agreement with the experiment. The spin orbit coupling has marginal influence on the optical properties. The ground state quantities such as lattice parameters (a, c and u), bulk modules B and its pressure derivative B^primeare evaluated.

General theory of feedback control of a nuclear spin ensemble in quantum dots

NASA Astrophysics Data System (ADS)

Yang, Wen; Sham, L. J.

2013-12-01

We present a microscopic theory of the nonequilibrium nuclear spin dynamics driven by the electron and/or hole under continuous-wave pumping in a quantum dot. We show the correlated dynamics of the nuclear spin ensemble and the electron and/or hole under optical excitation as a quantum feedback loop and investigate the dynamics of the many nuclear spins as a nonlinear collective motion. This gives rise to three observable effects: (i) hysteresis, (ii) locking (avoidance) of the pump absorption strength to (from) the natural resonance, and (iii) suppression (amplification) of the fluctuation of weakly polarized nuclear spins, leading to prolonged (shortened) electron-spin coherence time. A single nonlinear feedback function is constructed which determines the different outcomes of the three effects listed above depending on the feedback being negative or positive. The general theory also helps to put in perspective the wide range of existing theories on the problem of a single electron spin in a nuclear spin bath.

Nonlinear functional approximation with networks using adaptive neurons

NASA Technical Reports Server (NTRS)

Tawel, Raoul

1992-01-01

A novel mathematical framework for the rapid learning of nonlinear mappings and topological transformations is presented. It is based on allowing the neuron's parameters to adapt as a function of learning. This fully recurrent adaptive neuron model (ANM) has been successfully applied to complex nonlinear function approximation problems such as the highly degenerate inverse kinematics problem in robotics.

Nonlinear growth of zonal flows by secondary instability in general magnetic geometry

DOE PAGES

Plunk, G. G.; Navarro, A. Banon

2017-02-23

Here we present a theory of the nonlinear growth of zonal flows in magnetized plasma turbulence, by the mechanism of secondary instability. The theory is derived for general magnetic geometry, and is thus applicable to both tokamaks and stellarators. The predicted growth rate is shown to compare favorably with nonlinear gyrokinetic simulations, with the error scaling as expected with the small parameter of the theory.

Generation of Stationary Non-Gaussian Time Histories with a Specified Cross-spectral Density

DOE PAGES

Smallwood, David O.

1997-01-01

The paper reviews several methods for the generation of stationary realizations of sampled time histories with non-Gaussian distributions and introduces a new method which can be used to control the cross-spectral density matrix and the probability density functions (pdfs) of the multiple input problem. Discussed first are two methods for the specialized case of matching the auto (power) spectrum, the skewness, and kurtosis using generalized shot noise and using polynomial functions. It is then shown that the skewness and kurtosis can also be controlled by the phase of a complex frequency domain description of the random process. The general casemore » of matching a target probability density function using a zero memory nonlinear (ZMNL) function is then covered. Next methods for generating vectors of random variables with a specified covariance matrix for a class of spherically invariant random vectors (SIRV) are discussed. Finally the general case of matching the cross-spectral density matrix of a vector of inputs with non-Gaussian marginal distributions is presented.« less

From linear mechanics to nonlinear mechanics

NASA Technical Reports Server (NTRS)

Loeb, Julian

1955-01-01

Consideration is given to the techniques used in telecommunication where a nonlinear system (the modulator) results in a linear transposition of a signal. It is then shown that a similar method permits linearization of electromechanical devices or nonlinear mechanical devices. A sweep function plays the same role as the carrier wave in radio-electricity. The linearizations of certain nonlinear functionals are presented.

An exponential decay model for mediation.

PubMed

Fritz, Matthew S

2014-10-01

Mediation analysis is often used to investigate mechanisms of change in prevention research. Results finding mediation are strengthened when longitudinal data are used because of the need for temporal precedence. Current longitudinal mediation models have focused mainly on linear change, but many variables in prevention change nonlinearly across time. The most common solution to nonlinearity is to add a quadratic term to the linear model, but this can lead to the use of the quadratic function to explain all nonlinearity, regardless of theory and the characteristics of the variables in the model. The current study describes the problems that arise when quadratic functions are used to describe all nonlinearity and how the use of nonlinear functions, such as exponential decay, address many of these problems. In addition, nonlinear models provide several advantages over polynomial models including usefulness of parameters, parsimony, and generalizability. The effects of using nonlinear functions for mediation analysis are then discussed and a nonlinear growth curve model for mediation is presented. An empirical example using data from a randomized intervention study is then provided to illustrate the estimation and interpretation of the model. Implications, limitations, and future directions are also discussed.

An Exponential Decay Model for Mediation

PubMed Central

Fritz, Matthew S.

2013-01-01

Mediation analysis is often used to investigate mechanisms of change in prevention research. Results finding mediation are strengthened when longitudinal data are used because of the need for temporal precedence. Current longitudinal mediation models have focused mainly on linear change, but many variables in prevention change nonlinearly across time. The most common solution to nonlinearity is to add a quadratic term to the linear model, but this can lead to the use of the quadratic function to explain all nonlinearity, regardless of theory and the characteristics of the variables in the model. The current study describes the problems that arise when quadratic functions are used to describe all nonlinearity and how the use of nonlinear functions, such as exponential decay, addresses many of these problems. In addition, nonlinear models provide several advantages over polynomial models including usefulness of parameters, parsimony, and generalizability. The effects of using nonlinear functions for mediation analysis are then discussed and a nonlinear growth curve model for mediation is presented. An empirical example using data from a randomized intervention study is then provided to illustrate the estimation and interpretation of the model. Implications, limitations, and future directions are also discussed. PMID:23625557

Optical solitons and modulation instability analysis of an integrable model of (2+1)-Dimensional Heisenberg ferromagnetic spin chain equation

NASA Astrophysics Data System (ADS)

Inc, Mustafa; Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru

2017-12-01

This paper addresses the nonlinear Schrödinger type equation (NLSE) in (2+1)-dimensions which describes the nonlinear spin dynamics of Heisenberg ferromagnetic spin chains (HFSC) with anisotropic and bilinear interactions in the semiclassical limit. Two integration schemes are employed to study the equation. These are the complex envelope function ansatz and the generalized tanh methods. Dark, dark-bright or combined optical and singular soliton solutions of the equation are derived. Furthermore, the modulational instability (MI) is studied based on the standard linear-stability analysis and the MI gain is got. Numerical simulation of the obtained results are analyzed with interesting figures showing the physical meaning of the solutions.

Minimax terminal approach problem in two-level hierarchical nonlinear discrete-time dynamical system

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shorikov, A. F., E-mail: afshorikov@mail.ru

We consider a discrete–time dynamical system consisting of three controllable objects. The motions of all objects are given by the corresponding vector nonlinear or linear discrete–time recurrent vector relations, and control system for its has two levels: basic (first or I level) that is dominating and subordinate level (second or II level) and both have different criterions of functioning and united a priori by determined informational and control connections defined in advance. For the dynamical system in question, we propose a mathematical formalization in the form of solving a multistep problem of two-level hierarchical minimax program control over the terminalmore » approach process with incomplete information and give a general scheme for its solving.« less

Bound-preserving Legendre-WENO finite volume schemes using nonlinear mapping

NASA Astrophysics Data System (ADS)

Smith, Timothy; Pantano, Carlos

2017-11-01

We present a new method to enforce field bounds in high-order Legendre-WENO finite volume schemes. The strategy consists of reconstructing each field through an intermediate mapping, which by design satisfies realizability constraints. Determination of the coefficients of the polynomial reconstruction involves nonlinear equations that are solved using Newton's method. The selection between the original or mapped reconstruction is implemented dynamically to minimize computational cost. The method has also been generalized to fields that exhibit interdependencies, requiring multi-dimensional mappings. Further, the method does not depend on the existence of a numerical flux function. We will discuss details of the proposed scheme and show results for systems in conservation and non-conservation form. This work was funded by the NSF under Grant DMS 1318161.

Generalized hamming networks and applications.

PubMed

Koutroumbas, Konstantinos; Kalouptsidis, Nicholas

2005-09-01

In this paper the classical Hamming network is generalized in various ways. First, for the Hamming maxnet, a generalized model is proposed, which covers under its umbrella most of the existing versions of the Hamming Maxnet. The network dynamics are time varying while the commonly used ramp function may be replaced by a much more general non-linear function. Also, the weight parameters of the network are time varying. A detailed convergence analysis is provided. A bound on the number of iterations required for convergence is derived and its distribution functions are given for the cases where the initial values of the nodes of the Hamming maxnet stem from the uniform and the peak distributions. Stabilization mechanisms aiming to prevent the node(s) with the maximum initial value diverging to infinity or decaying to zero are described. Simulations demonstrate the advantages of the proposed extension. Also, a rough comparison between the proposed generalized scheme as well as the original Hamming maxnet and its variants is carried out in terms of the time required for convergence, in hardware implementations. Finally, the other two parts of the Hamming network, namely the competitors generating module and the decoding module, are briefly considered in the framework of various applications such as classification/clustering, vector quantization and function optimization.

Passive dendrites enable single neurons to compute linearly non-separable functions.

PubMed

Cazé, Romain Daniel; Humphries, Mark; Gutkin, Boris

2013-01-01

Local supra-linear summation of excitatory inputs occurring in pyramidal cell dendrites, the so-called dendritic spikes, results in independent spiking dendritic sub-units, which turn pyramidal neurons into two-layer neural networks capable of computing linearly non-separable functions, such as the exclusive OR. Other neuron classes, such as interneurons, may possess only a few independent dendritic sub-units, or only passive dendrites where input summation is purely sub-linear, and where dendritic sub-units are only saturating. To determine if such neurons can also compute linearly non-separable functions, we enumerate, for a given parameter range, the Boolean functions implementable by a binary neuron model with a linear sub-unit and either a single spiking or a saturating dendritic sub-unit. We then analytically generalize these numerical results to an arbitrary number of non-linear sub-units. First, we show that a single non-linear dendritic sub-unit, in addition to the somatic non-linearity, is sufficient to compute linearly non-separable functions. Second, we analytically prove that, with a sufficient number of saturating dendritic sub-units, a neuron can compute all functions computable with purely excitatory inputs. Third, we show that these linearly non-separable functions can be implemented with at least two strategies: one where a dendritic sub-unit is sufficient to trigger a somatic spike; another where somatic spiking requires the cooperation of multiple dendritic sub-units. We formally prove that implementing the latter architecture is possible with both types of dendritic sub-units whereas the former is only possible with spiking dendrites. Finally, we show how linearly non-separable functions can be computed by a generic two-compartment biophysical model and a realistic neuron model of the cerebellar stellate cell interneuron. Taken together our results demonstrate that passive dendrites are sufficient to enable neurons to compute linearly non-separable functions.

Passive Dendrites Enable Single Neurons to Compute Linearly Non-separable Functions

PubMed Central

Cazé, Romain Daniel; Humphries, Mark; Gutkin, Boris

2013-01-01

Local supra-linear summation of excitatory inputs occurring in pyramidal cell dendrites, the so-called dendritic spikes, results in independent spiking dendritic sub-units, which turn pyramidal neurons into two-layer neural networks capable of computing linearly non-separable functions, such as the exclusive OR. Other neuron classes, such as interneurons, may possess only a few independent dendritic sub-units, or only passive dendrites where input summation is purely sub-linear, and where dendritic sub-units are only saturating. To determine if such neurons can also compute linearly non-separable functions, we enumerate, for a given parameter range, the Boolean functions implementable by a binary neuron model with a linear sub-unit and either a single spiking or a saturating dendritic sub-unit. We then analytically generalize these numerical results to an arbitrary number of non-linear sub-units. First, we show that a single non-linear dendritic sub-unit, in addition to the somatic non-linearity, is sufficient to compute linearly non-separable functions. Second, we analytically prove that, with a sufficient number of saturating dendritic sub-units, a neuron can compute all functions computable with purely excitatory inputs. Third, we show that these linearly non-separable functions can be implemented with at least two strategies: one where a dendritic sub-unit is sufficient to trigger a somatic spike; another where somatic spiking requires the cooperation of multiple dendritic sub-units. We formally prove that implementing the latter architecture is possible with both types of dendritic sub-units whereas the former is only possible with spiking dendrites. Finally, we show how linearly non-separable functions can be computed by a generic two-compartment biophysical model and a realistic neuron model of the cerebellar stellate cell interneuron. Taken together our results demonstrate that passive dendrites are sufficient to enable neurons to compute linearly non-separable functions. PMID:23468600

Triphenylamine-based fluorescent NLO phores with ICT characteristics: Solvatochromic and theoretical study

NASA Astrophysics Data System (ADS)

Katariya, Santosh B.; Patil, Dinesh; Rhyman, Lydia; Alswaidan, Ibrahim A.; Ramasami, Ponnadurai; Sekar, Nagaiyan

2017-12-01

The static first and second hyperpolarizability and their related properties were calculated for triphenylamine-based "push-pull" dyes using the B3LYP, CAM-B3LYP and BHHLYP functionals in conjunction with the 6-311+G(d,p) basis set. The electronic coupling for the electron transfer reaction of the dyes were calculated with the generalized Mulliken-Hush method. The results obtained were correlated with the polarizability parameter αCT , first hyperpolarizability parameter βCT, and the solvatochromic descriptor of 〈 γ〉 SD obtained by the solvatochromic method. The dyes studied show a high total first order hyperpolarizability (70-238 times) and second order hyperpolarizability (412-778 times) compared to urea. Among the three functionals, the CAM-B3LYP and BHHLYP functionals show hyperpolarizability values closer to experimental values. Experimental absorption and emission wavelengths measured for all the synthesized dyes are in good agreement with those predicted using the time-dependent density functional theory. The theoretical examination on non-linear optical properties was performed on the key parameters of polarizability and hyperpolarizability. A remarkable increase in non-linear optical response is observed on insertion of benzothiazole unit compared to benzimidazole unit.

Using Approximations to Accelerate Engineering Design Optimization

NASA Technical Reports Server (NTRS)

Torczon, Virginia; Trosset, Michael W.

1998-01-01

Optimization problems that arise in engineering design are often characterized by several features that hinder the use of standard nonlinear optimization techniques. Foremost among these features is that the functions used to define the engineering optimization problem often are computationally intensive. Within a standard nonlinear optimization algorithm, the computational expense of evaluating the functions that define the problem would necessarily be incurred for each iteration of the optimization algorithm. Faced with such prohibitive computational costs, an attractive alternative is to make use of surrogates within an optimization context since surrogates can be chosen or constructed so that they are typically much less expensive to compute. For the purposes of this paper, we will focus on the use of algebraic approximations as surrogates for the objective. In this paper we introduce the use of so-called merit functions that explicitly recognize the desirability of improving the current approximation to the objective during the course of the optimization. We define and experiment with the use of merit functions chosen to simultaneously improve both the solution to the optimization problem (the objective) and the quality of the approximation. Our goal is to further improve the effectiveness of our general approach without sacrificing any of its rigor.

Optimizing cost-efficiency in mean exposure assessment - cost functions reconsidered

PubMed Central

2011-01-01

Background Reliable exposure data is a vital concern in medical epidemiology and intervention studies. The present study addresses the needs of the medical researcher to spend monetary resources devoted to exposure assessment with an optimal cost-efficiency, i.e. obtain the best possible statistical performance at a specified budget. A few previous studies have suggested mathematical optimization procedures based on very simple cost models; this study extends the methodology to cover even non-linear cost scenarios. Methods Statistical performance, i.e. efficiency, was assessed in terms of the precision of an exposure mean value, as determined in a hierarchical, nested measurement model with three stages. Total costs were assessed using a corresponding three-stage cost model, allowing costs at each stage to vary non-linearly with the number of measurements according to a power function. Using these models, procedures for identifying the optimally cost-efficient allocation of measurements under a constrained budget were developed, and applied on 225 scenarios combining different sizes of unit costs, cost function exponents, and exposure variance components. Results Explicit mathematical rules for identifying optimal allocation could be developed when cost functions were linear, while non-linear cost functions implied that parts of or the entire optimization procedure had to be carried out using numerical methods. For many of the 225 scenarios, the optimal strategy consisted in measuring on only one occasion from each of as many subjects as allowed by the budget. Significant deviations from this principle occurred if costs for recruiting subjects were large compared to costs for setting up measurement occasions, and, at the same time, the between-subjects to within-subject variance ratio was small. In these cases, non-linearities had a profound influence on the optimal allocation and on the eventual size of the exposure data set. Conclusions The analysis procedures developed in the present study can be used for informed design of exposure assessment strategies, provided that data are available on exposure variability and the costs of collecting and processing data. The present shortage of empirical evidence on costs and appropriate cost functions however impedes general conclusions on optimal exposure measurement strategies in different epidemiologic scenarios. PMID:21600023

Optimizing cost-efficiency in mean exposure assessment--cost functions reconsidered.

PubMed

Mathiassen, Svend Erik; Bolin, Kristian

2011-05-21

Reliable exposure data is a vital concern in medical epidemiology and intervention studies. The present study addresses the needs of the medical researcher to spend monetary resources devoted to exposure assessment with an optimal cost-efficiency, i.e. obtain the best possible statistical performance at a specified budget. A few previous studies have suggested mathematical optimization procedures based on very simple cost models; this study extends the methodology to cover even non-linear cost scenarios. Statistical performance, i.e. efficiency, was assessed in terms of the precision of an exposure mean value, as determined in a hierarchical, nested measurement model with three stages. Total costs were assessed using a corresponding three-stage cost model, allowing costs at each stage to vary non-linearly with the number of measurements according to a power function. Using these models, procedures for identifying the optimally cost-efficient allocation of measurements under a constrained budget were developed, and applied on 225 scenarios combining different sizes of unit costs, cost function exponents, and exposure variance components. Explicit mathematical rules for identifying optimal allocation could be developed when cost functions were linear, while non-linear cost functions implied that parts of or the entire optimization procedure had to be carried out using numerical methods.For many of the 225 scenarios, the optimal strategy consisted in measuring on only one occasion from each of as many subjects as allowed by the budget. Significant deviations from this principle occurred if costs for recruiting subjects were large compared to costs for setting up measurement occasions, and, at the same time, the between-subjects to within-subject variance ratio was small. In these cases, non-linearities had a profound influence on the optimal allocation and on the eventual size of the exposure data set. The analysis procedures developed in the present study can be used for informed design of exposure assessment strategies, provided that data are available on exposure variability and the costs of collecting and processing data. The present shortage of empirical evidence on costs and appropriate cost functions however impedes general conclusions on optimal exposure measurement strategies in different epidemiologic scenarios.

