Nonlinear dynamics non-integrable systems and chaotic dynamics
Borisov, Alexander
2017-01-01
This monograph reviews advanced topics in the area of nonlinear dynamics. Starting with theory of integrable systems – including methods to find and verify integrability – the remainder of the book is devoted to non-integrable systems with an emphasis on dynamical chaos. Topics include structural stability, mechanisms of emergence of irreversible behaviour in deterministic systems as well as chaotisation occurring in dissipative systems.
Non-integrability of measure preserving maps via Lie symmetries
Cima, Anna; Gasull, Armengol; Mañosa, Víctor
2015-11-01
We consider the problem of characterizing, for certain natural number m, the local Cm-non-integrability near elliptic fixed points of smooth planar measure preserving maps. Our criterion relates this non-integrability with the existence of some Lie Symmetries associated to the maps, together with the study of the finiteness of its periodic points. One of the steps in the proof uses the regularity of the period function on the whole period annulus for non-degenerate centers, question that we believe that is interesting by itself. The obtained criterion can be applied to prove the local non-integrability of the Cohen map and of several rational maps coming from second order difference equations.
Indian Academy of Sciences (India)
Ramaswamy Jaganathan; Sudeshna Sinha
2005-03-01
Motivated by studies on -deformed physical systems related to quantum group structures, and by the elements of Tsallis statistical mechanics, the concept of -deformed nonlinear maps is introduced. As a specific example, a -deformation procedure is applied to the logistic map. Compared to the canonical logistic map, the resulting family of -logistic maps is shown to have a wider spectrum of interesting behaviours, including the co-existence of attractors – a phenomenon rare in one-dimensional maps.
Energy Technology Data Exchange (ETDEWEB)
Makarov, V A; Petnikova, V M; Potravkin, N N; Shuvalov, V V [International Laser Center, M. V. Lomonosov Moscow State University, Moscow (Russian Federation)
2014-02-28
Using the linearization method, we obtain approximate solutions to a one-dimensional nonintegrable problem of propagation of elliptically polarised light waves in an isotropic gyrotropic medium with local and nonlocal components of the Kerr nonlinearity and group-velocity dispersion. The consistent evolution of two orthogonal circularly polarised components of the field is described analytically in the case when their phases vary linearly during propagation. The conditions are determined for the excitation of waves with a regular and 'chaotic' change in the polarisation state. The character of the corresponding nonlinear solutions, i.e., periodic analogues of multisoliton complexes, is analysed. (nonlinear optical phenomena)
Directory of Open Access Journals (Sweden)
Yong Huang
2012-01-01
Full Text Available The Bäcklund transformations and abundant exact explicit solutions for a class of nonlinear wave equation are obtained by the extended homogeneous balance method. These solutions include the solitary wave solution of rational function, the solitary wave solutions, singular solutions, and the periodic wave solutions of triangle function type. In addition to rederiving some known solutions, some entirely new exact solutions are also established. Explicit and exact particular solutions of many well-known nonlinear evolution equations which are of important physical significance, such as Kolmogorov-Petrovskii-Piskunov equation, FitzHugh-Nagumo equation, Burgers-Huxley equation, Chaffee-Infante reaction diffusion equation, Newell-Whitehead equation, Fisher equation, Fisher-Burgers equation, and an isothermal autocatalytic system, are obtained as special cases.
Invariant metric for nonlinear symplectic maps
Indian Academy of Sciences (India)
Govindan Rangarajan; Minita Sachidanand
2002-03-01
In this paper, we construct an invariant metric in the space of homogeneous polynomials of a given degree (≥ 3). The homogeneous polynomials specify a nonlinear symplectic map which in turn represents a Hamiltonian system. By minimizing the norm constructed out of this metric as a function of system parameters, we demonstrate that the performance of a nonlinear Hamiltonian system is enhanced.
Propagation and interaction of solitons for nonintegrable equations
Omel'yanov, G.
2016-04-01
We describe an approach to the construction of multi-soliton asymptotic solutions for nonintegrable equations. The general idea is realized in the case of N waves, N = 1, 2, 3, and for the KdV-type equation with nonlinearity u 4. A brief review of asymptotic methods as well as results of numerical simulation are included.
An Explicit Nonlinear Mapping for Manifold Learning.
Qiao, Hong; Zhang, Peng; Wang, Di; Zhang, Bo
2013-02-01
Manifold learning is a hot research topic in the held of computer science and has many applications in the real world. A main drawback of manifold learning methods is, however, that there are no explicit mappings from the input data manifold to the output embedding. This prohibits the application of manifold learning methods in many practical problems such as classification and target detection. Previously, in order to provide explicit mappings for manifold learning methods, many methods have been proposed to get an approximate explicit representation mapping with the assumption that there exists a linear projection between the high-dimensional data samples and their low-dimensional embedding. However, this linearity assumption may be too restrictive. In this paper, an explicit nonlinear mapping is proposed for manifold learning, based on the assumption that there exists a polynomial mapping between the high-dimensional data samples and their low-dimensional representations. As far as we know, this is the hrst time that an explicit nonlinear mapping for manifold learning is given. In particular, we apply this to the method of locally linear embedding and derive an explicit nonlinear manifold learning algorithm, which is named neighborhood preserving polynomial embedding. Experimental results on both synthetic and real-world data show that the proposed mapping is much more effective in preserving the local neighborhood information and the nonlinear geometry of the high-dimensional data samples than previous work.
Solitonlike solutions of the generalized discrete nonlinear Schrödinger equation
DEFF Research Database (Denmark)
Rasmussen, Kim; Henning, D.; Gabriel, H.
1996-01-01
We investigate the solution properties oi. a generalized discrete nonlinear Schrodinger equation describing a nonlinear lattice chain. The generalized equation interpolates between the integrable discrete Ablowitz-Ladik equation and the nonintegrable discrete Schrodinger equation. Special interest...... nonlinear Schrodinger equation. In this way eve are able to construct coherent solitonlike structures of profile determined by the map parameters....
Metric domains, holomorphic mappings and nonlinear semigroups
Directory of Open Access Journals (Sweden)
Simeon Reich
1998-01-01
Full Text Available We study nonlinear semigroups of holomorphic mappings on certain domains in complex Banach spaces. We examine, in particular, their differentiability and their representations by exponential and other product formulas. In addition, we also construct holomorphic retractions onto the stationary point sets of such semigroups.
Nonlinear functional mapping of the human brain
Allgaier, Nicholas; Banaschewski, Tobias; Barker, Gareth; Arun L W Bokde; Bongard, Josh C.; Bromberg, Uli; Büchel, Christian; Cattrell, Anna; Conrod, Patricia J.; Danforth, Christopher M.; Desrivières, Sylvane; Peter S. Dodds; Flor, Herta; Frouin, Vincent; Gallinat, Jürgen
2015-01-01
The field of neuroimaging has truly become data rich, and novel analytical methods capable of gleaning meaningful information from large stores of imaging data are in high demand. Those methods that might also be applicable on the level of individual subjects, and thus potentially useful clinically, are of special interest. In the present study, we introduce just such a method, called nonlinear functional mapping (NFM), and demonstrate its application in the analysis of resting state fMRI fro...
STOCHASTIC OPTIMAL CONTROL FOR THE RESPONSE OF QUASI NON-INTEGRABLE HAMILTONIAN SYSTEMS~
Institute of Scientific and Technical Information of China (English)
DengMaolin; HongMingchao; ZhuWeiqiu
2003-01-01
A strategy is proposed based on the stochastic averaging method for quasi nonintegrable Hamiltonian systems and the stochastic dynamical programming principle. The proposed strategy can be used to design nonlinear stochastic optimal control to minimize the response of quasi non-integrable Hamiltonian systems subject to Gaussian white noise excitation. By using the stochastic averaging method for quasi non-integrable Hamiltonian systems the equations of motion of a controlled quasi non-integrable Hamiltonian system is reduced to a one-dimensional averaged Ito stochastic differential equation. By using the stochastic dynamical programming principle the dynamical programming equation for minimizing the response of the system is formulated.The optimal control law is derived from the dynamical programming equation and the bounded control constraints. The response of optimally controlled systems is predicted through solving the FPK equation associated with It5 stochastic differential equation. An example is worked out in detail to illustrate the application of the control strategy proposed.
Learning Inverse Rig Mappings by Nonlinear Regression.
Holden, Daniel; Saito, Jun; Komura, Taku
2016-11-11
We present a framework to design inverse rig-functions - functions that map low level representations of a character's pose such as joint positions or surface geometry to the representation used by animators called the animation rig. Animators design scenes using an animation rig, a framework widely adopted in animation production which allows animators to design character poses and geometry via intuitive parameters and interfaces. Yet most state-of-the-art computer animation techniques control characters through raw, low level representations such as joint angles, joint positions, or vertex coordinates. This difference often stops the adoption of state-of-the-art techniques in animation production. Our framework solves this issue by learning a mapping between the low level representations of the pose and the animation rig. We use nonlinear regression techniques, learning from example animation sequences designed by the animators. When new motions are provided in the skeleton space, the learned mapping is used to estimate the rig controls that reproduce such a motion. We introduce two nonlinear functions for producing such a mapping: Gaussian process regression and feedforward neural networks. The appropriate solution depends on the nature of the rig and the amount of data available for training. We show our framework applied to various examples including articulated biped characters, quadruped characters, facial animation rigs, and deformable characters. With our system, animators have the freedom to apply any motion synthesis algorithm to arbitrary rigging and animation pipelines for immediate editing. This greatly improves the productivity of 3D animation, while retaining the flexibility and creativity of artistic input.
Recovering map static nonlinearities from chaotic data using dynamical models
Aguirre, Luis Antonio
1997-02-01
This paper is concerned with the estimation from chaotic data of maps with static nonlinearities. A number of issues concerning model construction such as structure selection, over-parametrization and model validation are discussed in the light of the shape of the static non-linearities reproduced by the estimated maps. A new interpretation of term clusters and cluster coefficients of polynomial models is provided based on this approach. The paper discusses model limitations and some useful principles to select the structure of nonlinear maps. Some of the ideas have been tested using several nonlinear systems including a boost voltage regulator map and a set of real data from a chaotic circuit.
Energy Technology Data Exchange (ETDEWEB)
Huan, Ronghua; Zhu, Weiqiu [Zhejiang University, Department of Mechanics, State Key Laboratory of Fluid Power Transmission and Control, Hangzhou (China); Wu, Yongjun [East China University of Science and Technology, School of Information Science and Engineering, Shanghai (China)
2009-02-15
A new bounded optimal control strategy for multi-degree-of-freedom (MDOF) quasi nonintegrable-Hamiltonian systems with actuator saturation is proposed. First, an n-degree-of-freedom (n-DOF) controlled quasi nonintegrable-Hamiltonian system is reduced to a partially averaged Ito stochastic differential equation by using the stochastic averaging method for quasi nonintegrable-Hamiltonian systems. Then, a dynamical programming equation is established by using the stochastic dynamical programming principle, from which the optimal control law consisting of optimal unbounded control and bang-bang control is derived. Finally, the response of the optimally controlled system is predicted by solving the Fokker-Planck-Kolmogorov (FPK) equation associated with the fully averaged Ito equation. An example of two controlled nonlinearly coupled Duffing oscillators is worked out in detail. Numerical results show that the proposed control strategy has high control effectiveness and efficiency and that chattering is reduced significantly compared with the bang-bang control strategy. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Romeo, Francesco [Dipartimento di Ingegneria Strutturale e Geotecnica, Universita di Roma ' La Sapienza' , Via Gramsci 53, 00197 Rome (Italy)] e-mail: francesco.romeo@uniromal.it; Rega, Giuseppe [Dipartimento di Ingegneria Strutturale e Geotecnica, Universita di Roma ' La Sapienza' , Via Gramsci 53, 00197 Rome (Italy)] e-mail: giuseppe.rega@uniromal.it
2006-02-01
Free wave propagation properties in one-dimensional chains of nonlinear oscillators are investigated by means of nonlinear maps. In this realm, the governing difference equations are regarded as symplectic nonlinear transformations relating the amplitudes in adjacent chain sites (n, n + 1) thereby considering a dynamical system where the location index n plays the role of the discrete time. Thus, wave propagation becomes synonymous of stability: finding regions of propagating wave solutions is equivalent to finding regions of linearly stable map solutions. Mechanical models of chains of linearly coupled nonlinear oscillators are investigated. Pass- and stop-band regions of the mono-coupled periodic system are analytically determined for period-q orbits as they are governed by the eigenvalues of the linearized 2D map arising from linear stability analysis of periodic orbits. Then, equivalent chains of nonlinear oscillators in complex domain are tackled. Also in this case, where a 4D real map governs the wave transmission, the nonlinear pass- and stop-bands for periodic orbits are analytically determined by extending the 2D map analysis. The analytical findings concerning the propagation properties are then compared with numerical results obtained through nonlinear map iteration.
Algebraic calculation of stroboscopic maps of ordinary, nonlinear differential equations
Energy Technology Data Exchange (ETDEWEB)
Wackerbauer, R. (Max-Planck-Institut fuer Extraterrestrische Physik, Garching (Germany)); Huebler, A. (Illinois Univ., Urbana, IL (United States). Center for Complex Systems Research); Mayer-Kress, G. (Los Alamos National Lab., NM (United States) California Univ., Santa Cruz, CA (United States). Dept. of Mathematics)
1991-07-25
The relation between the parameters of a differential equation and corresponding discrete maps are becoming increasingly important in the study of nonlinear dynamical systems. Maps are well adopted for numerical computation and several universal properties of them are known. Therefore some perturbation methods have been proposed to deduce them for physical systems, which can be modeled by an ordinary differential equation (ODE) with a small nonlinearity. A new iterative, rigorous algebraic method for the calculation of the coefficients of a Taylor expansion of a stroboscopic map from ODE's with not necessarily small nonlinearities is presented. It is shown analytically that most of the coefficients are small for a small integration time and grow slowly in the course of time if the flow vector field of the ODE is polynomial and if the ODE has fixed point in the origin. Approximations of different orders respectively of the rest term are investigated for several nonlinear systems. 31 refs., 16 figs.
Nonlinear feedback control of spatiotemporal chaos in coupled map lattices
Directory of Open Access Journals (Sweden)
Jin-Qing Fang
1998-01-01
Full Text Available We describe a nonlinear feedback functional method for study both of control and synchronization of spatiotemporal chaos. The method is illustrated by the coupled map lattices with five different connection forms. A key issue addressed is to find nonlinear feedback functions. Two large types of nonlinear feedback functions are introduced. The efficient and robustness of the method based on the flexibility of choices of nonlinear feedback functions are discussed. Various numerical results of nonlinear control are given. We have not found any difficulty for study both of control and synchronization using nonlinear feedback functional method. The method can also be extended to time continuous dynamical systems as well as to society problems.
Nonlinear Maps and their Applications 2011 International Workshop
Fournier-Prunaret, Daniele; Ueta, Tetsushi; Nishio, Yoshifumi
2014-01-01
In the field of Dynamical Systems, nonlinear iterative processes play an important role. Nonlinear mappings can be found as immediate models for many systems from different scientific areas, such as engineering, economics, biology, or can also be obtained via numerical methods permitting to solve non-linear differential equations. In both cases, the understanding of specific dynamical behaviors and phenomena is of the greatest interest for scientists. This volume contains papers that were presented at the International Workshop on Nonlinear Maps and their Applications (NOMA 2011) held in Évora, Portugal, on September 15-16, 2011. This kind of collaborative effort is of paramount importance in promoting communication among the various groups that work in dynamical systems and networks in their research theoretical studies as well as for applications. This volume is suitable for graduate students as well as researchers in the field.
An Explicit Nonlinear Mapping for Manifold Learning
Qiao, Hong; Zhang, Peng; Wang, Di; Zhang, Bo
2010-01-01
Manifold learning is a hot research topic in the field of computer science and has many applications in the real world. A main drawback of manifold learning methods is, however, that there is no explicit mappings from the input data manifold to the output embedding. This prohibits the application of manifold learning methods in many practical problems such as classification and target detection. Previously, in order to provide explicit mappings for manifold learning methods, many methods have...
An analytic map for space charge in a nonlinear lattice
Energy Technology Data Exchange (ETDEWEB)
Benedetti, C. [Dipartimento di Fisica Universita di Bologna and INFN, Via Irnerio 46, 40126 Bologna (Italy)]. E-mail: benedetti@bo.infn.it; Turchetti, G. [Dipartimento di Fisica Universita di Bologna and INFN, Via Irnerio 46, 40126 Bologna (Italy)
2005-06-13
We propose a simple analytical model for an intense beam in a lattice with localized nonlinearities. In the thin lens limit a single nonlinearity leads to a Henon like map. When the space charge is present and the core radius is small with respect to the dynamic aperture, the use of a frozen core distribution like KV is justified. In this case we define an analytic map M by composing the phase advance due to space charge, computed at the first perturbation order, with the kick due to the nonlinear force. The corresponding dynamics is almost indistinguishable from the dynamics of the 'exact' map, which requires an accurate symplectic integration, if the tune depression is weak enough. The same accuracy is preserved for parametric modulations of the perveance or the beam core radius. The extension to any other distribution is straightforward.
Chaos Suppression in a Sine Square Map through Nonlinear Coupling
Institute of Scientific and Technical Information of China (English)
Eduardo L. Brugnago; Paulo C. Rech
2011-01-01
We study a pair of nonlinearly coupled identical chaotic sine square maps.More specifically,we investigate the chaos suppression associated with the variation of two parameters.Two-dimensional parameter-space regions where the chaotic dynamics of the individual chaotic sine square map is driven towards regular dynamics are delimited.Additionally,the dynamics of the coupled system is numerically characterized as the parameters are changed.In recent years,many efforts have been devoted to chaos suppression in a nonlinear dynamics field.Iglesias et al.[1] reported a chaos suppression method through numerical truncation and rounding errors,with applications in discrete-time systems.Hénon map[2] and the Burgers map[3] were used to illustrate the method.A method of feedback impulsive chaos suppression was introduced by Osipov et al.[4]It is an algorithm of suppressing chaos in continuoustime dissipative systems with an external impulsive force,whose necessary condition is a reduction of the continuous flow to a discrete-time one-dimensional map.%We study a pair of nonlinearly coupled identical chaotic sine square maps. More specifically, we investigate the chaos suppression associated with the variation of two parameters. Two-dimensional parameter-space regions where the chaotic dynamics of the individual chaotic sine square map is driven towards regular dynamics are delimited. Additionally, the dynamics of the coupled system is numerically characterized as the parameters are changed.
Linear Algebraic Method for Non-Linear Map Analysis
Energy Technology Data Exchange (ETDEWEB)
Yu,L.; Nash, B.
2009-05-04
We present a newly developed method to analyze some non-linear dynamics problems such as the Henon map using a matrix analysis method from linear algebra. Choosing the Henon map as an example, we analyze the spectral structure, the tune-amplitude dependence, the variation of tune and amplitude during the particle motion, etc., using the method of Jordan decomposition which is widely used in conventional linear algebra.
Rational Expansion for Nonlinear Input-Output Maps
1988-01-01
This paper introduces a Rational Expansion for Nonlinear Input-Output MAPS. The method is new and is based on the rational expansion of functions of several complex variables. If truncated, this series reduces to a ratio of truncated Volterra series, A "feedback form" will be presented.
Visualization of nonlinear kernel models in neuroimaging by sensitivity maps
DEFF Research Database (Denmark)
Rasmussen, Peter Mondrup; Madsen, Kristoffer Hougaard; Lund, Torben Ellegaard
2011-01-01
There is significant current interest in decoding mental states from neuroimages. In this context kernel methods, e.g., support vector machines (SVM) are frequently adopted to learn statistical relations between patterns of brain activation and experimental conditions. In this paper we focus......, and conclude that the sensitivity map is a versatile and computationally efficient tool for visualization of nonlinear kernel models in neuroimaging....
An Adaptive Non-Linear Map and Its Application
Institute of Scientific and Technical Information of China (English)
YAN Xuefeng
2006-01-01
A novel adaptive non-linear mapping (ANLM),integrating an adaptive mapping error (AME) with a chaosgenetic algorithm (CGA) including chaotic variable, was proposed to overcome the deficiencies of non-linear mapping (NLM). The value of AME weight factor is determined according to the relative deviation square of distance between the two mapping points and the corresponding original objects distance. The larger the relative deviation square between two distances is, the larger the value of the corresponding weight factor is. Due to chaotic mapping operator, the evolutional process of CGA makes the individuals of subgenerations distributed ergodically in the defined space and circumvents the premature of the individuals of subgenerations. The comparison results demonstrated that the whole performance of CGA is better than that of traditional genetic algorithm. Furthermore, a typical example of mapping eight-dimensional olive oil samples onto two-dimensional plane was employed to verify the effectiveness of ANLM. The results showed that the topology-preserving map obtained by ANLM can well represent the classification of original objects and is much better than that obtained by NLM.
Energy Technology Data Exchange (ETDEWEB)
Leonel, Edson D; De Oliveira, Juliano A; Saif, Farhan, E-mail: edleonel@rc.unesp.br [Departamento de EstatIstica, Matematica Aplicada e Computacao, UNESP-Univ. Estadual Paulista, Av. 24A, 1515, Bela Vista, 13506-900 Rio Claro, Sao Paulo (Brazil)
2011-07-29
Critical exponents that describe a transition from integrability to non-integrability in a two-dimensional, nonlinear and area-preserving map are obtained via localization of the first invariant spanning curve (invariant tori) in the phase space. In a general class of systems, the position of the first invariant tori is estimated by reducing the mapping of the system to the standard mapping where a transition takes place from local to global chaos. The phase space of the mapping shows a large chaotic sea surrounding periodic islands and limited by a set of invariant tori whose position of the first of them depends on the control parameters. The formalism leads us to obtain analytically critical exponents that describe the behaviour of the average variable (action) along the chaotic sea. The result is compared to several models in the literature confirming the approach is of large interest. The formalism used is general and the procedure can be extended to many other different systems. (fast track communication)
Prethermalization in a Nonintegrable Quantum Spin Chain after a Quench
Marcuzzi, Matteo; Marino, Jamir; Gambassi, Andrea; Silva, Alessandro
2013-11-01
We study the dynamics of a quantum Ising chain after the sudden introduction of a nonintegrable long-range interaction. Via an exact mapping onto a fully connected lattice of hard-core bosons, we show that a prethermal state emerges and we investigate its features by focusing on a class of physically relevant observables. In order to gain insight into the eventual thermalization, we outline a diagrammatic approach which complements the study of the previous quasistationary state and provides the basis for a self-consistent solution of the kinetic equation. This analysis suggests that both the temporal decay towards the prethermal state and the crossover to the eventual thermal one may occur algebraically.
Chaotic Map Construction from Common Nonlinearities and Microcontroller Implementations
Ablay, Günyaz
2016-06-01
This work presents novel discrete-time chaotic systems with some known physical system nonlinearities. Dynamic behaviors of the models are examined with numerical methods and Arduino microcontroller-based experimental studies. Many new chaotic maps are generated in the form of x(k + 1) = rx(k) + f(x(k)) and high-dimensional chaotic systems are obtained by weak coupling or cross-coupling the same or different chaotic maps. An application of the chaotic maps is realized with Arduino for chaotic pulse width modulation to drive electrical machines. It is expected that the new chaotic maps and their microcontroller implementations will facilitate practical chaos-based applications in different fields.
High-resolution mapping of bifurcations in nonlinear biochemical circuits
Genot, A. J.; Baccouche, A.; Sieskind, R.; Aubert-Kato, N.; Bredeche, N.; Bartolo, J. F.; Taly, V.; Fujii, T.; Rondelez, Y.
2016-08-01
Analog molecular circuits can exploit the nonlinear nature of biochemical reaction networks to compute low-precision outputs with fewer resources than digital circuits. This analog computation is similar to that employed by gene-regulation networks. Although digital systems have a tractable link between structure and function, the nonlinear and continuous nature of analog circuits yields an intricate functional landscape, which makes their design counter-intuitive, their characterization laborious and their analysis delicate. Here, using droplet-based microfluidics, we map with high resolution and dimensionality the bifurcation diagrams of two synthetic, out-of-equilibrium and nonlinear programs: a bistable DNA switch and a predator-prey DNA oscillator. The diagrams delineate where function is optimal, dynamics bifurcates and models fail. Inverse problem solving on these large-scale data sets indicates interference from enzymatic coupling. Additionally, data mining exposes the presence of rare, stochastically bursting oscillators near deterministic bifurcations.
High-resolution mapping of bifurcations in nonlinear biochemical circuits.
Genot, A J; Baccouche, A; Sieskind, R; Aubert-Kato, N; Bredeche, N; Bartolo, J F; Taly, V; Fujii, T; Rondelez, Y
2016-08-01
Analog molecular circuits can exploit the nonlinear nature of biochemical reaction networks to compute low-precision outputs with fewer resources than digital circuits. This analog computation is similar to that employed by gene-regulation networks. Although digital systems have a tractable link between structure and function, the nonlinear and continuous nature of analog circuits yields an intricate functional landscape, which makes their design counter-intuitive, their characterization laborious and their analysis delicate. Here, using droplet-based microfluidics, we map with high resolution and dimensionality the bifurcation diagrams of two synthetic, out-of-equilibrium and nonlinear programs: a bistable DNA switch and a predator-prey DNA oscillator. The diagrams delineate where function is optimal, dynamics bifurcates and models fail. Inverse problem solving on these large-scale data sets indicates interference from enzymatic coupling. Additionally, data mining exposes the presence of rare, stochastically bursting oscillators near deterministic bifurcations.
Fixed Point Approximation of Nonexpansive Mappings on a Nonlinear Domain
Directory of Open Access Journals (Sweden)
Safeer Hussain Khan
2014-01-01
Full Text Available We use a three-step iterative process to prove some strong and Δ-convergence results for nonexpansive mappings in a uniformly convex hyperbolic space, a nonlinear domain. Three-step iterative processes have numerous applications and hyperbolic spaces contain Banach spaces (linear domains as well as CAT(0 spaces. Thus our results can be viewed as extension and generalization of several known results in uniformly convex Banach spaces as well as CAT(0 spaces.
Numerical simulation of a solitonic gas in some integrable and non-integrable models
Dutykh, Denys
2014-01-01
The collective behaviour of soliton ensembles (i.e. the solitonic gas) is studied using the methods of the direct numerical simulation. Traditionally this problem was addressed in the context of integrable models such as the celebrated KdV equation. We extend this analysis to non-integrable KdV--BBM type models. Some high resolution numerical results are presented in both integrable and nonintegrable cases. Moreover, the free surface elevation probability distribution is shown to be quasi-stationary. Finally, we employ the asymptotic methods along with the Monte--Carlo simulations in order to study quantitatively the dependence of some important statistical characteristics (such as the kurtosis and skewness) on the Stokes--Ursell number (which measures the relative importance of nonlinear effects compared to the dispersion) and also on the magnitude of the BBM term.
On the existence of localized excitations in nonlinear hamiltonian lattices
Flach, S
1994-01-01
We consider time-periodic nonlinear localized excitations (NLEs) on one-dimensional translationally invariant Hamiltonian lattices with arbitrary finite interaction range and arbitrary finite number of degrees of freedom per unit cell. We analyse a mapping of the Fourier coefficients of the NLE solution. NLEs correspond to homoclinic points in the phase space of this map. Using dimensionality properties of separatrix manifolds of the mapping we show the persistence of NLE solutions under perturbations of the system, provided NLEs exist for the given system. For a class of nonintegrable Fermi-Pasta-Ulam chains we rigorously prove the existence of NLE solutions.
Mapping deformation method and its application to nonlinear equations
Institute of Scientific and Technical Information of China (English)
李画眉
2002-01-01
An extended mapping deformation method is proposed for finding new exact travelling wave solutions of nonlinearpartial differential equations (PDEs). The key idea of this method is to take full advantage of the simple algebraicmapping relation between the solutions of the PDEs and those of the cubic nonlinear Klein-Gordon equation. This isapplied to solve a system of variant Boussinesq equations. As a result, many explicit and exact solutions are obtained,including solitary wave solutions, periodic wave solutions, Jacobian elliptic function solutions and other exact solutions.
Nonintegrability of the Zipoy-Voorhees metric
Lukes-Gerakopoulos, Georgios
2012-08-01
The low frequency gravitational wave detectors like the evolved Laser Interferometer Space Antenna/New Gravitational Wave Observatory (eLISA/NGO) will give us the opportunity to test whether the supermassive compact objects lying at the centers of galaxies are indeed Kerr black holes. One way to do such a test is to compare the gravitational wave signals with templates of perturbed black hole spacetimes, the so-called bumpy black hole spacetimes. The Zipoy-Voorhees (ZV) spacetime (known also as the γ spacetime) can be included in the bumpy black hole family, since it can be considered as a perturbation of the Schwarzschild spacetime background. Several authors have suggested that the ZV metric corresponds to an integrable system. Contrary to this integrability conjecture, the present article shows by numerical examples that, in general, ZV belongs to the family of nonintegrable systems.
Color image encryption based on Coupled Nonlinear Chaotic Map
Energy Technology Data Exchange (ETDEWEB)
Mazloom, Sahar [Faculty of Electrical, Computer and IT Engineering, Qazvin Islamic Azad University, Qazvin (Iran, Islamic Republic of)], E-mail: sahar.mazloom@gmail.com; Eftekhari-Moghadam, Amir Masud [Faculty of Electrical, Computer and IT Engineering, Qazvin Islamic Azad University, Qazvin (Iran, Islamic Republic of)], E-mail: eftekhari@qazviniau.ac.ir
2009-11-15
Image encryption is somehow different from text encryption due to some inherent features of image such as bulk data capacity and high correlation among pixels, which are generally difficult to handle by conventional methods. The desirable cryptographic properties of the chaotic maps such as sensitivity to initial conditions and random-like behavior have attracted the attention of cryptographers to develop new encryption algorithms. Therefore, recent researches of image encryption algorithms have been increasingly based on chaotic systems, though the drawbacks of small key space and weak security in one-dimensional chaotic cryptosystems are obvious. This paper proposes a Coupled Nonlinear Chaotic Map, called CNCM, and a novel chaos-based image encryption algorithm to encrypt color images by using CNCM. The chaotic cryptography technique which used in this paper is a symmetric key cryptography with a stream cipher structure. In order to increase the security of the proposed algorithm, 240 bit-long secret key is used to generate the initial conditions and parameters of the chaotic map by making some algebraic transformations to the key. These transformations as well as the nonlinearity and coupling structure of the CNCM have enhanced the cryptosystem security. For getting higher security and higher complexity, the current paper employs the image size and color components to cryptosystem, thereby significantly increasing the resistance to known/chosen-plaintext attacks. The results of several experimental, statistical analysis and key sensitivity tests show that the proposed image encryption scheme provides an efficient and secure way for real-time image encryption and transmission.
The homotopic mapping solution for the solitary wave for a generalized nonlinear evolution equation
Institute of Scientific and Technical Information of China (English)
Mo Jia-Qi; Lin Su-Rong
2009-01-01
This paper studies a generalized nonlinear evolution equation. Using the homotopic mapping method,it constructs a corresponding homotopic mapping transform. Selecting a suitable initial approximation and using homotopic mapping,it obtains an approximate solution with an arbitrary degree of accuracy for the solitary wave. From the approximate solution obtained by using the homotopic mapping method,it possesses a good accuracy.
Synchronizing spatiotemporal chaos in the coupled map lattices using nonlinear feedback functions
Institute of Scientific and Technical Information of China (English)
FangJin－Qing; MKAli
1997-01-01
In this paper the nonlinear feedback functional method is presented for study of synchronization of spatiotemporal chaos in coupled map lattices with five connection forms.Some of nonlinear feedback functions are given.The noise effect on synchronization and sporadic nonlinear feedback are discussed.
On input/output maps for nonlinear systems via continuity in a locally convex topology
Mazumdar, Ravi R.; Kannurpatti, Raghavan; Bagchi, Arunabha
1995-01-01
In this paper we show that the output of a nonlinear system with inputs in () whose state satisfies a nonlinear differential equation with standard smoothness conditions can be written as the composition of a nonlinear map with a linear Hilbert-Schmidt operator acting on the input. The result also e
Symplectic maps from cluster algebras
Fordy, Allan
2011-01-01
We consider nonlinear recurrences generated from the iteration of maps that arise from cluster algebras. More precisely, starting from a skew-symmetric integer matrix, or its corresponding %associated quiver, one can define a set of mutation operations, as well as a set of associated cluster mutations that are applied to a set of affine coordinates (the cluster variables). Fordy and Marsh recently provided a complete classification of all such quivers that have a certain periodicity property under sequences of mutations. This periodicity implies that a suitable sequence of cluster mutations is precisely equivalent to iteration of a nonlinear recurrence relation. Here we explain briefly how to introduce a % symplectic structure in this setting, which is preserved by a corresponding birational map (possibly on a space of lower dimension). We give examples of both integrable and non-integrable maps that arise from this construction. We use algebraic entropy as an approach to classifying integrable cases. The deg...
Detecting High-Order Epistasis in Nonlinear Genotype-Phenotype Maps.
Sailer, Zachary R; Harms, Michael J
2017-03-01
High-order epistasis has been observed in many genotype-phenotype maps. These multi-way interactions between mutations may be useful for dissecting complex traits and could have profound implications for evolution. Alternatively, they could be a statistical artifact. High-order epistasis models assume the effects of mutations should add, when they could in fact multiply or combine in some other nonlinear way. A mismatch in the "scale" of the epistasis model and the scale of the underlying map would lead to spurious epistasis. In this article, we develop an approach to estimate the nonlinear scales of arbitrary genotype-phenotype maps. We can then linearize these maps and extract high-order epistasis. We investigated seven experimental genotype-phenotype maps for which high-order epistasis had been reported previously. We find that five of the seven maps exhibited nonlinear scales. Interestingly, even after accounting for nonlinearity, we found statistically significant high-order epistasis in all seven maps. The contributions of high-order epistasis to the total variation ranged from 2.2 to 31.0%, with an average across maps of 12.7%. Our results provide strong evidence for extensive high-order epistasis, even after nonlinear scale is taken into account. Further, we describe a simple method to estimate and account for nonlinearity in genotype-phenotype maps.
Institute of Scientific and Technical Information of China (English)
XING Yong-Zhong; XU Gon-gOu; LI Jun-Qing
2001-01-01
The properties of the eigenspace of nonintegrable quantum systems are explored in detail in the light of the viewpoint of quantum-classical completely correspondence proposed recently by Xu et al. The changes of the topological structure in the state space of autonomous quantum system due to the nonlinear resonance are displayed numerically with the uncertainty measure ofa special initial state ρα(λ) and the transformation matrix U ( λ + δλ, λ - δλ). The statistical behavior of the subspace occupied by the state in eigenspace of quantum nonintegrable system is discussed carefully with the help of a special renormalization method. The results show that the randomness of effective Hamiltonian matrix, the transition matrix and the nearest level spacings in this region can be described by random matrix theory. And the extent of agreement of our calculation with the prediction of GOE is in correspondence to the extent of the classical torus violation.
46 CFR 128.430 - Non-integral keel cooler installations.
2010-10-01
... 46 Shipping 4 2010-10-01 2010-10-01 false Non-integral keel cooler installations. 128.430 Section... MARINE ENGINEERING: EQUIPMENT AND SYSTEMS Design Requirements for Specific Systems § 128.430 Non-integral keel cooler installations. (a) Each hull penetration for a non-integral keel cooler installation must...
46 CFR 169.608 - Non-integral keel cooler installations
2010-10-01
... 46 Shipping 7 2010-10-01 2010-10-01 false Non-integral keel cooler installations 169.608 Section... SCHOOL VESSELS Machinery and Electrical Internal Combustion Engine Installations § 169.608 Non-integral keel cooler installations (a) Hull penetrations for non-integral keel cooler installations must be made...
Nonlinear accelerator lattices with one and two analytic invariants
Energy Technology Data Exchange (ETDEWEB)
Danilov, V.; /SNS Project, Oak Ridge; Nagaitsev, S.; /Fermilab
2010-02-01
Integrable systems appeared in physics long ago at the onset of classical dynamics with examples being Kepler's and other famous problems. Unfortunately, the majority of nonlinear problems turned out to be nonintegrable. In accelerator terms, any 2D nonlinear nonintegrable mapping produces chaotic motion and a complex network of stable and unstable resonances. Nevertheless, in the proximity of an integrable system the full volume of such a chaotic network is small. Thus, the integrable nonlinear motion in accelerators has the potential to introduce a large betatron tune spread to suppress instabilities and to mitigate the effects of space charge and magnetic field errors. To create such an accelerator lattice one has to find magnetic and electric field combinations leading to a stable integrable motion. This paper presents families of lattices with one invariant where bounded motion can be easily created in large volumes of the phase space. In addition, it presents 3 families of integrable nonlinear accelerator lattices, realizable with longitudinal-coordinate-dependent magnetic or electric fields with the stable nonlinear motion, which can be solved in terms of separable variables.
Directory of Open Access Journals (Sweden)
Elsayed Mohamed Elsayed ZAYED
2014-07-01
Full Text Available In this article, many new exact solutions of the (2+1-dimensional nonlinear Boussinesq-Kadomtsev-Petviashvili equation and the (1+1-dimensional nonlinear heat conduction equation are constructed using the Riccati equation mapping method. By means of this method, many new exact solutions are successfully obtained. This method can be applied to many other nonlinear evolution equations in mathematical physics.doi:10.14456/WJST.2014.14
NERO a code for evaluation of nonlinear resonances in 4D symplectic mappings
Todesco, Ezio; Giovannozzi, Massimo
1998-01-01
A code to evaluate the stability, the position and the width of nonlinear resonances in four-dimensional symplectic mappings is described. NERO is based on the computation of the resonant perturbative series through the use of Lie transformation implemented in the code ARES, and on the analysis of the resonant orbits of the interpolating Hamiltonian. The code is aimed at studying the nonlinear moti on of a charged particle moving in a circular accelerator under the influence of nonlinear forces.
Integrability and Non-integrability of Hamiltonian Normal Forms
Verhulst, Ferdinand
2015-01-01
This paper summarizes the present state of integrability of Hamiltonian normal forms and it aims at characterizing non-integrable behaviour in higher-dimensional systems. Non-generic behaviour in Hamiltonian systems can be a sign of integrability, but it is not a conclusive indication. We will discu
Solitary waves in a nonintegrable Fermi-Pasta-Ulam chain
Truskinovsky, Lev; Vainchtein, Anna
2014-10-01
We present a family of exact solutions describing discrete solitary waves in a nonintegrable Fermi-Pasta-Ulam chain. The family is sufficiently rich to cover the whole spectrum of known behaviors from delocalized quasicontinuum waves moving with near-sonic velocities to highly localized anticontinuum excitations with only one particle moving at a time.
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
In this paper, we extend the mapping transformation method through introducing variable coefficients.By means of the extended mapping transformation method, many explicit and exact general solutions with arbitrary functions for some nonlinear partial differential equations, which contain solitary wave solutions, trigonometric function solutions, and rational solutions, are obtained.
Energy Technology Data Exchange (ETDEWEB)
Geniet, F; Leon, J [Physique Mathematique et Theorique, CNRS-UMR 5825, 34095 Montpellier (France)
2003-05-07
A nonlinear system possessing a natural forbidden band gap can transmit energy of a signal with a frequency in the gap, as recently shown for a nonlinear chain of coupled pendulums (Geniet and Leon 2002 Phys. Rev. Lett. 89 134102). This process of nonlinear supratransmission, occurring at a threshold that is exactly predictable in many cases, is shown to have a simple experimental realization with a mechanical chain of pendulums coupled by a coil spring. It is then analysed in more detail. First we go to different (nonintegrable) systems which do sustain nonlinear supratransmission. Then a Josephson transmission line (a one-dimensional array of short Josephson junctions coupled through superconducting wires) is shown to also sustain nonlinear supratransmission, though being related to a different class of boundary conditions, and despite the presence of damping, finiteness, and discreteness. Finally, the mechanism at the origin of nonlinear supratransmission is found to be a nonlinear instability, and this is briefly discussed here.
Quad-copter UAV BLDC Motor Control: Linear v/s non-linear control maps
Directory of Open Access Journals (Sweden)
Deep Parikh
2015-08-01
Full Text Available This paper presents some investigations and comparison of using linear versus non-linear static motor-control maps for the speed control of a BLDC (Brush Less Direct Current motors used in quad-copter UAV (Unmanned Aerial Vehicles. The motor-control map considered here is the inverse of the static map relating motor-speed output to motor-voltage input for a typical out-runner type Brushless DC Motors (BLDCM. Traditionally, quad-copter BLDC motor speed control uses simple linear motor-control map defined by the motor-constant specification. However, practical BLDC motors show non-linear characteristic, particularly when operated across wide operating speed-range as is commonly required in quad-copter UAV flight operations. In this paper, our investigations to compare performance of linear versus non-linear motor-control maps are presented. The investigations cover simulation-based and experimental study of BLDC motor speed control systems for quad-copter vehicle available. First the non-linear map relating rotor RPM to motor voltage for quad-copter BLDC motor is obtained experimentally using an optical speed encoder. The performance of the linear versus non-linear motor-control-maps for the speed control are studied. The investigations also cover study of time-responses for various standard test input-signals e.g. step, ramp and pulse inputs, applied as the reference speed-commands. Also, simple 2-degree of freedom test-bed is developed in our laboratory to help test the open-loop and closed-loop experimental investigations. The non-linear motor-control map is found to perform better in BLDC motor speed tracking control performance and thereby helping achieve better quad-copter roll-angle attitude control.
Evaluation of bias associated with capture maps derived from nonlinear groundwater flow models
Nadler, Cara; Allander, Kip K.; Pohll, Greg; Morway, Eric; Naranjo, Ramon C.; Huntington, Justin
2017-01-01
The impact of groundwater withdrawal on surface water is a concern of water users and water managers, particularly in the arid western United States. Capture maps are useful tools to spatially assess the impact of groundwater pumping on water sources (e.g., streamflow depletion) and are being used more frequently for conjunctive management of surface water and groundwater. Capture maps have been derived using linear groundwater flow models and rely on the principle of superposition to demonstrate the effects of pumping in various locations on resources of interest. However, nonlinear models are often necessary to simulate head-dependent boundary conditions and unconfined aquifers. Capture maps developed using nonlinear models with the principle of superposition may over- or underestimate capture magnitude and spatial extent. This paper presents new methods for generating capture difference maps, which assess spatial effects of model nonlinearity on capture fraction sensitivity to pumping rate, and for calculating the bias associated with capture maps. The sensitivity of capture map bias to selected parameters related to model design and conceptualization for the arid western United States is explored. This study finds that the simulation of stream continuity, pumping rates, stream incision, well proximity to capture sources, aquifer hydraulic conductivity, and groundwater evapotranspiration extinction depth substantially affect capture map bias. Capture difference maps demonstrate that regions with large capture fraction differences are indicative of greater potential capture map bias. Understanding both spatial and temporal bias in capture maps derived from nonlinear groundwater flow models improves their utility and defensibility as conjunctive-use management tools.
Strong Convergence of Modified Ishikawa Iterations for Nonlinear Mappings
Indian Academy of Sciences (India)
Yongfu Su; Xiaolong Qin
2007-02-01
In this paper, we prove a strong convergence theorem of modified Ishikawa iterations for relatively asymptotically nonexpansive mappings in Banach space. Our results extend and improve the recent results by Nakajo, Takahashi, Kim, $Xu$, Matsushita and some others.
Condition Monitoring of Turbines Using Nonlinear Mapping Method
Institute of Scientific and Technical Information of China (English)
Liao Guang-lan; Shi Tie-lin; Jiang Nan
2004-01-01
Aiming at the non-linear nature of the signals generated from turbines, curvilinear component analysis (CCA), a novel nonlinear projection method that favors local topology conservation is presented for turbines conditions monitoring. This is accomplished in two steps. Time domain features are extracted from raw vibration signals, and then they are projected into a two-dimensional output space by using CCA method and form regions indicative of specific conditions, which helps classify and identify turbine states visually. Therefore, the variation of turbine conditions can be observed clearly with the trajectory of image points for the feature data in the two-dimensional space, and the occurrence and development of failures can be monitored in time.
Nonlinear Dimensionality Reduction via Path-Based Isometric Mapping
2013-01-01
Nonlinear dimensionality reduction methods have demonstrated top-notch performance in many pattern recognition and image classification tasks. Despite their popularity, they suffer from highly expensive time and memory requirements, which render them inapplicable to large-scale datasets. To leverage such cases we propose a new method called "Path-Based Isomap". Similar to Isomap, we exploit geodesic paths to find the low-dimensional embedding. However, instead of preserving pairwise geodesic ...
Sparse PDF maps for non-linear multi-resolution image operations
Hadwiger, Markus
2012-11-01
We introduce a new type of multi-resolution image pyramid for high-resolution images called sparse pdf maps (sPDF-maps). Each pyramid level consists of a sparse encoding of continuous probability density functions (pdfs) of pixel neighborhoods in the original image. The encoded pdfs enable the accurate computation of non-linear image operations directly in any pyramid level with proper pre-filtering for anti-aliasing, without accessing higher or lower resolutions. The sparsity of sPDF-maps makes them feasible for gigapixel images, while enabling direct evaluation of a variety of non-linear operators from the same representation. We illustrate this versatility for antialiased color mapping, O(n) local Laplacian filters, smoothed local histogram filters (e.g., median or mode filters), and bilateral filters. © 2012 ACM.
Coastal tomographic mapping of nonlinear tidal currents and residual currents
Zhu, Ze-Nan; Zhu, Xiao-Hua; Guo, Xinyu
2017-07-01
Depth-averaged current data, which were obtained by coastal acoustic tomography (CAT) July 12-13, 2009 in Zhitouyang Bay on the western side of the East China Sea, are used to estimate the semidiurnal tidal current (M2) as well as its first two overtide currents (M4 and M6). Spatial mean amplitude ratios M2:M4:M6 in the bay are 1.00:0.15:0.11. The shallow-water equations are used to analyze the generation mechanisms of M4 and M6. In the deep area, where water depths are larger than 60 m, M4 velocity amplitudes measured by CAT agree well with those predicted by the advection terms in the shallow water equations, indicating that M4 in the deep area is predominantly generated by the advection terms. M6 measured by CAT and M6 predicted by the nonlinear quadratic bottom friction terms agree well in the area where water depths are less than 20 m, indicating that friction mechanisms are predominant for generating M6 in the shallow area. In addition, dynamic analysis of the residual currents using the tidally averaged momentum equation shows that spatial mean values of the horizontal pressure gradient due to residual sea level and of the advection of residual currents together contribute about 75% of the spatial mean values of the advection by the tidal currents, indicating that residual currents in this bay are induced mainly by the nonlinear effects of tidal currents. This is the first ever nonlinear tidal current study by CAT.
Generic convergence of iterates for a class of nonlinear mappings
Directory of Open Access Journals (Sweden)
Alexander J. Zaslavski
2004-08-01
Full Text Available Let K be a nonempty, bounded, closed, and convex subset of a Banach space. We show that the iterates of a typical element (in the sense of Baire's categories of a class of continuous self-mappings of K converge uniformly on K to the unique fixed point of this typical element.
Hooker, John C.
1990-01-01
A preliminary study of the applicability of nonlinear dynamic systems analysis techniques to low body negative pressure (LBNP) studies. In particular, the applicability of the heart rate delay map is investigated. It is suggested that the heart rate delay map has potential as a supplemental tool in the assessment of subject performance in LBNP tests and possibly in the determination of susceptibility to cardiovascular deconditioning with spaceflight.
NERO: a code for the nonlinear evaluation of resonances in one-turn mappings
Todesco, E.; Gemmi, M.; Giovannozzi, M.
1997-10-01
We describe a code that evaluates the stability, the position and the width of resonances in four-dimensional symplectic mappings. The code is based on the computation of the resonant perturbative series through the program ARES, and on the analysis of the resonant orbits of the interpolating Hamiltonian. The code is dedicated to the study and to the comparison of the nonlinear behaviour in one-turn betatronic maps.
Dynamics of a Skew Tent Map in the Nonlinear Frobenius-Perron Equation
Katsuragi, Daisuke
Return maps of the mean field in globally coupled map lattices (GCML) with a large system size were compared with those at the limit in a large system size. We adopted a nonlinear Frobenius-Perron equation (NFPE) for the limit in the large system size, and used a skew tent map as a chaotic map to simplify calculations in the NFPE. The return maps of the mean field for direct numerical calculations in the GCML usually fluctuate from those for numerical calculations in the NFPE. However, at some coupling strengths, there are totally different return maps between the GCML and the NFPE. We show that this strongly depends on the initial conditions at some coupling strengths.
Nonlinear Algorithms for Channel Equalization and Map Symbol Detection.
Giridhar, K.
The transfer of information through a communication medium invariably results in various kinds of distortion to the transmitted signal. In this dissertation, a feed -forward neural network-based equalizer, and a family of maximum a posteriori (MAP) symbol detectors are proposed for signal recovery in the presence of intersymbol interference (ISI) and additive white Gaussian noise. The proposed neural network-based equalizer employs a novel bit-mapping strategy to handle multilevel data signals in an equivalent bipolar representation. It uses a training procedure to learn the channel characteristics, and at the end of training, the multilevel symbols are recovered from the corresponding inverse bit-mapping. When the channel characteristics are unknown and no training sequences are available, blind estimation of the channel (or its inverse) and simultaneous data recovery is required. Convergence properties of several existing Bussgang-type blind equalization algorithms are studied through computer simulations, and a unique gain independent approach is used to obtain a fair comparison of their rates of convergence. Although simple to implement, the slow convergence of these Bussgang-type blind equalizers make them unsuitable for many high data-rate applications. Rapidly converging blind algorithms based on the principle of MAP symbol-by -symbol detection are proposed, which adaptively estimate the channel impulse response (CIR) and simultaneously decode the received data sequence. Assuming a linear and Gaussian measurement model, the near-optimal blind MAP symbol detector (MAPSD) consists of a parallel bank of conditional Kalman channel estimators, where the conditioning is done on each possible data subsequence that can convolve with the CIR. This algorithm is also extended to the recovery of convolutionally encoded waveforms in the presence of ISI. Since the complexity of the MAPSD algorithm increases exponentially with the length of the assumed CIR, a suboptimal
Quad-copter UAV BLDC Motor Control: Linear v/s non-linear control maps
Deep Parikh; Jignesh Patel; Jayesh Barve
2015-01-01
This paper presents some investigations and comparison of using linear versus non-linear static motor-control maps for the speed control of a BLDC (Brush Less Direct Current) motors used in quad-copter UAV (Unmanned Aerial Vehicles). The motor-control map considered here is the inverse of the static map relating motor-speed output to motor-voltage input for a typical out-runner type Brushless DC Motors (BLDCM). Traditionally, quad-copter BLDC motor speed control uses simple linear motor-cont...
Wang, Sijia; Peterson, Daniel J.; Gatenby, J. C.; Li, Wenbin; Grabowski, Thomas J.; Madhyastha, Tara M.
2017-01-01
Correction of echo planar imaging (EPI)-induced distortions (called “unwarping”) improves anatomical fidelity for diffusion magnetic resonance imaging (MRI) and functional imaging investigations. Commonly used unwarping methods require the acquisition of supplementary images during the scanning session. Alternatively, distortions can be corrected by nonlinear registration to a non-EPI acquired structural image. In this study, we compared reliability using two methods of unwarping: (1) nonlinear registration to a structural image using symmetric normalization (SyN) implemented in Advanced Normalization Tools (ANTs); and (2) unwarping using an acquired field map. We performed this comparison in two different test-retest data sets acquired at differing sites (N = 39 and N = 32). In both data sets, nonlinear registration provided higher test-retest reliability of the output fractional anisotropy (FA) maps than field map-based unwarping, even when accounting for the effect of interpolation on the smoothness of the images. In general, field map-based unwarping was preferable if and only if the field maps were acquired optimally.