Combined genetic algorithm and multiple linear regression (GA-MLR) optimizer: Application to multi-exponential fluorescence decay surface.

PubMed

Fisz, Jacek J

2006-12-07

The optimization approach based on the genetic algorithm (GA) combined with multiple linear regression (MLR) method, is discussed. The GA-MLR optimizer is designed for the nonlinear least-squares problems in which the model functions are linear combinations of nonlinear functions. GA optimizes the nonlinear parameters, and the linear parameters are calculated from MLR. GA-MLR is an intuitive optimization approach and it exploits all advantages of the genetic algorithm technique. This optimization method results from an appropriate combination of two well-known optimization methods. The MLR method is embedded in the GA optimizer and linear and nonlinear model parameters are optimized in parallel. The MLR method is the only one strictly mathematical "tool" involved in GA-MLR. The GA-MLR approach simplifies and accelerates considerably the optimization process because the linear parameters are not the fitted ones. Its properties are exemplified by the analysis of the kinetic biexponential fluorescence decay surface corresponding to a two-excited-state interconversion process. A short discussion of the variable projection (VP) algorithm, designed for the same class of the optimization problems, is presented. VP is a very advanced mathematical formalism that involves the methods of nonlinear functionals, algebra of linear projectors, and the formalism of Fréchet derivatives and pseudo-inverses. Additional explanatory comments are added on the application of recently introduced the GA-NR optimizer to simultaneous recovery of linear and weakly nonlinear parameters occurring in the same optimization problem together with nonlinear parameters. The GA-NR optimizer combines the GA method with the NR method, in which the minimum-value condition for the quadratic approximation to chi(2), obtained from the Taylor series expansion of chi(2), is recovered by means of the Newton-Raphson algorithm. The application of the GA-NR optimizer to model functions which are multi-linear combinations of nonlinear functions, is indicated. The VP algorithm does not distinguish the weakly nonlinear parameters from the nonlinear ones and it does not apply to the model functions which are multi-linear combinations of nonlinear functions.

Discrete-Time Stable Generalized Self-Learning Optimal Control With Approximation Errors.

PubMed

Wei, Qinglai; Li, Benkai; Song, Ruizhuo

2018-04-01

In this paper, a generalized policy iteration (GPI) algorithm with approximation errors is developed for solving infinite horizon optimal control problems for nonlinear systems. The developed stable GPI algorithm provides a general structure of discrete-time iterative adaptive dynamic programming algorithms, by which most of the discrete-time reinforcement learning algorithms can be described using the GPI structure. It is for the first time that approximation errors are explicitly considered in the GPI algorithm. The properties of the stable GPI algorithm with approximation errors are analyzed. The admissibility of the approximate iterative control law can be guaranteed if the approximation errors satisfy the admissibility criteria. The convergence of the developed algorithm is established, which shows that the iterative value function is convergent to a finite neighborhood of the optimal performance index function, if the approximate errors satisfy the convergence criterion. Finally, numerical examples and comparisons are presented.

Sequential bearings-only-tracking initiation with particle filtering method.

PubMed

Liu, Bin; Hao, Chengpeng

2013-01-01

The tracking initiation problem is examined in the context of autonomous bearings-only-tracking (BOT) of a single appearing/disappearing target in the presence of clutter measurements. In general, this problem suffers from a combinatorial explosion in the number of potential tracks resulted from the uncertainty in the linkage between the target and the measurement (a.k.a the data association problem). In addition, the nonlinear measurements lead to a non-Gaussian posterior probability density function (pdf) in the optimal Bayesian sequential estimation framework. The consequence of this nonlinear/non-Gaussian context is the absence of a closed-form solution. This paper models the linkage uncertainty and the nonlinear/non-Gaussian estimation problem jointly with solid Bayesian formalism. A particle filtering (PF) algorithm is derived for estimating the model's parameters in a sequential manner. Numerical results show that the proposed solution provides a significant benefit over the most commonly used methods, IPDA and IMMPDA. The posterior Cramér-Rao bounds are also involved for performance evaluation.

Impact of generalized Fourier's and Fick's laws on MHD 3D second grade nanofluid flow with variable thermal conductivity and convective heat and mass conditions

NASA Astrophysics Data System (ADS)

Ramzan, M.; Bilal, M.; Chung, Jae Dong; Lu, Dian Chen; Farooq, Umer

2017-09-01

A mathematical model has been established to study the magnetohydrodynamic second grade nanofluid flow past a bidirectional stretched surface. The flow is induced by Cattaneo-Christov thermal and concentration diffusion fluxes. Novel characteristics of Brownian motion and thermophoresis are accompanied by temperature dependent thermal conductivity and convective heat and mass boundary conditions. Apposite transformations are betrothed to transform a system of nonlinear partial differential equations to nonlinear ordinary differential equations. Analytic solutions of the obtained nonlinear system are obtained via a convergent method. Graphs are plotted to examine how velocity, temperature, and concentration distributions are affected by varied physical involved parameters. Effects of skin friction coefficients along the x- and y-direction versus various parameters are also shown through graphs and are well debated. Our findings show that velocities along both the x and y axes exhibit a decreasing trend for the Hartmann number. Moreover, temperature and concentration distributions are decreasing functions of thermal and concentration relaxation parameters.

Multivariate meta-analysis for non-linear and other multi-parameter associations

PubMed Central

Gasparrini, A; Armstrong, B; Kenward, M G

2012-01-01

In this paper, we formalize the application of multivariate meta-analysis and meta-regression to synthesize estimates of multi-parameter associations obtained from different studies. This modelling approach extends the standard two-stage analysis used to combine results across different sub-groups or populations. The most straightforward application is for the meta-analysis of non-linear relationships, described for example by regression coefficients of splines or other functions, but the methodology easily generalizes to any setting where complex associations are described by multiple correlated parameters. The modelling framework of multivariate meta-analysis is implemented in the package mvmeta within the statistical environment R. As an illustrative example, we propose a two-stage analysis for investigating the non-linear exposure–response relationship between temperature and non-accidental mortality using time-series data from multiple cities. Multivariate meta-analysis represents a useful analytical tool for studying complex associations through a two-stage procedure. Copyright © 2012 John Wiley & Sons, Ltd. PMID:22807043

Class of self-limiting growth models in the presence of nonlinear diffusion

NASA Astrophysics Data System (ADS)

Kar, Sandip; Banik, Suman Kumar; Ray, Deb Shankar

2002-06-01

The source term in a reaction-diffusion system, in general, does not involve explicit time dependence. A class of self-limiting growth models dealing with animal and tumor growth and bacterial population in a culture, on the other hand, are described by kinetics with explicit functions of time. We analyze a reaction-diffusion system to study the propagation of spatial front for these models.

Nonlinear stability of Gardner breathers

NASA Astrophysics Data System (ADS)

Alejo, Miguel A.

2018-01-01

We show that breather solutions of the Gardner equation, a natural generalization of the KdV and mKdV equations, are H2 (R) stable. Through a variational approach, we characterize Gardner breathers as minimizers of a new Lyapunov functional and we study the associated spectral problem, through (i) the analysis of the spectrum of explicit linear systems (spectral stability), and (ii) controlling degenerated directions by using low regularity conservation laws.

Combinatorial approaches to gene recognition.

PubMed

Roytberg, M A; Astakhova, T V; Gelfand, M S

1997-01-01

Recognition of genes via exon assembly approaches leads naturally to the use of dynamic programming. We consider the general graph-theoretical formulation of the exon assembly problem and analyze in detail some specific variants: multicriterial optimization in the case of non-linear gene-scoring functions; context-dependent schemes for scoring exons and related procedures for exon filtering; and highly specific recognition of arbitrary gene segments, oligonucleotide probes and polymerase chain reaction (PCR) primers.

Survey of digital filtering

NASA Technical Reports Server (NTRS)

Nagle, H. T., Jr.

1972-01-01

A three part survey is made of the state-of-the-art in digital filtering. Part one presents background material including sampled data transformations and the discrete Fourier transform. Part two, digital filter theory, gives an in-depth coverage of filter categories, transfer function synthesis, quantization and other nonlinear errors, filter structures and computer aided design. Part three presents hardware mechanization techniques. Implementations by general purpose, mini-, and special-purpose computers are presented.

Analytical approximate solutions for a general class of nonlinear delay differential equations.

PubMed

Căruntu, Bogdan; Bota, Constantin

2014-01-01

We use the polynomial least squares method (PLSM), which allows us to compute analytical approximate polynomial solutions for a very general class of strongly nonlinear delay differential equations. The method is tested by computing approximate solutions for several applications including the pantograph equations and a nonlinear time-delay model from biology. The accuracy of the method is illustrated by a comparison with approximate solutions previously computed using other methods.

Analysis of Nonlinear Periodic and Aperiodic Media: Application to Optical Logic Gates

NASA Astrophysics Data System (ADS)

Yu, Yisheng

This dissertation is about the analysis of nonlinear periodic and aperiodic media and their application to the design of intensity controlled all optical logic gates: AND, OR, and NOT. A coupled nonlinear differential equation that characterizes the electromagnetic wave propagation in a nonlinear periodic (and aperiodic) medium has been derived from the first principle. The equations are general enough that it reflects the effect of transverse modal fields and can be used to analyze both co-propagating and counter propagating waves. A numerical technique based on the finite differences method and absorbing boundary condition has been developed to solve the coupled differential equations here. The numerical method is simple and accurate. Unlike the method based on characteristics that has been reported in the literature, this method does not involve integration and step sizes of time and space coordinates are decoupled. The decoupling provides independent choice for time and space step sizes. The concept of "gap soliton" has also been re-examined. The dissertation consists of four manuscripts. Manuscript I reports on the design of all optical logic gates: AND, OR, and NOT based on the bistability property of nonlinear periodic and aperiodic waveguiding structures. The functioning of the logic gates has been shown by analysis. The numerical technique that has been developed to solve the nonlinear differential equations are addressed in manuscript II. The effect of transverse modal fields on the bistable property of nonlinear periodic medium is reported in manuscript III. The concept of "gap soliton" that are generated in a nonlinear periodic medium has been re-examined. The details on the finding of the re-examination are discussed in manuscript IV.

Nonlinear analysis of structures. [within framework of finite element method

NASA Technical Reports Server (NTRS)

Armen, H., Jr.; Levine, H.; Pifko, A.; Levy, A.

1974-01-01

The development of nonlinear analysis techniques within the framework of the finite-element method is reported. Although the emphasis is concerned with those nonlinearities associated with material behavior, a general treatment of geometric nonlinearity, alone or in combination with plasticity is included, and applications presented for a class of problems categorized as axisymmetric shells of revolution. The scope of the nonlinear analysis capabilities includes: (1) a membrane stress analysis, (2) bending and membrane stress analysis, (3) analysis of thick and thin axisymmetric bodies of revolution, (4) a general three dimensional analysis, and (5) analysis of laminated composites. Applications of the methods are made to a number of sample structures. Correlation with available analytic or experimental data range from good to excellent.

Optical soliton solutions of the cubic-quintic non-linear Schrödinger's equation including an anti-cubic term

NASA Astrophysics Data System (ADS)

Kaplan, Melike; Hosseini, Kamyar; Samadani, Farzan; Raza, Nauman

2018-07-01

A wide range of problems in different fields of the applied sciences especially non-linear optics is described by non-linear Schrödinger's equations (NLSEs). In the present paper, a specific type of NLSEs known as the cubic-quintic non-linear Schrödinger's equation including an anti-cubic term has been studied. The generalized Kudryashov method along with symbolic computation package has been exerted to carry out this objective. As a consequence, a series of optical soliton solutions have formally been retrieved. It is corroborated that the generalized form of Kudryashov method is a direct, effectual, and reliable technique to deal with various types of non-linear Schrödinger's equations.

A framework for optimal kernel-based manifold embedding of medical image data.

PubMed

Zimmer, Veronika A; Lekadir, Karim; Hoogendoorn, Corné; Frangi, Alejandro F; Piella, Gemma

2015-04-01

Kernel-based dimensionality reduction is a widely used technique in medical image analysis. To fully unravel the underlying nonlinear manifold the selection of an adequate kernel function and of its free parameters is critical. In practice, however, the kernel function is generally chosen as Gaussian or polynomial and such standard kernels might not always be optimal for a given image dataset or application. In this paper, we present a study on the effect of the kernel functions in nonlinear manifold embedding of medical image data. To this end, we first carry out a literature review on existing advanced kernels developed in the statistics, machine learning, and signal processing communities. In addition, we implement kernel-based formulations of well-known nonlinear dimensional reduction techniques such as Isomap and Locally Linear Embedding, thus obtaining a unified framework for manifold embedding using kernels. Subsequently, we present a method to automatically choose a kernel function and its associated parameters from a pool of kernel candidates, with the aim to generate the most optimal manifold embeddings. Furthermore, we show how the calculated selection measures can be extended to take into account the spatial relationships in images, or used to combine several kernels to further improve the embedding results. Experiments are then carried out on various synthetic and phantom datasets for numerical assessment of the methods. Furthermore, the workflow is applied to real data that include brain manifolds and multispectral images to demonstrate the importance of the kernel selection in the analysis of high-dimensional medical images. Copyright © 2014 Elsevier Ltd. All rights reserved.

Nonlinear association criterion, nonlinear Granger causality and related issues with applications to neuroimage studies.

PubMed

Tao, Chenyang; Feng, Jianfeng

2016-03-15

Quantifying associations in neuroscience (and many other scientific disciplines) is often challenged by high-dimensionality, nonlinearity and noisy observations. Many classic methods have either poor power or poor scalability on data sets of the same or different scales such as genetical, physiological and image data. Based on the framework of reproducing kernel Hilbert spaces we proposed a new nonlinear association criteria (NAC) with an efficient numerical algorithm and p-value approximation scheme. We also presented mathematical justification that links the proposed method to related methods such as kernel generalized variance, kernel canonical correlation analysis and Hilbert-Schmidt independence criteria. NAC allows the detection of association between arbitrary input domain as long as a characteristic kernel is defined. A MATLAB package was provided to facilitate applications. Extensive simulation examples and four real world neuroscience examples including functional MRI causality, Calcium imaging and imaging genetic studies on autism [Brain, 138(5):13821393 (2015)] and alcohol addiction [PNAS, 112(30):E4085-E4093 (2015)] are used to benchmark NAC. It demonstrates the superior performance over the existing procedures we tested and also yields biologically significant results for the real world examples. NAC beats its linear counterparts when nonlinearity is presented in the data. It also shows more robustness against different experimental setups compared with its nonlinear counterparts. In this work we presented a new and robust statistical approach NAC for measuring associations. It could serve as an interesting alternative to the existing methods for datasets where nonlinearity and other confounding factors are present. Copyright © 2016 Elsevier B.V. All rights reserved.

Probability Weighting Functions Derived from Hyperbolic Time Discounting: Psychophysical Models and Their Individual Level Testing.

PubMed

Takemura, Kazuhisa; Murakami, Hajime

2016-01-01

A probability weighting function (w(p)) is considered to be a nonlinear function of probability (p) in behavioral decision theory. This study proposes a psychophysical model of probability weighting functions derived from a hyperbolic time discounting model and a geometric distribution. The aim of the study is to show probability weighting functions from the point of view of waiting time for a decision maker. Since the expected value of a geometrically distributed random variable X is 1/p, we formulized the probability weighting function of the expected value model for hyperbolic time discounting as w(p) = (1 - k log p)(-1). Moreover, the probability weighting function is derived from Loewenstein and Prelec's (1992) generalized hyperbolic time discounting model. The latter model is proved to be equivalent to the hyperbolic-logarithmic weighting function considered by Prelec (1998) and Luce (2001). In this study, we derive a model from the generalized hyperbolic time discounting model assuming Fechner's (1860) psychophysical law of time and a geometric distribution of trials. In addition, we develop median models of hyperbolic time discounting and generalized hyperbolic time discounting. To illustrate the fitness of each model, a psychological experiment was conducted to assess the probability weighting and value functions at the level of the individual participant. The participants were 50 university students. The results of individual analysis indicated that the expected value model of generalized hyperbolic discounting fitted better than previous probability weighting decision-making models. The theoretical implications of this finding are discussed.

A class of all digital phase locked loops - Modeling and analysis

NASA Technical Reports Server (NTRS)

Reddy, C. P.; Gupta, S. C.

1973-01-01

An all digital phase locked loop which tracks the phase of the incoming signal once per carrier cycle is proposed. The different elements and their functions, and the phase lock operation are explained in detail. The general digital loop operation is governed by a nonlinear difference equation from which a suitable model is developed. The lock range for the general model is derived. The performance of the digital loop for phase step and frequency step inputs for different levels of quantization without loop filter are studied. The analytical results are checked by simulating the actual system on the digital computer.

Development of a winter wheat adjustable crop calendar model

NASA Technical Reports Server (NTRS)

Baker, J. R. (Principal Investigator)

1978-01-01

The author has identified the following significant results. After parameter estimation, tests were conducted with variances from the fits, and on independent data. From these tests, it was generally concluded that exponential functions have little advantage over polynomials. Precipitation was not found to significantly affect the fits. The Robertson's triquadratic form, in general use for spring wheat, was found to show promise for winter wheat, but special techniques and care were required for its use. In most instances, equations with nonlinear effects were found to yield erratic results when utilized with daily environmental values as independent variables.

Chirped femtosecond pulses in the higher-order nonlinear Schrödinger equation with non-Kerr nonlinear terms and cubic-quintic-septic nonlinearities

NASA Astrophysics Data System (ADS)

Triki, Houria; Biswas, Anjan; Milović, Daniela; Belić, Milivoj

2016-05-01

We consider a high-order nonlinear Schrödinger equation with competing cubic-quintic-septic nonlinearities, non-Kerr quintic nonlinearity, self-steepening, and self-frequency shift. The model describes the propagation of ultrashort (femtosecond) optical pulses in highly nonlinear optical fibers. A new ansatz is adopted to obtain nonlinear chirp associated with the propagating femtosecond soliton pulses. It is shown that the resultant elliptic equation of the problem is of high order, contains several new terms and is more general than the earlier reported results, thus providing a systematic way to find exact chirped soliton solutions of the septic model. Novel soliton solutions, including chirped bright, dark, kink and fractional-transform soliton solutions are obtained for special choices of parameters. Furthermore, we present the parameter domains in which these optical solitons exist. The nonlinear chirp associated with each of the solitonic solutions is also determined. It is shown that the chirping is proportional to the intensity of the wave and depends on higher-order nonlinearities. Of special interest is the soliton solution of the bright and dark type, determined for the general case when all coefficients in the equation have nonzero values. These results can be useful for possible chirped-soliton-based applications of highly nonlinear optical fiber systems.