Analytical description of critical dynamics for two-dimensional dissipative nonlinear maps
Energy Technology Data Exchange (ETDEWEB)
Méndez-Bermúdez, J.A. [Instituto de Física, Benemérita Universidad Autónoma de Puebla, Apartado Postal J-48, Puebla 72570 (Mexico); Oliveira, Juliano A. de [UNESP – Univ. Estadual Paulista, Câmpus de São João da Boa Vista, Av. Professora Isette Corrêa Fontão, 505, Jardim Santa Rita das Areias, 13876-750 São João da Boa Vista, SP (Brazil); Leonel, Edson D. [Departamento de Física, UNESP – Univ. Estadual Paulista, Av. 24A, 1515, Bela Vista, 13506-900 Rio Claro, SP (Brazil); Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34151 Trieste (Italy)
2016-05-20
The critical dynamics near the transition from unlimited to limited action diffusion for two families of well known dissipative nonlinear maps, namely the dissipative standard and dissipative discontinuous maps, is characterized by the use of an analytical approach. The approach is applied to explicitly obtain the average squared action as a function of the (discrete) time and the parameters controlling nonlinearity and dissipation. This allows to obtain a set of critical exponents so far obtained numerically in the literature. The theoretical predictions are verified by extensive numerical simulations. We conclude that all possible dynamical cases, independently on the map parameter values and initial conditions, collapse into the universal exponential decay of the properly normalized average squared action as a function of a normalized time. The formalism developed here can be extended to many other different types of mappings therefore making the methodology generic and robust. - Highlights: • We analytically approach scaling properties of a family of two-dimensional dissipative nonlinear maps. • We derive universal scaling functions that were obtained before only approximately. • We predict the unexpected condition where diffusion and dissipation compensate each other exactly. • We find a new universal scaling function that embraces all possible dissipative behaviors.
46 CFR 182.422 - Integral and non-integral keel cooler installations.
2010-10-01
... 46 Shipping 7 2010-10-01 2010-10-01 false Integral and non-integral keel cooler installations. 182... VESSELS (UNDER 100 GROSS TONS) MACHINERY INSTALLATION Specific Machinery Requirements § 182.422 Integral and non-integral keel cooler installations. (a) A keel cooler installation used for engine cooling...
46 CFR 119.422 - Integral and non-integral keel cooler installations.
2010-10-01
... 46 Shipping 4 2010-10-01 2010-10-01 false Integral and non-integral keel cooler installations. 119... MACHINERY INSTALLATION Specific Machinery Requirements § 119.422 Integral and non-integral keel cooler... connections for a keel cooler installation. (e) Shutoff valves are not required for integral keel coolers. A...
Imprint of non-linear effects on HI intensity mapping on large scales
Umeh, Obinna
2016-01-01
Intensity mapping of the HI brightness temperature provides a unique way of tracing large-scale structures of the Universe up to the largest possible scales. This is achieved by using a low angular resolution radio telescopes to detect emission line from cosmic neutral Hydrogen in the post-reionization Universe. We consider how non-linear effects associated with the HI bias and redshift space distortions contribute to the clustering of cosmic neutral Hydrogen on large scales. We use general relativistic perturbation theory techniques to derive for the first time the full expression for the HI brightness temperature up to third order in perturbation theory without making any plane-parallel approximation. We use this result to show how mode coupling at nonlinear order due to nonlinear bias parameters and redshift space distortions leads to about 10\\% modulation of the HI power spectrum on large scales.
Imprint of non-linear effects on HI intensity mapping on large scales
Umeh, Obinna
2017-06-01
Intensity mapping of the HI brightness temperature provides a unique way of tracing large-scale structures of the Universe up to the largest possible scales. This is achieved by using a low angular resolution radio telescopes to detect emission line from cosmic neutral Hydrogen in the post-reionization Universe. We use general relativistic perturbation theory techniques to derive for the first time the full expression for the HI brightness temperature up to third order in perturbation theory without making any plane-parallel approximation. We use this result and the renormalization prescription for biased tracers to study the impact of nonlinear effects on the power spectrum of HI brightness temperature both in real and redshift space. We show how mode coupling at nonlinear order due to nonlinear bias parameters and redshift space distortion terms modulate the power spectrum on large scales. The large scale modulation may be understood to be due to the effective bias parameter and effective shot noise.
Block and parallel modelling of broad domain nonlinear continuous mapping based on NN
Institute of Scientific and Technical Information of China (English)
Yang Guowei; Tu Xuyan; Wang Shoujue
2006-01-01
The necessity of the use of the block and parallel modeling of the nonlinear continuous mappings with NN is firstly expounded quantitatively. Then, a practical approach for the block and parallel modeling of the nonlinear continuous mappings with NN is proposed. Finally, an example indicating that the method raised in this paper can be realized by suitable existed software is given. The results of the experiment of the model discussed on the 3-D Mexican straw hat indicate that the block and parallel modeling based on NN is more precise and faster in computation than the direct ones and it is obviously a concrete example and the development of the large-scale general model established by Tu Xuyan.
Self-mapping the longitudinal field structure of a nonlinear plasma accelerator cavity.
Clayton, C E; Adli, E; Allen, J; An, W; Clarke, C I; Corde, S; Frederico, J; Gessner, S; Green, S Z; Hogan, M J; Joshi, C; Litos, M; Lu, W; Marsh, K A; Mori, W B; Vafaei-Najafabadi, N; Xu, X; Yakimenko, V
2016-08-16
The preservation of emittance of the accelerating beam is the next challenge for plasma-based accelerators envisioned for future light sources and colliders. The field structure of a highly nonlinear plasma wake is potentially suitable for this purpose but has not been yet measured. Here we show that the longitudinal variation of the fields in a nonlinear plasma wakefield accelerator cavity produced by a relativistic electron bunch can be mapped using the bunch itself as a probe. We find that, for much of the cavity that is devoid of plasma electrons, the transverse force is constant longitudinally to within ±3% (r.m.s.). Moreover, comparison of experimental data and simulations has resulted in mapping of the longitudinal electric field of the unloaded wake up to 83 GV m(-1) to a similar degree of accuracy. These results bode well for high-gradient, high-efficiency acceleration of electron bunches while preserving their emittance in such a cavity.
Self-mapping the longitudinal field structure of a nonlinear plasma accelerator cavity
Clayton, C. E.; Adli, E.; Allen, J.; An, W.; Clarke, C. I.; Corde, S.; Frederico, J.; Gessner, S.; Green, S. Z.; Hogan, M. J.; Joshi, C.; Litos, M.; Lu, W.; Marsh, K. A.; Mori, W. B.; Vafaei-Najafabadi, N.; Xu, X.; Yakimenko, V.
2016-08-01
The preservation of emittance of the accelerating beam is the next challenge for plasma-based accelerators envisioned for future light sources and colliders. The field structure of a highly nonlinear plasma wake is potentially suitable for this purpose but has not been yet measured. Here we show that the longitudinal variation of the fields in a nonlinear plasma wakefield accelerator cavity produced by a relativistic electron bunch can be mapped using the bunch itself as a probe. We find that, for much of the cavity that is devoid of plasma electrons, the transverse force is constant longitudinally to within +/-3% (r.m.s.). Moreover, comparison of experimental data and simulations has resulted in mapping of the longitudinal electric field of the unloaded wake up to 83 GV m-1 to a similar degree of accuracy. These results bode well for high-gradient, high-efficiency acceleration of electron bunches while preserving their emittance in such a cavity.
Frequency map analysis of resonances in a nonlinear lattice with space charge
Energy Technology Data Exchange (ETDEWEB)
Turchetti, G. E-mail: turchetti@bo.infn.it; Bazzani, A.; Bergamini, F.; Rambaldi, S.; Hofmann, I.; Bongini, L.; Franchetti, G
2001-05-21
In storage rings for heavy ion fusion beam losses must be minimized. During bunch compression high space charge is reached and the reciprocal effects between the collective modes of the beam and the single particle lattice nonlinearities must be considered to understand the problem of resonance crossing and halo formation. We show that the frequency map analysis of particle in core models gives an adequate description of the resonance network and of the chaotic regions where the halo particles can diffuse.
A new mapping method and its applications to nonlinear partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Zeng Xin [Department of Mathematics, Zhengzhou University, Zhengzhou 450052 (China)], E-mail: zeng79723@163.com; Yong Xuelin [Department of Mathematics and Physics, North China Electric Power University, Beijing 102206 (China)
2008-10-27
In this Letter, a new mapping method is proposed for constructing more exact solutions of nonlinear partial differential equations. With the aid of symbolic computation, we choose the (2+1)-dimensional Konopelchenko-Dubrovsky equation and the (2+1)-dimensional KdV equations to illustrate the validity and advantages of the method. As a result, many new and more general exact solutions are obtained.
Nonlinear Maps for Design of Discrete-Time Models of Neuronal Network Dynamics
2016-03-31
responsive tiring patterns . We propose to use modern DSP ideas to develop new efficient approaches to the design of such discrete-time models for...2016 Performance/Technic~ 03-01-2016- 03-31-2016 4. TITLE AND SUBTITLE Sa. CONTRACT NUMBER Nonlinear Maps for Design of Discrete-Time Models of...simulations is to design a neuronal model in the form of difference equations that generates neuronal states in discrete moments of time. In this
AxiSketcher: Interactive Nonlinear Axis Mapping of Visualizations through User Drawings.
Kwon, Bum Chul; Kim, Hannah; Wall, Emily; Choo, Jaegul; Park, Haesun; Endert, Alex
2017-01-01
Visual analytics techniques help users explore high-dimensional data. However, it is often challenging for users to express their domain knowledge in order to steer the underlying data model, especially when they have little attribute-level knowledge. Furthermore, users' complex, high-level domain knowledge, compared to low-level attributes, posits even greater challenges. To overcome these challenges, we introduce a technique to interpret a user's drawings with an interactive, nonlinear axis mapping approach called AxiSketcher. This technique enables users to impose their domain knowledge on a visualization by allowing interaction with data entries rather than with data attributes. The proposed interaction is performed through directly sketching lines over the visualization. Using this technique, users can draw lines over selected data points, and the system forms the axes that represent a nonlinear, weighted combination of multidimensional attributes. In this paper, we describe our techniques in three areas: 1) the design space of sketching methods for eliciting users' nonlinear domain knowledge; 2) the underlying model that translates users' input, extracts patterns behind the selected data points, and results in nonlinear axes reflecting users' complex intent; and 3) the interactive visualization for viewing, assessing, and reconstructing the newly formed, nonlinear axes.
The non-integrability of the Zipoy-Voorhees metric
Lukes-Gerakopoulos, Georgios
2012-01-01
The low frequency gravitational wave detectors like eLISA/NGO will give us the opportunity to test whether the supermassive compact objects lying at the centers of galaxies are indeed Kerr black holes. A way to do such a test is to compare the gravitational wave signals with templates of perturbed black hole spacetimes, the so-called bumpy black hole spacetimes. The Zipoy-Voorhees (ZV) spacetime (known also as the $\\gamma$ spacetime) can be included in the bumpy black hole family, because it can be considered as a perturbation of the Schwarzschild spacetime background. Several authors have suggested that the ZV metric corresponds to an integrable system. Contrary to this integrability conjecture, in the present article it is shown by numerical examples that in general ZV belongs to the family of non-integrable systems.
Non-integral dimensions ultrasonic phased arrays in a borehole
Institute of Scientific and Technical Information of China (English)
ZHANG Bixing; ZHANG Chengguang; Deng Fangqing
2009-01-01
The non-integral dimensions ultrasonic phased arrays and their scanning and test-ing methods in a borehole are studied. First, the focusing acoustic fields excited by the 1.25D, 1.5D, and 1.75D phased arrays are analyzed, and then the imaging resolution in the elevation direction and the influence of the dynamic elements are investigated. Second, the focusing and deflexion characteristics of the acoustic fields excited by the annular and segmented annular phased arrays are studied, and they are compared with those excited by the 2D surface array. The application method of the 1.25D, 1.5D, and 1.75D, annular and segmented annular phased arrays in acoustic logging are analyzed and discussed. It provides a theoretical foundation for the application of the ultrasonic phased arrays in acoustic logging.
On thermalization in a nonintegrable quantum system: who thermalizes?
Kim, Hyungwon; Banuls, Mari Carmen; Huse, David; Cirac, Ignacio
2014-03-01
We study properties of local operators with a nonintegrable Hamiltonian. We look for the cases where non-thermal (nonequilibrium) behaviors may be persistent even in the long time limit. First, we consider eigenstates which do not obey the Eigenstate Thermalization Hypothesis (ETH) in a finite size system. We show that the expectation values of local observable of these ``outliers'' converge to the scenario of ETH as we increase the system size. Next, we construct a local operator that gives the smallest value of commutator with the Hamiltonian. As we increase the range of the operator, the commutator quickly decreases with the range. This may imply the existence of local operators which may take fairly long to thermalize.
Wang, X.; Zheng, G. T.
2016-02-01
A simple and general Equivalent Dynamic Stiffness Mapping technique is proposed for identifying the parameters or the mathematical model of a nonlinear structural element with steady-state primary harmonic frequency response functions (FRFs). The Equivalent Dynamic Stiffness is defined as the complex ratio between the internal force and the displacement response of unknown element. Obtained with the test data of responses' frequencies and amplitudes, the real and imaginary part of Equivalent Dynamic Stiffness are plotted as discrete points in a three dimensional space over the displacement amplitude and the frequency, which are called the real and the imaginary Equivalent Dynamic Stiffness map, respectively. These points will form a repeatable surface as the Equivalent Dynamic stiffness is only a function of the corresponding data as derived in the paper. The mathematical model of the unknown element can then be obtained by surface-fitting these points with special functions selected by priori knowledge of the nonlinear type or with ordinary polynomials if the type of nonlinearity is not pre-known. An important merit of this technique is its capability of dealing with strong nonlinearities owning complicated frequency response behaviors such as jumps and breaks in resonance curves. In addition, this technique could also greatly simplify the test procedure. Besides there is no need to pre-identify the underlying linear parameters, the method uses the measured data of excitation forces and responses without requiring a strict control of the excitation force during the test. The proposed technique is demonstrated and validated with four classical single-degree-of-freedom (SDOF) numerical examples and one experimental example. An application of this technique for identification of nonlinearity from multiple-degree-of-freedom (MDOF) systems is also illustrated.
Automated, non-linear registration between 3-dimensional brain map and medical head image
Energy Technology Data Exchange (ETDEWEB)
Mizuta, Shinobu; Urayama, Shin-ichi; Zoroofi, R.A.; Uyama, Chikao [National Cardiovascular Center, Suita, Osaka (Japan)
1998-05-01
In this paper, we propose an automated, non-linear registration method between 3-dimensional medical head image and brain map in order to efficiently extract the regions of interest. In our method, input 3-dimensional image is registered into a reference image extracted from a brain map. The problems to be solved are automated, non-linear image matching procedure, and cost function which represents the similarity between two images. Non-linear matching is carried out by dividing the input image into connected partial regions, transforming the partial regions preserving connectivity among the adjacent images, evaluating the image similarity between the transformed regions of the input image and the correspondent regions of the reference image, and iteratively searching the optimal transformation of the partial regions. In order to measure the voxelwise similarity of multi-modal images, a cost function is introduced, which is based on the mutual information. Some experiments using MR images presented the effectiveness of the proposed method. (author)
Directory of Open Access Journals (Sweden)
Ebrahim Parcham
2014-07-01
Full Text Available Classifying similar images is one of the most interesting and essential image processing operations. Presented methods have some disadvantages like: low accuracy in analysis step and low speed in feature extraction process. In this paper, a new method for image classification is proposed in which similarity weight is revised by means of information in related and unrelated images. Based on researchers’ idea, most of real world similarity measurement systems are nonlinear. Thus, traditional linear methods are not capable of recognizing nonlinear relationship and correlation in such systems. Undoubtedly, Self Organizing Map neural networks are strongest networks for data mining and nonlinear analysis of sophisticated spaces purposes. In our proposed method, we obtain images with the most similarity measure by extracting features of our target image and comparing them with the features of other images. We took advantage of NLPCA algorithm for feature extraction which is a nonlinear algorithm that has the ability to recognize the smallest variations even in noisy images. Finally, we compare the run time and efficiency of our proposed method with previous proposed methods.
Institute of Scientific and Technical Information of China (English)
LI Hua-Mei
2003-01-01
In this paper, we extend the mapping deformation method proposed by Lou. It is used to find new exacttravelling wave solutions of nonlinear partial differential equation or coupled nonlinear partial differential equations(PDEs). Based on the idea of the homogeneous balance method, we construct the general mapping relation betweenthe solutions of the PDEs and those of the cubic nonlinear Klein-Gordon (NKG) equation. By using this relation andthe abundant solutions of the cubic NKG equation, many explicit and exact travelling wave solutions of three systemsof coupled PDEs, which contain solitary wave solutions, trigonometric function solutions, Jacobian elliptic functionsolutions, and rational solutions, are obtained.
A large U3 deletion causes increased in vivo expression from a nonintegrating lentiviral vector.
Bayer, Matthew; Kantor, Boris; Cockrell, Adam; Ma, Hong; Zeithaml, Brian; Li, Xiangping; McCown, Thomas; Kafri, Tal
2008-12-01
The feasibility of using nonintegrating lentiviral vectors has been demonstrated by recent studies showing their ability to maintain transgene expression both in vitro and in vivo. Furthermore, human immunodeficiency virus-1 (HIV-1) vectors packaged with a mutated integrase were able to correct retinal disease in a mouse model. Interestingly, these results differ from earlier studies in which first-generation nonintegrating lentiviral vectors yielded insignificant levels of transduction. However, to date, a rigorous characterization of transgene expression from the currently used self-inactivating (SIN) nonintegrating lentiviral vectors has not been published. In this study, we characterize transgene expression from SIN nonintegrating lentiviral vectors. Overall, we found that nonintegrating vectors express transgenes at a significantly lower level than their integrating counterparts. Expression from nonintegrating vectors was improved upon introducing a longer deletion in the vector's U3 region. A unique shuttle-vector assay indicated that the relative abundance of the different episomal forms was not altered by the longer U3 deletion. Interestingly, the longer U3 deletion did not enhance expression in the corpus callosum of the rat brain, suggesting that the extent of silencing of episomal transcription is influenced by tissue-specific factors. Finally, and for the first time, episomal expression in the mouse liver was potent and sustained.
Nonlinear Maps for Design of Discrete Time Models of Neuronal Network Dynamics
2016-02-29
and K+ pumps responsible for generation of action potential (spike). This map is of the form Xn+l = fa(Xn, y), where Xn is a dynamical variable and...function fa(. . ) is a piecewise nonlinear function containing three segments . In the original form the function is { a 1 + y, Xn ~ 0, fa(Xn,y...a~~~ 0 < Xn <a+ y and Xn-1 ~ 0, -1, Xn 2:: a+ y or Xn- 1 > 0, where variable Xn_ 1 is used to define a condition that prevents system to remain at
The new integrable symplectic map and the symmetry of integrable nonlinear lattice equation
Dong, Huanhe; Zhang, Yong; Zhang, Xiaoen
2016-07-01
A discrete matrix spectral problem is presented and the hierarchy of discrete integrable systems is derived. Their Hamiltonian structures are established. As to the discrete integrable system, nonlinearization of the spatial parts of the Lax pairs and the adjoint Lax pairs generate a new integrable symplectic map. Based on the theory, a new integrable symplectic map and a family of finite-dimension completely integrable systems are given. Especially, two explicit equations are obtained under the Bargmann constraint. Finally, the symmetry of the discrete equation is provided according to the recursion operator and the seed symmetry. Although the solutions of the discrete equations have been gained by many methods, there are few articles that solving the discrete equation via the symmetry. So the solution of the discrete lattice equation is obtained through the symmetry theory.
Directory of Open Access Journals (Sweden)
Lin Liang
2015-01-01
Full Text Available A new method for extracting the low-dimensional feature automatically with self-organization mapping manifold is proposed for the detection of rotating mechanical nonlinear faults (such as rubbing, pedestal looseness. Under the phase space reconstructed by single vibration signal, the self-organization mapping (SOM with expectation maximization iteration algorithm is used to divide the local neighborhoods adaptively without manual intervention. After that, the local tangent space alignment algorithm is adopted to compress the high-dimensional phase space into low-dimensional feature space. The proposed method takes advantages of the manifold learning in low-dimensional feature extraction and adaptive neighborhood construction of SOM and can extract intrinsic fault features of interest in two dimensional projection space. To evaluate the performance of the proposed method, the Lorenz system was simulated and rotation machinery with nonlinear faults was obtained for test purposes. Compared with the holospectrum approaches, the results reveal that the proposed method is superior in identifying faults and effective for rotating machinery condition monitoring.
Finding zeros of nonlinear functions using the hybrid parallel cell mapping method
Xiong, Fu-Rui; Schütze, Oliver; Ding, Qian; Sun, Jian-Qiao
2016-05-01
Analysis of nonlinear dynamical systems including finding equilibrium states and stability boundaries often leads to a problem of finding zeros of vector functions. However, finding all the zeros of a set of vector functions in the domain of interest is quite a challenging task. This paper proposes a zero finding algorithm that combines the cell mapping methods and the subdivision techniques. Both the simple cell mapping (SCM) and generalized cell mapping (GCM) methods are used to identify a covering set of zeros. The subdivision technique is applied to enhance the solution resolution. The parallel implementation of the proposed method is discussed extensively. Several examples are presented to demonstrate the application and effectiveness of the proposed method. We then extend the study of finding zeros to the problem of finding stability boundaries of potential fields. Examples of two and three dimensional potential fields are studied. In addition to the effectiveness in finding the stability boundaries, the proposed method can handle several millions of cells in just a few seconds with the help of parallel computing in graphics processing units (GPUs).
Theory and praxis of map analsys in CHEF part 2: Nonlinear normal form
Energy Technology Data Exchange (ETDEWEB)
Michelotti, Leo; /FERMILAB
2009-04-01
This is the second of three memos describing how normal form map analysis is implemented in CHEF. The first [1] explained the manipulations required to assure that initial, linear transformations preserved Poincare invariants, thereby confirming correct normalization of action-angle coordinates. In this one, the transformation will be extended to nonlinear terms. The third, describing how the algorithms were implemented within the software of CHEF's libraries, most likely will never be written. The first section, Section 2, quickly lays out preliminary concepts and relationships. In Section 3, we shall review the perturbation theory - an iterative sequence of transformations that converts a nonlinear mapping into its normal form - and examine the equation which moves calculations from one step to the next. Following that is a section titled 'Interpretation', which identifies connections between the normalized mappings and idealized, integrable, fictitious Hamiltonian models. A final section contains closing comments, some of which may - but probably will not - preview work to be done later. My reasons for writing this memo and its predecessor have already been expressed. [1] To them can be added this: 'black box code' encourages users to proceed with little or no understanding of what it does or how it operates. So far, CHEF has avoided this trap admirably by failing to attract potential users. However, we reached a watershed last year: even I now have difficulty following the software through its maze of operations. Extensions to CHEF's physics functionalities, software upgrades, and even simple maintenance are becoming more difficult than they should. I hope these memos will mark parts of the maze for easier navigation in the future. Despite appearances to the contrary, I tried to include no (or very little) more than the minimum needed to understand what CHEF's nonlinear analysis modules do.1 As with the first memo, material
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.
Wu, Tsai-Chin; Anderson, Rae
We use active microrheology coupled to single-molecule fluorescence imaging to elucidate the microscale dynamics of entangled DNA. DNA naturally exists in a wide range of lengths and topologies, and is often confined in cell nucleui, forming highly concentrated and entangled biopolymer networks. Thus, DNA is the model polymer for understanding entangled polymer dynamics as well as the crowded environment of cells. These networks display complex viscoelastic properties that are not well understood, especially at the molecular-level and in response to nonlinear perturbations. Specifically, how microscopic stresses and strains propagate through entangled networks, and what molecular deformations lead to the network stress responses are unknown. To answer these important questions, we optically drive a microsphere through entangled DNA, perturbing the system far from equilibrium, while measuring the resistive force the DNA exerts on the bead during and after bead motion. We simultaneously image single fluorescent-labeled DNA molecules throughout the network to directly link the microscale stress response to molecular deformations. We characterize the deformation of the network from the molecular-level to the mesoscale, and map the stress propagation throughout the network. We further study the impact of DNA length (11 - 115 kbp) and topology (linear vs ring DNA) on deformation and propagation dynamics, exploring key nonlinear features such as tube dilation and power-law relaxation.
Kantor, Boris; Bayer, Matthew; Ma, Hong; Samulski, Jude; Li, Chengwen; McCown, Thomas; Kafri, Tal
2011-03-01
Nonintegrating lentiviral vectors present a means of reducing the risk of insertional mutagenesis in nondividing cells and enabling short-term expression of potentially hazardous gene products. However, residual, integrase-independent integration raises a concern that may limit the usefulness of this system. Here we present a novel 3' polypurine tract (PPT)-deleted lentiviral vector that demonstrates impaired integration efficiency and, when packaged into integrase-deficient particles, significantly reduced illegitimate integration. Cells transduced with PPT-deleted vectors exhibited predominantly 1-long terminal repeat (LTR) circles and a low level of linear genomes after reverse transcription (RT). Importantly, the PPT-deleted vector exhibited titers and in vitro and in vivo expression levels matching those of conventional nonintegrating lentiviral vectors. This safer nonintegrating lentiviral vector system will support emerging technologies, such as those based on transient expression of zinc-finger nucleases (ZFNs) for gene editing, as well as reprogramming factors for inducing pluripotency.
Scaling properties of a simplified bouncer model and of Chirikov's standard map
Energy Technology Data Exchange (ETDEWEB)
Ladeira, Denis Gouvea; Silva, Jafferson Kamphorst Leal da [Departamento de FIsica, ICEx, Universidade Federal de Minas Gerais (UFMG), CP 702, 30.123-970 Belo Horizonte, MG (Brazil)
2007-09-21
Scaling properties of Chirikov's standard map are investigated by studying the average value of I{sup 2}, where I is the action variable, for initial conditions in (a) the stability island and (b) the chaotic component. Scaling behavior appears in three regimes, defined by the value of the control parameter K: (i) the integrable to non-integrable transition (K {approx} 0) and K < K{sub c} (K{sub c} {approx} 0.9716); (ii) the transition from limited to unlimited growth of I{sup 2}, K {approx}> K{sub c}; (iii) the regime of strong nonlinearity, K >> K{sub c}. Our scaling results are also applicable to Pustylnikov's bouncer model, since it is globally equivalent to the standard map. We also describe the scaling properties of a stochastic version of the standard map, which exhibits unlimited growth of I{sup 2} even for small values of K.