Using recurrent neural networks for adaptive communication channel equalization.

PubMed

Kechriotis, G; Zervas, E; Manolakos, E S

1994-01-01

Nonlinear adaptive filters based on a variety of neural network models have been used successfully for system identification and noise-cancellation in a wide class of applications. An important problem in data communications is that of channel equalization, i.e., the removal of interferences introduced by linear or nonlinear message corrupting mechanisms, so that the originally transmitted symbols can be recovered correctly at the receiver. In this paper we introduce an adaptive recurrent neural network (RNN) based equalizer whose small size and high performance makes it suitable for high-speed channel equalization. We propose RNN based structures for both trained adaptation and blind equalization, and we evaluate their performance via extensive simulations for a variety of signal modulations and communication channel models. It is shown that the RNN equalizers have comparable performance with traditional linear filter based equalizers when the channel interferences are relatively mild, and that they outperform them by several orders of magnitude when either the channel's transfer function has spectral nulls or severe nonlinear distortion is present. In addition, the small-size RNN equalizers, being essentially generalized IIR filters, are shown to outperform multilayer perceptron equalizers of larger computational complexity in linear and nonlinear channel equalization cases.

On the nonlinear three dimensional instability of Stokes layers and other shear layers to pairs of oblique waves

NASA Technical Reports Server (NTRS)

Wu, Xuesong; Lee, Sang Soo; Cowley, Stephen J.

1992-01-01

The nonlinear evolution of a pair of initially oblique waves in a high Reynolds Number Stokes layer is studied. Attention is focused on times when disturbances of amplitude epsilon have O(epsilon(exp 1/3)R) growth rates, where R is the Reynolds number. The development of a pair of oblique waves is then controlled by nonlinear critical-layer effects. Viscous effects are included by studying the distinguished scaling epsilon = O(R(exp -1)). This leads to a complicated modification of the kernel function in the integro-differential amplitude equation. When viscosity is not too large, solutions to the amplitude equation develop a finite-time singularity, indicating that an explosive growth can be introduced by nonlinear effects; we suggest that such explosive growth can lead to the bursts observed in experiments. Increasing the importance of viscosity generally delays the occurrence of the finite-time singularity, and sufficiently large viscosity may lead to the disturbance decaying exponentially. For the special case when the streamwise and spanwise wavenumbers are equal, the solution can evolve into a periodic oscillation. A link between the unsteady critical-layer approach to high-Reynolds-number flow instability, and the wave vortex approach is identified.

Non-linear eigensolver-based alternative to traditional SCF methods

NASA Astrophysics Data System (ADS)

Gavin, Brendan; Polizzi, Eric

2013-03-01

The self-consistent iterative procedure in Density Functional Theory calculations is revisited using a new, highly efficient and robust algorithm for solving the non-linear eigenvector problem (i.e. H(X)X = EX;) of the Kohn-Sham equations. This new scheme is derived from a generalization of the FEAST eigenvalue algorithm, and provides a fundamental and practical numerical solution for addressing the non-linearity of the Hamiltonian with the occupied eigenvectors. In contrast to SCF techniques, the traditional outer iterations are replaced by subspace iterations that are intrinsic to the FEAST algorithm, while the non-linearity is handled at the level of a projected reduced system which is orders of magnitude smaller than the original one. Using a series of numerical examples, it will be shown that our approach can outperform the traditional SCF mixing techniques such as Pulay-DIIS by providing a high converge rate and by converging to the correct solution regardless of the choice of the initial guess. We also discuss a practical implementation of the technique that can be achieved effectively using the FEAST solver package. This research is supported by NSF under Grant #ECCS-0846457 and Intel Corporation.

Dissipative behavior of some fully non-linear KdV-type equations

NASA Astrophysics Data System (ADS)

Brenier, Yann; Levy, Doron

2000-03-01

The KdV equation can be considered as a special case of the general equation u t+f(u) x-δg(u xx) x=0, δ>0, where f is non-linear and g is linear, namely f( u)= u2/2 and g( v)= v. As the parameter δ tends to 0, the dispersive behavior of the KdV equation has been throughly investigated (see, e.g., [P.G. Drazin, Solitons, London Math. Soc. Lect. Note Ser. 85, Cambridge University Press, Cambridge, 1983; P.D. Lax, C.D. Levermore, The small dispersion limit of the Korteweg-de Vries equation, III, Commun. Pure Appl. Math. 36 (1983) 809-829; G.B. Whitham, Linear and Nonlinear Waves, Wiley/Interscience, New York, 1974] and the references therein). We show through numerical evidence that a completely different, dissipative behavior occurs when g is non-linear, namely when g is an even concave function such as g( v)=-∣ v∣ or g( v)=- v2. In particular, our numerical results hint that as δ→0 the solutions strongly converge to the unique entropy solution of the formal limit equation, in total contrast with the solutions of the KdV equation.

Variational Bayesian identification and prediction of stochastic nonlinear dynamic causal models.

PubMed

Daunizeau, J; Friston, K J; Kiebel, S J

2009-11-01

In this paper, we describe a general variational Bayesian approach for approximate inference on nonlinear stochastic dynamic models. This scheme extends established approximate inference on hidden-states to cover: (i) nonlinear evolution and observation functions, (ii) unknown parameters and (precision) hyperparameters and (iii) model comparison and prediction under uncertainty. Model identification or inversion entails the estimation of the marginal likelihood or evidence of a model. This difficult integration problem can be finessed by optimising a free-energy bound on the evidence using results from variational calculus. This yields a deterministic update scheme that optimises an approximation to the posterior density on the unknown model variables. We derive such a variational Bayesian scheme in the context of nonlinear stochastic dynamic hierarchical models, for both model identification and time-series prediction. The computational complexity of the scheme is comparable to that of an extended Kalman filter, which is critical when inverting high dimensional models or long time-series. Using Monte-Carlo simulations, we assess the estimation efficiency of this variational Bayesian approach using three stochastic variants of chaotic dynamic systems. We also demonstrate the model comparison capabilities of the method, its self-consistency and its predictive power.

Probabilistic density function method for nonlinear dynamical systems driven by colored noise.

PubMed

Barajas-Solano, David A; Tartakovsky, Alexandre M

2016-05-01

We present a probability density function (PDF) method for a system of nonlinear stochastic ordinary differential equations driven by colored noise. The method provides an integrodifferential equation for the temporal evolution of the joint PDF of the system's state, which we close by means of a modified large-eddy-diffusivity (LED) closure. In contrast to the classical LED closure, the proposed closure accounts for advective transport of the PDF in the approximate temporal deconvolution of the integrodifferential equation. In addition, we introduce the generalized local linearization approximation for deriving a computable PDF equation in the form of a second-order partial differential equation. We demonstrate that the proposed closure and localization accurately describe the dynamics of the PDF in phase space for systems driven by noise with arbitrary autocorrelation time. We apply the proposed PDF method to analyze a set of Kramers equations driven by exponentially autocorrelated Gaussian colored noise to study nonlinear oscillators and the dynamics and stability of a power grid. Numerical experiments show the PDF method is accurate when the noise autocorrelation time is either much shorter or longer than the system's relaxation time, while the accuracy decreases as the ratio of the two timescales approaches unity. Similarly, the PDF method accuracy decreases with increasing standard deviation of the noise.

Halo correlations in nonlinear cosmic density fields

NASA Astrophysics Data System (ADS)

Bernardeau, F.; Schaeffer, R.

1999-09-01

The question we address in this paper is the determination of the correlation properties of the dark matter halos appearing in cosmic density fields once they underwent a strongly nonlinear evolution induced by gravitational dynamics. A series of previous works have given indications that kind of non-Gaussian features are induced by nonlinear evolution in term of the high-order correlation functions. Assuming such patterns for the matter field, i.e. that the high-order correlation functions behave as products of two-body correlation functions, we derive the correlation properties of the halos, that are assumed to represent the correlation properties of galaxies or clusters. The hierarchical pattern originally induced by gravity is shown to be conserved for the halos. The strength of their correlations at any order varies, however, but is found to depend only on their internal properties, namely on the parameter x~ m/r(3-gamma ) where m is the mass of the halo, r its size and gamma is the power law index of the two-body correlation function. This internal parameter is seen to be close to the depth of the internal potential well of virialized objects. We were able to derive the explicit form of the generating function of the moments of the halo counts probability distribution function. In particular we show explicitly that, generically, S_P(x)-> P(P-2) in the rare halo limit. Various illustrations of our general results are presented. As a function of the properties of the underlying matter field, we construct the count probabilities for halos and in particular discuss the halo void probability. We evaluate the dependence of the halo mass function on the environment: within clusters, hierarchical clustering implies the higher masses are favored. These properties solely arise from what is a natural bias (ie, naturally induced by gravity) between the observed objects and the unseen matter field, and how it manifests itself depending on which selection effects are imposed.

Filtering Non-Linear Transfer Functions on Surfaces.

PubMed

Heitz, Eric; Nowrouzezahrai, Derek; Poulin, Pierre; Neyret, Fabrice

2014-07-01

Applying non-linear transfer functions and look-up tables to procedural functions (such as noise), surface attributes, or even surface geometry are common strategies used to enhance visual detail. Their simplicity and ability to mimic a wide range of realistic appearances have led to their adoption in many rendering problems. As with any textured or geometric detail, proper filtering is needed to reduce aliasing when viewed across a range of distances, but accurate and efficient transfer function filtering remains an open problem for several reasons: transfer functions are complex and non-linear, especially when mapped through procedural noise and/or geometry-dependent functions, and the effects of perspective and masking further complicate the filtering over a pixel's footprint. We accurately solve this problem by computing and sampling from specialized filtering distributions on the fly, yielding very fast performance. We investigate the case where the transfer function to filter is a color map applied to (macroscale) surface textures (like noise), as well as color maps applied according to (microscale) geometric details. We introduce a novel representation of a (potentially modulated) color map's distribution over pixel footprints using Gaussian statistics and, in the more complex case of high-resolution color mapped microsurface details, our filtering is view- and light-dependent, and capable of correctly handling masking and occlusion effects. Our approach can be generalized to filter other physical-based rendering quantities. We propose an application to shading with irradiance environment maps over large terrains. Our framework is also compatible with the case of transfer functions used to warp surface geometry, as long as the transformations can be represented with Gaussian statistics, leading to proper view- and light-dependent filtering results. Our results match ground truth and our solution is well suited to real-time applications, requires only a few lines of shader code (provided in supplemental material, which can be found on the Computer Society Digital Library at http://doi.ieeecomputersociety.org/10.1109/TVCG.2013.102), is high performance, and has a negligible memory footprint.

The heritability of the functional connectome is robust to common nonlinear registration methods

NASA Astrophysics Data System (ADS)

Hafzalla, George W.; Prasad, Gautam; Baboyan, Vatche G.; Faskowitz, Joshua; Jahanshad, Neda; McMahon, Katie L.; de Zubicaray, Greig I.; Wright, Margaret J.; Braskie, Meredith N.; Thompson, Paul M.

2016-03-01

Nonlinear registration algorithms are routinely used in brain imaging, to align data for inter-subject and group comparisons, and for voxelwise statistical analyses. To understand how the choice of registration method affects maps of functional brain connectivity in a sample of 611 twins, we evaluated three popular nonlinear registration methods: Advanced Normalization Tools (ANTs), Automatic Registration Toolbox (ART), and FMRIB's Nonlinear Image Registration Tool (FNIRT). Using both structural and functional MRI, we used each of the three methods to align the MNI152 brain template, and 80 regions of interest (ROIs), to each subject's T1-weighted (T1w) anatomical image. We then transformed each subject's ROIs onto the associated resting state functional MRI (rs-fMRI) scans and computed a connectivity network or functional connectome for each subject. Given the different degrees of genetic similarity between pairs of monozygotic (MZ) and same-sex dizygotic (DZ) twins, we used structural equation modeling to estimate the additive genetic influences on the elements of the function networks, or their heritability. The functional connectome and derived statistics were relatively robust to nonlinear registration effects.

Robust Adaptive Modified Newton Algorithm for Generalized Eigendecomposition and Its Application

NASA Astrophysics Data System (ADS)

Yang, Jian; Yang, Feng; Xi, Hong-Sheng; Guo, Wei; Sheng, Yanmin

2007-12-01

We propose a robust adaptive algorithm for generalized eigendecomposition problems that arise in modern signal processing applications. To that extent, the generalized eigendecomposition problem is reinterpreted as an unconstrained nonlinear optimization problem. Starting from the proposed cost function and making use of an approximation of the Hessian matrix, a robust modified Newton algorithm is derived. A rigorous analysis of its convergence properties is presented by using stochastic approximation theory. We also apply this theory to solve the signal reception problem of multicarrier DS-CDMA to illustrate its practical application. The simulation results show that the proposed algorithm has fast convergence and excellent tracking capability, which are important in a practical time-varying communication environment.

Orbital stability and energy estimate of ground states of saturable nonlinear Schrödinger equations with intensity functions in R2

NASA Astrophysics Data System (ADS)

Lin, Tai-Chia; Wang, Xiaoming; Wang, Zhi-Qiang

2017-10-01

Conventionally, the existence and orbital stability of ground states of nonlinear Schrödinger (NLS) equations with power-law nonlinearity (subcritical case) can be proved by an argument using strict subadditivity of the ground state energy and the concentration compactness method of Cazenave and Lions [4]. However, for saturable nonlinearity, such an argument is not applicable because strict subadditivity of the ground state energy fails in this case. Here we use a convexity argument to prove the existence and orbital stability of ground states of NLS equations with saturable nonlinearity and intensity functions in R2. Besides, we derive the energy estimate of ground states of saturable NLS equations with intensity functions using the eigenvalue estimate of saturable NLS equations without intensity function.

Multi-Lagrangians for integrable systems

NASA Astrophysics Data System (ADS)

Nutku, Y.; Pavlov, M. V.

2002-03-01

We propose a general scheme to construct multiple Lagrangians for completely integrable nonlinear evolution equations that admit multi-Hamiltonian structure. The recursion operator plays a fundamental role in this construction. We use a conserved quantity higher/lower than the Hamiltonian in the potential part of the new Lagrangian and determine the corresponding kinetic terms by generating the appropriate momentum map. This leads to some remarkable new developments. We show that nonlinear evolutionary systems that admit N-fold first order local Hamiltonian structure can be cast into variational form with 2N-1 Lagrangians which will be local functionals of Clebsch potentials. This number increases to 3N-2 when the Miura transformation is invertible. Furthermore we construct a new Lagrangian for polytropic gas dynamics in 1+1 dimensions which is a free, local functional of the physical field variables, namely density and velocity, thus dispensing with the necessity of introducing Clebsch potentials entirely. This is a consequence of bi-Hamiltonian structure with a compatible pair of first and third order Hamiltonian operators derived from Sheftel's recursion operator.

A diffusion model of protected population on bilocal habitat with generalized resource

NASA Astrophysics Data System (ADS)

Vasilyev, Maxim D.; Trofimtsev, Yuri I.; Vasilyeva, Natalya V.

2017-11-01

A model of population distribution in a two-dimensional area divided by an ecological barrier, i.e. the boundaries of natural reserve, is considered. Distribution of the population is defined by diffusion, directed migrations and areal resource. The exchange of specimens occurs between two parts of the habitat. The mathematical model is presented in the form of a boundary value problem for a system of non-linear parabolic equations with variable parameters of diffusion and growth function. The splitting space variables, sweep method and simple iteration methods were used for the numerical solution of a system. A set of programs was coded in Python. Numerical simulation results for the two-dimensional unsteady non-linear problem are analyzed in detail. The influence of migration flow coefficients and functions of natural birth/death ratio on the distributions of population densities is investigated. The results of the research would allow to describe the conditions of the stable and sustainable existence of populations in bilocal habitat containing the protected and non-protected zones.

Flow Equation Approach to the Statistics of Nonlinear Dynamical Systems

NASA Astrophysics Data System (ADS)

Marston, J. B.; Hastings, M. B.

2005-03-01

The probability distribution function of non-linear dynamical systems is governed by a linear framework that resembles quantum many-body theory, in which stochastic forcing and/or averaging over initial conditions play the role of non-zero . Besides the well-known Fokker-Planck approach, there is a related Hopf functional methodootnotetextUriel Frisch, Turbulence: The Legacy of A. N. Kolmogorov (Cambridge University Press, 1995) chapter 9.5.; in both formalisms, zero modes of linear operators describe the stationary non-equilibrium statistics. To access the statistics, we investigate the method of continuous unitary transformationsootnotetextS. D. Glazek and K. G. Wilson, Phys. Rev. D 48, 5863 (1993); Phys. Rev. D 49, 4214 (1994). (also known as the flow equation approachootnotetextF. Wegner, Ann. Phys. 3, 77 (1994).), suitably generalized to the diagonalization of non-Hermitian matrices. Comparison to the more traditional cumulant expansion method is illustrated with low-dimensional attractors. The treatment of high-dimensional dynamical systems is also discussed.

Linearized Programming of Memristors for Artificial Neuro-Sensor Signal Processing

PubMed Central

Yang, Changju; Kim, Hyongsuk

2016-01-01

A linearized programming method of memristor-based neural weights is proposed. Memristor is known as an ideal element to implement a neural synapse due to its embedded functions of analog memory and analog multiplication. Its resistance variation with a voltage input is generally a nonlinear function of time. Linearization of memristance variation about time is very important for the easiness of memristor programming. In this paper, a method utilizing an anti-serial architecture for linear programming is proposed. The anti-serial architecture is composed of two memristors with opposite polarities. It linearizes the variation of memristance due to complimentary actions of two memristors. For programming a memristor, additional memristor with opposite polarity is employed. The linearization effect of weight programming of an anti-serial architecture is investigated and memristor bridge synapse which is built with two sets of anti-serial memristor architecture is taken as an application example of the proposed method. Simulations are performed with memristors of both linear drift model and nonlinear model. PMID:27548186

Linearized Programming of Memristors for Artificial Neuro-Sensor Signal Processing.