A Robust Hash Function Using Cross-Coupled Chaotic Maps with Absolute-Valued Sinusoidal Nonlinearity
Directory of Open Access Journals (Sweden)
Wimol San-Um
2016-01-01
Full Text Available This paper presents a compact and effective chaos-based keyed hash function implemented by a cross-coupled topology of chaotic maps, which employs absolute-value of sinusoidal nonlinearity, and offers robust chaotic regions over broad parameter spaces with high degree of randomness through chaoticity measurements using the Lyapunov exponent. Hash function operations involve an initial stage when the chaotic map accepts initial conditions and a hashing stage that accepts input messages and generates the alterable-length hash values. Hashing performances are evaluated in terms of original message condition changes, statistical analyses, and collision analyses. The results of hashing performances show that the mean changed probabilities are very close to 50%, and the mean number of bit changes is also close to a half of hash value lengths. The collision tests reveal the mean absolute difference of each character values for the hash values of 128, 160 and 256 bits are close to the ideal value of 85.43. The proposed keyed hash function enhances the collision resistance, comparing to MD5 and SHA1, and the other complicated chaos-based approaches. An implementation of hash function Android application is demonstrated.
Directory of Open Access Journals (Sweden)
Qiaomei Su
2017-07-01
Full Text Available Landslide susceptibility mapping is the first and most important step involved in landslide hazard assessment. The purpose of the present study is to compare three nonlinear approaches for landslide susceptibility mapping and test whether coal mining has a significant impact on landslide occurrence in coal mine areas. Landslide data collected by the Bureau of Land and Resources are represented by the X, Y coordinates of its central point; causative factors were calculated from topographic and geologic maps, as well as satellite imagery. The five-fold cross-validation method was adopted and the landslide/non-landslide datasets were randomly split into a ratio of 80:20. From this, five subsets for 20 times were acquired for training and validating models by GIS Geostatistical analysis methods, and all of the subsets were employed in a spatially balanced sample design. Three landslide models were built using support vector machine (SVM, logistic regression (LR, and artificial neural network (ANN models by selecting the median of the performance measures. Then, the three fitted models were compared using the area under the receiver operating characteristics (ROC curves (AUC and the performance measures. The results show that the prediction accuracies are between 73.43% and 87.45% in the training stage, and 67.16% to 73.13% in the validating stage for the three models. AUCs vary from 0.807 to 0.906 and 0.753 to 0.944 in the two stages, respectively. Additionally, three landslide susceptibility maps were obtained by classifying the range of landslide probabilities into four classes representing low (0–0.02, medium (0.02–0.1, high (0.1–0.85, and very high (0.85–1 probabilities of landslides. For the distributions of landslide and area percentages under different susceptibility standards, the SVM model has more relative balance in the four classes compared to the LR and the ANN models. The result reveals that the SVM model possesses better
Romanov, Dmitri; Smith, Stanley; Brady, John; Levis, Robert J.
2008-02-01
We have studied the application of the diffusion mapping technique to dimensionality reduction and clustering in multidimensional optical datasets. The combinational (input-output) data were obtained by sampling search spaces related to optimization of a nonlinear physical process, short-pulse second harmonic generation. The diffusion mapping technique hierarchically reduces the dimensionality of the data set and unifies the statistics of input (the pulse shape) and output (the integral output intensity) parameters. The information content of the emerging clustered pattern can be optimized by modifying the parameters of the mapping procedure. The low-dimensional pattern captures essential features of the nonlinear process, based on a finite sampling set. In particular, the apparently parabolic two-dimensional projection of this pattern exhibits regular evolution with the increase of higher-intensity data in the sampling set. The basic shape of the pattern and the evolution are relatively insensitive to the size of the sampling set, as well as to the details of the mapping procedure. Moreover, the experimental data sets and the sets produced numerically on the basis of a theoretical model are mapped into patterns of remarkable similarity (as quantified by the similarity of the related quadratic-form coefficients). The diffusion mapping method is robust and capable of predicting higher-intensity points from a set of low-intensity points. With these attractive features, diffusion mapping stands poised to become a helpful statistical tool for preprocessing analysis of vast and multidimensional combinational optical datasets.
The Quench Map in an Integrable Classical Field Theory: Nonlinear Schr\\"odinger Equation
Caudrelier, Vincent
2016-01-01
We study the non-equilibrium dynamics obtained by an abrupt change (a {\\em quench}) in the parameters of an integrable classical field theory, the nonlinear Schr\\"odinger equation. We first consider explicit one-soliton examples, which we fully describe by solving the direct part of the inverse scattering problem. We then develop some aspects of the general theory using elements of the inverse scattering method. For this purpose, we introduce the {\\em quench map} which acts on the space of scattering data and represents the change of parameter with fixed field configuration (initial condition). We describe some of its analytic properties by implementing a higher level version of the inverse scattering method, and we discuss the applications of Darboux-B\\"acklund transformations, Gelfand-Levitan-Marchenko equations and the Rosales series solution to a related, dual quench problem. Finally, we comment on the interplay between quantum and classical tools around the theme of quenches and on the usefulness of the ...
The quench map in an integrable classical field theory: nonlinear Schrödinger equation
Caudrelier, Vincent; Doyon, Benjamin
2016-11-01
We study the non-equilibrium dynamics obtained by an abrupt change (a quench) in the parameters of an integrable classical field theory, the nonlinear Schrödinger equation. We first consider explicit one-soliton examples, which we fully describe by solving the direct part of the inverse scattering problem. We then develop some aspects of the general theory using elements of the inverse scattering method. For this purpose, we introduce the quench map which acts on the space of scattering data and represents the change of parameter with fixed field configuration (initial condition). We describe some of its analytic properties by implementing a higher level version of the inverse scattering method, and we discuss the applications of Darboux–Bäcklund transformations, Gelfand–Levitan–Marchenko equations and the Rosales series solution to a related, dual quench problem. Finally, we comment on the interplay between quantum and classical tools around the theme of quenches and on the usefulness of the quantization of our classical approach to the quantum quench problem.
Effects of Analog-to-Digital Converter Nonlinearities on Radar Range-Doppler Maps
Energy Technology Data Exchange (ETDEWEB)
Doerry, Armin Walter [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Dubbert, Dale F. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Tise, Bertice L. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2014-07-01
Radar operation, particularly Ground Moving Target Indicator (GMTI) radar modes, are very sensitive to anomalous effects of system nonlinearities. These throw off harmonic spurs that are sometimes detected as false alarms. One significant source of nonlinear behavior is the Analog to Digital Converter (ADC). One measure of its undesired nonlinearity is its Integral Nonlinearity (INL) specification. We examine in this report the relationship of INL to GMTI performance.
Kengne, Emmanuel; Saydé, Michel; Ben Hamouda, Fathi; Lakhssassi, Ahmed
2013-11-01
Analytical entire traveling wave solutions to the 1+1 density-dependent nonlinear reaction-diffusion equation via the extended generalized Riccati equation mapping method are presented in this paper. This equation can be regarded as an extension case of the Fisher-Kolmogoroff equation, which is used for studying insect and animal dispersal with growth dynamics. The analytical solutions are then used to investigate the effect of equation parameters on the population distribution.
Angelis, Georgios I; Matthews, Julian C; Kotasidis, Fotis A; Markiewicz, Pawel J; Lionheart, William R; Reader, Andrew J
2014-11-01
Estimation of nonlinear micro-parameters is a computationally demanding and fairly challenging process, since it involves the use of rather slow iterative nonlinear fitting algorithms and it often results in very noisy voxel-wise parametric maps. Direct reconstruction algorithms can provide parametric maps with reduced variance, but usually the overall reconstruction is impractically time consuming with common nonlinear fitting algorithms. In this work we employed a recently proposed direct parametric image reconstruction algorithm to estimate the parametric maps of all micro-parameters of a two-tissue compartment model, used to describe the kinetics of [[Formula: see text]F]FDG. The algorithm decouples the tomographic and the kinetic modelling problems, allowing the use of previously developed post-reconstruction methods, such as the generalised linear least squares (GLLS) algorithm. Results on both clinical and simulated data showed that the proposed direct reconstruction method provides considerable quantitative and qualitative improvements for all micro-parameters compared to the conventional post-reconstruction fitting method. Additionally, region-wise comparison of all parametric maps against the well-established filtered back projection followed by post-reconstruction non-linear fitting, as well as the direct Patlak method, showed substantial quantitative agreement in all regions. The proposed direct parametric reconstruction algorithm is a promising approach towards the estimation of all individual microparameters of any compartment model. In addition, due to the linearised nature of the GLLS algorithm, the fitting step can be very efficiently implemented and, therefore, it does not considerably affect the overall reconstruction time.
Analysis of the small dispersion limit of a non-integrable generalized Korteweg-de Vries equation
Zakeri, Gholam-Ali; Yomba, Emmanuel
2013-08-01
A generalized non-integrable Korteweg-de Vries (KdV) equation is investigated for the qualitative behavior of its solutions with a small dispersion limit. We obtained two reduced ordinary differential equations using a similarity analysis and discussed the solutions of generalized KdV (gKdV) by employing singular perturbation and asymptotic methods. We found a new closed form solution and provided various approximate solutions. We have shown that for sech-type initial value data the cumulative primitive function of the gKdV solution converges point-wise as the coefficient of the dispersive term goes to zero. Our numerical experiments provide strong evidence that for each fixed time, the solutions of gKdV are bounded by well-defined envelopes as the coefficient of the dispersion term goes to zero. We have shown that for a higher order of nonlinearity, the soliton becomes shaper, with a larger amplitude, but remains bounded. Comparatively, for a smaller coefficient of the dispersion term, its base gets smaller and the soliton becomes narrower, but the amplitude of the soliton remains the same.
Exact periodic solution in coupled nonlinear Schrodinger equations
Institute of Scientific and Technical Information of China (English)
Li Qi-Liang; Chen Jun-Lang; Sun Li-Li; Yu Shu-Yi; Qian Sheng
2007-01-01
The coupled nonlinear Schrodinger equations (CNLSEs) of two symmetrical optical fibres are nonintegrable, however the transformed CNLSEs have integrability. Integrability of the transformed CNLSEs is proved by the Hamilton dynamics theory and Galilei transform. Making use of a transform for CNLSEs and using the ansatz with Jacobi elliptic function form, this paper obtains the exact optical pulse solutions.
A highly nonlinear differentially 4 uniform power mapping that permutes fields of even degree
DEFF Research Database (Denmark)
Leander, Gregor; Bracken, Carl
2010-01-01
cryptosystem should be a permutation. Also, it is required that the function is highly nonlinear so that it is resistant to Matsui’s linear attack. In this article we demonstrate that the highly nonlinear permutation f (x) = x22k+2k+1 on the field F24k , discovered by Hans Dobbertin (1998) [1], has...
Lasue, Jeremie; Wiens, Roger; Stepinski, Tom; Forni, Olivier; Clegg, Samuel; Maurice, Sylvestre; Chemcam Team
2011-02-01
ChemCam is a remote laser-induced breakdown spectroscopy (LIBS) instrument that will arrive on Mars in 2012, on-board the Mars Science Laboratory Rover. The LIBS technique is crucial to accurately identify samples and quantify elemental abundances at various distances from the rover. In this study, we compare different linear and nonlinear multivariate techniques to visualize and discriminate clusters in two dimensions (2D) from the data obtained with ChemCam. We have used principal components analysis (PCA) and independent components analysis (ICA) for the linear tools and compared them with the nonlinear Sammon's map projection technique. We demonstrate that the Sammon's map gives the best 2D representation of the data set, with optimization values from 2.8% to 4.3% (0% is a perfect representation), together with an entropy value of 0.81 for the purity of the clustering analysis. The linear 2D projections result in three (ICA) and five times (PCA) more stress, and their clustering purity is more than twice higher with entropy values about 1.8. We show that the Sammon's map algorithm is faster and gives a slightly better representation of the data set if the initial conditions are taken from the ICA projection rather than the PCA projection. We conclude that the nonlinear Sammon's map projection is the best technique for combining data visualization and clustering assessment of the ChemCam LIBS data in 2D. PCA and ICA projections on more dimensions would improve on these numbers at the cost of the intuitive interpretation of the 2D projection by a human operator.
Baranes, Edmond; Bardey, David
2015-12-01
This article examines a model of competition between two types of health insurer: Health Maintenance Organizations (HMOs) and nonintegrated insurers. HMOs vertically integrate health care providers and pay them at a competitive price, while nonintegrated health insurers work as indemnity plans and pay the health care providers freely chosen by policyholders at a wholesale price. Such difference is referred to as an input price effect which, at first glance, favors HMOs. Moreover, we assume that policyholders place a positive value on the provider diversity supplied by their health insurance plan and that this value increases with the probability of disease. Due to the restricted choice of health care providers in HMOs a risk segmentation occurs: policyholders who choose nonintegrated health insurers are characterized by higher risk, which also tends to favor HMOs. Our equilibrium analysis reveals that the equilibrium allocation only depends on the number of HMOs in the case of exclusivity contracts between HMOs and providers. Surprisingly, our model shows that the interplay between risk segmentation and input price effects may generate ambiguous results. More precisely, we reveal that vertical integration in health insurance markets may decrease health insurers' premiums.
Directory of Open Access Journals (Sweden)
Jurado-Piña, R.
2014-12-01
Full Text Available When designing a tension structure the shape is not known at the beginning of the process. Form-finding methods allow the designer to obtain an initial shape from given boundary conditions. Several form-finding methods for tension structures are already available in the technical literature; all of them posses certain limitations and drawbacks and no single method is optimal for all problems. The engineer may select the proper combination of methods best suited to the designer’s needs. In this paper it is proposed a combined method to achieve satisfactory equilibrium configurations for fabric tension structures. The force density method (FDM implemented with topological mapping (TM is used as a search engine for the preliminary design, and a procedure that employs nonlinear structural analysis is proposed for final refinement of the initial equilibrium configuration hence allowing the use of the same analysis tool for both refinement of the solution and analysis under loading.Al diseñar una estructura tensada la forma inicial es normalmente desconocida. Los métodos de búsqueda de forma permiten al ingeniero obtener una geometría inicial dadas unas condiciones de contorno. Existen diferentes métodos de búsqueda de formas de equilibrio, pero todos tienen limitaciones y no existe uno único óptimo para cualquier tipo de problema. El ingeniero debe elegir la combinación de métodos que mejor se adapte a sus necesidades. En este artículo se propone un método combinado para generar configuraciones de equilibrio satisfactorias en estructuras tensadas. Como motor de búsqueda para el diseño preliminar se emplea el método de las densidades de fuerza (FDM implementado con mallado en topología (TM, y se propone un procedimiento basado en análisis no lineal de estructuras para el refinamiento de la configuración inicial de equilibrio, permitiéndose así el empleo de las mismas herramientas tanto para el refinamiento de la solución inicial
Yan, Chaowen; Wang, Jianping; Lu, Huimin; Shi, Yinjia; Zhang, Yini
2016-05-01
A joint algorithm, integrating selective mapping (SLM) and restorable clipping (RC), is proposed for the direct current-biased optical orthogonal frequency division multiplexing (DCO-OFDM) and visible light communication (VLC) system to reduce the nonlinearity impacts of light-emitting diode (LED) aggravated by high peak-to-average power ratio (PAPR) and DC-bias. The performance of DCO-OFDM VLC system is analyzed and discussed with different techniques of LED nonlinearity alleviation. The simulation results show that compared to the original DCO-OFDM VLC system, the system with the proposed scheme can achieve about 4.8 dB improvement of PAPR reduction and 7 dB improvement of bit error rate (BER) performance. The reason is that the signals acquiring the desired shape in LED linear region can be recovered correctly without distortion induced by LED nonlinearity. It is demonstrated that the proposed SLM-RC technique effectively reduces not only PAPR but also the impacts of LED nonlinearity without BER deterioration.
Asaki, SAITO; Future University-Hakodate
2006-01-01
We introduce a modified Bernoulli map, which presents f^ spectrum. This map is equivalent to a certain symbolic operation of continued fraction representation. From this fact, we can derive various properties of the map, e.g., concerning residence times, from the theory of continued fractions. Furthermore, we can generate true chaotic orbits with intermittent behavior long enough to investigate their statistical properties.
Frankel, Arthur D.; Stephenson, William J.; Carver, David L.; Williams, Robert A.; Odum, Jack K.; Rhea, Susan
2007-01-01
This report presents probabilistic seismic hazard maps for Seattle, Washington, based on over 500 3D simulations of ground motions from scenario earthquakes. These maps include 3D sedimentary basin effects and rupture directivity. Nonlinear site response for soft-soil sites of fill and alluvium was also applied in the maps. The report describes the methodology for incorporating source and site dependent amplification factors into a probabilistic seismic hazard calculation. 3D simulations were conducted for the various earthquake sources that can affect Seattle: Seattle fault zone, Cascadia subduction zone, South Whidbey Island fault, and background shallow and deep earthquakes. The maps presented in this document used essentially the same set of faults and distributed-earthquake sources as in the 2002 national seismic hazard maps. The 3D velocity model utilized in the simulations was validated by modeling the amplitudes and waveforms of observed seismograms from five earthquakes in the region, including the 2001 M6.8 Nisqually earthquake. The probabilistic seismic hazard maps presented here depict 1 Hz response spectral accelerations with 10%, 5%, and 2% probabilities of exceedance in 50 years. The maps are based on determinations of seismic hazard for 7236 sites with a spacing of 280 m. The maps show that the most hazardous locations for this frequency band (around 1 Hz) are soft-soil sites (fill and alluvium) within the Seattle basin and along the inferred trace of the frontal fault of the Seattle fault zone. The next highest hazard is typically found for soft-soil sites in the Duwamish Valley south of the Seattle basin. In general, stiff-soil sites in the Seattle basin exhibit higher hazard than stiff-soil sites outside the basin. Sites with shallow bedrock outside the Seattle basin have the lowest estimated hazard for this frequency band.
Koch, Herbert; Vişan, Monica
2014-01-01
The first part of the book provides an introduction to key tools and techniques in dispersive equations: Strichartz estimates, bilinear estimates, modulation and adapted function spaces, with an application to the generalized Korteweg-de Vries equation and the Kadomtsev-Petviashvili equation. The energy-critical nonlinear Schrödinger equation, global solutions to the defocusing problem, and scattering are the focus of the second part. Using this concrete example, it walks the reader through the induction on energy technique, which has become the essential methodology for tackling large data critical problems. This includes refined/inverse Strichartz estimates, the existence and almost periodicity of minimal blow up solutions, and the development of long-time Strichartz inequalities. The third part describes wave and Schrödinger maps. Starting by building heuristics about multilinear estimates, it provides a detailed outline of this very active area of geometric/dispersive PDE. It focuses on concepts and ide...
Energy Technology Data Exchange (ETDEWEB)
Klofai, Yerima [Department of Physics, Higher Teacher Training College, University of Maroua, PO Box 46 Maroua (Cameroon); Essimbi, B Z [Department of Physics, Faculty of Science, University of Yaounde 1, PO Box 812 Yaounde (Cameroon); Jaeger, D, E-mail: bessimb@yahoo.fr [ZHO, Optoelectronik, Universitaet Duisburg-Essen, D-47048 Duisburg (Germany)
2011-10-15
Pulse propagation on high-frequency dissipative nonlinear transmission lines (NLTLs)/resonant tunneling diode line cascaded maps is investigated for long-distance propagation of short pulses. Applying perturbative analysis, we show that the dynamics of each line is reduced to an expanded Korteweg-de Vries-Burgers equation. Moreover, it is found by computer experiments that the soliton developed in NLTLs experiences an exponential amplitude decay on the one hand and an exponential amplitude growth on the other. As a result, the behavior of a pulse in special electrical networks made of concatenated pieces of lines is closely similar to the transmission of information in optical/electrical communication systems.
Non-linear Maps on Borel Subalgebras of Simple Lie Algebras Preserving Abelin Ideals
Institute of Scientific and Technical Information of China (English)
ZHAO Yan-xia; WANG Deng-yin
2012-01-01
Let g be a complex simple Lie algebra of rank l,b the standard Borel subalgebra.An invertible map on b is said to preserve abelian ideals if it maps each abelian ideal to some such ideal of the same dimension.In this article,by using some results of Chevalley groups,the theory of root systems and root space decomposition,the author gives an explicit description on such maps of b.
Energy Technology Data Exchange (ETDEWEB)
Guo, Kong-Ming, E-mail: kmguo@xidian.edu.cn [School of Electromechanical Engineering, Xidian University, P.O. Box 187, Xi' an 710071 (China); Jiang, Jun, E-mail: jun.jiang@mail.xjtu.edu.cn [State Key Laboratory for Strength and Vibration, Xi' an Jiaotong University, Xi' an 710049 (China)
2014-07-04
To apply stochastic sensitivity function method, which can estimate the probabilistic distribution of stochastic attractors, to non-autonomous dynamical systems, a 1/N-period stroboscopic map for a periodic motion is constructed in order to discretize the continuous cycle into a discrete one. In this way, the sensitivity analysis of a cycle for discrete map can be utilized and a numerical algorithm for the stochastic sensitivity analysis of periodic solutions of non-autonomous nonlinear dynamical systems under stochastic disturbances is devised. An external excited Duffing oscillator and a parametric excited laser system are studied as examples to show the validity of the proposed method. - Highlights: • A method to analyze sensitivity of stochastic periodic attractors in non-autonomous dynamical systems is proposed. • Probabilistic distribution around periodic attractors in an external excited Φ{sup 6} Duffing system is obtained. • Probabilistic distribution around a periodic attractor in a parametric excited laser system is determined.
Mapping nonlinear shallow-water tides: a look at the past and future
DEFF Research Database (Denmark)
Andersen, Ole Baltazar; Egbert, G.D.; Erofeeva, S.Y.;
2006-01-01
these two interests. After a brief review, we describe initial steps toward the assimilation of altimetry into models of nonlinear tides via generalized inverse methods. A series of barotropic inverse solutions is computed for the M-4 tide over the northwest European Shelf. Future applications of altimetry...
Li, Kang; Petersen, Gitte; Barco, Lisa; Hvidtfeldt, Kristian; Liu, Liping; Dalsgaard, Anders
2017-08-01
Integrated tilapia-pig farming, which uses manure from pigs as fertilizers in fish pond, is a traditional and common production system practised by small-scale farmers in South-east Asia. Although such systems may be environmentally sustainable, they also pose potential food safety hazards including transmission of faecal zoonotic pathogens and accumulation of antimicrobial and other chemical residues. This study aimed to determine differences in occurrence and characteristics of Salmonella spp. isolated from tilapia-pig and non-integrated aquaculture systems in Guangdong province, China. A total of 77 samples (9 pig feed, 19 fish feed, 9 pig faeces, 20 fish mucus and 20 fish intestine) from 10 tilapia-pig ponds and 10 non-integrated ponds were analysed. Salmonella spp. was found in fish mucus (20.0%), fish intestine (40.0%) and pig faeces (11.1%) from integrated ponds, and from fish mucus (40.0%) and fish intestine (40.0%) from non-integrated ponds. S. Weltevreden (76.5%) was by far the most common serovar showing limited antimicrobial resistance. One pig faeces sample contained S. Typhimurium whereas feed samples were found free of Salmonella spp.. DNA fingerprinting by the PFGE method showed a clonal relationship of S. Weltevreden which was supported by similar antimicrobial resistance patterns (sulfamethoxazole and trimethoprim resistance) as well as most isolates harbouring a 147-kb sized plasmid. The common finding of S. Weltevreden in both tilapia production systems indicates that this serovar may have a different ecology and increased survival in aquaculture environments in comparison with other Salmonella serovars. Further in vivo studies of the ecology of S. Weltevreden in aquaculture environments are needed.
Signatures of chaos and non-integrability in two-dimensional gravity with dynamical boundary
Directory of Open Access Journals (Sweden)
Fitkevich Maxim
2016-01-01
Full Text Available We propose a model of two-dimensional dilaton gravity with a boundary. In the bulk our model coincides with the classically integrable CGHS model; the dynamical boundary cuts of the CGHS strong-coupling region. As a result, classical dynamics in our model reminds that in the spherically-symmetric gravity: wave packets of matter fields either reflect from the boundary or form black holes. We find large integrable sector of multisoliton solutions in this model. At the same time, we argue that the model is globally non-integrable because solutions at the verge of black hole formation display chaotic properties.
Institute of Scientific and Technical Information of China (English)
GE Jian-Ya; WANG Rui-Min; DAI Chao-Qing; ZHANG Jie-Fang
2006-01-01
In this paper, by means of the variable-coefficient mapping method based on elliptical equation, we obtain explicit solutions of nonlinear Schr(o)dinger equation with variable-coefficient. These solutions include Jacobian elliptic function solutions, solitary wave solutions, soliton-like solutions, and trigonometric function solutions, among which some are found for the first time. Six figures are given to illustrate some features of these solutions. The method can be applied to other nonlinear evolution equations in mathematical physics.
Mapping nonlinear receptive field structure in primate retina at single cone resolution.
Freeman, Jeremy; Field, Greg D; Li, Peter H; Greschner, Martin; Gunning, Deborah E; Mathieson, Keith; Sher, Alexander; Litke, Alan M; Paninski, Liam; Simoncelli, Eero P; Chichilnisky, E J
2015-01-01
The function of a neural circuit is shaped by the computations performed by its interneurons, which in many cases are not easily accessible to experimental investigation. Here, we elucidate the transformation of visual signals flowing from the input to the output of the primate retina, using a combination of large-scale multi-electrode recordings from an identified ganglion cell type, visual stimulation targeted at individual cone photoreceptors, and a hierarchical computational model. The results reveal nonlinear subunits in the circuity of OFF midget ganglion cells, which subserve high-resolution vision. The model explains light responses to a variety of stimuli more accurately than a linear model, including stimuli targeted to cones within and across subunits. The recovered model components are consistent with known anatomical organization of midget bipolar interneurons. These results reveal the spatial structure of linear and nonlinear encoding, at the resolution of single cells and at the scale of complete circuits.
An Improved Ishikawa-type Iteration for Nonlinear Quase-Contraction Mappings%非线性拟压缩映射的改进Ishikawa型迭代
Institute of Scientific and Technical Information of China (English)
田有先
2001-01-01
在凸度量空间内，引入了非线性拟压缩映射序列和改进的Ishikawa型迭代序列，证明了改进的Ishikawa型迭代序列收敛于非线性拟压缩映射序列的唯一公共不动点。%The notion of nonlinear qusi-contraction mappings squence and improved Ishikawa-type iteration are introduced in convex matric space.The result that the improved lshikawa-type iteration sequence converges to unique common fixed point of nonlinear quasi-contraction-mappings sequence is also given.