PubMed

Yang, Changju; Kim, Hyongsuk

2016-08-19

A linearized programming method of memristor-based neural weights is proposed. Memristor is known as an ideal element to implement a neural synapse due to its embedded functions of analog memory and analog multiplication. Its resistance variation with a voltage input is generally a nonlinear function of time. Linearization of memristance variation about time is very important for the easiness of memristor programming. In this paper, a method utilizing an anti-serial architecture for linear programming is proposed. The anti-serial architecture is composed of two memristors with opposite polarities. It linearizes the variation of memristance due to complimentary actions of two memristors. For programming a memristor, additional memristor with opposite polarity is employed. The linearization effect of weight programming of an anti-serial architecture is investigated and memristor bridge synapse which is built with two sets of anti-serial memristor architecture is taken as an application example of the proposed method. Simulations are performed with memristors of both linear drift model and nonlinear model.

A reduced-order model from high-dimensional frictional hysteresis

PubMed Central

Biswas, Saurabh; Chatterjee, Anindya

2014-01-01

Hysteresis in material behaviour includes both signum nonlinearities as well as high dimensionality. Available models for component-level hysteretic behaviour are empirical. Here, we derive a low-order model for rate-independent hysteresis from a high-dimensional massless frictional system. The original system, being given in terms of signs of velocities, is first solved incrementally using a linear complementarity problem formulation. From this numerical solution, to develop a reduced-order model, basis vectors are chosen using the singular value decomposition. The slip direction in generalized coordinates is identified as the minimizer of a dissipation-related function. That function includes terms for frictional dissipation through signum nonlinearities at many friction sites. Luckily, it allows a convenient analytical approximation. Upon solution of the approximated minimization problem, the slip direction is found. A final evolution equation for a few states is then obtained that gives a good match with the full solution. The model obtained here may lead to new insights into hysteresis as well as better empirical modelling thereof. PMID:24910522

DOE Office of Scientific and Technical Information (OSTI.GOV)

Huang, Kuo -Ling; Mehrotra, Sanjay

We present a homogeneous algorithm equipped with a modified potential function for the monotone complementarity problem. We show that this potential function is reduced by at least a constant amount if a scaled Lipschitz condition (SLC) is satisfied. A practical algorithm based on this potential function is implemented in a software package named iOptimize. The implementation in iOptimize maintains global linear and polynomial time convergence properties, while achieving practical performance. It either successfully solves the problem, or concludes that the SLC is not satisfied. When compared with the mature software package MOSEK (barrier solver version 6.0.0.106), iOptimize solves convex quadraticmore » programming problems, convex quadratically constrained quadratic programming problems, and general convex programming problems in fewer iterations. Moreover, several problems for which MOSEK fails are solved to optimality. In addition, we also find that iOptimize detects infeasibility more reliably than the general nonlinear solvers Ipopt (version 3.9.2) and Knitro (version 8.0).« less

Phase dynamics of coupled oscillators reconstructed from data

NASA Astrophysics Data System (ADS)

Rosenblum, Michael; Kralemann, Bjoern; Pikovsky, Arkady

2013-03-01

We present a technique for invariant reconstruction of the phase dynamics equations for coupled oscillators from data. The invariant description is achieved by means of a transformation of phase estimates (protophases) obtained from general scalar observables to genuine phases. Staring from the bivariate data, we obtain the coupling functions in terms of these phases. We discuss the importance of the protophase-to-phase transformation for characterization of strength and directionality of interaction. To illustrate the technique we analyse the cardio-respiratory interaction on healthy humans. Our invariant approach is confirmed by high similarity of the coupling functions obtained from different observables of the cardiac system. Next, we generalize the technique to cover the case of small networks of coupled periodic units. We use the partial norms of the reconstructed coupling functions to quantify directed coupling between the oscillators. We illustrate the method by different network motifs for three coupled oscillators. We also discuss nonlinear effects in coupling.

Wavelets and distributed approximating functionals

NASA Astrophysics Data System (ADS)

Wei, G. W.; Kouri, D. J.; Hoffman, D. K.

1998-07-01

A general procedure is proposed for constructing father and mother wavelets that have excellent time-frequency localization and can be used to generate entire wavelet families for use as wavelet transforms. One interesting feature of our father wavelets (scaling functions) is that they belong to a class of generalized delta sequences, which we refer to as distributed approximating functionals (DAFs). We indicate this by the notation wavelet-DAFs. Correspondingly, the mother wavelets generated from these wavelet-DAFs are appropriately called DAF-wavelets. Wavelet-DAFs can be regarded as providing a pointwise (localized) spectral method, which furnishes a bridge between the traditional global methods and local methods for solving partial differential equations. They are shown to provide extremely accurate numerical solutions for a number of nonlinear partial differential equations, including the Korteweg-de Vries (KdV) equation, for which a previous method has encountered difficulties (J. Comput. Phys. 132 (1997) 233).

Flexible link functions in nonparametric binary regression with Gaussian process priors.

PubMed

Li, Dan; Wang, Xia; Lin, Lizhen; Dey, Dipak K

2016-09-01

In many scientific fields, it is a common practice to collect a sequence of 0-1 binary responses from a subject across time, space, or a collection of covariates. Researchers are interested in finding out how the expected binary outcome is related to covariates, and aim at better prediction in the future 0-1 outcomes. Gaussian processes have been widely used to model nonlinear systems; in particular to model the latent structure in a binary regression model allowing nonlinear functional relationship between covariates and the expectation of binary outcomes. A critical issue in modeling binary response data is the appropriate choice of link functions. Commonly adopted link functions such as probit or logit links have fixed skewness and lack the flexibility to allow the data to determine the degree of the skewness. To address this limitation, we propose a flexible binary regression model which combines a generalized extreme value link function with a Gaussian process prior on the latent structure. Bayesian computation is employed in model estimation. Posterior consistency of the resulting posterior distribution is demonstrated. The flexibility and gains of the proposed model are illustrated through detailed simulation studies and two real data examples. Empirical results show that the proposed model outperforms a set of alternative models, which only have either a Gaussian process prior on the latent regression function or a Dirichlet prior on the link function. © 2015, The International Biometric Society.

Flexible Link Functions in Nonparametric Binary Regression with Gaussian Process Priors

PubMed Central

Li, Dan; Lin, Lizhen; Dey, Dipak K.

2015-01-01

Summary In many scientific fields, it is a common practice to collect a sequence of 0-1 binary responses from a subject across time, space, or a collection of covariates. Researchers are interested in finding out how the expected binary outcome is related to covariates, and aim at better prediction in the future 0-1 outcomes. Gaussian processes have been widely used to model nonlinear systems; in particular to model the latent structure in a binary regression model allowing nonlinear functional relationship between covariates and the expectation of binary outcomes. A critical issue in modeling binary response data is the appropriate choice of link functions. Commonly adopted link functions such as probit or logit links have fixed skewness and lack the flexibility to allow the data to determine the degree of the skewness. To address this limitation, we propose a flexible binary regression model which combines a generalized extreme value link function with a Gaussian process prior on the latent structure. Bayesian computation is employed in model estimation. Posterior consistency of the resulting posterior distribution is demonstrated. The flexibility and gains of the proposed model are illustrated through detailed simulation studies and two real data examples. Empirical results show that the proposed model outperforms a set of alternative models, which only have either a Gaussian process prior on the latent regression function or a Dirichlet prior on the link function. PMID:26686333

Nonlinearly Activated Neural Network for Solving Time-Varying Complex Sylvester Equation.

PubMed

Li, Shuai; Li, Yangming

2013-10-28

The Sylvester equation is often encountered in mathematics and control theory. For the general time-invariant Sylvester equation problem, which is defined in the domain of complex numbers, the Bartels-Stewart algorithm and its extensions are effective and widely used with an O(n³) time complexity. When applied to solving the time-varying Sylvester equation, the computation burden increases intensively with the decrease of sampling period and cannot satisfy continuous realtime calculation requirements. For the special case of the general Sylvester equation problem defined in the domain of real numbers, gradient-based recurrent neural networks are able to solve the time-varying Sylvester equation in real time, but there always exists an estimation error while a recently proposed recurrent neural network by Zhang et al [this type of neural network is called Zhang neural network (ZNN)] converges to the solution ideally. The advancements in complex-valued neural networks cast light to extend the existing real-valued ZNN for solving the time-varying real-valued Sylvester equation to its counterpart in the domain of complex numbers. In this paper, a complex-valued ZNN for solving the complex-valued Sylvester equation problem is investigated and the global convergence of the neural network is proven with the proposed nonlinear complex-valued activation functions. Moreover, a special type of activation function with a core function, called sign-bi-power function, is proven to enable the ZNN to converge in finite time, which further enhances its advantage in online processing. In this case, the upper bound of the convergence time is also derived analytically. Simulations are performed to evaluate and compare the performance of the neural network with different parameters and activation functions. Both theoretical analysis and numerical simulations validate the effectiveness of the proposed method.

Generalized Appended Product Indicator Procedure for Nonlinear Structural Equation Analysis.

ERIC Educational Resources Information Center

Wall, Melanie M.; Amemiya, Yasuo

2001-01-01

Considers the estimation of polynomial structural models and shows a limitation of an existing method. Introduces a new procedure, the generalized appended product indicator procedure, for nonlinear structural equation analysis. Addresses statistical issues associated with the procedure through simulation. (SLD)

A generalized nonlinear model-based mixed multinomial logit approach for crash data analysis.

PubMed

Zeng, Ziqiang; Zhu, Wenbo; Ke, Ruimin; Ash, John; Wang, Yinhai; Xu, Jiuping; Xu, Xinxin

2017-02-01

The mixed multinomial logit (MNL) approach, which can account for unobserved heterogeneity, is a promising unordered model that has been employed in analyzing the effect of factors contributing to crash severity. However, its basic assumption of using a linear function to explore the relationship between the probability of crash severity and its contributing factors can be violated in reality. This paper develops a generalized nonlinear model-based mixed MNL approach which is capable of capturing non-monotonic relationships by developing nonlinear predictors for the contributing factors in the context of unobserved heterogeneity. The crash data on seven Interstate freeways in Washington between January 2011 and December 2014 are collected to develop the nonlinear predictors in the model. Thirteen contributing factors in terms of traffic characteristics, roadway geometric characteristics, and weather conditions are identified to have significant mixed (fixed or random) effects on the crash density in three crash severity levels: fatal, injury, and property damage only. The proposed model is compared with the standard mixed MNL model. The comparison results suggest a slight superiority of the new approach in terms of model fit measured by the Akaike Information Criterion (12.06 percent decrease) and Bayesian Information Criterion (9.11 percent decrease). The predicted crash densities for all three levels of crash severities of the new approach are also closer (on average) to the observations than the ones predicted by the standard mixed MNL model. Finally, the significance and impacts of the contributing factors are analyzed. Copyright © 2016 Elsevier Ltd. All rights reserved.

Brittle failure of rock: A review and general linear criterion

NASA Astrophysics Data System (ADS)

Labuz, Joseph F.; Zeng, Feitao; Makhnenko, Roman; Li, Yuan

2018-07-01

A failure criterion typically is phenomenological since few models exist to theoretically derive the mathematical function. Indeed, a successful failure criterion is a generalization of experimental data obtained from strength tests on specimens subjected to known stress states. For isotropic rock that exhibits a pressure dependence on strength, a popular failure criterion is a linear equation in major and minor principal stresses, independent of the intermediate principal stress. A general linear failure criterion called Paul-Mohr-Coulomb (PMC) contains all three principal stresses with three material constants: friction angles for axisymmetric compression ϕc and extension ϕe and isotropic tensile strength V0. PMC provides a framework to describe a nonlinear failure surface by a set of planes "hugging" the curved surface. Brittle failure of rock is reviewed and multiaxial test methods are summarized. Equations are presented to implement PMC for fitting strength data and determining the three material parameters. A piecewise linear approximation to a nonlinear failure surface is illustrated by fitting two planes with six material parameters to form either a 6- to 12-sided pyramid or a 6- to 12- to 6-sided pyramid. The particular nature of the failure surface is dictated by the experimental data.

On a generalized Ablowitz-Kaup-Newell-Segur hierarchy in inhomogeneities of media: soliton solutions and wave propagation influenced from coefficient functions and scattering data

NASA Astrophysics Data System (ADS)

Zhang, Sheng; Hong, Siyu

2018-07-01

In this paper, a generalized Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy in inhomogeneities of media described by variable coefficients is investigated, which includes some important nonlinear evolution equations as special cases, for example, the celebrated Korteweg-de Vries equation modeling waves on shallow water surfaces. To be specific, the known AKNS spectral problem and its time evolution equation are first generalized by embedding a finite number of differentiable and time-dependent functions. Starting from the generalized AKNS spectral problem and its generalized time evolution equation, a generalized AKNS hierarchy with variable coefficients is then derived. Furthermore, based on a systematic analysis on the time dependence of related scattering data of the generalized AKNS spectral problem, exact solutions of the generalized AKNS hierarchy are formulated through the inverse scattering transform method. In the case of reflectionless potentials, the obtained exact solutions are reduced to n-soliton solutions. It is graphically shown that the dynamical evolutions of such soliton solutions are influenced by not only the time-dependent coefficients but also the related scattering data in the process of propagations.

Linear and nonlinear dynamo properties of time-dependent ABC flows

NASA Astrophysics Data System (ADS)

Brummell, N. H.; Cattaneo, F.; Tobias, S. M.

2001-04-01

The linear and nonlinear dynamo properties of a class of periodically forced flows is considered. The forcing functions are chosen to drive, in the absence of magnetic effects (kinematic regime), a time-dependent version of the ABC flow with A= B= C=1. The time-dependence consists of a harmonic displacement of the origin along the line x= y= z=1 with amplitude ɛ and frequency Ω. The finite-time Lyapunov exponents are computed for several values of ɛ and Ω. It is found that for values of these parameters near unity chaotic streamlines occupy most of the volume. In this parameter range, and for moderate kinetic and magnetic Reynolds numbers, the basic flow is both hydrodynamically and hydromagnetically unstable. However, the dynamo instability has a higher growth rate than the hydrodynamic one, so that the nonlinear regime can be reached with negligible departures from the basic ABC flow. In the nonlinear regime, two distinct classes of behaviour are observed. In one, the exponential growth of the magnetic field saturates and the dynamo settles to a stationary state whereby the magnetic energy is maintained indefinitely. In the other the velocity field evolves to a nondynamo state and the magnetic field, following an initial amplification, decays to zero. The transition from the dynamo to the nondynamo state can be mediated by the hydrodynamic instability or by magnetic perturbations. The properties of the ensuing nonlinear dynamo states are investigated for different parameter values. The implications for a general theory of nonlinear dynamos are discussed.

Study of cumulative fatigue damage detection for used parts with nonlinear output frequency response functions based on NARMAX modelling

NASA Astrophysics Data System (ADS)

Huang, Honglan; Mao, Hanying; Mao, Hanling; Zheng, Weixue; Huang, Zhenfeng; Li, Xinxin; Wang, Xianghong

2017-12-01

Cumulative fatigue damage detection for used parts plays a key role in the process of remanufacturing engineering and is related to the service safety of the remanufactured parts. In light of the nonlinear properties of used parts caused by cumulative fatigue damage, the based nonlinear output frequency response functions detection approach offers a breakthrough to solve this key problem. First, a modified PSO-adaptive lasso algorithm is introduced to improve the accuracy of the NARMAX model under impulse hammer excitation, and then, an effective new algorithm is derived to estimate the nonlinear output frequency response functions under rectangular pulse excitation, and a based nonlinear output frequency response functions index is introduced to detect the cumulative fatigue damage in used parts. Then, a novel damage detection approach that integrates the NARMAX model and the rectangular pulse is proposed for nonlinear output frequency response functions identification and cumulative fatigue damage detection of used parts. Finally, experimental studies of fatigued plate specimens and used connecting rod parts are conducted to verify the validity of the novel approach. The obtained results reveal that the new approach can detect cumulative fatigue damages of used parts effectively and efficiently and that the various values of the based nonlinear output frequency response functions index can be used to detect the different fatigue damages or working time. Since the proposed new approach can extract nonlinear properties of systems by only a single excitation of the inspected system, it shows great promise for use in remanufacturing engineering applications.

Research on Nonlinear Time Series Forecasting of Time-Delay NN Embedded with Bayesian Regularization

NASA Astrophysics Data System (ADS)

Jiang, Weijin; Xu, Yusheng; Xu, Yuhui; Wang, Jianmin

Based on the idea of nonlinear prediction of phase space reconstruction, this paper presented a time delay BP neural network model, whose generalization capability was improved by Bayesian regularization. Furthermore, the model is applied to forecast the imp&exp trades in one industry. The results showed that the improved model has excellent generalization capabilities, which not only learned the historical curve, but efficiently predicted the trend of business. Comparing with common evaluation of forecasts, we put on a conclusion that nonlinear forecast can not only focus on data combination and precision improvement, it also can vividly reflect the nonlinear characteristic of the forecasting system. While analyzing the forecasting precision of the model, we give a model judgment by calculating the nonlinear characteristic value of the combined serial and original serial, proved that the forecasting model can reasonably 'catch' the dynamic characteristic of the nonlinear system which produced the origin serial.

Nonlinear Curvature Expressions for Combined Flapwise Bending, Chordwise Bending, Torsion and Extension of Twisted Rotor Blades

NASA Technical Reports Server (NTRS)

Kvaternik, R. G.; Kaza, K. R. V.

1976-01-01

The nonlinear curvature expressions for a twisted rotor blade or a beam undergoing transverse bending in two planes, torsion, and extension were developed. The curvature expressions were obtained using simple geometric considerations. The expressions were first developed in a general manner using the geometrical nonlinear theory of elasticity. These general nonlinear expressions were then systematically reduced to four levels of approximation by imposing various simplifying assumptions, and in each of these levels the second degree nonlinear expressions were given. The assumptions were carefully stated and their implications with respect to the nonlinear theory of elasticity as applied to beams were pointed out. The transformation matrices between the deformed and undeformed blade-fixed coordinates, which were needed in the development of the curvature expressions, were also given for three of the levels of approximation. The present curvature expressions and transformation matrices were compared with corresponding expressions existing in the literature.

Acoustic-radiation stress in solids. I - Theory

NASA Technical Reports Server (NTRS)

Cantrell, J. H., Jr.