Loss of adiabaticity with increasing tunneling gap in nonintegrable multistate Landau-Zener models
Malla, Rajesh K.; Raikh, M. E.
2017-09-01
We consider the simplest nonintegrable model of the multistate Landau-Zener transition. In this model, two pairs of levels in two tunnel-coupled quantum dots are swept past each other by the gate voltage. Although this 2 ×2 model is nonintegrable, it can be solved analytically in the limit when the interlevel energy distance is much smaller than their tunnel splitting. The result is contrasted to the similar 2 ×1 model, in which one of the dots contains only one level. The latter model does not allow interference of the virtual transition amplitudes, and it is exactly solvable. In the 2 ×1 model, the probability for a particle, residing at time t →-∞ in one dot, to remain in the same dot at t →∞ , falls off exponentially with tunnel coupling. By contrast, in the 2 ×2 model, this probability grows rapidly with tunnel coupling. The physical origin of this growth is the formation of the tunneling-induced collective states in the system of two dots. This can be viewed as a manifestation of the Dicke effect.
Meraviglia, Viviana; Zanon, Alessandra; Lavdas, Alexandros A; Schwienbacher, Christine; Silipigni, Rosamaria; Di Segni, Marina; Chen, Huei-Sheng Vincent; Pramstaller, Peter P; Hicks, Andrew A; Rossini, Alessandra
2015-06-05
Somatic cells can be reprogrammed into induced pluripotent stem cells (iPSCs) by forcing the expression of four transcription factors (Oct-4, Sox-2, Klf-4, and c-Myc), typically expressed by human embryonic stem cells (hESCs). Due to their similarity with hESCs, iPSCs have become an important tool for potential patient-specific regenerative medicine, avoiding ethical issues associated with hESCs. In order to obtain cells suitable for clinical application, transgene-free iPSCs need to be generated to avoid transgene reactivation, altered gene expression and misguided differentiation. Moreover, a highly efficient and inexpensive reprogramming method is necessary to derive sufficient iPSCs for therapeutic purposes. Given this need, an efficient non-integrating episomal plasmid approach is the preferable choice for iPSC derivation. Currently the most common cell type used for reprogramming purposes are fibroblasts, the isolation of which requires tissue biopsy, an invasive surgical procedure for the patient. Therefore, human peripheral blood represents the most accessible and least invasive tissue for iPSC generation. In this study, a cost-effective and viral-free protocol using non-integrating episomal plasmids is reported for the generation of iPSCs from human peripheral blood mononuclear cells (PBMNCs) obtained from frozen buffy coats after whole blood centrifugation and without density gradient separation.
Institute of Scientific and Technical Information of China (English)
TANG Xiao-Yan; LOU Sen-Yue
2002-01-01
We study the localized coherent structures ofa generally nonintegrable (2+ 1 )-dimensional KdV equation via a variable separation approach. In a special integrable case, the entrance of some arbitrary functions leads to abundant coherent structures. However, in the general nonintegrable case, an additional condition has to be introduced for these arbitrary functions. Although the additional condition has been introduced into the solutions of the nonintegrable KdV equation, there still exist many interesting solitary wave structures. Especially, the nonintegrable KdV equation possesses the breather-like localized excitations, and the similar static ring soliton solutions as in the integrable case. Furthermor,in the integrable case, the interaction between two travelling ring solitons is elastic, while in the nonintegrable case we cannot find even the single travelling ring soliton solution.
Using MatContM in the study of a nonlinear map in economics
Neirynck, Niels; Al-Hdaibat, Bashir; Govaerts, Willy; Kouznetsov, Yuri A.; Meijer, Hil G.E.
2016-01-01
MatContM is a MATLAB interactive toolbox for the numerical study of iterated smooth maps, their Lyapunov exponents, fixed points, and periodic, homoclinic and heteroclinic orbits as well as their stable and unstable invariant manifolds. The bifurcation analysis is based on continuation methods, trac
Using MatContM in the study of a nonlinear map in economics
Neirynck, N.; Al Hdaibat, Bashir; Govaerts, W.; Kuznetsov, Yu.A.; Meijer, H.G.E.
2016-01-01
MatContM is a MATLAB interactive toolbox for the numerical study of iterated smooth maps, their Lyapunov exponents, fixed points, and periodic, homoclinic and heteroclitic orbits as well as their stable and unstable invariant manifolds. The bifurcation analysis is based on continuation methods, trac
Directory of Open Access Journals (Sweden)
Ali Volkan Bilgili
2013-07-01
Full Text Available In the Harran Plain, southeastern Turkey, soil salinisation causes land degradation threatening the sustainability of agricultural production. According to a recent survey, approximately 18000 ha area has been affected by soil salinity and sodicity at various levels. Determining the distribution of saline and sodic soils in the study area is the first step for effective management of these soils. Over 200 soil samples have been randomly selected across the plain and analyzed for selected soil salinity and sodicity variables in soil salinity laboratory. Indicator kriging (IK, a non-linear interpolation technique, was used to map the probability levels of occurrence of saline and sodic soils across the plain. The results of IK showed the probability distributions of risky areas under different types of soil salinity classes; nonsaline, saline, saline – sodic and sodic.
SPATIO-TEMPORAL DATA ANALYSIS WITH NON-LINEAR FILTERS: BRAIN MAPPING WITH fMRI DATA
Directory of Open Access Journals (Sweden)
Karsten Rodenacker
2011-05-01
Full Text Available Spatio-temporal digital data from fMRI (functional Magnetic Resonance Imaging are used to analyse and to model brain activation. To map brain functions, a well-defined sensory activation is offered to a test person and the hemodynamic response to neuronal activity is studied. This so-called BOLD effect in fMRI is typically small and characterised by a very low signal to noise ratio. Hence the activation is repeated and the three dimensional signal (multi-slice 2D is gathered during relatively long time ranges (3-5 min. From the noisy and distorted spatio-temporal signal the expected response has to be filtered out. Presented methods of spatio-temporal signal processing base on non-linear concepts of data reconstruction and filters of mathematical morphology (e.g. alternating sequential morphological filters. Filters applied are compared by classifications of activations.
Barros, A. P.; Wilson, A. M.; Miller, D. K.; Tao, J.; Genereux, D. P.; Prat, O.; Petersen, W. A.; Brunsell, N. A.; Petters, M. D.; Duan, Y.
2015-12-01
Using the planet as a study domain and collecting observations over unprecedented ranges of spatial and temporal scales, NASA's EOS (Earth Observing System) program was an agent of transformational change in Earth Sciences over the last thirty years. The remarkable space-time organization and variability of atmospheric and terrestrial moist processes that emerged from the analysis of comprehensive satellite observations provided much impetus to expand the scope of land-atmosphere interaction studies in Hydrology and Hydrometeorology. Consequently, input and output terms in the mass and energy balance equations evolved from being treated as fluxes that can be used as boundary conditions, or forcing, to being viewed as dynamic processes of a coupled system interacting at multiple scales. Measurements of states or fluxes are most useful if together they map, reveal and/or constrain the underlying physical processes and their interactions. This can only be accomplished through an integrated observing system designed to capture the coupled physics, including nonlinear feedbacks and tipping points. Here, we first review and synthesize lessons learned from hydrometeorology studies in the Southern Appalachians and in the Southern Great Plains using both ground-based and satellite observations, physical models and data-assimilation systems. We will specifically focus on mapping and understanding nonlinearity and multiscale memory of rainfall-runoff processes in mountainous regions. It will be shown that beyond technical rigor, variety, quantity and duration of measurements, the utility of observing systems is determined by their interpretive value in the context of physical models to describe the linkages among different observations. Second, we propose a framework for designing science-grade and science-minded process-oriented integrated observing and modeling platforms for hydrometeorological studies.
Accurate 3D maps from depth images and motion sensors via nonlinear Kalman filtering
Hervier, Thibault; Goulette, François
2012-01-01
This paper investigates the use of depth images as localisation sensors for 3D map building. The localisation information is derived from the 3D data thanks to the ICP (Iterative Closest Point) algorithm. The covariance of the ICP, and thus of the localization error, is analysed, and described by a Fisher Information Matrix. It is advocated this error can be much reduced if the data is fused with measurements from other motion sensors, or even with prior knowledge on the motion. The data fusion is performed by a recently introduced specific extended Kalman filter, the so-called Invariant EKF, and is directly based on the estimated covariance of the ICP. The resulting filter is very natural, and is proved to possess strong properties. Experiments with a Kinect sensor and a three-axis gyroscope prove clear improvement in the accuracy of the localization, and thus in the accuracy of the built 3D map.
Nonlinear imaging and 3D-mapping of terahertz fields with Kerr media
Clerici, Matteo; Caspani, Lucia; Peccianti, Marco; Rubino, Eleonora; Razzari, Luca; Légaré, François; Ozaki, Tsuneyuki; Morandotti, Roberto
2013-01-01
We investigate the spatially and temporally resolved four-wave mixing of terahertz fields and optical pulses in large band-gap dielectrics, such as diamond. We show that it is possible to perform beam profiling and space-time resolved mapping of terahertz fields with sub-wavelength THz resolution by encoding the spatial information into an optical signal, which can then be recorded by a standard CCD camera.
Nonlinear Maps Satisfying Derivability on the Parabolic Subalgebras of the Full Matrix Algebras
Institute of Scientific and Technical Information of China (English)
Zheng Xin CHEN; Yu E ZHAO
2011-01-01
Let F be a field of characteristic O,Mn(F) the full matrix algebra over F,t the subalgebra of Mn(F) consisting of all upper triangular matrices.Any subalgebra of Mn(F) containing t is called a parabolic subalgebra of Mn(F).Let P be a parabolic subalgebra of Mn(F).A map φ on P is said to satisfy derivability if φ(x·y) =φ(x).y+x·φ(y) for all x,y ∈ P,where φ is not necessarily linear.Note that a map satisfying derivability on P is not necessarily a derivation on P.In this paper,we prove that a map φ on P satisfies derivability if and only if φ is a sum of an inner derivation and an additive quasi-derivation on P.In particular,any derivation of parabolic subalgebras of Mn (F) is an inner derivation.
[The presence of non-integrated SV40 viral DNA in nonproductive cells transformed by this virus].
Daya-Grosjean, L; Bénichou, D; Monier, R
1975-09-08
The hot phenol extraction of nuclic acids reveals the presence of small amounts of nonintegrated SV 40 DNA in transformed syrian hamster or mouse cells. The extractibility of the viral DNA is influenced by its conformation; SV 40 DNA, form I is preferentially extracted by contrast with form III DNA.
Feuerverger, Grace
1989-01-01
A study examined the relationship between language experiences of Italo-Canadian students at home and school and their perceptions of group vitality and ethnic language maintenance. Subjects were in grade eight integrated and non-integrated heritage language programs. (58 references) (Author/MSE)
Prigogine, Ilya
2002-01-01
Hamiltonian systems can be classified according Poincaré into integrable and non-integrable systems. On the other hand, our previous work introduced a formulation of dynamics based on the evolution of correlations. It is shown that for integrable systems this method is equivalent to the diagonalisation problem of the Hamiltonian for integrable systems but our method can be easily extended to non-integrable systems through analytic continuation. This leads to a description of unstable dressed excited states, as well as to excitations for interacting fields. The mechanism of the formation of dressed objects will be analysed in terms of two different time scales. The analogy with these dissipative structures will be emphasized. We may distinguish two levels in the formulation of laws of nature. The first is in terms of Hamiltonian dynamics, the second, necessary for classes of non-integrable systems, The first is in terms of Hamiltonian dynamics, the second, necessary for classes of non-integrable systems, aris...
Xu, Zhen; Chen, Feng; Zhang, Lingling; Lu, Jing; Xu, Peng; Liu, Guang; Xie, Xuemin; Mu, Wenli; Wang, Yajun; Liu, Depei
2016-10-01
Safe and efficient gene transfer systems are the basis of gene therapy applications. Non-integrating lentiviral (NIL) vectors are among the most promising candidates for gene transfer tools, because they exhibit high transfer efficiency in both dividing and non-dividing cells and do not present a risk of insertional mutagenesis. However, non-integrating lentiviral vectors cannot introduce stable exogenous gene expression to dividing cells, thereby limiting their application. Here, we report the design of a non-integrating lentiviral vector that contains the minimal scaffold/matrix attachment region (S/MAR) sequence (SNIL), and this SNIL vector is able to retain episomal transgene expression in dividing cells. Using SNIL vectors, we detected the expression of the eGFP gene for 61 days in SNIL-transduced stable CHO cells, either with selection or not. In the NIL group without the S/MAR sequence, however, the transduced cells died under selection for the transient expression of NIL vectors. Furthermore, Southern blot assays demonstrated that the SNIL vectors were retained extrachromosomally in the CHO cells. In conclusion, the minimal S/MAR sequence retained the non-integrating lentiviral vectors in dividing cells, which indicates that SNIL vectors have the potential for use as a gene transfer tool.
Using MatContM in the study of a nonlinear map in economics
Neirynck, Niels; Al-Hdaibat, Bashir; Govaerts, Willy; Kuznetsov, Yuri A.; Meijer, Hil G. E.
2016-02-01
MatContM is a MATLAB interactive toolbox for the numerical study of iterated smooth maps, their Lyapunov exponents, fixed points, and periodic, homoclinic and heteroclinic orbits as well as their stable and unstable invariant manifolds. The bifurcation analysis is based on continuation methods, tracing out solution manifolds of various types of objects while some of the parameters of the map vary. In particular, MatContM computes codimension 1 bifurcation curves of cycles and supports the computation of the normal form coefficients of their codimension two bifurcations, and allows branch switching from codimension 2 points to secondary curves. MatContM builds on an earlier command-line MATLAB package CL MatContM but provides new computational routines and functionalities, as well as a graphical user interface, enabling interactive control of all computations, data handling and archiving. We apply MatContM in our study of the monopoly model of T. Puu with cubic price and quadratic marginal cost functions. Using MatContM, we analyze the fixed points and their stability and we compute branches of solutions of period 5, 10, 13 17. The chaotic and periodic behavior of the monopoly model is further analyzed by computing the largest Lyapunov exponents.
Šimara, P; Tesařová, L; Padourová, S; Koutná, I
2014-01-01
Preclinical studies have demonstrated the promising potential of human induced pluripotent stem cells (hiPSCs) for clinical application. To fulfil this goal, efficient and safe methods to generate them must be established. Various reprogramming techniques were presented during seven years of hiPSCs research. Genome non-integrating and completely xeno-free protocols from the first biopsy to stable hiPSC clones are highly preferable in terms of future clinical application. In this short communication, we summarize the reprogramming experiments performed in our laboratories. We successfully generated hiPSCs using STEMCCA lentivirus, Sendai virus or episomal vectors. Human neonatal fibroblasts and CD34(+) blood progenitors were used as cell sources and were maintained either on mouse embryonic feeder cells or in feeder-free conditions. The reprogramming efficiency was comparable for all three methods and both cell types, while the best results were obtained in feeder-free conditions.
Chaos and the continuum limit in the gravitational N-body problem II. Nonintegrable potentials
Sideris, I V; Sideris, Ioannis V.; Kandrup, Henry E.
2002-01-01
This paper continues a numerical investigation of orbits evolved in `frozen,' time-independent N-body realisations of smooth time-independent density distributions corresponding to both integrable and nonintegrable potentials, allowing for N as large as 300,000. The principal focus is on distinguishing between, and quantifying, the effects of graininess on initial conditions corresponding, in the continuum limit, to regular and chaotic orbits. Ordinary Lyapunov exponents X do not provide a useful diagnostic for distinguishing between regular and chaotic behaviour. Frozen-N orbits corresponding in the continuum limit to both regular and chaotic characteristics have large positive X even though, for large N, the `regular' frozen-N orbits closely resemble regular characteristics in the smooth potential. Viewed macroscopically both `regular' and `chaotic' frozen-N orbits diverge as a power law in time from smooth orbits with the same initial condition. There is, however, an important difference between `regular' ...
Algebraic approach to non-integrability of Bajer-Moffattʼs steady Stokes flow
Nishiyama, Takahiro
2014-12-01
Non-integrability of the streamline system of equations for a steady Stokes flow, which Bajer and Moffatt introduced by the name of stretch-twist-fold flow, is discussed by an algebraic method without assuming its closeness to an integrable system. In the author's previous paper, the non-existence of a real meromorphic first integral of the streamline system was proved on the basis of Ziglin's theory and the differential Galois theory, where a parameter was assumed not to belong to a set of exceptional values. In this paper, this assumption is proved to be removable by making further use of some results from the differential Galois theory. The road to this result is explained in the form of a recipe in order to make clear how the differential Galois theory is applied.
Zhu, Hong-Ming; Pen, Ue-Li; Chen, Xuelei; Yu, Hao-Ran
2016-01-01
We present a direct approach to non-parametrically reconstruct the linear density field from an observed non-linear map. We solve for the unique displacement potential consistent with the non-linear density and positive definite coordinate transformation using a multigrid algorithm. We show that we recover the linear initial conditions up to $k\\sim 1\\ h/\\mathrm{Mpc}$ with minimal computational cost. This reconstruction approach generalizes the linear displacement theory to fully non-linear fields, potentially substantially expanding the BAO and RSD information content of dense large scale structure surveys, including for example SDSS main sample and 21cm intensity mapping.
DEFF Research Database (Denmark)
Marschler, Christian; Vollmer, Jürgen
2014-01-01
, the Reynolds number for pipe flow, and with transitions from bounded chaotic patches to an invasion of space of irregular motion. Dynamical systems models are unique tools in this respect because they can provide insight into the origin of the very long lifetime of puffs, and the dynamical mechanism leading......Recently, highly resolved experiments and simulations have provided detailed insight into the dynamics of turbulent pipe flow. This has revived the interest in identifying mechanisms that generate chaotic transients with superexponential growth of lifetime as a function of a control parameter...... to the transition from puffs to slugs in pipe flow. The present paper contributes to this enterprise by introducing a unidirectionally coupled map lattice. It mimics three of the salient features of pipe-flow turbulence: (i) the transition from laminar flow to puffs, (ii) a superexponential scaling of puff lifetime...
Marschler, Christian
2014-01-01
Recently, highly resolved experiments and simulations have provided detailed insight into the dynamics of turbulent pipe flow. This has revived the interest to identify mechanisms that generate chaotic transients with super-exponential growth of lifetime as a function of a control parameter, the Reynolds number for pipe flow, and with transitions from bounded chaotic patches to an invasion of space of irregular motion. Dynamical systems models are unique tools in this respect because they can provide insight into the origin of the very long life time of puffs, and the dynamical mechanism leading to the transition from puffs to slugs in pipe flow. The present paper contributes to this enterprise by introducing a unidirectionally coupled map lattice. It mimics three of the salient features of pipe-flow turbulence: (i) the transition from laminar flow to puffs, (ii) a super-exponential scaling of puff lifetime, and (iii) the transition from puffs to slugs by an unbinding transition in an intermittency scenario. ...
Singularity analysis of a new discrete nonlinear Schrodinger equation
Sakovich, Sergei
2001-01-01
We apply the Painleve test for integrability to a new discrete (differential-difference) nonlinear Schrodinger equation introduced by Leon and Manna. Since the singular expansions of solutions of this equation turn out to contain nondominant logarithmic terms, we conclude that the studied equation is nonintegrable. This result supports the observation of Levi and Yamilov that the Leon-Manna equation does not admit high-order generalized symmetries. As a byproduct of the singularity analysis c...
Institute of Scientific and Technical Information of China (English)
李志斌; 陈天华
2002-01-01
An algorithm for constructing exact solitary wave solutions and singular solutions for a class of nonlinear dissipative-dispersive system is presented. With the aid of symbolic manipulation system Maple, some explicit solutions are obtained for the system in physically interesting but non-integrable cases.
Neural Network Nonlinear Predictive Control Based on Tent-map Chaos Optimization%基于Tent混沌优化的神经网络预测控制
Institute of Scientific and Technical Information of China (English)
宋莹; 陈增强; 袁著祉
2007-01-01
With the unique ergodicity, irregularity, and special ability to avoid being trapped in local optima, chaos optimization has been a novel global optimization technique and has attracted considerable attention for application in various fields, such as nonlinear programming problems. In this article, a novel neural network nonlinear predictive control (NNPC) strategy based on the new Tent-map chaos optimization algorithm (TCOA) is presented. The feedforward neural network is used as the multi-step predictive model. In addition, the TCOA is applied to perform the nonlinear rolling optimization to enhance the convergence and accuracy in the NNPC. Simulation on a laboratory-scale liquid-level system is given to illustrate the effectiveness of the proposed method.
Directory of Open Access Journals (Sweden)
Nicolae Nistor
2014-11-01
Full Text Available Online knowledge building communities (OKBC reunite participants engaged in collaborative discourse. OKBCs can be made „smart“ by adding tools that predict how likely an OKBC is to integrate newcomers in existing dialogues and socio-cognitive structures. Starting from Bakhtin’s dialogical approach and polyphony theory, and building on the concept of inter- animation of voices, this study explores the relationship between newcomer integration and dialogue quality in OKBCs. The automated analysis tool “Important Moments” was employed to compare two dialogues, from an integrative and from a non-integrative blog-based OKBC. In the former, the concepts, lexical chains and inter-animation moments occurred more frequently than in the latter. Also, newcomer comments were linked to less lexical chains in the integrative community than in the non-integrative OKBC. These findings suggest close relationships between dialogue quality and newcomer integration, which can be used for designing smart OKBCs.
Da Costa, Godwin Clovis; Aras, Meena Ajay; Chalakkal, Paul; Da Costa, Michelle Clovis
2017-01-01
The article highlights a new method for the fabrication of an ocular prosthesis by the incorporation of a ceramic scleral veneer. The steps of fabrication include impression making, wax try-in, performing a "cut-back" on a selected stock eye, insertion of the IPS e-max press scleral veneer, finishing and insertion. It also includes a detailed review on non-integrated ocular prostheses.
Da Costa, Godwin Clovis; Aras, Meena Ajay; Chalakkal, Paul; Da Costa, Michelle Clovis
2017-01-01
The article highlights a new method for the fabrication of an ocular prosthesis by the incorporation of a ceramic scleral veneer. The steps of fabrication include impression making, wax try-in, performing a “cut-back” on a selected stock eye, insertion of the IPS e-max press scleral veneer, finishing and insertion. It also includes a detailed review on non-integrated ocular prostheses. PMID:28149792
Zou, Rui; Riverson, John; Liu, Yong; Murphy, Ryan; Sim, Youn
2015-03-01
Integrated continuous simulation-optimization models can be effective predictors of a process-based responses for cost-benefit optimization of best management practices (BMPs) selection and placement. However, practical application of simulation-optimization model is computationally prohibitive for large-scale systems. This study proposes an enhanced Nonlinearity Interval Mapping Scheme (NIMS) to solve large-scale watershed simulation-optimization problems several orders of magnitude faster than other commonly used algorithms. An efficient interval response coefficient (IRC) derivation method was incorporated into the NIMS framework to overcome a computational bottleneck. The proposed algorithm was evaluated using a case study watershed in the Los Angeles County Flood Control District. Using a continuous simulation watershed/stream-transport model, Loading Simulation Program in C++ (LSPC), three nested in-stream compliance points (CP)—each with multiple Total Maximum Daily Loads (TMDL) targets—were selected to derive optimal treatment levels for each of the 28 subwatersheds, so that the TMDL targets at all the CP were met with the lowest possible BMP implementation cost. Genetic Algorithm (GA) and NIMS were both applied and compared. The results showed that the NIMS took 11 iterations (about 11 min) to complete with the resulting optimal solution having a total cost of 67.2 million, while each of the multiple GA executions took 21-38 days to reach near optimal solutions. The best solution obtained among all the GA executions compared had a minimized cost of 67.7 million—marginally higher, but approximately equal to that of the NIMS solution. The results highlight the utility for decision making in large-scale watershed simulation-optimization formulations.
Universal behavior of the Shannon mutual information in nonintegrable self-dual quantum chains
Alcaraz, F. C.
2016-09-01
An existing conjecture states that the Shannon mutual information contained in the ground-state wave function of conformally invariant quantum chains, on periodic lattices, has a leading finite-size scaling behavior that, similarly as the von Neumann entanglement entropy, depends on the value of the central charge of the underlying conformal field theory describing the physical properties. This conjecture applies whenever the ground-state wave function is expressed in some special basis (conformal basis). Its formulation comes mainly from numerical evidences on exactly integrable quantum chains. In this paper, the above conjecture was tested for several general nonintegrable quantum chains. We introduce new families of self-dual Z (Q ) symmetric quantum chains (Q =2 ,3 ,... ). These quantum chains contain nearest-neighbor as well next-nearest-neighbor interactions (coupling constant p ). In the cases Q =2 and Q =3 , they are extensions of the standard quantum Ising and three-state Potts chains, respectively. For Q =4 and Q ≥5 , they are extensions of the Ashkin-Teller and Z (Q ) parafermionic quantum chains. Our studies indicate that these models are interesting on their own. They are critical, conformally invariant, and share the same universality class in a continuous critical line. Moreover, our numerical analysis for Q =2 -8 indicate that the Shannon mutual information exhibits the conjectured behavior irrespective if the conformally invariant quantum chain is exactly integrable or not. For completeness we also calculated, for these new families of quantum chains, the two existing generalizations of the Shannon mutual information, which are based on the Rényi entropy and on the Rényi divergence.
Nonintegral stoichiometry in CFTR gating revealed by a pore-lining mutation.
Jih, Kang-Yang; Sohma, Yoshiro; Hwang, Tzyh-Chang
2012-10-01
Cystic fibrosis transmembrane conductance regulator (CFTR) is a unique member of the ATP-binding cassette (ABC) protein superfamily. Unlike most other ABC proteins that function as active transporters, CFTR is an ATP-gated chloride channel. The opening of CFTR's gate is associated with ATP-induced dimerization of its two nucleotide-binding domains (NBD1 and NBD2), whereas gate closure is facilitated by ATP hydrolysis-triggered partial separation of the NBDs. This generally held theme of CFTR gating-a strict coupling between the ATP hydrolysis cycle and the gating cycle-is put to the test by our recent finding of a short-lived, post-hydrolytic state that can bind ATP and reenter the ATP-induced original open state. We accidentally found a mutant CFTR channel that exhibits two distinct open conductance states, the smaller O1 state and the larger O2 state. In the presence of ATP, the transition between the two states follows a preferred O1→O2 order, a telltale sign of a violation of microscopic reversibility, hence demanding an external energy input likely from ATP hydrolysis, as such preferred gating transition was abolished in a hydrolysis-deficient mutant. Interestingly, we also observed a considerable amount of opening events that contain more than one O1→O2 transition, indicating that more than one ATP molecule may be hydrolyzed within an opening burst. We thus conclude a nonintegral stoichiometry between the gating cycle and ATP consumption. Our results lead to a six-state gating model conforming to the classical allosteric mechanism: both NBDs and transmembrane domains hold a certain degree of autonomy, whereas the conformational change in one domain will facilitate the conformational change in the other domain.