1984-01-01

The general case of acoustic-radiation stress associated with quasi-compressional and quasi-shear waves propagating in infinite and semiinfinite lossless solids of arbitrary crystalline symmetry is studied. The Boussinesq radiation stress is defined and found to depend directly on an acoustic nonlinearity parameter which characterizes the radiation-induced static strain, a stress-generalized nonlinearity parameter which characterizes the stress nonlinearity, and the energy density of the propagating wave. Application of the Boltzmann-Ehrenfest principle of adiabatic invariance to a self-constrained system described by the nonlinear equations of motion allows the acoustic-radiation-induced static strain to be identified with a self-constrained variation in the time-averaged product of the internal energy density and displacement gradient. The time-averaged product is scaled by the acoustic nonlinearity parameter and represents the first-order nonlinearity in the virial theorem. Finally, the relationship between the Boussinesq and the Cauchy radiation stress is obtained in a closed three-dimensional form.

Stochastic foundations of undulatory transport phenomena: generalized Poisson-Kac processes—part III extensions and applications to kinetic theory and transport

NASA Astrophysics Data System (ADS)

Giona, Massimiliano; Brasiello, Antonio; Crescitelli, Silvestro

2017-08-01

This third part extends the theory of Generalized Poisson-Kac (GPK) processes to nonlinear stochastic models and to a continuum of states. Nonlinearity is treated in two ways: (i) as a dependence of the parameters (intensity of the stochastic velocity, transition rates) of the stochastic perturbation on the state variable, similarly to the case of nonlinear Langevin equations, and (ii) as the dependence of the stochastic microdynamic equations of motion on the statistical description of the process itself (nonlinear Fokker-Planck-Kac models). Several numerical and physical examples illustrate the theory. Gathering nonlinearity and a continuum of states, GPK theory provides a stochastic derivation of the nonlinear Boltzmann equation, furnishing a positive answer to the Kac’s program in kinetic theory. The transition from stochastic microdynamics to transport theory within the framework of the GPK paradigm is also addressed.

Gap-metric-based robustness analysis of nonlinear systems with full and partial feedback linearisation

NASA Astrophysics Data System (ADS)

Al-Gburi, A.; Freeman, C. T.; French, M. C.

2018-06-01

This paper uses gap metric analysis to derive robustness and performance margins for feedback linearising controllers. Distinct from previous robustness analysis, it incorporates the case of output unstructured uncertainties, and is shown to yield general stability conditions which can be applied to both stable and unstable plants. It then expands on existing feedback linearising control schemes by introducing a more general robust feedback linearising control design which classifies the system nonlinearity into stable and unstable components and cancels only the unstable plant nonlinearities. This is done in order to preserve the stabilising action of the inherently stabilising nonlinearities. Robustness and performance margins are derived for this control scheme, and are expressed in terms of bounds on the plant nonlinearities and the accuracy of the cancellation of the unstable plant nonlinearity by the controller. Case studies then confirm reduced conservatism compared with standard methods.

Broad-band simulation of M7.2 earthquake on the North Tehran fault, considering non-linear soil effects

NASA Astrophysics Data System (ADS)

Majidinejad, A.; Zafarani, H.; Vahdani, S.

2018-05-01

The North Tehran fault (NTF) is known to be one of the most drastic sources of seismic hazard on the city of Tehran. In this study, we provide broad-band (0-10 Hz) ground motions for the city as a consequence of probable M7.2 earthquake on the NTF. Low-frequency motions (0-2 Hz) are provided from spectral element dynamic simulation of 17 scenario models. High-frequency (2-10 Hz) motions are calculated with a physics-based method based on S-to-S backscattering theory. Broad-band ground motions at the bedrock level show amplifications, both at low and high frequencies, due to the existence of deep Tehran basin in the vicinity of the NTF. By employing soil profiles obtained from regional studies, effect of shallow soil layers on broad-band ground motions is investigated by both linear and non-linear analyses. While linear soil response overestimate ground motion prediction equations, non-linear response predicts plausible results within one standard deviation of empirical relationships. Average Peak Ground Accelerations (PGAs) at the northern, central and southern parts of the city are estimated about 0.93, 0.59 and 0.4 g, respectively. Increased damping caused by non-linear soil behaviour, reduces the soil linear responses considerably, in particular at frequencies above 3 Hz. Non-linear deamplification reduces linear spectral accelerations up to 63 per cent at stations above soft thick sediments. By performing more general analyses, which exclude source-to-site effects on stations, a correction function is proposed for typical site classes of Tehran. Parameters for the function which reduces linear soil response in order to take into account non-linear soil deamplification are provided for various frequencies in the range of engineering interest. In addition to fully non-linear analyses, equivalent-linear calculations were also conducted which their comparison revealed appropriateness of the method for large peaks and low frequencies, but its shortage for small to medium peaks and motions with higher than 3 Hz frequencies.

Non-Linear Interactions Determine the Impact of Sea-Level Rise on Estuarine Benthic Biodiversity and Ecosystem Processes

PubMed Central

Yamanaka, Tsuyuko; Raffaelli, David; White, Piran C. L.

2013-01-01

Sea-level rise induced by climate change may have significant impacts on the ecosystem functions and ecosystem services provided by intertidal sediment ecosystems. Accelerated sea-level rise is expected to lead to steeper beach slopes, coarser particle sizes and increased wave exposure, with consequent impacts on intertidal ecosystems. We examined the relationships between abundance, biomass, and community metabolism of benthic fauna with beach slope, particle size and exposure, using samples across a range of conditions from three different locations in the UK, to determine the significance of sediment particle size beach slope and wave exposure in affecting benthic fauna and ecosystem function in different ecological contexts. Our results show that abundance, biomass and oxygen consumption of intertidal macrofauna and meiofauna are affected significantly by interactions among sediment particle size, beach slope and wave exposure. For macrofauna on less sloping beaches, the effect of these physical constraints is mediated by the local context, although for meiofauna and for macrofauna on intermediate and steeper beaches, the effects of physical constraints dominate. Steeper beach slopes, coarser particle sizes and increased wave exposure generally result in decreases in abundance, biomass and oxygen consumption, but these relationships are complex and non-linear. Sea-level rise is likely to lead to changes in ecosystem structure with generally negative impacts on ecosystem functions and ecosystem services. However, the impacts of sea-level rise will also be affected by local ecological context, especially for less sloping beaches. PMID:23861863

Non-linear interactions determine the impact of sea-level rise on estuarine benthic biodiversity and ecosystem processes.

PubMed

Yamanaka, Tsuyuko; Raffaelli, David; White, Piran C L

2013-01-01

Sea-level rise induced by climate change may have significant impacts on the ecosystem functions and ecosystem services provided by intertidal sediment ecosystems. Accelerated sea-level rise is expected to lead to steeper beach slopes, coarser particle sizes and increased wave exposure, with consequent impacts on intertidal ecosystems. We examined the relationships between abundance, biomass, and community metabolism of benthic fauna with beach slope, particle size and exposure, using samples across a range of conditions from three different locations in the UK, to determine the significance of sediment particle size beach slope and wave exposure in affecting benthic fauna and ecosystem function in different ecological contexts. Our results show that abundance, biomass and oxygen consumption of intertidal macrofauna and meiofauna are affected significantly by interactions among sediment particle size, beach slope and wave exposure. For macrofauna on less sloping beaches, the effect of these physical constraints is mediated by the local context, although for meiofauna and for macrofauna on intermediate and steeper beaches, the effects of physical constraints dominate. Steeper beach slopes, coarser particle sizes and increased wave exposure generally result in decreases in abundance, biomass and oxygen consumption, but these relationships are complex and non-linear. Sea-level rise is likely to lead to changes in ecosystem structure with generally negative impacts on ecosystem functions and ecosystem services. However, the impacts of sea-level rise will also be affected by local ecological context, especially for less sloping beaches.

Reconstructing biochemical pathways from time course data.

PubMed

Srividhya, Jeyaraman; Crampin, Edmund J; McSharry, Patrick E; Schnell, Santiago

2007-03-01

Time series data on biochemical reactions reveal transient behavior, away from chemical equilibrium, and contain information on the dynamic interactions among reacting components. However, this information can be difficult to extract using conventional analysis techniques. We present a new method to infer biochemical pathway mechanisms from time course data using a global nonlinear modeling technique to identify the elementary reaction steps which constitute the pathway. The method involves the generation of a complete dictionary of polynomial basis functions based on the law of mass action. Using these basis functions, there are two approaches to model construction, namely the general to specific and the specific to general approach. We demonstrate that our new methodology reconstructs the chemical reaction steps and connectivity of the glycolytic pathway of Lactococcus lactis from time course experimental data.

Combining Biomarkers Linearly and Nonlinearly for Classification Using the Area Under the ROC Curve

PubMed Central

Fong, Youyi; Yin, Shuxin; Huang, Ying

2016-01-01

In biomedical studies, it is often of interest to classify/predict a subject’s disease status based on a variety of biomarker measurements. A commonly used classification criterion is based on AUC - Area under the Receiver Operating Characteristic Curve. Many methods have been proposed to optimize approximated empirical AUC criteria, but there are two limitations to the existing methods. First, most methods are only designed to find the best linear combination of biomarkers, which may not perform well when there is strong nonlinearity in the data. Second, many existing linear combination methods use gradient-based algorithms to find the best marker combination, which often result in sub-optimal local solutions. In this paper, we address these two problems by proposing a new kernel-based AUC optimization method called Ramp AUC (RAUC). This method approximates the empirical AUC loss function with a ramp function, and finds the best combination by a difference of convex functions algorithm. We show that as a linear combination method, RAUC leads to a consistent and asymptotically normal estimator of the linear marker combination when the data is generated from a semiparametric generalized linear model, just as the Smoothed AUC method (SAUC). Through simulation studies and real data examples, we demonstrate that RAUC out-performs SAUC in finding the best linear marker combinations, and can successfully capture nonlinear pattern in the data to achieve better classification performance. We illustrate our method with a dataset from a recent HIV vaccine trial. PMID:27058981

On Various Nonlinearity Measures for Boolean Functions*

PubMed Central

Boyar, Joan; Find, Magnus Gausdal; Peralta, René

2016-01-01

A necessary condition for the security of cryptographic functions is to be “sufficiently distant” from linear, and cryptographers have proposed several measures for this distance. In this paper, we show that six common measures, nonlinearity, algebraic degree, annihilator immunity, algebraic thickness, normality, and multiplicative complexity, are incomparable in the sense that for each pair of measures, μ1, μ2, there exist functions f1, f2 with f1 being more nonlinear than f2 according to μ1, but less nonlinear according to μ2. We also present new connections between two of these measures. Additionally, we give a lower bound on the multiplicative complexity of collision-free functions. PMID:27458499

Traveling wave and exact solutions for the perturbed nonlinear Schrödinger equation with Kerr law nonlinearity

NASA Astrophysics Data System (ADS)

Akram, Ghazala; Mahak, Nadia

2018-06-01

The nonlinear Schrödinger equation (NLSE) with the aid of three order dispersion terms is investigated to find the exact solutions via the extended (G'/G2)-expansion method and the first integral method. Many exact traveling wave solutions, such as trigonometric, hyperbolic, rational, soliton and complex function solutions, are characterized with some free parameters of the problem studied. It is corroborated that the proposed techniques are manageable, straightforward and powerful tools to find the exact solutions of nonlinear partial differential equations (PDEs). Some figures are plotted to describe the propagation of traveling wave solutions expressed by the hyperbolic functions, trigonometric functions and rational functions.

A Multi-Resolution Nonlinear Mapping Technique for Design and Analysis Applications

NASA Technical Reports Server (NTRS)

Phan, Minh Q.

1998-01-01

This report describes a nonlinear mapping technique where the unknown static or dynamic system is approximated by a sum of dimensionally increasing functions (one-dimensional curves, two-dimensional surfaces, etc.). These lower dimensional functions are synthesized from a set of multi-resolution basis functions, where the resolutions specify the level of details at which the nonlinear system is approximated. The basis functions also cause the parameter estimation step to become linear. This feature is taken advantage of to derive a systematic procedure to determine and eliminate basis functions that are less significant for the particular system under identification. The number of unknown parameters that must be estimated is thus reduced and compact models obtained. The lower dimensional functions (identified curves and surfaces) permit a kind of "visualization" into the complexity of the nonlinearity itself.

A Multi-Resolution Nonlinear Mapping Technique for Design and Analysis Application

NASA Technical Reports Server (NTRS)

Phan, Minh Q.

1997-01-01

This report describes a nonlinear mapping technique where the unknown static or dynamic system is approximated by a sum of dimensionally increasing functions (one-dimensional curves, two-dimensional surfaces, etc.). These lower dimensional functions are synthesized from a set of multi-resolution basis functions, where the resolutions specify the level of details at which the nonlinear system is approximated. The basis functions also cause the parameter estimation step to become linear. This feature is taken advantage of to derive a systematic procedure to determine and eliminate basis functions that are less significant for the particular system under identification. The number of unknown parameters that must be estimated is thus reduced and compact models obtained. The lower dimensional functions (identified curves and surfaces) permit a kind of "visualization" into the complexity of the nonlinearity itself.

Becoming angular momentum density flow through nonlinear mass transfer into a gravitating spheroidal body

NASA Astrophysics Data System (ADS)

Krot, A. M.

2009-04-01

A statistical theory for a cosmological body forming based on the spheroidal body model has been proposed in the works [1]-[4]. This work studies a slowly evolving process of gravitational condensation of a spheroidal body from an infinitely distributed gas-dust substance in space. The equation for an initial evolution of mass density function of a gas-dust cloud is considered here. It is found this equation coincides completely with the analogous equation for a slowly gravitational compressed spheroidal body [5]. A conductive flow in dissipative systems was investigated by I. Prigogine in his works (see, for example, [6], [7]). As it has been found in [2], [5], there exists a conductive antidiffusion flow in a slowly compressible gravitating spheroidal body. Applying the equation of continuity to this conductive flow density we obtain a linear antidiffusion equation [5]. However, if an intensity of conductive flow density increases sharply then the linear antidiffusion equation becomes a nonlinear one. Really, it was pointed to [6] analogous linear equations of diffusion or thermal conductivity transform in nonlinear equations respectively. In this case, the equation of continuity describes a nonlinear mass flow being a source of instabilities into a gravitating spheroidal body because the gravitational compression factor G is a function of not only time but a mass density. Using integral substitution we can reduce a nonlinear antidiffusion equation to the linear antidiffusion equation relative to a new function. If the factor G can be considered as a specific angular momentum then the new function is an angular momentum density. Thus, a nonlinear momentum density flow induces a flow of angular momentum density because streamlines of moving continuous substance come close into a gravitating spheroidal body. Really, the streamline approach leads to more tight interactions of "liquid particles" that implies a superposition of their specific angular momentums. This superposition forms an antidiffusion flow of an angular momentum density into a gravitating spheroidal body. References: [1] Krot, A.M. The statistical model of gravitational interaction of particles. Achievement in Modern Radioelectronics (spec.issue"Cosmic Radiophysics", Moscow), 1996, no.8, pp. 66-81 (in Russian). [2] Krot, A.M. Statistical description of gravitational field: a new approach. Proc. SPIE's 14th Annual Intern.Symp. "AeroSense", Orlando, Florida, USA, 2000, vol.4038, pp.1318-1329. [3] Krot, A.M. The statistical model of rotating and gravitating spheroidal body with the point of view of general relativity. Proc.35th COSPAR Scientific Assembly, Paris, France, 2004, Abstract A-00162. [4] Krot, A. The statistical approach to exploring formation of Solar system. Proc.EGU General Assembly, Vienna, Austria, 2006, Geophys.Res.Abstracts, vol.8, A-00216; SRef-ID: 1607-7962/gra/. [5] Krot, A.M. A statistical approach to investigate the formation of the solar system. Chaos, Solitons and Fractals, 2008, doi:10.1016/j.chaos.2008.06.014. [6] Glansdorff, P. and Prigogine, I. Thermodynamic Theory of Structure, Stability and Fluctuations. London, 1971. [7] Nicolis, G. and Prigogine, I. Self-organization in Nonequilibrium Systems:From Dissipative Structures to Order through Fluctuation. John Willey and Sons, New York etc., 1977.

Virtual-pulse time integral methodology: A new explicit approach for computational dynamics - Theoretical developments for general nonlinear structural dynamics

NASA Technical Reports Server (NTRS)

Chen, Xiaoqin; Tamma, Kumar K.; Sha, Desong

1993-01-01

The present paper describes a new explicit virtual-pulse time integral methodology for nonlinear structural dynamics problems. The purpose of the paper is to provide the theoretical basis of the methodology and to demonstrate applicability of the proposed formulations to nonlinear dynamic structures. Different from the existing numerical methods such as direct time integrations or mode superposition techniques, the proposed methodology offers new perspectives and methodology of development, and possesses several unique and attractive computational characteristics. The methodology is tested and compared with the implicit Newmark method (trapezoidal rule) through a nonlinear softening and hardening spring dynamic models. The numerical results indicate that the proposed explicit virtual-pulse time integral methodology is an excellent alternative for solving general nonlinear dynamic problems.

Nonlinear effective theory of dark energy

NASA Astrophysics Data System (ADS)

Cusin, Giulia; Lewandowski, Matthew; Vernizzi, Filippo

2018-04-01

We develop an approach to parametrize cosmological perturbations beyond linear order for general dark energy and modified gravity models characterized by a single scalar degree of freedom. We derive the full nonlinear action, focusing on Horndeski theories. In the quasi-static, non-relativistic limit, there are a total of six independent relevant operators, three of which start at nonlinear order. The new nonlinear couplings modify, beyond linear order, the generalized Poisson equation relating the Newtonian potential to the matter density contrast. We derive this equation up to cubic order in perturbations and, in a companion article [1], we apply it to compute the one-loop matter power spectrum. Within this approach, we also discuss the Vainshtein regime around spherical sources and the relation between the Vainshtein scale and the nonlinear scale for structure formation.

Identity effects dominate the impacts of multiple species extinctions on the functioning of complex food webs.

PubMed

Harvey, Eric; Séguin, Annie; Nozais, Christian; Archambault, Philippe; Gravel, Dominique

2013-01-01

Understanding the impacts of species extinctions on the functioning of food webs is a challenging task because of the complexity of ecological interactions. We report the impacts of experimental species extinctions on the functioning of two food webs of freshwater and marine systems. We used a linear model to partition the variance among the multiple components of the diversity effect (linear group richness, nonlinear group richness, and identity). The identity of each functional group was the best explaining variable of ecosystem functioning for both systems. We assessed the contribution of each functional group in multifunctional space and found that, although the effect of functional group varied across ecosystem functions, some functional groups shared common effects on functions. This study is the first experimental demonstration that functional identity dominates the effects of extinctions on ecosystem functioning, suggesting that generalizations are possible despite the inherent complexity of interactions.

Functional Nonlinear Mixed Effects Models For Longitudinal Image Data

PubMed Central

Luo, Xinchao; Zhu, Lixing; Kong, Linglong; Zhu, Hongtu

2015-01-01

Motivated by studying large-scale longitudinal image data, we propose a novel functional nonlinear mixed effects modeling (FN-MEM) framework to model the nonlinear spatial-temporal growth patterns of brain structure and function and their association with covariates of interest (e.g., time or diagnostic status). Our FNMEM explicitly quantifies a random nonlinear association map of individual trajectories. We develop an efficient estimation method to estimate the nonlinear growth function and the covariance operator of the spatial-temporal process. We propose a global test and a simultaneous confidence band for some specific growth patterns. We conduct Monte Carlo simulation to examine the finite-sample performance of the proposed procedures. We apply FNMEM to investigate the spatial-temporal dynamics of white-matter fiber skeletons in a national database for autism research. Our FNMEM may provide a valuable tool for charting the developmental trajectories of various neuropsychiatric and neurodegenerative disorders. PMID:26213453

Optimal Averages for Nonlinear Signal Decompositions - Another Alternative for Empirical Mode Decomposition

DTIC Science & Technology

2014-10-01

nonlinear and non-stationary signals. It aims at decomposing a signal, via an iterative sifting procedure, into several intrinsic mode functions ...stationary signals. It aims at decomposing a signal, via an iterative sifting procedure into several intrinsic mode functions (IMFs), and each of the... function , optimization. 1 Introduction It is well known that nonlinear and non-stationary signal analysis is important and difficult. His- torically

Curved Displacement Transfer Functions for Geometric Nonlinear Large Deformation Structure Shape Predictions

NASA Technical Reports Server (NTRS)

Ko, William L.; Fleischer, Van Tran; Lung, Shun-Fat

2017-01-01

For shape predictions of structures under large geometrically nonlinear deformations, Curved Displacement Transfer Functions were formulated based on a curved displacement, traced by a material point from the undeformed position to deformed position. The embedded beam (depth-wise cross section of a structure along a surface strain-sensing line) was discretized into multiple small domains, with domain junctures matching the strain-sensing stations. Thus, the surface strain distribution could be described with a piecewise linear or a piecewise nonlinear function. The discretization approach enabled piecewise integrations of the embedded-beam curvature equations to yield the Curved Displacement Transfer Functions, expressed in terms of embedded beam geometrical parameters and surface strains. By entering the surface strain data into the Displacement Transfer Functions, deflections along each embedded beam can be calculated at multiple points for mapping the overall structural deformed shapes. Finite-element linear and nonlinear analyses of a tapered cantilever tubular beam were performed to generate linear and nonlinear surface strains and the associated deflections to be used for validation. The shape prediction accuracies were then determined by comparing the theoretical deflections with the finiteelement- generated deflections. The results show that the newly developed Curved Displacement Transfer Functions are very accurate for shape predictions of structures under large geometrically nonlinear deformations.

Solution of a few nonlinear problems in aerodynamics by the finite elements and functional least squares methods. Ph.D. Thesis - Paris Univ.; [mathematical models of transonic flow using nonlinear equations

NASA Technical Reports Server (NTRS)

Periaux, J.

1979-01-01

The numerical simulation of the transonic flows of idealized fluids and of incompressible viscous fluids, by the nonlinear least squares methods is presented. The nonlinear equations, the boundary conditions, and the various constraints controlling the two types of flow are described. The standard iterative methods for solving a quasi elliptical nonlinear equation with partial derivatives are reviewed with emphasis placed on two examples: the fixed point method applied to the Gelder functional in the case of compressible subsonic flows and the Newton method used in the technique of decomposition of the lifting potential. The new abstract least squares method is discussed. It consists of substituting the nonlinear equation by a problem of minimization in a H to the minus 1 type Sobolev functional space.

Nonlinear oscillator with power-form elastic-term: Fourier series expansion of the exact solution

NASA Astrophysics Data System (ADS)

Beléndez, Augusto; Francés, Jorge; Beléndez, Tarsicio; Bleda, Sergio; Pascual, Carolina; Arribas, Enrique

2015-05-01

A family of conservative, truly nonlinear, oscillators with integer or non-integer order nonlinearity is considered. These oscillators have only one odd power-form elastic-term and exact expressions for their period and solution were found in terms of Gamma functions and a cosine-Ateb function, respectively. Only for a few values of the order of nonlinearity, is it possible to obtain the periodic solution in terms of more common functions. However, for this family of conservative truly nonlinear oscillators we show in this paper that it is possible to obtain the Fourier series expansion of the exact solution, even though this exact solution is unknown. The coefficients of the Fourier series expansion of the exact solution are obtained as an integral expression in which a regularized incomplete Beta function appears. These coefficients are a function of the order of nonlinearity only and are computed numerically. One application of this technique is to compare the amplitudes for the different harmonics of the solution obtained using approximate methods with the exact ones computed numerically as shown in this paper. As an example, the approximate amplitudes obtained via a modified Ritz method are compared with the exact ones computed numerically.

Discriminative analysis of non-linear brain connectivity for leukoaraiosis with resting-state fMRI

NASA Astrophysics Data System (ADS)

Lai, Youzhi; Xu, Lele; Yao, Li; Wu, Xia

2015-03-01

Leukoaraiosis (LA) describes diffuse white matter abnormalities on CT or MR brain scans, often seen in the normal elderly and in association with vascular risk factors such as hypertension, or in the context of cognitive impairment. The mechanism of cognitive dysfunction is still unclear. The recent clinical studies have revealed that the severity of LA was not corresponding to the cognitive level, and functional connectivity analysis is an appropriate method to detect the relation between LA and cognitive decline. However, existing functional connectivity analyses of LA have been mostly limited to linear associations. In this investigation, a novel measure utilizing the extended maximal information coefficient (eMIC) was applied to construct non-linear functional connectivity in 44 LA subjects (9 dementia, 25 mild cognitive impairment (MCI) and 10 cognitively normal (CN)). The strength of non-linear functional connections for the first 1% of discriminative power increased in MCI compared with CN and dementia, which was opposed to its linear counterpart. Further functional network analysis revealed that the changes of the non-linear and linear connectivity have similar but not completely the same spatial distribution in human brain. In the multivariate pattern analysis with multiple classifiers, the non-linear functional connectivity mostly identified dementia, MCI and CN from LA with a relatively higher accuracy rate than the linear measure. Our findings revealed the non-linear functional connectivity provided useful discriminative power in classification of LA, and the spatial distributed changes between the non-linear and linear measure may indicate the underlying mechanism of cognitive dysfunction in LA.

Theory of multinonlinear media and its application to the soliton processes in ferrite–ferroelectric structures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cherkasskii, M. A., E-mail: macherkasskii@hotmail.com; Nikitin, A. A.; Kalinikos, B. A.

A theory is developed to describe the wave processes that occur in waveguide media having several types of nonlinearity, specifically, multinonlinear media. It is shown that the nonlinear Schrödinger equation can be used to describe the general wave process that occurs in such media. The competition between the electric wave nonlinearity and the magnetic wave nonlinearity in a layered multinonlinear ferrite–ferroelectric structure is found to change a total repulsive nonlinearity into a total attractive nonlinearity.

Energy spectra of X-ray clusters of galaxies

NASA Technical Reports Server (NTRS)

Avni, Y.

1976-01-01

A procedure for estimating the ranges of parameters that describe the spectra of X-rays from clusters of galaxies is presented. The applicability of the method is proved by statistical simulations of cluster spectra; such a proof is necessary because of the nonlinearity of the spectral functions. Implications for the spectra of the Perseus, Coma, and Virgo clusters are discussed. The procedure can be applied in more general problems of parameter estimation.

Differential Equations and Computational Simulations

DTIC Science & Technology

1999-06-18

divergence operator of a vector field, which can be defined in terms of the Levi - Civita connection. Let $(x, t) be the orbit passing through x g M...differential equations 31 Junping Chen and Dadi Yang The limit cycle of two species predator-prey model with general functional response > 34 S. S...analysis of two -species nonlinear competition system with periodic coefficients 286 X. H. Tang and J. S. Yu Oscillation of first order delay

A quasi-Newton approach to optimization problems with probability density constraints. [problem solving in mathematical programming

NASA Technical Reports Server (NTRS)

Tapia, R. A.; Vanrooy, D. L.

1976-01-01

A quasi-Newton method is presented for minimizing a nonlinear function while constraining the variables to be nonnegative and sum to one. The nonnegativity constraints were eliminated by working with the squares of the variables and the resulting problem was solved using Tapia's general theory of quasi-Newton methods for constrained optimization. A user's guide for a computer program implementing this algorithm is provided.

Theory, Methods, and Applications of Nonlinear Control

DTIC Science & Technology

2012-08-29

an application to Lotka - Volterra systems,” in Proceedings of the American Control Conference (St. Louis, MO, 10-12 June 2009), pp. 96-101. [MM10a...Mazenc, F., and M. Malisoff, “Strict Lyapunov function constructions under LaSalle conditions with an application to Lotka - Volterra systems,” IEEE...the tracking dynamics, (d) the applicability of the theory to a very general class of reference trajectories, and (e) the use of input-to-state

Parametric reduced models for the nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Harlim, John; Li, Xiantao

2015-05-01

Reduced models for the (defocusing) nonlinear Schrödinger equation are developed. In particular, we develop reduced models that only involve the low-frequency modes given noisy observations of these modes. The ansatz of the reduced parametric models are obtained by employing a rational approximation and a colored-noise approximation, respectively, on the memory terms and the random noise of a generalized Langevin equation that is derived from the standard Mori-Zwanzig formalism. The parameters in the resulting reduced models are inferred from noisy observations with a recently developed ensemble Kalman filter-based parametrization method. The forecasting skill across different temperature regimes are verified by comparing the moments up to order four, a two-time correlation function statistics, and marginal densities of the coarse-grained variables.

Temperature Induced Syllable Breaking Unveils Nonlinearly Interacting Timescales in Birdsong Motor Pathway

PubMed Central

Goldin, Matías A.; Alonso, Leandro M.; Alliende, Jorge A.; Goller, Franz; Mindlin, Gabriel B.

2013-01-01

The nature of telencephalic control over premotor and motor circuits is debated. Hypotheses range from complete usurping of downstream circuitry to highly interactive mechanisms of control. We show theoretically and experimentally, that telencephalic song motor control in canaries is consistent with a highly interactive strategy. As predicted from a theoretical model of respiratory control, mild cooling of a forebrain nucleus (HVC) led to song stretching, but further cooling caused progressive restructuring of song, consistent with the hypothesis that respiratory gestures are subharmonic responses to a timescale present in the output of HVC. This interaction between a life-sustaining motor function (respiration) and telencephalic song motor control suggests a more general mechanism of how nonlinear integration of evolutionarily new brain structures into existing circuitry gives rise to diverse, new behavior. PMID:23818988

Parametric reduced models for the nonlinear Schrödinger equation.

PubMed

Harlim, John; Li, Xiantao

2015-05-01

Reduced models for the (defocusing) nonlinear Schrödinger equation are developed. In particular, we develop reduced models that only involve the low-frequency modes given noisy observations of these modes. The ansatz of the reduced parametric models are obtained by employing a rational approximation and a colored-noise approximation, respectively, on the memory terms and the random noise of a generalized Langevin equation that is derived from the standard Mori-Zwanzig formalism. The parameters in the resulting reduced models are inferred from noisy observations with a recently developed ensemble Kalman filter-based parametrization method. The forecasting skill across different temperature regimes are verified by comparing the moments up to order four, a two-time correlation function statistics, and marginal densities of the coarse-grained variables.

Temperature induced syllable breaking unveils nonlinearly interacting timescales in birdsong motor pathway.

PubMed

Goldin, Matías A; Alonso, Leandro M; Alliende, Jorge A; Goller, Franz; Mindlin, Gabriel B

2013-01-01

The nature of telencephalic control over premotor and motor circuits is debated. Hypotheses range from complete usurping of downstream circuitry to highly interactive mechanisms of control. We show theoretically and experimentally, that telencephalic song motor control in canaries is consistent with a highly interactive strategy. As predicted from a theoretical model of respiratory control, mild cooling of a forebrain nucleus (HVC) led to song stretching, but further cooling caused progressive restructuring of song, consistent with the hypothesis that respiratory gestures are subharmonic responses to a timescale present in the output of HVC. This interaction between a life-sustaining motor function (respiration) and telencephalic song motor control suggests a more general mechanism of how nonlinear integration of evolutionarily new brain structures into existing circuitry gives rise to diverse, new behavior.

Smoothing tautologies, hidden dynamics, and sigmoid asymptotics for piecewise smooth systems

NASA Astrophysics Data System (ADS)

Jeffrey, Mike R.

2015-10-01

Switches in real systems take many forms, such as impacts, electronic relays, mitosis, and the implementation of decisions or control strategies. To understand what is lost, and what can be retained, when we model a switch as an instantaneous event, requires a consideration of so-called hidden terms. These are asymptotically vanishing outside the switch, but can be encoded in the form of nonlinear switching terms. A general expression for the switch can be developed in the form of a series of sigmoid functions. We review the key steps in extending Filippov's method of sliding modes to such systems. We show how even slight nonlinear effects can hugely alter the behaviour of an electronic control circuit, and lead to "hidden" attractors inside the switching surface.

Smoothing tautologies, hidden dynamics, and sigmoid asymptotics for piecewise smooth systems.

PubMed

Jeffrey, Mike R

2015-10-01

Switches in real systems take many forms, such as impacts, electronic relays, mitosis, and the implementation of decisions or control strategies. To understand what is lost, and what can be retained, when we model a switch as an instantaneous event, requires a consideration of so-called hidden terms. These are asymptotically vanishing outside the switch, but can be encoded in the form of nonlinear switching terms. A general expression for the switch can be developed in the form of a series of sigmoid functions. We review the key steps in extending Filippov's method of sliding modes to such systems. We show how even slight nonlinear effects can hugely alter the behaviour of an electronic control circuit, and lead to "hidden" attractors inside the switching surface.

Smoothing tautologies, hidden dynamics, and sigmoid asymptotics for piecewise smooth systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jeffrey, Mike R., E-mail: mike.jeffrey@bristol.ac.uk

2015-10-15

Switches in real systems take many forms, such as impacts, electronic relays, mitosis, and the implementation of decisions or control strategies. To understand what is lost, and what can be retained, when we model a switch as an instantaneous event, requires a consideration of so-called hidden terms. These are asymptotically vanishing outside the switch, but can be encoded in the form of nonlinear switching terms. A general expression for the switch can be developed in the form of a series of sigmoid functions. We review the key steps in extending Filippov's method of sliding modes to such systems. We showmore » how even slight nonlinear effects can hugely alter the behaviour of an electronic control circuit, and lead to “hidden” attractors inside the switching surface.« less

Three-dimensional vibration analysis of a uniform beam with offset inertial masses at the ends

NASA Technical Reports Server (NTRS)

Robertson, D. K.

1985-01-01

Analysis of a flexible beam with displaced end-located inertial masses is presented. The resulting three-dimensional mode shape is shown to consist of two one-plane bending modes and one torsional mode. These three components of the mode shapes are shown to be linear combinations of trigonometric and hyperbolic sine and cosine functions. Boundary conditions are derived to obtain nonlinear algebraic equations through kinematic coupling of the general solutions of the three governing partial differential equations. A method of solution which takes these boundary conditions into account is also presented. A computer program has been written to obtain unique solutions to the resulting nonlinear algebraic equations. This program, which calculates natural frequencies and three-dimensional mode shapes for any number of modes, is presented and discussed.

A critical blow-up exponent in a chemotaxis system with nonlinear signal production

NASA Astrophysics Data System (ADS)

Winkler, Michael

2018-05-01

This paper is concerned with radially symmetric solutions of the Keller–Segel system with nonlinear signal production, as given by in the ball for and R  >  0, where f is a suitably regular function generalizing the prototype determined by the choice , , with . The main results assert that if in this setting the number κ satisfies then for any prescribed mass level m  >  0, there exist initial data u 0 with , for which the solution of the corresponding Neumann initial-boundary value problem blows up in finite time. The condition in () is essentially optimal and is indicated by a complementary result according to which in the case , for widely arbitrary initial data, a global bounded classical solution can always be found.

Optical rogue waves for the inhomogeneous generalized nonlinear Schrödinger equation.

PubMed

Loomba, Shally; Kaur, Harleen

2013-12-01

We present optical rogue wave solutions for a generalized nonlinear Schrodinger equation by using similarity transformation. We have predicted the propagation of rogue waves through a nonlinear optical fiber for three cases: (i) dispersion increasing (decreasing) fiber, (ii) periodic dispersion parameter, and (iii) hyperbolic dispersion parameter. We found that the rogue waves and their interactions can be tuned by properly choosing the parameters. We expect that our results can be used to realize improved signal transmission through optical rogue waves.

Numerical realization of the variational method for generating self-trapped beams

NASA Astrophysics Data System (ADS)

Duque, Erick I.; Lopez-Aguayo, Servando; Malomed, Boris A.

2018-03-01

We introduce a numerical variational method based on the Rayleigh-Ritz optimization principle for predicting two-dimensional self-trapped beams in nonlinear media. This technique overcomes the limitation of the traditional variational approximation in performing analytical Lagrangian integration and differentiation. Approximate soliton solutions of a generalized nonlinear Schr\\"odinger equation are obtained, demonstrating robustness of the beams of various types (fundamental, vortices, multipoles, azimuthons) in the course of their propagation. The algorithm offers possibilities to produce more sophisticated soliton profiles in general nonlinear models.