Directory of Open Access Journals (Sweden)
Frédéric Coutant
Full Text Available Trials testing the RTS,S candidate malaria vaccine and radiation-attenuated sporozoites (RAS have shown that protective immunity against malaria can be induced and that an effective vaccine is not out of reach. However, longer-term protection and higher protection rates are required to eradicate malaria from the endemic regions. It implies that there is still a need to explore new vaccine strategies. Lentiviral vectors are very potent at inducing strong immunological memory. However their integrative status challenges their safety profile. Eliminating the integration step obviates the risk of insertional oncogenesis. Providing they confer sterile immunity, nonintegrative lentiviral vectors (NILV hold promise as mass pediatric vaccine by meeting high safety standards. In this study, we have assessed the protective efficacy of NILV against malaria in a robust pre-clinical model. Mice were immunized with NILV encoding Plasmodium yoelii Circumsporozoite Protein (Py CSP and challenged with sporozoites one month later. In two independent protective efficacy studies, 50% (37.5-62.5 of the animals were fully protected (p = 0.0072 and p = 0.0008 respectively when compared to naive mice. The remaining mice with detectable parasitized red blood cells exhibited a prolonged patency and reduced parasitemia. Moreover, protection was long-lasting with 42.8% sterile protection six months after the last immunization (p = 0.0042. Post-challenge CD8+ T cells to CSP, in contrast to anti-CSP antibodies, were associated with protection (r = -0.6615 and p = 0.0004 between the frequency of IFN-g secreting specific T cells in spleen and parasitemia. However, while NILV and RAS immunizations elicited comparable immunity to CSP, only RAS conferred 100% of sterile protection. Given that a better protection can be anticipated from a multi-antigen vaccine and an optimized vector design, NILV appear as a promising malaria vaccine.
Jabur, Ghazwan Ns; Sidhu, Karishma; Willcox, Timothy W; Mitchell, Simon J
2016-07-01
To compare the emboli filtration efficiency of five integrated or non-integrated oxygenator-filter combinations in cardiopulmonary bypass circuits. Fifty-one adult patients underwent surgery using a circuit with an integrated filtration oxygenator or non-integrated oxygenator with a separate 20 µm arterial line filter (Sorin Dideco Avant D903 + Pall AL20 (n=12), Sorin Inspire 6 M + Pall AL20 (n=10), Sorin Inspire 6M F (n=9), Terumo FX25 (n=10), Medtronic Fusion (n=10)). The Emboli Detection and Classification quantifier was used to count emboli upstream and downstream of the primary filter throughout cardiopulmonary bypass. The primary outcome measure was to compare the devices in respect of the median proportion of emboli removed. One device (Sorin Inspire 6 M + Pall AL20) exhibited a significantly greater median percentage reduction (96.77%, IQR=95.48 - 98.45) in total emboli counts compared to all other devices tested (p=0.0062 - 0.0002). In comparisons between the other units, they all removed a greater percentage of emboli than one device (Medtronic Fusion), but there were no other significant differences. The new generation Sorin Inspire 6 M, with a stand-alone 20 µm arterial filter, appeared most efficient at removing incoming emboli from the circuit. No firm conclusions can be drawn about the relative efficacy of emboli removal by units categorised by class (integrated vs non-integrated); however, the stand-alone 20 µm arterial filter presently sets a contemporary standard against which other configurations of equipment can be judged. © The Author(s) 2015.
Directory of Open Access Journals (Sweden)
Xiangjin Kang
Full Text Available Human-induced pluripotent stem cells (iPSCs are derived from differentiated somatic cells using defined factors and provide a renewable source of autologous cells for cell therapy. Many reprogramming methods have been employed to generate human iPSCs, including the use of integrating vectors and non-integrating vectors. Maintenance of the genomic integrity of iPSCs is highly desirable if the cells are to be used in clinical applications. Here, using the Affymetrix Cytoscan HD array, we investigated the genomic aberration profiles of 19 human cell lines: 5 embryonic stem cell (ESC lines, 6 iPSC lines derived using integrating vectors ("integrating iPSC lines", 6 iPSC lines derived using non-integrating vectors ("non-integrating iPSC lines", and the 2 parental cell lines from which the iPSCs were derived. The genome-wide copy number variation (CNV, loss of heterozygosity (LOH and mosaicism patterns of integrating and non-integrating iPSC lines were investigated. The maximum sizes of CNVs in the genomes of the integrating iPSC lines were 20 times higher than those of the non-integrating iPSC lines. Moreover, the total number of CNVs was much higher in integrating iPSC lines than in other cell lines. The average numbers of novel CNVs with a low degree of overlap with the DGV and of likely pathogenic CNVs with a high degree of overlap with the ISCA (International Symposium on Computer Architecture database were highest in integrating iPSC lines. Different single nucleotide polymorphisms (SNP calls revealed that, using the parental cell genotype as a reference, integrating iPSC lines displayed more single nucleotide variations and mosaicism than did non-integrating iPSC lines. This study describes the genome stability of human iPSCs generated using either a DNA-integrating or non-integrating reprogramming method, of the corresponding somatic cells, and of hESCs. Our results highlight the importance of using a high-resolution method to monitor genomic
Kang, Xiangjin; Yu, Qian; Huang, Yuling; Song, Bing; Chen, Yaoyong; Gao, Xingcheng; He, Wenyin; Sun, Xiaofang; Fan, Yong
2015-01-01
Human-induced pluripotent stem cells (iPSCs) are derived from differentiated somatic cells using defined factors and provide a renewable source of autologous cells for cell therapy. Many reprogramming methods have been employed to generate human iPSCs, including the use of integrating vectors and non-integrating vectors. Maintenance of the genomic integrity of iPSCs is highly desirable if the cells are to be used in clinical applications. Here, using the Affymetrix Cytoscan HD array, we investigated the genomic aberration profiles of 19 human cell lines: 5 embryonic stem cell (ESC) lines, 6 iPSC lines derived using integrating vectors ("integrating iPSC lines"), 6 iPSC lines derived using non-integrating vectors ("non-integrating iPSC lines"), and the 2 parental cell lines from which the iPSCs were derived. The genome-wide copy number variation (CNV), loss of heterozygosity (LOH) and mosaicism patterns of integrating and non-integrating iPSC lines were investigated. The maximum sizes of CNVs in the genomes of the integrating iPSC lines were 20 times higher than those of the non-integrating iPSC lines. Moreover, the total number of CNVs was much higher in integrating iPSC lines than in other cell lines. The average numbers of novel CNVs with a low degree of overlap with the DGV and of likely pathogenic CNVs with a high degree of overlap with the ISCA (International Symposium on Computer Architecture) database were highest in integrating iPSC lines. Different single nucleotide polymorphisms (SNP) calls revealed that, using the parental cell genotype as a reference, integrating iPSC lines displayed more single nucleotide variations and mosaicism than did non-integrating iPSC lines. This study describes the genome stability of human iPSCs generated using either a DNA-integrating or non-integrating reprogramming method, of the corresponding somatic cells, and of hESCs. Our results highlight the importance of using a high-resolution method to monitor genomic aberrations
Institute of Scientific and Technical Information of China (English)
Jianqin Lü; Xiaosong Zhao
2008-01-01
Nonlinear transport of intense continuous beam in the axial-symmetric electrostatic fields is analyzed with the Lie algebraic method.The K-V particle distribution is adopted in the analysis. The results obtained can be used in the calculations of the intense continuous beam dynamics in the beam optical systems consisting of drift spaces, electrostatic lenses, and DC electrostatic accelerating tubes. A com-puter code has been designed for practical simulations. To meet the needs of accurate calculation, all the elements are divided into many small segments, the electric fields in each segment are regarded as uniform fields, and the dividing points are treated as thin lenses. Iter-ation procedures are adopted in the code to obtain self-consistent solutions. The code can be used to design low energy dc beam transport systems, electrostatic accelerators, and ion implantation machines.
booc.io: An Education System with Hierarchical Concept Maps and Dynamic Non-linear Learning Plans.
Schwab, Michail; Strobelt, Hendrik; Tompkin, James; Fredericks, Colin; Huff, Connor; Higgins, Dana; Strezhnev, Anton; Komisarchik, Mayya; King, Gary; Pfister, Hanspeter
2017-01-01
Information hierarchies are difficult to express when real-world space or time constraints force traversing the hierarchy in linear presentations, such as in educational books and classroom courses. We present booc.io, which allows linear and non-linear presentation and navigation of educational concepts and material. To support a breadth of material for each concept, booc.io is Web based, which allows adding material such as lecture slides, book chapters, videos, and LTIs. A visual interface assists the creation of the needed hierarchical structures. The goals of our system were formed in expert interviews, and we explain how our design meets these goals. We adapt a real-world course into booc.io, and perform introductory qualitative evaluation with students.
Stationary solutions and self-trapping in discrete quadratic nonlinear systems
DEFF Research Database (Denmark)
Bang, Ole; Christiansen, Peter Leth; Clausen, Carl A. Balslev
1998-01-01
the nonintegrable dimer reduce to the discrete nonlinear Schrodinger (DNLS) equation with two degrees of freedom, which is integrable. We show how the stationary solutions to the two systems correspond to each other and how the self-trapped DNLS solutions gradually develop chaotic dynamics in the chi((2)) system......We consider the simplest equations describing coupled quadratic nonlinear (chi((2))) systems, which each consists of a fundamental mode resonantly interacting with its second harmonic. Such discrete equations apply, e.g., to optics, where they can describe arrays of chi((2)) waveguides...
Energy Technology Data Exchange (ETDEWEB)
Oliveira, Diego F.M., E-mail: diegofregolente@gmail.co [Departamento de Fisica, Instituto de Geociencias e Ciencias Exatas, Universidade Estadual Paulista, Av. 24A, 1515 Bela Vista, CEP, 13506-900 Rio Claro, SP (Brazil); Leonel, Edson D., E-mail: edleonel@rc.unesp.b [Departamento de Estatistica, Matematica Aplicada e Computacao, Instituto de Geociencias e Ciencias Exatas, Universidade Estadual Paulista, Av. 24A, 1515 Bela Vista, CEP, 13506-900 Rio Claro, SP (Brazil)
2010-07-05
Some dynamical properties for a dissipative time-dependent oval-shaped billiard are studied. The system is described in terms of a four-dimensional nonlinear mapping. Dissipation is introduced via inelastic collisions of the particle with the boundary, thus implying that the particle has a fractional loss of energy upon collision. The dissipation causes profound modifications in the dynamics of the particle as well as in the phase space of the non-dissipative system. In particular, inelastic collisions can be assumed as an efficient mechanism to suppress Fermi acceleration of the particle. The dissipation also creates attractors in the system, including chaotic. We show that a slightly modification of the intensity of the damping coefficient yields a drastic and sudden destruction of the chaotic attractor, thus leading the system to experience a boundary crisis. We have characterized such a boundary crisis via a collision of the chaotic attractor with its own basin of attraction and confirmed that inelastic collisions do indeed suppress Fermi acceleration in two-dimensional time-dependent billiards.
Peres Penteado, Alissa; Fábio Maciel, Rafael; Erbs, João; Feijó Ortolani, Cristina Lucia; Aguiar Roza, Bartira; Torres Pisa, Ivan
2015-01-01
The entire kidney transplantation process in Brazil is defined through laws, decrees, ordinances, and resolutions, but there is no defined theoretical map describing this process. From this representation it's possible to perform analysis, such as the identification of bottlenecks and information and communication technologies (ICTs) that support this process. The aim of this study was to analyze and represent the kidney transplantation workflow using business process modeling notation (BPMN) and then to identify the ICTs involved in the process. This study was conducted in eight steps, including document analysis and professional evaluation. The results include the BPMN model of the kidney transplantation process in Brazil and the identification of ICTs. We discovered that there are great delays in the process due to there being many different ICTs involved, which can cause information to be poorly integrated.
The scaling limit of the energy correlations in non-integrable Ising models
Giuliani, Alessandro; Greenblatt, Rafael L.; Mastropietro, Vieri
2012-09-01
We obtain an explicit expression for the multipoint energy correlations of a non-solvable two-dimensional Ising models with nearest neighbor ferromagnetic interactions plus a weak finite range interaction of strength λ, in a scaling limit in which we send the lattice spacing to zero and the temperature to the critical one. Our analysis is based on an exact mapping of the model into an interacting lattice fermionic theory, which generalizes the one originally used by Schultz, Mattis, and Lieb for the nearest neighbor Ising model. The interacting model is then analyzed by a multiscale method first proposed by Pinson and Spencer. If the lattice spacing is finite, then the correlations cannot be computed in closed form: rather, they are expressed in terms of infinite, convergent, power series in λ. In the scaling limit, these infinite expansions radically simplify and reduce to the limiting energy correlations of the integrable Ising model, up to a finite renormalization of the parameters. Explicit bounds on the speed of convergence to the scaling limit are derived.
Wang, Aixing; Fang, Chao; Liu, Yibao
2017-01-07
In this article the dynamic features of the highly excited vibrational states of the hypochlorous acid (HOCl) non-integrable system are studied using the dynamic potential and Lyapunov exponent approaches. On the condition that the 3:1 resonance between the H-O stretching and H-O-Cl bending modes accompany the 2:1 Fermi resonance between the O-Cl stretching and H-O-Cl bending modes, it is found that the dynamic potentials of the highly excited vibrational states vary regularly with different Polyad numbers (P numbers). As the P number increases, the dynamic potentials of the H-O stretching mode remain the same, but those of the H-O-Cl bending mode gradually become complex. In order to investigate the chaotic and stable features of the highly excited vibrational states of the HOCl non-integrable system, the Lyapunov exponents of different energy levels lying in the dynamic potentials of the H-O-Cl bending mode (P = 4 and 5) are calculated. It is shown that the Lyapunov exponents of the energy levels staying in the junction of Morse potential and inverse Morse potential are relative large, which indicates the degrees of chaos for these energy levels is relatively high, but the stabilities of the corresponding states are good. These results could be interpreted as the intramolecular vibrational relaxation (IVR) acting strongly via the HOCl bending motion and causing energy transfers among different modes. Based on the previous studies, these conclusions seem to be generally valid to some extent for non-integrable triatomic molecules.
Directory of Open Access Journals (Sweden)
Tea Soon Park
Full Text Available Nonviral conversion of skin or blood cells into clinically useful human induced pluripotent stem cells (hiPSC occurs in only rare fractions (~0.001%-0.5% of donor cells transfected with non-integrating reprogramming factors. Pluripotency induction of developmentally immature stem-progenitors is generally more efficient than differentiated somatic cell targets. However, the nature of augmented progenitor reprogramming remains obscure, and its potential has not been fully explored for improving the extremely slow pace of non-integrated reprogramming. Here, we report highly optimized four-factor reprogramming of lineage-committed cord blood (CB myeloid progenitors with bulk efficiencies of ~50% in purified episome-expressing cells. Lineage-committed CD33(+CD45(+CD34(- myeloid cells and not primitive hematopoietic stem-progenitors were the main targets of a rapid and nearly complete non-integrated reprogramming. The efficient conversion of mature myeloid populations into NANOG(+TRA-1-81(+ hiPSC was mediated by synergies between hematopoietic growth factor (GF, stromal activation signals, and episomal Yamanaka factor expression. Using a modular bioinformatics approach, we demonstrated that efficient myeloid reprogramming correlated not to increased proliferation or endogenous Core factor expressions, but to poised expression of GF-activated transcriptional circuits that commonly regulate plasticity in both hematopoietic progenitors and embryonic stem cells (ESC. Factor-driven conversion of myeloid progenitors to a high-fidelity pluripotent state was further accelerated by soluble and contact-dependent stromal signals that included an implied and unexpected role for Toll receptor-NFκB signaling. These data provide a paradigm for understanding the augmented reprogramming capacity of somatic progenitors, and reveal that efficient induced pluripotency in other cell types may also require extrinsic activation of a molecular framework that commonly
Directory of Open Access Journals (Sweden)
Shoukry Ibrahim Atia El-Ganaini
2013-01-01
Full Text Available The first integral method introduced by Feng is adopted for solving some important nonlinear systems of partial differential equations, including classical Drinfel'd-Sokolov-Wilson system (DSWE, (2 + 1-dimensional Davey-Stewartson system, and generalized Hirota-Satsuma coupled KdV system. This method provides polynomial first integrals for autonomous planar systems. Through the established first integrals, exact traveling wave solutions are formally derived in a concise manner. This method can also be applied to nonintegrable equations as well as integrable ones.
Institute of Scientific and Technical Information of China (English)
陈岁生; 卢建刚; 楼晓春
2012-01-01
New localization algorithms for wireless sensor networks which combine multidimensional scal-ing-map (MDS-MAP) and nonlinear filtering were studied to improve the localization accuracy of sensor nodes. According to the nonlinear relationship between the sensor node distances and the node localized coordinates, the extended Kalman filter (EKF) and the unscented Kalman filter (UKF) were applied to refine the localized coordinates obtained by the MDS-MAP algorithm. The localization accuracies of these three different localization algorithms, MDS-MAP, MDS-EKF (combination of MDS-MAP and EKF) and MDS-UKF (combination of MDS-MAP and UKF), were compared. Experimental results show that the implementation of nonlinear filtering algorithms (EKF and UKF) can improve the localization accuracy. Under the same conditions, the MDS-UKF localization algorithm achieves the best accuracy and its generated network topology is the closest to the actual network topology.%为提高传感器网络节点的定位精度,对MDS-MAP结合非线性滤波方法的多种传感器网络定位算法进行研究.根据传感器节点间距离与节点定位坐标之间存在的非线性关系,在MDS-MAP定位算法的基础上,引入扩展卡尔曼滤波(EKF)求精算法和不敏卡尔曼滤波(UKF)求精算法,对MDS- MAP求得的节点坐标进行求精.对MDS-MAP定位算法、MDS-MAP和EKF相结合的定位算法(MDS-EKF)、MDS-MAP和UKF相结合的定位算法(MDS-UKF)的定位精度进行比较.实验结果表明:EKF和UKF等非线性滤波方法的应用可以提高定位精度,在相同条件下MDS-UKF定位算法的定位精度更高并且其生成的网络拓扑图最接近于实际网络拓扑图.
Directory of Open Access Journals (Sweden)
Özgür Gürsu
2013-01-01
Full Text Available Background. Innovative cardiopulmonary bypass (CPB settings have been developed in order to integrate the concepts of “surface-coating,” “blood-filtration,” and “miniaturization.” Objectives. To compare integrated and nonintegrated arterial line filters in terms of peri- and postoperative clinical variables, inflammatory response, and transfusion needs. Material and Methods. Thirty-six patients who underwent coronary bypass surgery were randomized into integrated (Group In and nonintegrated arterial line filter (Group NIn groups. Arterial blood samples for the assessments of complete hemogram, biochemical screening, interleukin-6, interleukin-2R, and C-reactive protein were analyzed before and after surgery. Need for postoperative dialysis, inotropic therapy and transfusion, in addition to extubation time, total amount of drainage (mL, length of intensive care unit, and hospital stay, and mortality rates was also recorded for each patient. Results. Prime volume was significantly higher and mean intraoperative hematocrit value was lower in Group NIn, but need for erythrocyte transfusion was significantly higher in Group NIn. C-reactive protein values did not differ significantly except for postoperative second day's results, which were found significantly lower in Group In than in Group NIn. Conclusion. Intraoperative hematocrit levels were higher and need for postoperative erythrocyte transfusion was decreased in Group In.
Global Analysis of Nonlinear Dynamics
Luo, Albert
2012-01-01
Global Analysis of Nonlinear Dynamics collects chapters on recent developments in global analysis of non-linear dynamical systems with a particular emphasis on cell mapping methods developed by Professor C.S. Hsu of the University of California, Berkeley. This collection of contributions prepared by a diverse group of internationally recognized researchers is intended to stimulate interests in global analysis of complex and high-dimensional nonlinear dynamical systems, whose global properties are largely unexplored at this time. This book also: Presents recent developments in global analysis of non-linear dynamical systems Provides in-depth considerations and extensions of cell mapping methods Adopts an inclusive style accessible to non-specialists and graduate students Global Analysis of Nonlinear Dynamics is an ideal reference for the community of nonlinear dynamics in different disciplines including engineering, applied mathematics, meteorology, life science, computational science, and medicine.
Diffusion Based Photon Mapping
DEFF Research Database (Denmark)
Schjøth, Lars; Olsen, Ole Fogh; Sporring, Jon
2006-01-01
. To address this problem we introduce a novel photon mapping algorithm based on nonlinear anisotropic diffusion. Our algorithm adapts according to the structure of the photon map such that smoothing occurs along edges and structures and not across. In this way we preserve the important illumination features......, while eliminating noise. We call our method diffusion based photon mapping....
Diffusion Based Photon Mapping
DEFF Research Database (Denmark)
Schjøth, Lars; Fogh Olsen, Ole; Sporring, Jon
2007-01-01
. To address this problem we introduce a novel photon mapping algorithm based on nonlinear anisotropic diffusion. Our algorithm adapts according to the structure of the photon map such that smoothing occurs along edges and structures and not across. In this way we preserve the important illumination features......, while eliminating noise. We call our method diffusion based photon mapping....
The quasi-equilibrium phase of nonlinear chains
Indian Academy of Sciences (India)
T R Krishna Mohan; Surajit Sen
2005-03-01
We show that time evolution initiated via kinetic energy perturbations in conservative, discrete, spring-mass chains with purely nonlinear, non-integrable, algebraic potentials of the form ( − +1 ∼ $(_{} − _{+1})^{2}$, ≥ 2 and an integer, occurs via discrete solitary waves (DSWs) and discrete antisolitary waves (DASWs). Presence of reflecting and periodic boundaries in the system leads to collisions between the DSWs and DASWs. Such collisions lead to the breakage and subsequent reformation of (different) DSWs and DASWs. Our calculations show that the system eventually reaches a stable `quasi-equilibrium' phase that appears to be independent of initial conditions, possesses Gaussian velocity distribution, and has a higher mean kinetic energy and larger range of kinetic energy fluctuations as compared to the pure harmonic system with = 1; the latter indicates possible violation of equipartition.
Directory of Open Access Journals (Sweden)
Giulia Coppiello
2017-05-01
Full Text Available We generated ATCi-MF1 induced pluripotent stem (iPS cell line from Macaca fascicularis adult skin fibroblasts using non-integrative Sendai viruses carrying OCT3/4, KLF4, SOX2 and c-MYC. Once established, ATCi-MF1 cells present a normal karyotype, are Sendai virus-free and express pluripotency associated markers. Microsatellite markers analysis confirmed the origin of the iPS cells from the parental fibroblasts. Pluripotency was tested with the in vivo teratoma formation assay. ATCi-MF1 cell line may be a useful primate iPS cell model to test different experimental conditions where the use of human cells can imply ethical issues, as microinjection of pluripotent stem cells in pre-implantational embryos.
Slamecka, Jaroslav; Salimova, Lilia; McClellan, Steven; van Kelle, Mathieu; Kehl, Debora; Laurini, Javier; Cinelli, Paolo; Owen, Laurie; Hoerstrup, Simon P; Weber, Benedikt
2016-01-01
Amniotic fluid stem cells (AFSC) represent an attractive potential cell source for fetal and pediatric cell-based therapies. However, upgrading them to pluripotency confers refractoriness toward senescence, higher proliferation rate and unlimited differentiation potential. AFSC were observed to rapidly and efficiently reacquire pluripotency which together with their easy recovery makes them an attractive cell source for reprogramming. The reprogramming process as well as the resulting iPSC epigenome could potentially benefit from the unspecialized nature of AFSC. iPSC derived from AFSC also have potential in disease modeling, such as Down syndrome or β-thalassemia. Previous experiments involving AFSC reprogramming have largely relied on integrative vector transgene delivery and undefined serum-containing, feeder-dependent culture. Here, we describe non-integrative oriP/EBNA-1 episomal plasmid-based reprogramming of AFSC into iPSC and culture in fully chemically defined xeno-free conditions represented by vitronectin coating and E8 medium, a system that we found uniquely suited for this purpose. The derived AF-iPSC lines uniformly expressed a set of pluripotency markers Oct3/4, Nanog, Sox2, SSEA-1, SSEA-4, TRA-1-60, TRA-1-81 in a pattern typical for human primed PSC. Additionally, the cells formed teratomas, and were deemed pluripotent by PluriTest, a global expression microarray-based in-silico pluripotency assay. However, we found that the PluriTest scores were borderline, indicating a unique pluripotent signature in the defined condition. In the light of potential future clinical translation of iPSC technology, non-integrating reprogramming and chemically defined culture are more acceptable.
Nonlinear robust hierarchical control for nonlinear uncertain systems
Directory of Open Access Journals (Sweden)
Leonessa Alexander
1999-01-01
Full Text Available A nonlinear robust control-system design framework predicated on a hierarchical switching controller architecture parameterized over a set of moving nominal system equilibria is developed. Specifically, using equilibria-dependent Lyapunov functions, a hierarchical nonlinear robust control strategy is developed that robustly stabilizes a given nonlinear system over a prescribed range of system uncertainty by robustly stabilizing a collection of nonlinear controlled uncertain subsystems. The robust switching nonlinear controller architecture is designed based on a generalized (lower semicontinuous Lyapunov function obtained by minimizing a potential function over a given switching set induced by the parameterized nominal system equilibria. The proposed framework robustly stabilizes a compact positively invariant set of a given nonlinear uncertain dynamical system with structured parametric uncertainty. Finally, the efficacy of the proposed approach is demonstrated on a jet engine propulsion control problem with uncertain pressure-flow map data.