Compatible Models of Carbon Content of Individual Trees on a Cunninghamia lanceolata Plantation in Fujian Province, China

PubMed Central

Zhuo, Lin; Tao, Hong; Wei, Hong; Chengzhen, Wu

2016-01-01

We tried to establish compatible carbon content models of individual trees for a Chinese fir (Cunninghamia lanceolata (Lamb.) Hook.) plantation from Fujian province in southeast China. In general, compatibility requires that the sum of components equal the whole tree, meaning that the sum of percentages calculated from component equations should equal 100%. Thus, we used multiple approaches to simulate carbon content in boles, branches, foliage leaves, roots and the whole individual trees. The approaches included (i) single optimal fitting (SOF), (ii) nonlinear adjustment in proportion (NAP) and (iii) nonlinear seemingly unrelated regression (NSUR). These approaches were used in combination with variables relating diameter at breast height (D) and tree height (H), such as D, D2H, DH and D&H (where D&H means two separate variables in bivariate model). Power, exponential and polynomial functions were tested as well as a new general function model was proposed by this study. Weighted least squares regression models were employed to eliminate heteroscedasticity. Model performances were evaluated by using mean residuals, residual variance, mean square error and the determination coefficient. The results indicated that models with two dimensional variables (DH, D2H and D&H) were always superior to those with a single variable (D). The D&H variable combination was found to be the most useful predictor. Of all the approaches, SOF could establish a single optimal model separately, but there were deviations in estimating results due to existing incompatibilities, while NAP and NSUR could ensure predictions compatibility. Simultaneously, we found that the new general model had better accuracy than others. In conclusion, we recommend that the new general model be used to estimate carbon content for Chinese fir and considered for other vegetation types as well. PMID:26982054

Separation of the low-frequency atmospheric variability into non-Gaussian multidimensional sources by Independent Subspace Analysis

NASA Astrophysics Data System (ADS)

Pires, Carlos; Ribeiro, Andreia

2016-04-01

An efficient nonlinear method of statistical source separation of space-distributed non-Gaussian distributed data is proposed. The method relies in the so called Independent Subspace Analysis (ISA), being tested on a long time-series of the stream-function field of an atmospheric quasi-geostrophic 3-level model (QG3) simulating the winter's monthly variability of the Northern Hemisphere. ISA generalizes the Independent Component Analysis (ICA) by looking for multidimensional and minimally dependent, uncorrelated and non-Gaussian distributed statistical sources among the rotated projections or subspaces of the multivariate probability distribution of the leading principal components of the working field whereas ICA restrict to scalar sources. The rationale of that technique relies upon the projection pursuit technique, looking for data projections of enhanced interest. In order to accomplish the decomposition, we maximize measures of the sources' non-Gaussianity by contrast functions which are given by squares of nonlinear, cross-cumulant-based correlations involving the variables spanning the sources. Therefore sources are sought matching certain nonlinear data structures. The maximized contrast function is built in such a way that it provides the minimization of the mean square of the residuals of certain nonlinear regressions. The issuing residuals, followed by spherization, provide a new set of nonlinear variable changes that are at once uncorrelated, quasi-independent and quasi-Gaussian, representing an advantage with respect to the Independent Components (scalar sources) obtained by ICA where the non-Gaussianity is concentrated into the non-Gaussian scalar sources. The new scalar sources obtained by the above process encompass the attractor's curvature thus providing improved nonlinear model indices of the low-frequency atmospheric variability which is useful since large circulation indices are nonlinearly correlated. The non-Gaussian tested sources (dyads and triads, respectively of two and three dimensions) lead to a dense data concentration along certain curves or surfaces, nearby which the clusters' centroids of the joint probability density function tend to be located. That favors a better splitting of the QG3 atmospheric model's weather regimes: the positive and negative phases of the Arctic Oscillation and positive and negative phases of the North Atlantic Oscillation. The leading model's non-Gaussian dyad is associated to a positive correlation between: 1) the squared anomaly of the extratropical jet-stream and 2) the meridional jet-stream meandering. Triadic sources coming from maximized third-order cross cumulants between pairwise uncorrelated components reveal situations of triadic wave resonance and nonlinear triadic teleconnections, only possible thanks to joint non-Gaussianity. That kind of triadic synergies are accounted for an Information-Theoretic measure: the Interaction Information. The dominant model's triad occurs between anomalies of: 1) the North Pole anomaly pressure 2) the jet-stream intensity at the Eastern North-American boundary and 3) the jet-stream intensity at the Eastern Asian boundary. Publication supported by project FCT UID/GEO/50019/2013 - Instituto Dom Luiz.

Generalized t-statistic for two-group classification.

PubMed

Komori, Osamu; Eguchi, Shinto; Copas, John B

2015-06-01

In the classic discriminant model of two multivariate normal distributions with equal variance matrices, the linear discriminant function is optimal both in terms of the log likelihood ratio and in terms of maximizing the standardized difference (the t-statistic) between the means of the two distributions. In a typical case-control study, normality may be sensible for the control sample but heterogeneity and uncertainty in diagnosis may suggest that a more flexible model is needed for the cases. We generalize the t-statistic approach by finding the linear function which maximizes a standardized difference but with data from one of the groups (the cases) filtered by a possibly nonlinear function U. We study conditions for consistency of the method and find the function U which is optimal in the sense of asymptotic efficiency. Optimality may also extend to other measures of discriminatory efficiency such as the area under the receiver operating characteristic curve. The optimal function U depends on a scalar probability density function which can be estimated non-parametrically using a standard numerical algorithm. A lasso-like version for variable selection is implemented by adding L1-regularization to the generalized t-statistic. Two microarray data sets in the study of asthma and various cancers are used as motivating examples. © 2014, The International Biometric Society.

Chaos, patterns, coherent structures, and turbulence: Reflections on nonlinear science.

PubMed

Ecke, Robert E

2015-09-01

The paradigms of nonlinear science were succinctly articulated over 25 years ago as deterministic chaos, pattern formation, coherent structures, and adaptation/evolution/learning. For chaos, the main unifying concept was universal routes to chaos in general nonlinear dynamical systems, built upon a framework of bifurcation theory. Pattern formation focused on spatially extended nonlinear systems, taking advantage of symmetry properties to develop highly quantitative amplitude equations of the Ginzburg-Landau type to describe early nonlinear phenomena in the vicinity of critical points. Solitons, mathematically precise localized nonlinear wave states, were generalized to a larger and less precise class of coherent structures such as, for example, concentrated regions of vorticity from laboratory wake flows to the Jovian Great Red Spot. The combination of these three ideas was hoped to provide the tools and concepts for the understanding and characterization of the strongly nonlinear problem of fluid turbulence. Although this early promise has been largely unfulfilled, steady progress has been made using the approaches of nonlinear science. I provide a series of examples of bifurcations and chaos, of one-dimensional and two-dimensional pattern formation, and of turbulence to illustrate both the progress and limitations of the nonlinear science approach. As experimental and computational methods continue to improve, the promise of nonlinear science to elucidate fluid turbulence continues to advance in a steady manner, indicative of the grand challenge nature of strongly nonlinear multi-scale dynamical systems.

Stochastic P-bifurcation and stochastic resonance in a noisy bistable fractional-order system

NASA Astrophysics Data System (ADS)

Yang, J. H.; Sanjuán, Miguel A. F.; Liu, H. G.; Litak, G.; Li, X.

2016-12-01

We investigate the stochastic response of a noisy bistable fractional-order system when the fractional-order lies in the interval (0, 2]. We focus mainly on the stochastic P-bifurcation and the phenomenon of the stochastic resonance. We compare the generalized Euler algorithm and the predictor-corrector approach which are commonly used for numerical calculations of fractional-order nonlinear equations. Based on the predictor-corrector approach, the stochastic P-bifurcation and the stochastic resonance are investigated. Both the fractional-order value and the noise intensity can induce an stochastic P-bifurcation. The fractional-order may lead the stationary probability density function to turn from a single-peak mode to a double-peak mode. However, the noise intensity may transform the stationary probability density function from a double-peak mode to a single-peak mode. The stochastic resonance is investigated thoroughly, according to the linear and the nonlinear response theory. In the linear response theory, the optimal stochastic resonance may occur when the value of the fractional-order is larger than one. In previous works, the fractional-order is usually limited to the interval (0, 1]. Moreover, the stochastic resonance at the subharmonic frequency and the superharmonic frequency are investigated respectively, by using the nonlinear response theory. When it occurs at the subharmonic frequency, the resonance may be strong and cannot be ignored. When it occurs at the superharmonic frequency, the resonance is weak. We believe that the results in this paper might be useful for the signal processing of nonlinear systems.

Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control.

PubMed

Brunton, Steven L; Brunton, Bingni W; Proctor, Joshua L; Kutz, J Nathan

2016-01-01

In this wIn this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control.ork, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control.

B-spline goal-oriented error estimators for geometrically nonlinear rods

DTIC Science & Technology

2011-04-01

respectively, for the output functionals q2–q4 (linear and nonlinear with the trigonometric functions sine and cosine) in all the tests considered...of the errors resulting from the linear, quadratic and nonlinear (with trigonometric functions sine and cosine) outputs and for p = 1, 2. If the... Portugal . References [1] A.T. Adams. Sobolev Spaces. Academic Press, Boston, 1975. [2] M. Ainsworth and J.T. Oden. A posteriori error estimation in

Kurtosis Approach for Nonlinear Blind Source Separation

NASA Technical Reports Server (NTRS)

Duong, Vu A.; Stubbemd, Allen R.

2005-01-01

In this paper, we introduce a new algorithm for blind source signal separation for post-nonlinear mixtures. The mixtures are assumed to be linearly mixed from unknown sources first and then distorted by memoryless nonlinear functions. The nonlinear functions are assumed to be smooth and can be approximated by polynomials. Both the coefficients of the unknown mixing matrix and the coefficients of the approximated polynomials are estimated by the gradient descent method conditional on the higher order statistical requirements. The results of simulation experiments presented in this paper demonstrate the validity and usefulness of our approach for nonlinear blind source signal separation.

Order reduction, identification and localization studies of dynamical systems

NASA Astrophysics Data System (ADS)

Ma, Xianghong

In this thesis methods are developed for performing order reduction, system identification and induction of nonlinear localization in complex mechanical dynamic systems. General techniques are proposed for constructing low-order models of linear and nonlinear mechanical systems; in addition, novel mechanical designs are considered for inducing nonlinear localization phenomena for the purpose of enhancing their dynamical performance. The thesis is in three major parts. In the first part, the transient dynamics of an impulsively loaded multi-bay truss is numerically computed by employing the Direct Global Matrix (DGM) approach. The approach is applicable to large-scale flexible structures with periodicity. Karhunen-Loeve (K-L) decomposition is used to discretize the dynamics of the truss and to create the low-order models of the truss. The leading order K-L modes are recovered by an experiment, which shows the feasibility of K-L based order reduction technique. In the second part of the thesis, nonlinear localization in dynamical systems is studied through two applications. In the seismic base isolation study, it is shown that the dynamics are sensitive to the presence of nonlinear elements and that passive motion confinement can be induced under proper design. In the coupled rod system, numerical simulation of the transient dynamics shows that a nonlinear backlash spring can induce either nonlinear localization or delocalization in the form of beat phenomena. K-L decomposition and poincare maps are utilized to study the nonlinear effects. The study shows that nonlinear localization can be induced in complex structures through backlash. In the third and final part of the thesis, a new technique based on Green!s function method is proposed to identify the dynamics of practical bolted joints. By modeling the difference between the dynamics of the bolted structure and the corresponding unbolted one, one constructs a nonparametric model for the joint dynamics. Two applications are given with a bolted beam and a truss joint in order to show the applicability of the technique.

Theoretical and software considerations for nonlinear dynamic analysis

NASA Technical Reports Server (NTRS)

Schmidt, R. J.; Dodds, R. H., Jr.

1983-01-01

In the finite element method for structural analysis, it is generally necessary to discretize the structural model into a very large number of elements to accurately evaluate displacements, strains, and stresses. As the complexity of the model increases, the number of degrees of freedom can easily exceed the capacity of present-day software system. Improvements of structural analysis software including more efficient use of existing hardware and improved structural modeling techniques are discussed. One modeling technique that is used successfully in static linear and nonlinear analysis is multilevel substructuring. This research extends the use of multilevel substructure modeling to include dynamic analysis and defines the requirements for a general purpose software system capable of efficient nonlinear dynamic analysis. The multilevel substructuring technique is presented, the analytical formulations and computational procedures for dynamic analysis and nonlinear mechanics are reviewed, and an approach to the design and implementation of a general purpose structural software system is presented.

Bi-orthogonal approach to non-Hermitian Hamiltonians with the oscillator spectrum: Generalized coherent states for nonlinear algebras

NASA Astrophysics Data System (ADS)

Rosas-Ortiz, Oscar; Zelaya, Kevin

2018-01-01

A set of Hamiltonians that are not self-adjoint but have the spectrum of the harmonic oscillator is studied. The eigenvectors of these operators and those of their Hermitian conjugates form a bi-orthogonal system that provides a mathematical procedure to satisfy the superposition principle. In this form the non-Hermitian oscillators can be studied in much the same way as in the Hermitian approaches. Two different nonlinear algebras generated by properly constructed ladder operators are found and the corresponding generalized coherent states are obtained. The non-Hermitian oscillators can be steered to the conventional one by the appropriate selection of parameters. In such limit, the generators of the nonlinear algebras converge to generalized ladder operators that would represent either intensity-dependent interactions or multi-photon processes if the oscillator is associated with single mode photon fields in nonlinear media.

A generalized partially linear mean-covariance regression model for longitudinal proportional data, with applications to the analysis of quality of life data from cancer clinical trials.

PubMed

Zheng, Xueying; Qin, Guoyou; Tu, Dongsheng

2017-05-30

Motivated by the analysis of quality of life data from a clinical trial on early breast cancer, we propose in this paper a generalized partially linear mean-covariance regression model for longitudinal proportional data, which are bounded in a closed interval. Cholesky decomposition of the covariance matrix for within-subject responses and generalized estimation equations are used to estimate unknown parameters and the nonlinear function in the model. Simulation studies are performed to evaluate the performance of the proposed estimation procedures. Our new model is also applied to analyze the data from the cancer clinical trial that motivated this research. In comparison with available models in the literature, the proposed model does not require specific parametric assumptions on the density function of the longitudinal responses and the probability function of the boundary values and can capture dynamic changes of time or other interested variables on both mean and covariance of the correlated proportional responses. Copyright © 2017 John Wiley & Sons, Ltd. Copyright © 2017 John Wiley & Sons, Ltd.

Four-dimensional black holes in Einsteinian cubic gravity

NASA Astrophysics Data System (ADS)

Bueno, Pablo; Cano, Pablo A.

2016-12-01

We construct static and spherically symmetric generalizations of the Schwarzschild- and Reissner-Nordström-(anti-)de Sitter [RN-(A)dS] black-hole solutions in four-dimensional Einsteinian cubic gravity (ECG). The solutions are characterized by a single function which satisfies a nonlinear second-order differential equation. Interestingly, we are able to compute independently the Hawking temperature T , the Wald entropy S and the Abbott-Deser mass M of the solutions analytically as functions of the horizon radius and the ECG coupling constant λ . Using these we show that the first law of black-hole mechanics is exactly satisfied. Some of the solutions have positive specific heat, which makes them thermodynamically stable, even in the uncharged and asymptotically flat case. Further, we claim that, up to cubic order in curvature, ECG is the most general four-dimensional theory of gravity which allows for nontrivial generalizations of Schwarzschild- and RN-(A)dS characterized by a single function which reduce to the usual Einstein gravity solutions when the corresponding higher-order couplings are set to zero.

A kinetic equation with kinetic entropy functions for scalar conservation laws

NASA Technical Reports Server (NTRS)

Perthame, Benoit; Tadmor, Eitan

1990-01-01

A nonlinear kinetic equation is constructed and proved to be well-adapted to describe general multidimensional scalar conservation laws. In particular, it is proved to be well-posed uniformly in epsilon - the microscopic scale. It is also shown that the proposed kinetic equation is equipped with a family of kinetic entropy functions - analogous to Boltzmann's microscopic H-function, such that they recover Krushkov-type entropy inequality on the macroscopic scale. Finally, it is proved by both - BV compactness arguments in the one-dimensional case, that the local density of kinetic particles admits a continuum limit, as it converges strongly with epsilon below 0 to the unique entropy solution of the corresponding conservation law.

Diffusion in different models of active Brownian motion

NASA Astrophysics Data System (ADS)

Lindner, B.; Nicola, E. M.

2008-04-01

Active Brownian particles (ABP) have served as phenomenological models of self-propelled motion in biology. We study the effective diffusion coefficient of two one-dimensional ABP models (simplified depot model and Rayleigh-Helmholtz model) differing in their nonlinear friction functions. Depending on the choice of the friction function the diffusion coefficient does or does not attain a minimum as a function of noise intensity. We furthermore discuss the case of an additional bias breaking the left-right symmetry of the system. We show that this bias induces a drift and that it generally reduces the diffusion coefficient. For a finite range of values of the bias, both models can exhibit a maximum in the diffusion coefficient vs. noise intensity.

Numerical solution of the general coupled nonlinear Schrödinger equations on unbounded domains.

PubMed

Li, Hongwei; Guo, Yue

2017-12-01

The numerical solution of the general coupled nonlinear Schrödinger equations on unbounded domains is considered by applying the artificial boundary method in this paper. In order to design the local absorbing boundary conditions for the coupled nonlinear Schrödinger equations, we generalize the unified approach previously proposed [J. Zhang et al., Phys. Rev. E 78, 026709 (2008)PLEEE81539-375510.1103/PhysRevE.78.026709]. Based on the methodology underlying the unified approach, the original problem is split into two parts, linear and nonlinear terms, and we then achieve a one-way operator to approximate the linear term to make the wave out-going, and finally we combine the one-way operator with the nonlinear term to derive the local absorbing boundary conditions. Then we reduce the original problem into an initial boundary value problem on the bounded domain, which can be solved by the finite difference method. The stability of the reduced problem is also analyzed by introducing some auxiliary variables. Ample numerical examples are presented to verify the accuracy and effectiveness of our proposed method.

Generalized Nonlinear Yule Models

NASA Astrophysics Data System (ADS)

Lansky, Petr; Polito, Federico; Sacerdote, Laura

2016-11-01

With the aim of considering models related to random graphs growth exhibiting persistent memory, we propose a fractional nonlinear modification of the classical Yule model often studied in the context of macroevolution. Here the model is analyzed and interpreted in the framework of the development of networks such as the World Wide Web. Nonlinearity is introduced by replacing the linear birth process governing the growth of the in-links of each specific webpage with a fractional nonlinear birth process with completely general birth rates. Among the main results we derive the explicit distribution of the number of in-links of a webpage chosen uniformly at random recognizing the contribution to the asymptotics and the finite time correction. The mean value of the latter distribution is also calculated explicitly in the most general case. Furthermore, in order to show the usefulness of our results, we particularize them in the case of specific birth rates giving rise to a saturating behaviour, a property that is often observed in nature. The further specialization to the non-fractional case allows us to extend the Yule model accounting for a nonlinear growth.