DEFF Research Database (Denmark)
Mosegaard, Klaus
2012-01-01
For non-linear inverse problems, the mathematical structure of the mapping from model parameters to data is usually unknown or partly unknown. Absence of information about the mathematical structure of this function prevents us from presenting an analytical solution, so our solution depends on our......-heuristics are inefficient for large-scale, non-linear inverse problems, and that the 'no-free-lunch' theorem holds. We discuss typical objections to the relevance of this theorem. A consequence of the no-free-lunch theorem is that algorithms adapted to the mathematical structure of the problem perform more efficiently than...
Bloembergen, Nicolaas
1996-01-01
Nicolaas Bloembergen, recipient of the Nobel Prize for Physics (1981), wrote Nonlinear Optics in 1964, when the field of nonlinear optics was only three years old. The available literature has since grown by at least three orders of magnitude.The vitality of Nonlinear Optics is evident from the still-growing number of scientists and engineers engaged in the study of new nonlinear phenomena and in the development of new nonlinear devices in the field of opto-electronics. This monograph should be helpful in providing a historical introduction and a general background of basic ideas both for expe
Diffusion Based Photon Mapping
DEFF Research Database (Denmark)
Schjøth, Lars; Sporring, Jon; Fogh Olsen, Ole
2008-01-01
. To address this problem, we introduce a photon mapping algorithm based on nonlinear anisotropic diffusion. Our algorithm adapts according to the structure of the photon map such that smoothing occurs along edges and structures and not across. In this way, we preserve important illumination features, while...
2016-07-01
Advanced Research Projects Agency (DARPA) Dynamics-Enabled Frequency Sources (DEFYS) program is focused on the convergence of nonlinear dynamics and...Early work in this program has shown that nonlinear dynamics can provide performance advantages. However, the pathway from initial results to...dependent nonlinear stiffness observed in these devices. This work is ongoing, and will continue through the final period of this program . Reference 9
Nonlinear stochastic optimal bounded control of hysteretic systems with actuator saturation
Institute of Scientific and Technical Information of China (English)
Rong-hua HUAN; Wei-qiu ZHU; Yong-jun WU
2008-01-01
A modified nonlinear stochastic optimal bounded control strategy for random excited hysteretic systems with actuator saturation is proposed. First, a controlled hysteretic system is converted into an equivalent nonlinear nonhysteretic stochastic system. Then, the partially averaged It6 stochastic differential equation and dynamical programming equation are established, respectively, by using the stochastic averaging method for quasi non-integrable Hamiltonian systems and stochastic dynamical programming principle, from which the optimal control law consisting of optimal unbounded control and bang-bang control is derived. Finally, the response of optimally controlled system is predicted by solving the Fokker-Planck-Kolmogorov (FPK) equation associated with the fully averaged It6 equation. Numerical results show that the proposed control strategy has high control effectiveness and efficiency.
Nayfeh, Ali Hasan
1995-01-01
Nonlinear Oscillations is a self-contained and thorough treatment of the vigorous research that has occurred in nonlinear mechanics since 1970. The book begins with fundamental concepts and techniques of analysis and progresses through recent developments and provides an overview that abstracts and introduces main nonlinear phenomena. It treats systems having a single degree of freedom, introducing basic concepts and analytical methods, and extends concepts and methods to systems having degrees of freedom. Most of this material cannot be found in any other text. Nonlinear Oscillations uses sim
Yoshida, Zensho
2010-01-01
This book gives a general, basic understanding of the mathematical structure "nonlinearity" that lies in the depths of complex systems. Analyzing the heterogeneity that the prefix "non" represents with respect to notions such as the linear space, integrability and scale hierarchy, "nonlinear science" is explained as a challenge of deconstruction of the modern sciences. This book is not a technical guide to teach mathematical tools of nonlinear analysis, nor a zoology of so-called nonlinear phenomena. By critically analyzing the structure of linear theories, and cl
Nanda, Sudarsan
2013-01-01
"Nonlinear analysis" presents recent developments in calculus in Banach space, convex sets, convex functions, best approximation, fixed point theorems, nonlinear operators, variational inequality, complementary problem and semi-inner-product spaces. Nonlinear Analysis has become important and useful in the present days because many real world problems are nonlinear, nonconvex and nonsmooth in nature. Although basic concepts have been presented here but many results presented have not appeared in any book till now. The book could be used as a text for graduate students and also it will be useful for researchers working in this field.
Energy Technology Data Exchange (ETDEWEB)
Zhu Shundong [Department of Physics, Zhejiang Lishui University, Lishui 323000 (China)], E-mail: zhusd1965@sina.com
2008-09-15
The tanh method is used to find travelling wave solutions to various wave equations. In this paper, the extended tanh function method is further improved by the generalizing Riccati equation mapping method and picking up its new solutions. In order to test the validity of this approach, the (2 + 1)-dimensional Boiti-Leon-Pempinelle equation is considered. As a result, the abundant new non-travelling wave solutions are obtained.
Institute of Scientific and Technical Information of China (English)
Yongjie Piao∗
2015-01-01
A classΦof 5-dimensional functions was introduced and an existence and uniqueness of common fixed points for a family of non-self mappings satisfying aφi-quasi-contractive condition and a certain boundary condition was given on complete metrically convex metric spaces, and from which, more general unique common fixed point theorems were obtained.Our main results generalize and improve many same type common fixed point theorems in references.
Classification of Lipschitz mappings
Piasecki, Lukasz
2013-01-01
The Lipschitz Condition Nonlinear spectral radius Uniformly lipschitzian mappings Basic Facts on Banach Spaces Convexity The operator norm Dual spaces, reexivity, the weak, and weak* topologiesMean Lipschitz Condition Nonexpansive and mean nonexpansive mappings in Banach spaces General case On the Lipschitz Constants for Iterates of Mean Lipschitzian Mappings A bound for Lipschitz constants of iterates A bound for the constant k∞(T)Moving averages in Bana
Energy Technology Data Exchange (ETDEWEB)
Later, D.W.
1985-01-01
This document reports the results from chemical analyses and biological testing of process materials sampled during operation of the Wilsonville Advanced Coal Liquefaction Research and Development Facility (Wilsonville, Alabama) in both the noncoupled or nonintegrated (NTSL Run 241) and coupled or integrated (ITSL Run 242) two-stage liquefaction operating modes. Mutagenicity and carcinogenicity assays were conducted in conjunction with chromatographic and mass spectrometric analyses to provide detailed, comparative chemical and biological assessments of several NTSL and ITSL process materials. In general, the NTSL process materials were biologically more active and chemically more refractory than analogous ITSL process materials. To provide perspective, the NTSL and ITSL results are compared with those from similar testing and analyses of other direct coal liquefaction materials from the solvent refined coal (SRC) I, SRC II and EDS processes. Comparisons are also made between two-stage coal liquefaction materials from the Wilsonville pilot plant and the C.E. Lummus PDU-ITSL Facility in an effort to assess scale-up effects in these two similar processes. 36 references, 26 figures, 37 tables.
Boyd, Robert W
2013-01-01
Nonlinear Optics is an advanced textbook for courses dealing with nonlinear optics, quantum electronics, laser physics, contemporary and quantum optics, and electrooptics. Its pedagogical emphasis is on fundamentals rather than particular, transitory applications. As a result, this textbook will have lasting appeal to a wide audience of electrical engineering, physics, and optics students, as well as those in related fields such as materials science and chemistry.Key Features* The origin of optical nonlinearities, including dependence on the polarization of light* A detailed treatment of the q
Generalized Strongly Nonlinear Implicit Quasivariational Inequalities
Directory of Open Access Journals (Sweden)
Salahuddin
2009-01-01
Full Text Available We prove an existence theorem for solution of generalized strongly nonlinear implicit quasivariational inequality problems and convergence of iterative sequences with errors, involving Lipschitz continuous, generalized pseudocontractive and generalized -pseudocontractive mappings in Hilbert spaces.
GLOBAL SOLUTIONS OF NONLINEAR SCHRODINGER EQUATIONS
Institute of Scientific and Technical Information of China (English)
Ye Yaojun
2005-01-01
In this paper we study the existence of global solutions to the Cauchy problem of nonlinear Schrodinger equation by establishing time weight function spaces and using the contraction mapping principle.
Ruszczynski, Andrzej
2011-01-01
Optimization is one of the most important areas of modern applied mathematics, with applications in fields from engineering and economics to finance, statistics, management science, and medicine. While many books have addressed its various aspects, Nonlinear Optimization is the first comprehensive treatment that will allow graduate students and researchers to understand its modern ideas, principles, and methods within a reasonable time, but without sacrificing mathematical precision. Andrzej Ruszczynski, a leading expert in the optimization of nonlinear stochastic systems, integrates t
Boundary controllability for a nonlinear beam equation
Directory of Open Access Journals (Sweden)
Xiao-Min Cao
2015-09-01
Full Text Available This article concerns a nonlinear system modeling the bending vibrations of a nonlinear beam of length $L>0$. First, we derive the existence of long time solutions near an equilibrium. Then we prove that the nonlinear beam is locally exact controllable around the equilibrium in $H^4(0,L$ and with control functions in $H^2(0,T$. The approach we used are open mapping theorem, local controllability established by linearization, and the induction.
Nonlinear science an interactive Mathematica notebook
Campbell, David K; Tanury, Thomas A
2012-01-01
This interactive Mathematica(TM) notebook provides a ready-made tool by which users can undertake their own mathematical experiments and explore the behavior of non-linear systems, from chaos in low-dimensional maps and coupled ordinary differential equations to solitons and coherent structures in nonlinear partial differential equations and "intrisic localized modes" and "discrete breathers" in extended lattice systems.
Wismüller, Axel; Abidin, Anas Z.; D'Souza, Adora M.; Wang, Xixi; Hobbs, Susan K.; Leistritz, Lutz; Nagarajan, Mahesh B.
2015-03-01
We explore a computational framework for functional connectivity analysis in resting-state functional MRI (fMRI) data acquired from the human brain for recovering the underlying network structure and understanding causality between network components. Termed mutual connectivity analysis (MCA), this framework involves two steps, the first of which is to evaluate the pair-wise cross-prediction performance between fMRI pixel time series within the brain. In a second step, the underlying network structure is subsequently recovered from the affinity matrix using non-metric network clustering approaches, such as the so-called Louvain method. Finally, we use convergent cross-mapping (CCM) to study causality between different network components. We demonstrate our MCA framework in the problem of recovering the motor cortex network associated with hand movement from resting state fMRI data. Results are compared with a ground truth of active motor cortex regions as identified by a task-based fMRI sequence involving a finger-tapping stimulation experiment. Our results regarding causation between regions of the motor cortex revealed a significant directional variability and were not readily interpretable in a consistent manner across subjects. However, our results on whole-slice fMRI analysis demonstrate that MCA-based model-free recovery of regions associated with the primary motor cortex and supplementary motor area are in close agreement with localization of similar regions achieved with a task-based fMRI acquisition. Thus, we conclude that our MCA methodology can extract and visualize valuable information concerning the underlying network structure between different regions of the brain in resting state fMRI.
In, Visarath; Longhini, Patrick; Kho, Andy; Neff, Joseph D.; Leung, Daniel; Liu, Norman; Meadows, Brian K.; Gordon, Frank; Bulsara, Adi R.; Palacios, Antonio
2012-12-01
The nonlinear channelizer is an integrated circuit made up of large parallel arrays of analog nonlinear oscillators, which, collectively, serve as a broad-spectrum analyzer with the ability to receive complex signals containing multiple frequencies and instantaneously lock-on or respond to a received signal in a few oscillation cycles. The concept is based on the generation of internal oscillations in coupled nonlinear systems that do not normally oscillate in the absence of coupling. In particular, the system consists of unidirectionally coupled bistable nonlinear elements, where the frequency and other dynamical characteristics of the emergent oscillations depend on the system's internal parameters and the received signal. These properties and characteristics are being employed to develop a system capable of locking onto any arbitrary input radio frequency signal. The system is efficient by eliminating the need for high-speed, high-accuracy analog-to-digital converters, and compact by making use of nonlinear coupled systems to act as a channelizer (frequency binning and channeling), a low noise amplifier, and a frequency down-converter in a single step which, in turn, will reduce the size, weight, power, and cost of the entire communication system. This paper covers the theory, numerical simulations, and some engineering details that validate the concept at the frequency band of 1-4 GHz.
Directory of Open Access Journals (Sweden)
Victor Kardashov
2002-01-01
Full Text Available This paper has considered a novel approach to structural recognition and control of nonlinear reaction-diffusion systems (systems with density dependent diffusion. The main consistence of the approach is interactive variation of the nonlinear diffusion and sources structural parameters that allows to implement a qualitative control and recognition of transitional system conditions (transients. The method of inverse solutions construction allows formulating the new analytic conditions of compactness and periodicity of the transients that is also available for nonintegrated systems. On the other hand, using of energy conservations laws, allows transfer to nonlinear dynamics models that gives the possiblity to apply the modern deterministic chaos theory (particularly the Feigenboum's universal constants and scenario of chaotic transitions.
Energy Technology Data Exchange (ETDEWEB)
Turchetti, G. (Bologna Univ. (Italy). Dipt. di Fisica)
1989-01-01
Research in nonlinear dynamics is rapidly expanding and its range of applications is extending beyond the traditional areas of science where it was first developed. Indeed while linear analysis and modelling, which has been very successful in mathematical physics and engineering, has become a mature science, many elementary phenomena of intrinsic nonlinear nature were recently experimentally detected and investigated, suggesting new theoretical work. Complex systems, as turbulent fluids, were known to be governed by intrinsically nonlinear laws since a long time ago, but received purely phenomenological descriptions. The pioneering works of Boltzmann and Poincare, probably because of their intrinsic difficulty, did not have a revolutionary impact at their time; it is only very recently that their message is reaching a significant number of mathematicians and physicists. Certainly the development of computers and computer graphics played an important role in developing geometric intuition of complex phenomena through simple numerical experiments, while a new mathematical framework to understand them was being developed.
Fractal scattering of Gaussian solitons in directional couplers with logarithmic nonlinearities
Energy Technology Data Exchange (ETDEWEB)
Teixeira, Rafael M.P.; Cardoso, Wesley B., E-mail: wesleybcardoso@gmail.com
2016-08-12
In this paper we study the interaction of Gaussian solitons in a dispersive and nonlinear media with log-law nonlinearity. The model is described by the coupled logarithmic nonlinear Schrödinger equations, which is a nonintegrable system that allows the observation of a very rich scenario in the collision patterns. By employing a variational approach and direct numerical simulations, we observe a fractal-scattering phenomenon from the exit velocities of each soliton as a function of the input velocities. Furthermore, we introduce a linearization model to identify the position of the reflection/transmission window that emerges within the chaotic region. This enables us the possibility of controlling the scattering of solitons as well as the lifetime of bound states. - Highlights: • We study the interaction of Gaussian solitons in a system with log-law nonlinearity. • The model is described by the coupled logarithmic nonlinear Schrödinger equations. • We observe a fractal-scattering phenomenon of the solitons.
Exact Solution of a Generalized Nonlinear Schrodinger Equation Dimer
DEFF Research Database (Denmark)
Christiansen, Peter Leth; Maniadis, P.; Tsironis, G.P.
1998-01-01
We present exact solutions for a nonlinear dimer system defined throught a discrete nonlinear Schrodinger equation that contains also an integrable Ablowitz-Ladik term. The solutions are obtained throught a transformation that maps the dimer into a double Sine-Gordon like ordinary nonlinear...... differential equation....
Developments of VLBI synthesis mapping.
Jiang, Dongrong; Wan, Tongshan
1992-12-01
The authors review the developments of VLBI synthesis mapping. First they give a brief history of VLBI techniques and a summary of some technical parameters frequently used in VLBI synthesis mapping. They then mention problems, namely, (u,v) coverage, correction of errors in visibility data, image quality, GFF (Global Fringe Fitting), field of view, etc. The new developments which are presented include the improvements of (u,v) coverage and angular resolution, Mk III GFF, phase reference mapping, wide field mapping, difference mapping, the potential of space VLBI mapping, mosaicing and non-linear deconvolution.
Seider, Warren D.; Ungar, Lyle H.
1987-01-01
Describes a course in nonlinear mathematics courses offered at the University of Pennsylvania which provides an opportunity for students to examine the complex solution spaces that chemical engineers encounter. Topics include modeling many chemical processes, especially those involving reaction and diffusion, auto catalytic reactions, phase…
Institute of Scientific and Technical Information of China (English)
赵明
2014-01-01
This paper studies two types of models of the non-integrated supply chain without or with a transporter. Firstly, in the absence of a transporter,we establish the non-integrated supply chain models that the retailor and the manufacturer respectively acts as the transporter.Secondly, with a transporter participating in the supply chain,we set up the non-integrated supply chain models that the retailor and the manufacturer respectively bears the transportation service charges.Finally,by comparing the optimal solutions of the two types of models,we analyze the effects of the different transportation sponsors and the different undertakers of transportation service expenses on the retailor’s, manufacturer’s and the supply chain’s total profits.%研究了没有运输商和有运输商参与的两类非一体化供应链模型。首先，在没有运输商参与情况下，构建了零售商和制造商分别作为运输主体的非一体化供应链模型；其次，在有运输商参与的情况下，构建了零售商和制造商分别承担运输服务费用下的非一体化供应链模型；最后，通过对两类模型最优解的比较，分析了运输主体的不同和运输服务费用承担主体的不同对零售商、制造商以及供应链整体利润的影响。
Wijk, Jarke J. van; Telea, Alexandru
2001-01-01
The visualization of scalar functions of two variables is a classic and ubiquitous application. We present a new method to visualize such data. The method is based on a non-linear mapping of the function to a height field, followed by visualization as a shaded mountain landscape. The method is easy
Energy Technology Data Exchange (ETDEWEB)
Edelman, Mark, E-mail: edelman@cims.nyu.ed [Courant Institute of Mathematical Sciences, New York University, 251 Mercer St., New York, NY 10012 (United States)] [Department of Physics, Stern College at Yeshiva University, 245 Lexington Avenue, New York, NY 10016 (United States); Tarasov, Vasily E. [Courant Institute of Mathematical Sciences, New York University, 251 Mercer St., New York, NY 10012 (United States)] [Skobeltsyn Institute of Nuclear Physics, Moscow State University, Moscow 119991 (Russian Federation)
2009-12-28
Properties of the phase space of the standard map with memory are investigated. This map was obtained from a kicked fractional differential equation. Depending on the value of the map parameter and the fractional order of the derivative in the original differential equation, this nonlinear dynamical system demonstrates attractors (fixed points, stable periodic trajectories, slow converging and slow diverging trajectories, ballistic trajectories, and fractal-like structures) and/or chaotic trajectories. At least one type of fractal-like sticky attractors in the chaotic sea was observed.
2015-01-01
From the Back Cover: The emphasis throughout the present volume is on the practical application of theoretical mathematical models helping to unravel the underlying mechanisms involved in processes from mathematical physics and biosciences. It has been conceived as a unique collection of abstract methods dealing especially with nonlinear partial differential equations (either stationary or evolutionary) that are applied to understand concrete processes involving some important applications re...
Ronald, John A.; Cusso, Lorena; Chuang, Hui-Yen; Yan, Xinrui; Dragulescu-Andrasi, Anca; Gambhir, Sanjiv Sam
2013-01-01
Reporter gene (RG) imaging of cell-based therapies provides a direct readout of therapeutic efficacy by assessing the fate of implanted cells. To permit long-term cellular imaging, RGs are traditionally required to be integrated into the cellular genome. This poses a potential safety risk and regulatory bottleneck for clinical translation as integration can lead to cellular transformation. To address this issue, we have developed non-integrative, replicating minicircles (MCs) as an alternative platform for safer monitoring of cells in living subjects. We developed both plasmids and minicircles containing the scaffold/matrix attachment regions (S/MAR) of the human interferon-beta gene, driven by the CMV promoter, and expressing the bioluminescence RG firefly luciferase. Constructs were transfected into breast cancer cells, and expanded S/MAR minicircle clones showed luciferase signal for greater than 3 months in culture and minicircles remained as episomes. Importantly, luciferase activity in clonal populations was slowly lost over time and this corresponded to a loss of episome, providing a way to reversibly label cells. To monitor cell proliferation in vivo, 1.5×106 cells carrying the S/MAR minicircle were implanted subcutaneously into mice (n = 5) and as tumors developed significantly more bioluminescence signal was noted at day 35 and 43 compared to day 7 post-implant (p<0.05). To our knowledge, this is the first work examining the use of episomal, self-limited, replicating minicircles to track the proliferation of cells using non-invasive imaging in living subjects. Continued development of S/MAR minicircles will provide a broadly applicable vector platform amenable with any of the numerous RG technologies available to allow therapeutic cell fate to be assessed in individual patients, and to achieve this without the need to manipulate the cell's genome so that safety concerns are minimized. This will lead to safe tools to assess treatment response at
Directory of Open Access Journals (Sweden)
Sayed M. Arafat
2014-06-01
Full Text Available Land cover map of North Sinai was produced based on the FAO-Land Cover Classification System (LCCS of 2004. The standard FAO classification scheme provides a standardized system of classification that can be used to analyze spatial and temporal land cover variability in the study area. This approach also has the advantage of facilitating the integration of Sinai land cover mapping products to be included with the regional and global land cover datasets. The total study area is covering a total area of 20,310.4 km2 (203,104 hectare. The landscape classification was based on SPOT4 data acquired in 2011 using combined multispectral bands of 20 m spatial resolution. Geographic Information System (GIS was used to manipulate the attributed layers of classification in order to reach the maximum possible accuracy. GIS was also used to include all necessary information. The identified vegetative land cover classes of the study area are irrigated herbaceous crops, irrigated tree crops and rain fed tree crops. The non-vegetated land covers in the study area include bare rock, bare soils (stony, very stony and salt crusts, loose and shifting sands and sand dunes. The water bodies were classified as artificial perennial water bodies (fish ponds and irrigated canals and natural perennial water bodies as lakes (standing. The artificial surfaces include linear and non-linear features.
Nonlinearity detection in hyperspectral images using a polynomial post-nonlinear mixing model.
Altmann, Yoann; Dobigeon, Nicolas; Tourneret, Jean-Yves
2013-04-01
This paper studies a nonlinear mixing model for hyperspectral image unmixing and nonlinearity detection. 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 by polynomials leading to a polynomial post-nonlinear mixing model. We have shown in a previous paper that the parameters involved in the resulting model can be estimated using least squares methods. A generalized likelihood ratio test based on the estimator of the nonlinearity parameter is proposed to decide whether a pixel of the image results from the commonly used linear mixing model or from a more general nonlinear mixing model. To compute the test statistic associated with the nonlinearity detection, we propose to approximate the variance of the estimated nonlinearity parameter by its constrained Cramér-Rao bound. The performance of the detection strategy is evaluated via simulations conducted on synthetic and real data. More precisely, synthetic data have been generated according to the standard linear mixing model and three nonlinear models from the literature. The real data investigated in this study are extracted from the Cuprite image, which shows that some minerals seem to be nonlinearly mixed in this image. Finally, it is interesting to note that the estimated abundance maps obtained with the post-nonlinear mixing model are in good agreement with results obtained in previous studies.
Institute of Scientific and Technical Information of China (English)
郭祖华; 王辉
2015-01-01
Current chaotic map cryptographies are commonly difficult to balance high computation efficiency and high security and cannot meet the real-time transmission requirement of internet as well.In light of these shortcomings, we design the synchronised pseudo-random number generator and the parallelised masking technology, and introduce periodic boundary conditions, according to 2D chaotic map and nearest-neighbouring coupled map lattices we derive the coupling model of the algorithm proposed in the paper, and present an image encryption algorithm in which the 2D piecewise nonlinear chaotic map couples the nearest-neighbouring coupled map lattices.Through synchronised pseudo-random number generator we generate the initial conditions and parameters of the proposed algorithm, and then according to the coupling model we derive a group of pseudo-random numbers by iterating the initial values; finally, we use these pseudo-random numbers to carry out bidirectional encryption on plaintext image based on encryption transformation function, and use S-box to substitute the encryption elements, and conduct the masking process.Simulation results show that compared with current chaotic cryptography, the proposed algorithm has higher security and computation efficiency;and can meet the real-time transmission requirement of internet as well.%针对当前的混沌映射加密算法普遍难以兼顾高计算效率和高安全性,无法满足互联网实时性传输要求等不足. 设计了伪随机数同步生成器和并行化掩蔽技术;并引入周期性边界条件,根据2D混沌映射与最邻近耦合映像格子推导出耦合模型,提出一种2D分段非线性混沌映射耦合最邻近耦合映像格子的图像加密算法. 通过伪随机数同步生成器生成算法的初始条件与参数,然后根据该耦合模型迭代初始值,得到一组伪随机数;最后利用该伪随机数根据加密变换函数对明文图像进行双向加密,利
Nonlinear dynamics and chaotic phenomena an introduction
Shivamoggi, Bhimsen K
2014-01-01
This book starts with a discussion of nonlinear ordinary differential equations, bifurcation theory and Hamiltonian dynamics. It then embarks on a systematic discussion of the traditional topics of modern nonlinear dynamics -- integrable systems, Poincaré maps, chaos, fractals and strange attractors. The Baker’s transformation, the logistic map and Lorenz system are discussed in detail in view of their central place in the subject. There is a detailed discussion of solitons centered around the Korteweg-deVries equation in view of its central place in integrable systems. Then, there is a discussion of the Painlevé property of nonlinear differential equations which seems to provide a test of integrability. Finally, there is a detailed discussion of the application of fractals and multi-fractals to fully-developed turbulence -- a problem whose understanding has been considerably enriched by the application of the concepts and methods of modern nonlinear dynamics. On the application side, there is a special...
Institute of Scientific and Technical Information of China (English)
姜劲
2016-01-01
舰载雷达一般要同时承担对空和对海目标搜索预警任务，雷达资源十分紧张。在圈扫模式下进行海面目标检测时，同一波位上的相参脉冲数很少，导致目标的多普勒信息难以利用，加上海杂波本身的非高斯性，使得海面低速小目标检测较为困难。提出了一种基于目标扩展的非线性映射检测方法，该方法在抑制杂波单元的同时保留目标特征的强散射单元，在实距离像互相关矩阵基础上构造了一个新的统计量用于决策，基于实测数据的分析结果表明该检测算法优于传统的平均恒虚警检测。%The main task for shipborne radar is searching and warning both air and sea targets, therefore,the system resource is in short supply.The number of coherent pulses in the same beam position is limited for Doppler analysis,as well as the non-Gaussian nature of sea clutter, which together cause detection problem for low speed target in sea clutter.A nonlinear mapping method is proposed for range-spread target in sea clutter.The feature of the proposed method is that it can maintain the character of strong scattering unit while suppressing sea clut-ter.A new detection statistics is built on the basis of cross-correlation matrix of real range pro-file,which is used for making final decision.The analysis result of real radar data shows the proposed method is better than traditional CA-CFAR.