Predicting radiotherapy outcomes using statistical learning techniques

NASA Astrophysics Data System (ADS)

El Naqa, Issam; Bradley, Jeffrey D.; Lindsay, Patricia E.; Hope, Andrew J.; Deasy, Joseph O.

2009-09-01

Radiotherapy outcomes are determined by complex interactions between treatment, anatomical and patient-related variables. A common obstacle to building maximally predictive outcome models for clinical practice is the failure to capture potential complexity of heterogeneous variable interactions and applicability beyond institutional data. We describe a statistical learning methodology that can automatically screen for nonlinear relations among prognostic variables and generalize to unseen data before. In this work, several types of linear and nonlinear kernels to generate interaction terms and approximate the treatment-response function are evaluated. Examples of institutional datasets of esophagitis, pneumonitis and xerostomia endpoints were used. Furthermore, an independent RTOG dataset was used for 'generalizabilty' validation. We formulated the discrimination between risk groups as a supervised learning problem. The distribution of patient groups was initially analyzed using principle components analysis (PCA) to uncover potential nonlinear behavior. The performance of the different methods was evaluated using bivariate correlations and actuarial analysis. Over-fitting was controlled via cross-validation resampling. Our results suggest that a modified support vector machine (SVM) kernel method provided superior performance on leave-one-out testing compared to logistic regression and neural networks in cases where the data exhibited nonlinear behavior on PCA. For instance, in prediction of esophagitis and pneumonitis endpoints, which exhibited nonlinear behavior on PCA, the method provided 21% and 60% improvements, respectively. Furthermore, evaluation on the independent pneumonitis RTOG dataset demonstrated good generalizabilty beyond institutional data in contrast with other models. This indicates that the prediction of treatment response can be improved by utilizing nonlinear kernel methods for discovering important nonlinear interactions among model variables. These models have the capacity to predict on unseen data. Part of this work was first presented at the Seventh International Conference on Machine Learning and Applications, San Diego, CA, USA, 11-13 December 2008.

Plastic and Large-Deflection Analysis of Nonlinear Structures

NASA Technical Reports Server (NTRS)

Thomson, R. G.; Hayduk, R. J.; Robinson, M. P.; Durling, B. J.; Pifko, A.; Levine, H. S.; Armen, H. J.; Levy, A.; Ogilvie, P.

1982-01-01

Plastic and Large Deflection Analysis of Nonlinear Structures (PLANS) system is collection of five computer programs for finite-element static-plastic and large deflection analysis of variety of nonlinear structures. System considers bending and membrane stresses, general three-dimensional bodies, and laminated composites.

Exact solutions to three-dimensional generalized nonlinear Schrödinger equations with varying potential and nonlinearities.

PubMed

Yan, Zhenya; Konotop, V V

2009-09-01

It is shown that using the similarity transformations, a set of three-dimensional p-q nonlinear Schrödinger (NLS) equations with inhomogeneous coefficients can be reduced to one-dimensional stationary NLS equation with constant or varying coefficients, thus allowing for obtaining exact localized and periodic wave solutions. In the suggested reduction the original coordinates in the (1+3) space are mapped into a set of one-parametric coordinate surfaces, whose parameter plays the role of the coordinate of the one-dimensional equation. We describe the algorithm of finding solutions and concentrate on power (linear and nonlinear) potentials presenting a number of case examples. Generalizations of the method are also discussed.

Nonlinear layered lattice model and generalized solitary waves in imperfectly bonded structures.

PubMed

Khusnutdinova, Karima R; Samsonov, Alexander M; Zakharov, Alexey S

2009-05-01

We study nonlinear waves in a two-layered imperfectly bonded structure using a nonlinear lattice model. The key element of the model is an anharmonic chain of oscillating dipoles, which can be viewed as a basic lattice analog of a one-dimensional macroscopic waveguide. Long nonlinear longitudinal waves in a layered lattice with a soft middle (or bonding) layer are governed by a system of coupled Boussinesq-type equations. For this system we find conservation laws and show that pure solitary waves, which exist in a single equation and can exist in the coupled system in the symmetric case, are structurally unstable and are replaced with generalized solitary waves.

PREDICTION OF NONLINEAR SPATIAL FUNCTIONALS. (R827257)

EPA Science Inventory

Spatial statistical methodology can be useful in the arena of environmental regulation. Some regulatory questions may be addressed by predicting linear functionals of the underlying signal, but other questions may require the prediction of nonlinear functionals of the signal. ...

Finite-time H∞ filtering for non-linear stochastic systems

NASA Astrophysics Data System (ADS)

Hou, Mingzhe; Deng, Zongquan; Duan, Guangren

2016-09-01

This paper describes the robust H∞ filtering analysis and the synthesis of general non-linear stochastic systems with finite settling time. We assume that the system dynamic is modelled by Itô-type stochastic differential equations of which the state and the measurement are corrupted by state-dependent noises and exogenous disturbances. A sufficient condition for non-linear stochastic systems to have the finite-time H∞ performance with gain less than or equal to a prescribed positive number is established in terms of a certain Hamilton-Jacobi inequality. Based on this result, the existence of a finite-time H∞ filter is given for the general non-linear stochastic system by a second-order non-linear partial differential inequality, and the filter can be obtained by solving this inequality. The effectiveness of the obtained result is illustrated by a numerical example.

A Physics-driven Neural Networks-based Simulation System (PhyNNeSS) for multimodal interactive virtual environments involving nonlinear deformable objects

PubMed Central

De, Suvranu; Deo, Dhannanjay; Sankaranarayanan, Ganesh; Arikatla, Venkata S.

2012-01-01

Background While an update rate of 30 Hz is considered adequate for real time graphics, a much higher update rate of about 1 kHz is necessary for haptics. Physics-based modeling of deformable objects, especially when large nonlinear deformations and complex nonlinear material properties are involved, at these very high rates is one of the most challenging tasks in the development of real time simulation systems. While some specialized solutions exist, there is no general solution for arbitrary nonlinearities. Methods In this work we present PhyNNeSS - a Physics-driven Neural Networks-based Simulation System - to address this long-standing technical challenge. The first step is an off-line pre-computation step in which a database is generated by applying carefully prescribed displacements to each node of the finite element models of the deformable objects. In the next step, the data is condensed into a set of coefficients describing neurons of a Radial Basis Function network (RBFN). During real-time computation, these neural networks are used to reconstruct the deformation fields as well as the interaction forces. Results We present realistic simulation examples from interactive surgical simulation with real time force feedback. As an example, we have developed a deformable human stomach model and a Penrose-drain model used in the Fundamentals of Laparoscopic Surgery (FLS) training tool box. Conclusions A unique computational modeling system has been developed that is capable of simulating the response of nonlinear deformable objects in real time. The method distinguishes itself from previous efforts in that a systematic physics-based pre-computational step allows training of neural networks which may be used in real time simulations. We show, through careful error analysis, that the scheme is scalable, with the accuracy being controlled by the number of neurons used in the simulation. PhyNNeSS has been integrated into SoFMIS (Software Framework for Multimodal Interactive Simulation) for general use. PMID:22629108

Solution of the nonlinear mixed Volterra-Fredholm integral equations by hybrid of block-pulse functions and Bernoulli polynomials.

PubMed

Mashayekhi, S; Razzaghi, M; Tripak, O

2014-01-01

A new numerical method for solving the nonlinear mixed Volterra-Fredholm integral equations is presented. This method is based upon hybrid functions approximation. The properties of hybrid functions consisting of block-pulse functions and Bernoulli polynomials are presented. The operational matrices of integration and product are given. These matrices are then utilized to reduce the nonlinear mixed Volterra-Fredholm integral equations to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.

Solution of the Nonlinear Mixed Volterra-Fredholm Integral Equations by Hybrid of Block-Pulse Functions and Bernoulli Polynomials

PubMed Central

Mashayekhi, S.; Razzaghi, M.; Tripak, O.

2014-01-01

A new numerical method for solving the nonlinear mixed Volterra-Fredholm integral equations is presented. This method is based upon hybrid functions approximation. The properties of hybrid functions consisting of block-pulse functions and Bernoulli polynomials are presented. The operational matrices of integration and product are given. These matrices are then utilized to reduce the nonlinear mixed Volterra-Fredholm integral equations to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique. PMID:24523638

Four points function fitted and first derivative procedure for determining the end points in potentiometric titration curves: statistical analysis and method comparison.

PubMed

Kholeif, S A

2001-06-01

A new method that belongs to the differential category for determining the end points from potentiometric titration curves is presented. It uses a preprocess to find first derivative values by fitting four data points in and around the region of inflection to a non-linear function, and then locate the end point, usually as a maximum or minimum, using an inverse parabolic interpolation procedure that has an analytical solution. The behavior and accuracy of the sigmoid and cumulative non-linear functions used are investigated against three factors. A statistical evaluation of the new method using linear least-squares method validation and multifactor data analysis are covered. The new method is generally applied to symmetrical and unsymmetrical potentiometric titration curves, and the end point is calculated using numerical procedures only. It outperforms the "parent" regular differential method in almost all factors levels and gives accurate results comparable to the true or estimated true end points. Calculated end points from selected experimental titration curves compatible with the equivalence point category of methods, such as Gran or Fortuin, are also compared with the new method.

Time-sliced perturbation theory for large scale structure I: general formalism

DOE Office of Scientific and Technical Information (OSTI.GOV)

Blas, Diego; Garny, Mathias; Sibiryakov, Sergey

2016-07-01

We present a new analytic approach to describe large scale structure formation in the mildly non-linear regime. The central object of the method is the time-dependent probability distribution function generating correlators of the cosmological observables at a given moment of time. Expanding the distribution function around the Gaussian weight we formulate a perturbative technique to calculate non-linear corrections to cosmological correlators, similar to the diagrammatic expansion in a three-dimensional Euclidean quantum field theory, with time playing the role of an external parameter. For the physically relevant case of cold dark matter in an Einstein-de Sitter universe, the time evolution ofmore » the distribution function can be found exactly and is encapsulated by a time-dependent coupling constant controlling the perturbative expansion. We show that all building blocks of the expansion are free from spurious infrared enhanced contributions that plague the standard cosmological perturbation theory. This paves the way towards the systematic resummation of infrared effects in large scale structure formation. We also argue that the approach proposed here provides a natural framework to account for the influence of short-scale dynamics on larger scales along the lines of effective field theory.« less

Optimization-Based Robust Nonlinear Control

DTIC Science & Technology

2006-08-01

ABSTRACT New control algorithms were developed for robust stabilization of nonlinear dynamical systems . Novel, linear matrix inequality-based synthesis...was to further advance optimization-based robust nonlinear control design, for general nonlinear systems (especially in discrete time ), for linear...Teel, IEEE Transactions on Control Systems Technology, vol. 14, no. 3, p. 398-407, May 2006. 3. "A unified framework for input-to-state stability in

Linear and nonlinear properties of the ULF waves driven by ring-beam distribution functions

NASA Technical Reports Server (NTRS)

Killen, K.; Omidi, N.; Krauss-Varban, D.; Karimabadi, H.

1995-01-01

The problem of the exitation of obliquely propagating magnetosonic waves which can steepen up (also known as shocklets) is considered. Shocklets have been observed upstream of the Earth's bow shock and at comets Giacobini-Zinner and Grigg-Skjellerup. Linear theory as well as two-dimensional (2-D) hybrid (fluid electrons, particle ions) simulations are used to determine the properties of waves generated by ring-beam velocity distributions in great detail. The effects of both proton and oxygen ring-beams are considered. The study of instabilities excited by a proton ring-beam is relevant to the region upstream of the Earth's bow shock, whereas the oxygen ring-beam corresponds to cometary ions picked up by the solar wind. Linear theory has shown that for a ring-beam, four instabilities are found, one on the nonresonant mode, one on the Alfven mode, and two along the magnetosonic/whistler branch. The relative growth rate of these instabilities is a sensitive function of parameters. Although one of the magnetosonic instabilities has maximum growth along the magnetic field, the other has maximum growth in oblique directions. We have studied the competition of these instabilities in the nonlinear regime using 2-D simulations. As in the linear limit, the nonlinear results are a function of beam density and distribution function. By performing the simulations as both initial value and driven systems, we have found that the outcome of the simulations can vary, suggesting that the latter type simulations is needed to address the observations. A general conclusion of the simulation results is that field-aligned beams do not result in the formation of shocklets, whereas ring-beam distributions can.

Fatigue crack detection by nonlinear spectral correlation with a wideband input

NASA Astrophysics Data System (ADS)

Liu, Peipei; Sohn, Hoon

2017-04-01

Due to crack-induced nonlinearity, ultrasonic wave can distort, create accompanying harmonics, multiply waves of different frequencies, and, under resonance conditions, change resonance frequencies as a function of driving amplitude. All these nonlinear ultrasonic features have been widely studied and proved capable of detecting fatigue crack at its very early stage. However, in noisy environment, the nonlinear features might be drown in the noise, therefore it is difficult to extract those features using a conventional spectral density function. In this study, nonlinear spectral correlation is defined as a new nonlinear feature, which considers not only nonlinear modulations in ultrasonic waves but also spectral correlation between the nonlinear modulations. The proposed nonlinear feature is associated with the following two advantages: (1) stationary noise in the ultrasonic waves has little effect on nonlinear spectral correlation; and (2) the contrast of nonlinear spectral correlation between damage and intact conditions can be enhanced simply by using a wideband input. To validate the proposed nonlinear feature, micro fatigue cracks are introduced to aluminum plates by repeated tensile loading, and the experiment is conducted using surface-mounted piezoelectric transducers for ultrasonic wave generation and measurement. The experimental results confirm that the nonlinear spectral correlation can successfully detect fatigue crack with a higher sensitivity than the classical nonlinear coefficient.

Linear parameter varying representations for nonlinear control design

NASA Astrophysics Data System (ADS)

Carter, Lance Huntington

Linear parameter varying (LPV) systems are investigated as a framework for gain-scheduled control design and optimal hybrid control. An LPV system is defined as a linear system whose dynamics depend upon an a priori unknown but measurable exogenous parameter. A gain-scheduled autopilot design is presented for a bank-to-turn (BTT) missile. The method is novel in that the gain-scheduled design does not involve linearizations about operating points. Instead, the missile dynamics are brought to LPV form via a state transformation. This idea is applied to the design of a coupled longitudinal/lateral BTT missile autopilot. The pitch and yaw/roll dynamics are separately transformed to LPV form, where the cross axis states are treated as "exogenous" parameters. These are actually endogenous variables, so such a plant is called "quasi-LPV." Once in quasi-LPV form, a family of robust controllers using mu synthesis is designed for both the pitch and yaw/roll channels, using angle-of-attack and roll rate as the scheduling variables. The closed-loop time response is simulated using the original nonlinear model and also using perturbed aerodynamic coefficients. Modeling and control of engine idle speed is investigated using LPV methods. It is shown how generalized discrete nonlinear systems may be transformed into quasi-LPV form. A discrete nonlinear engine model is developed and expressed in quasi-LPV form with engine speed as the scheduling variable. An example control design is presented using linear quadratic methods. Simulations are shown comparing the LPV based controller performance to that using PID control. LPV representations are also shown to provide a setting for hybrid systems. A hybrid system is characterized by control inputs consisting of both analog signals and discrete actions. A solution is derived for the optimal control of hybrid systems with generalized cost functions. This is shown to be computationally intensive, so a suboptimal strategy is proposed that neglects a subset of possible parameter trajectories. A computational algorithm is constructed for this suboptimal solution applied to a class of linear non-quadratic cost functions.

Phenomenological modeling of nonlinear holograms based on metallic geometric metasurfaces.

PubMed

Ye, Weimin; Li, Xin; Liu, Juan; Zhang, Shuang

2016-10-31

Benefiting from efficient local phase and amplitude control at the subwavelength scale, metasurfaces offer a new platform for computer generated holography with high spatial resolution. Three-dimensional and high efficient holograms have been realized by metasurfaces constituted by subwavelength meta-atoms with spatially varying geometries or orientations. Metasurfaces have been recently extended to the nonlinear optical regime to generate holographic images in harmonic generation waves. Thus far, there has been no vector field simulation of nonlinear metasurface holograms because of the tremendous computational challenge in numerically calculating the collective nonlinear responses of the large number of different subwavelength meta-atoms in a hologram. Here, we propose a general phenomenological method to model nonlinear metasurface holograms based on the assumption that every meta-atom could be described by a localized nonlinear polarizability tensor. Applied to geometric nonlinear metasurfaces, we numerically model the holographic images formed by the second-harmonic waves of different spins. We show that, in contrast to the metasurface holograms operating in the linear optical regime, the wavelength of incident fundamental light should be slightly detuned from the fundamental resonant wavelength to optimize the efficiency and quality of nonlinear holographic images. The proposed modeling provides a general method to simulate nonlinear optical devices based on metallic metasurfaces.

Orbital stability of solitary waves for generalized Boussinesq equation with two nonlinear terms

NASA Astrophysics Data System (ADS)

Zhang, Weiguo; Li, Xiang; Li, Shaowei; Chen, Xu

2018-06-01

This paper investigates the orbital stability and instability of solitary waves for the generalized Boussinesq equation with two nonlinear terms. Firstly, according to the theory of Grillakis-Shatah-Strauss orbital stability, we present the general results to judge orbital stability of the solitary waves. Further, we deduce the explicit expression of discrimination d‧‧(c) to judge the stability of the two solitary waves, and give the stable wave speed interval. Moreover, we analyze the influence of the interaction between two nonlinear terms on the stable wave speed interval, and give the maximal stable range for the wave speed. Finally, some conclusions are given in this paper.

Auxiliary variables for numerically solving nonlinear equations with softly broken symmetries.

PubMed

Olum, Ken D; Masoumi, Ali

2017-06-01

General methods for solving simultaneous nonlinear equations work by generating a sequence of approximate solutions that successively improve a measure of the total error. However, if the total error function has a narrow curved valley, the available techniques tend to find the solution after a very large number of steps, if ever. The solver first converges rapidly to the valley, but once there it converges extremely slowly to the solution. In this paper we show that in the specific physically important case where these valleys are the result of a softly broken symmetry, the solution can often be found much more quickly by adding the generators of the softly broken symmetry as auxiliary variables. This makes the number of variables more than the equations and hence there will be a family of solutions, any one of which would be acceptable. We present a procedure for finding solutions in this case and apply it to several simple examples and an important problem in the physics of false vacuum decay. We also provide a Mathematica package that implements Powell's hybrid method with the generalization to allow more variables than equations.