Directory of Open Access Journals (Sweden)
2006-01-01
Full Text Available The maps of the form f( x = ∑ i=1 n a i ⋅x⋅ b i , called 1-degree maps, are introduced and investigated. For noncommutative algebras and modules over them 1-degree maps give an analogy of linear maps and differentials. Under some conditions on the algebra 𝒜 , contractibility of the group of 1-degree isomorphisms is proved for the module l 2 ( 𝒜 . It is shown that these conditions are fulfilled for the algebra of linear maps of a finite-dimensional linear space. The notion of 1-degree map gives a possibility to define a nonlinear Fredholm map of l 2 ( 𝒜 and a Fredholm manifold modelled by l 2 ( 𝒜 . 1-degree maps are also applied to some problems of Markov chains.
Rajasekar, Shanmuganathan
2016-01-01
This introductory text presents the basic aspects and most important features of various types of resonances and anti-resonances in dynamical systems. In particular, for each resonance, it covers the theoretical concepts, illustrates them with case studies, and reviews the available information on mechanisms, characterization, numerical simulations, experimental realizations, possible quantum analogues, applications and significant advances made over the years. Resonances are one of the most fundamental phenomena exhibited by nonlinear systems and refer to specific realizations of maximum response of a system due to the ability of that system to store and transfer energy received from an external forcing source. Resonances are of particular importance in physical, engineering and biological systems - they can prove to be advantageous in many applications, while leading to instability and even disasters in others. The book is self-contained, providing the details of mathematical derivations and techniques invo...
Institute of Scientific and Technical Information of China (English)
1996-01-01
3.1 A Unified Nonlinear Feedback Functional Method for Study Both Control and Synchronization of Spatiotemporal Chaos Fang Jinqing Ali M. K. (Department of Physics, The University of Lethbridge,Lethbridge, Alberta T1K 3M4,Canada) Two fundamental questions dominate future chaos control theories.The first is the problem of controlling hyperchaos in higher dimensional systems.The second question has yet to be addressed:the problem of controlling spatiotemporal chaos in a spatiotemporal system.In recent years, control and synchronization of spatiotemporal chaos and hyperchaos have became a much more important and challenging subject. The reason for this is the control and synchronism of such behaviours have extensive and great potential of interdisciplinary applications, such as security communication, information processing, medicine and so on. However, this subject is not much known and remains an outstanding open.
Discretization and implicit mapping dynamics
Luo, Albert C J
2015-01-01
This unique book presents the discretization of continuous systems and implicit mapping dynamics of periodic motions to chaos in continuous nonlinear systems. The stability and bifurcation theory of fixed points in discrete nonlinear dynamical systems is reviewed, and the explicit and implicit maps of continuous dynamical systems are developed through the single-step and multi-step discretizations. The implicit dynamics of period-m solutions in discrete nonlinear systems are discussed. The book also offers a generalized approach to finding analytical and numerical solutions of stable and unstable periodic flows to chaos in nonlinear systems with/without time-delay. The bifurcation trees of periodic motions to chaos in the Duffing oscillator are shown as a sample problem, while the discrete Fourier series of periodic motions and chaos are also presented. The book offers a valuable resource for university students, professors, researchers and engineers in the fields of applied mathematics, physics, mechanics,...
DSP Approach to the Design of Nonlinear Optical Devices
Directory of Open Access Journals (Sweden)
Steve Blair
2005-06-01
Full Text Available Discrete-time signal processing (DSP tools have been used to analyze numerous optical filter configurations in order to optimize their linear response. In this paper, we propose a DSP approach to design nonlinear optical devices by treating the desired nonlinear response in the weak perturbation limit as a discrete-time filter. Optimized discrete-time filters can be designed and then mapped onto a specific optical architecture to obtain the desired nonlinear response. This approach is systematic and intuitive for the design of nonlinear optical devices. We demonstrate this approach by designing autoregressive (AR and autoregressive moving average (ARMA lattice filters to obtain a nonlinear phase shift response.
NONLINEAR DATA RECONCILIATION METHOD BASED ON KERNEL PRINCIPAL COMPONENT ANALYSIS
Institute of Scientific and Technical Information of China (English)
无
2003-01-01
In the industrial process situation, principal component analysis (PCA) is a general method in data reconciliation.However, PCA sometime is unfeasible to nonlinear feature analysis and limited in application to nonlinear industrial process.Kernel PCA (KPCA) is extension of PCA and can be used for nonlinear feature analysis.A nonlinear data reconciliation method based on KPCA is proposed.The basic idea of this method is that firstly original data are mapped to high dimensional feature space by nonlinear function, and PCA is implemented in the feature space.Then nonlinear feature analysis is implemented and data are reconstructed by using the kernel.The data reconciliation method based on KPCA is applied to ternary distillation column.Simulation results show that this method can filter the noise in measurements of nonlinear process and reconciliated data can represent the true information of nonlinear process.
Nonlinear Materials Characterization Facility
Federal Laboratory Consortium — The Nonlinear Materials Characterization Facility conducts photophysical research and development of nonlinear materials operating in the visible spectrum to protect...
Nonlinear singular vectors and nonlinear singular values
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
A novel concept of nonlinear singular vector and nonlinear singular value is introduced, which is a natural generalization of the classical linear singular vector and linear singular value to the nonlinear category. The optimization problem related to the determination of nonlinear singular vectors and singular values is formulated. The general idea of this approach is demonstrated by a simple two-dimensional quasigeostrophic model in the atmospheric and oceanic sciences. The advantage and its applications of the new method to the predictability, ensemble forecast and finite-time nonlinear instability are discussed. This paper makes a necessary preparation for further theoretical and numerical investigations.
Novel Localized Excitations of Nonlinear Coupled Scalar Fields
Institute of Scientific and Technical Information of China (English)
ZHU Ren-Gui; LI Jin-Hua; WANG An-Min; WU Huang-Jiao
2008-01-01
Some extended solution mapping relations of the nonlinear coupled scalar field and the well-known φ4 model are presented. Simultaneously, inspired by the new solutions of the famous φ4 model recently proposed by Jia, Huang and Lou, five kinds of new localized excitations of the nonlinear coupled scalar field (NCSF) system are obtained.
Quantification of unidirectional nonlinear associations between multidimensional signals.
S.N. Kalitzin; J. Parra; D.N. Velis; F.H. Lopes da Silva
2007-01-01
In this paper, we present a rigorous, general definition of the nonlinear association index, known as h2. Proving equivalence between different definitions we show that the index measures the best dynamic range of any nonlinear map between signals. We present also a construction for removing the inf
Linearization of Systems of Nonlinear Diffusion Equations
Institute of Scientific and Technical Information of China (English)
KANG Jing; QU Chang-Zheng
2007-01-01
We investigate the linearization of systems of n-component nonlinear diffusion equations; such systems have physical applications in soil science, mathematical biology and invariant curve flows. Equivalence transformations of their auxiliary systems are used to identify the systems that can be linearized. We also provide several examples of systems with two-component equations, and show how to linearize them by nonlocal mappings.
Topological invariants in nonlinear boundary value problems
Energy Technology Data Exchange (ETDEWEB)
Vinagre, Sandra [Departamento de Matematica, Universidade de Evora, Rua Roma-tilde o Ramalho 59, 7000-671 Evora (Portugal)]. E-mail: smv@uevora.pt; Severino, Ricardo [Departamento de Matematica, Universidade do Minho, Campus de Gualtar, 4710-057 Braga (Portugal)]. E-mail: ricardo@math.uminho.pt; Ramos, J. Sousa [Departamento de Matematica, Instituto Superior Tecnico, Av. Rovisco Pais 1, 1049-001 Lisbon (Portugal)]. E-mail: sramos@math.ist.utl.pt
2005-07-01
We consider a class of boundary value problems for partial differential equations, whose solutions are, basically, characterized by the iteration of a nonlinear function. We apply methods of symbolic dynamics of discrete bimodal maps in the interval in order to give a topological characterization of its solutions.
Nonlinear transient analysis of joint dominated structures
Chapman, J. M.; Shaw, F. H.; Russell, W. C.
1987-01-01
A residual force technique is presented that can perform the transient analyses of large, flexible, and joint dominated structures. The technique permits substantial size reduction in the number of degrees of freedom describing the nonlinear structural models and can account for such nonlinear joint phenomena as free-play and hysteresis. In general, joints can have arbitrary force-state map representations but these are used in the form of residual force maps. One essential feature of the technique is to replace the arbitrary force-state maps describing the nonlinear joints with residual force maps describing the truss links. The main advantage of this replacement is that the incrementally small relative displacements and velocities across a joint are not monitored directly thereby avoiding numerical difficulties. Instead, very small and 'soft' residual forces are defined giving a numerically attractive form for the equations of motion and thereby permitting numerically stable integration algorithms. The technique was successfully applied to the transient analyses of a large 58 bay, 60 meter truss having nonlinear joints. A method to perform link testing is also presented.
Perturbations of normally solvable nonlinear operators, I
Directory of Open Access Journals (Sweden)
William O. Ray
1985-01-01
Full Text Available Let X and Y be Banach spaces and let ℱ and be Gateaux differentiable mappings from X to Y In this note we study when the operator ℱ+ is surjective for sufficiently small perturbations of a surjective operator ℱ The methods extend previous results in the area of normal solvability for nonlinear operators.
NONLINEAR EXPECTATIONS AND NONLINEAR MARKOV CHAINS
Institute of Scientific and Technical Information of China (English)
PENG SHIGE
2005-01-01
This paper deals with nonlinear expectations. The author obtains a nonlinear generalization of the well-known Kolmogorov's consistent theorem and then use it to construct filtration-consistent nonlinear expectations via nonlinear Markov chains. Compared to the author's previous results, i.e., the theory of g-expectations introduced via BSDE on a probability space, the present framework is not based on a given probability measure. Many fully nonlinear and singular situations are covered. The induced topology is a natural generalization of Lp-norms and L∞-norm in linear situations.The author also obtains the existence and uniqueness result of BSDE under this new framework and develops a nonlinear type of von Neumann-Morgenstern representation theorem to utilities and present dynamic risk measures.
On some nonlinear potential problems
Directory of Open Access Journals (Sweden)
M. A. Efendiev
1999-05-01
Full Text Available The degree theory of mappings is applied to a two-dimensional semilinear elliptic problem with the Laplacian as principal part subject to a nonlinear boundary condition of Robin type. Under some growth conditions we obtain existence. The analysis is based on an equivalent coupled system of domain--boundary variational equations whose principal parts are the Dirichlet bilinear form in the domain and the single layer potential bilinear form on the boundary, respectively. This system consists of a monotone and a compact part. Additional monotonicity implies convergence of an appropriate Richardson iteration.
Haar basis and nonlinear modeling of complex systems
García, P.; Merlitti, A.
2007-04-01
In this work we introduce a technique to perform nonlinear modeling of chaotic time series using the kernel method. The basic idea behind this method is to map the data into a high dimensional space via nonlinear mapping and do a linear regression in this space. Here we use a Haar wavelet-like kernel to achieve the task. This strategy, in contrast to Support Vector Machines technique, shows the conceptual simplicity of least mean square algoritm for linear regression but allows local nonlinear aproximation of the system evolution, with low computational cost.
On the convergence of nonlinear Beltrami type operators
Directory of Open Access Journals (Sweden)
Riccardo De Arcangelis
1986-11-01
Full Text Available One of the results proved is the following: if (fh is a sequence of K-quasiregular mappings, converging to f in L1loc , whose jacobians verify a weak integrability condition, then the solutions of Dirichlet problems for the nonlinear Laplace-Beltrami operator associated to each fh converge to the solution of the Dirichlet problem for the nonlinear Laplace-Beltrami operator associated to f. Such result is deduced as a particular case of a more general theorem concerning nonlinear operators. The case of K-quasiconformal functions fh is also treated. A class of weighted Sobolev spaces associated to quasiconformal mappings is studied.
... Fact Sheets Fact Sheets En Español: Mapeo Genético Genetic Mapping What is genetic mapping? How do researchers create ... genetic map? What are genetic markers? What is genetic mapping? Among the main goals of the Human Genome ...
Visualizing the Logistic Map with a Microcontroller
Serna, Juan D.; Joshi, Amitabh
2012-01-01
The logistic map is one of the simplest nonlinear dynamical systems that clearly exhibits the route to chaos. In this paper, we explore the evolution of the logistic map using an open-source microcontroller connected to an array of light-emitting diodes (LEDs). We divide the one-dimensional domain interval [0,1] into ten equal parts, an associate…
Info-quantifiers’ map-characterization revisited
Rosso, Osvaldo A.; De Micco, Luciana; Plastino, A.; Larrondo, Hilda A.
2010-11-01
We highlight the potentiality of a special Information Theory (IT) approach in order to unravel the intricacies of nonlinear dynamics, the methodology being illustrated with reference to the logistic map. A rather surprising dynamic feature→plane- topography map becomes available.
Visualizing the Logistic Map with a Microcontroller
Serna, Juan D.; Joshi, Amitabh
2012-01-01
The logistic map is one of the simplest nonlinear dynamical systems that clearly exhibits the route to chaos. In this paper, we explore the evolution of the logistic map using an open-source microcontroller connected to an array of light-emitting diodes (LEDs). We divide the one-dimensional domain interval [0,1] into ten equal parts, an associate…
Schwendimann, Beat Adrian
2014-01-01
A concept map is a node-link diagram showing the semantic relationships among concepts. The technique for constructing concept maps is called "concept mapping". A concept map consists of nodes, arrows as linking lines, and linking phrases that describe the relationship between nodes. Two nodes connected with a labeled arrow are called a proposition. Concept maps are versatile graphic organizers that can represent many different forms of relationships between concepts. The relationship between...
Geometric properties of Banach spaces and nonlinear iterations
Chidume, Charles
2009-01-01
Nonlinear functional analysis and applications is an area of study that has provided fascination for many mathematicians across the world. This monograph delves specifically into the topic of the geometric properties of Banach spaces and nonlinear iterations, a subject of extensive research over the past thirty years. Chapters 1 to 5 develop materials on convexity and smoothness of Banach spaces, associated moduli and connections with duality maps. Key results obtained are summarized at the end of each chapter for easy reference. Chapters 6 to 23 deal with an in-depth, comprehensive and up-to-date coverage of the main ideas, concepts and results on iterative algorithms for the approximation of fixed points of nonlinear nonexpansive and pseudo-contractive-type mappings. This includes detailed workings on solutions of variational inequality problems, solutions of Hammerstein integral equations, and common fixed points (and common zeros) of families of nonlinear mappings. Carefully referenced and full of recent,...
Characterization of nonlinear dynamic systems using artificial neural networks
Energy Technology Data Exchange (ETDEWEB)
Urbina, A. [Univ. of Texas, El Paso, TX (United States); Hunter, N.F. [Los Alamos National Lab., NM (United States). Engineering Science and Analysis Div.; Paez, T.L. [Sandia National Labs., Albuquerque, NM (United States). Experimental Structural Dynamics Dept.
1998-12-01
The efficient characterization of nonlinear systems is an important goal of vibration and model testing. The authors build a nonlinear system model based on the acceleration time series response of a single input, multiple output system. A series of local linear models are used as a template to train artificial neutral networks (ANNs). The trained ANNs map measured time series responses into states of a nonlinear system. Another NN propagates response states in time, and a third ANN inverts the original map, transforming states into acceleration predictions in the measurement domain. The technique is illustrated using a nonlinear oscillator, in which quadratic and cubic stiffness terms play a major part in the system`s response. Reasonable maps are obtained for the states, and accurate, long-term response predictions are made for data outside the training data set.
Numerical Analysis of Nonlinear Rotor-bearing-seal System
Institute of Scientific and Technical Information of China (English)
CHENG Mei; MENG Guang; JING Jian-ping
2008-01-01
The system state trajectory, Poincaré maps, largest Lyapunov exponents, frequency spectra and bifurcation diagrams were used to investigate the non-linear dynamic behaviors of a rotor-bearing-seal coupled system and to analyze the influence of the seal and bearing on the nonlinear characteristics of the rotor system. Various nonlinear phenomena in the rotor-bearing-seal system, such as periodic motion, double-periodicmotion, multi-periodic motion and quasi-periodic motion were investigated. The results may contribute to a further understanding of the non-linear dynamics of the rotor-bearing-seal coupled system.
Deimling, Klaus
1985-01-01
topics. However, only a modest preliminary knowledge is needed. In the first chapter, where we introduce an important topological concept, the so-called topological degree for continuous maps from subsets ofRn into Rn, you need not know anything about functional analysis. Starting with Chapter 2, where infinite dimensions first appear, one should be familiar with the essential step of consider ing a sequence or a function of some sort as a point in the corresponding vector space of all such sequences or functions, whenever this abstraction is worthwhile. One should also work out the things which are proved in § 7 and accept certain basic principles of linear functional analysis quoted there for easier references, until they are applied in later chapters. In other words, even the 'completely linear' sections which we have included for your convenience serve only as a vehicle for progress in nonlinearity. Another point that makes the text introductory is the use of an essentially uniform mathematical languag...
Meyer, George
1997-01-01
The paper describes a method for guiding a dynamic system through a given set of points. The paradigm is a fully automatic aircraft subject to air traffic control (ATC). The ATC provides a sequence of way points through which the aircraft trajectory must pass. The way points typically specify time, position, and velocity. The guidance problem is to synthesize a system state trajectory which satisfies both the ATC and aircraft constraints. Complications arise because the controlled process is multi-dimensional, multi-axis, nonlinear, highly coupled, and the state space is not flat. In addition, there is a multitude of possible operating modes, which may number in the hundreds. Each such mode defines a distinct state space model of the process by specifying the state space coordinatization, the partition of the controls into active controls and configuration controls, and the output map. Furthermore, mode transitions must be smooth. The guidance algorithm is based on the inversion of the pure feedback approximations, which is followed by iterative corrections for the effects of zero dynamics. The paper describes the structure and modules of the algorithm, and the performance is illustrated by several example aircraft maneuvers.
Chen, Xianfeng; Zeng, Heping; Guo, Qi; She, Weilong
2015-01-01
This book presents an overview of the state of the art of nonlinear optics from weak light nonlinear optics, ultrafast nonlinear optics to electro-optical theory and applications. Topics range from the fundamental studies of the interaction between matter and radiation to the development of devices, components, and systems of tremendous commercial interest for widespread applications in optical telecommunications, medicine, and biotechnology.
Distributed nonlinear optical response
DEFF Research Database (Denmark)
Nikolov, Nikola Ivanov
2005-01-01
The purpose of the research presented here is to investigate basic physical properties in nonlinear optical materials with delayed or nonlocal nonlinearity. Soliton propagation, spectral broadening and the influence of the nonlocality or delay of the nonlinearity are the main focusses in the work...
Noncommutative Nonlinear Supersymmetry
Nishino, H; Nishino, Hitoshi; Rajpoot, Subhash
2002-01-01
We present noncommutative nonlinear supersymmetric theories. The first example is a non-polynomial Akulov-Volkov-type lagrangian with noncommutative nonlinear global supersymmetry in arbitrary space-time dimensions. The second example is the generalization of this lagrangian to Dirac-Born-Infeld lagrangian with nonlinear supersymmetry realized in dimensions D=2,3,4 and 6 (mod 8).
Fiber Nonlinearities: A Tutorial
Institute of Scientific and Technical Information of China (English)
Govind P. Agrawal
2003-01-01
Fiber nonlinearities have long been regarded as being mostly harmful for fiber-optic communication systems. Over the last few years, however, the nonlinear effects are increasingly being used for practical telecommunications applications,the Raman amplification being only one of the recent examples. In this tutorial I review the vario us nonlinear effects occurring in optical fibers from both standpoints..
Fiber Nonlinearities: A Tutorial
Institute of Scientific and Technical Information of China (English)
Govind; P.; Agrawal
2003-01-01
Fiber nonlinearities have long been regarded as being mostly harmful for fiber-optic communication systems. Over the last few years, however, the nonlinear effects are increasingly being used for practical telecommunications applications, the Raman amplification being only one of the recent examples. In this tutorial I review the various nonlinear effects occurring in optical fibers from both standpoints..
PBH tests for nonlinear systems
Kawano, Yu; Ohtsuka, Toshiyuki
2017-01-01
Recently, concepts of nonlinear eigenvalues and eigenvectors are introduced. In this paper, we establish connections between the nonlinear eigenvalues and nonlinear accessibility/observability. In particular, we provide a generalization of Popov- Belevitch-Hautus (PBH) test to nonlinear accessibilit
Nonlinear dynamics and complexity
Luo, Albert; Fu, Xilin
2014-01-01
This important collection presents recent advances in nonlinear dynamics including analytical solutions, chaos in Hamiltonian systems, time-delay, uncertainty, and bio-network dynamics. Nonlinear Dynamics and Complexity equips readers to appreciate this increasingly main-stream approach to understanding complex phenomena in nonlinear systems as they are examined in a broad array of disciplines. The book facilitates a better understanding of the mechanisms and phenomena in nonlinear dynamics and develops the corresponding mathematical theory to apply nonlinear design to practical engineering.
Profiling a Mind Map User: A Descriptive Appraisal
Tucker, Joanne M.; Armstrong, Gary R.; Massad, Victor J.
2010-01-01
Whether manually or through the use of software, a non-linear information organization framework known as mind mapping offers an alternative method for capturing thoughts, ideas and information to linear thinking modes such as outlining. Mind mapping is brainstorming, organizing, and problem solving. This paper examines mind mapping techniques,…
Ghaderpour, Ebrahim
2014-01-01
In this paper, we introduce some known map projections from a model of the Earth to a flat sheet of paper or map and derive the plotting equations for these projections. The first fundamental form and the Gaussian fundamental quantities are defined and applied to obtain the plotting equations and distortions in length, shape and size for some of these map projections.
Nonlinear Elliptic Differential Equations with Multivalued Nonlinearities
Indian Academy of Sciences (India)
Antonella Fiacca; Nikolaos Matzakos; Nikolaos S Papageorgiou; Raffaella Servadei
2001-11-01
In this paper we study nonlinear elliptic boundary value problems with monotone and nonmonotone multivalued nonlinearities. First we consider the case of monotone nonlinearities. In the first result we assume that the multivalued nonlinearity is defined on all $\\mathbb{R}$. Assuming the existence of an upper and of a lower solution, we prove the existence of a solution between them. Also for a special version of the problem, we prove the existence of extremal solutions in the order interval formed by the upper and lower solutions. Then we drop the requirement that the monotone nonlinearity is defined on all of $\\mathbb{R}$. This case is important because it covers variational inequalities. Using the theory of operators of monotone type we show that the problem has a solution. Finally in the last part we consider an eigenvalue problem with a nonmonotone multivalued nonlinearity. Using the critical point theory for nonsmooth locally Lipschitz functionals we prove the existence of at least two nontrivial solutions (multiplicity theorem).
,
2008-01-01
The U.S. Geological Survey (USGS) produced its first topographic map in 1879, the same year it was established. Today, more than 100 years and millions of map copies later, topographic mapping is still a central activity for the USGS. The topographic map remains an indispensable tool for government, science, industry, and leisure. Much has changed since early topographers traveled the unsettled West and carefully plotted the first USGS maps by hand. Advances in survey techniques, instrumentation, and design and printing technologies, as well as the use of aerial photography and satellite data, have dramatically improved mapping coverage, accuracy, and efficiency. Yet cartography, the art and science of mapping, may never before have undergone change more profound than today.
Coupled Oscillator Model for Nonlinear Gravitational Perturbations
Yang, Huan; Green, Stephen R; Lehner, Luis
2015-01-01
Motivated by the gravity/fluid correspondence, we introduce a new method for characterizing nonlinear gravitational interactions. Namely we map the nonlinear perturbative form of the Einstein equation to the equations of motion of a collection of nonlinearly-coupled harmonic oscillators. These oscillators correspond to the quasinormal or normal modes of the background spacetime. We demonstrate the mechanics and the utility of this formalism within the context of perturbed asymptotically anti-de Sitter black brane spacetimes. We confirm in this case that the boundary fluid dynamics are equivalent to those of the hydrodynamic quasinormal modes of the bulk spacetime. We expect this formalism to remain valid in more general spacetimes, including those without a fluid dual. In other words, although borne out of the gravity/fluid correspondence, the formalism is fully independent and it has a much wider range of applicability. In particular, as this formalism inspires an especially transparent physical intuition, w...
High resolution 3D nonlinear integrated inversion
Institute of Scientific and Technical Information of China (English)
Li Yong; Wang Xuben; Li Zhirong; Li Qiong; Li Zhengwen
2009-01-01
The high resolution 3D nonlinear integrated inversion method is based on nonlinear theory. Under layer control, the log data from several wells (or all wells) in the study area and seismic trace data adjacent to the wells are input to a network with multiple inputs and outputs and are integratedly trained to obtain an adaptive weight function of the entire study area. Integrated nonlinear mapping relationships are built and updated by the lateral and vertical geologic variations of the reservoirs. Therefore, the inversion process and its inversion results can be constrained and controlled and a stable seismic inversion section with high resolution with velocity inversion, impedance inversion, and density inversion sections, can be gained. Good geologic effects have been obtained in model computation tests and real data processing, which verified that this method has high precision, good practicality, and can be used for quantitative reservoir analysis.
Non-linear (loop) quantum cosmology
Bojowald, Martin; Dantas, Christine C; Jaffe, Matthew; Simpson, David
2012-01-01
Inhomogeneous quantum cosmology is modeled as a dynamical system of discrete patches, whose interacting many-body equations can be mapped to a non-linear minisuperspace equation by methods analogous to Bose-Einstein condensation. Complicated gravitational dynamics can therefore be described by more-manageable equations for finitely many degrees of freedom, for which powerful solution procedures are available, including effective equations. The specific form of non-linear and non-local equations suggests new questions for mathematical and computational investigations, and general properties of non-linear wave equations lead to several new options for physical effects and tests of the consistency of loop quantum gravity. In particular, our quantum cosmological methods show how sizeable quantum corrections in a low-curvature universe can arise from tiny local contributions adding up coherently in large regions.
Bacteriorhodopsin: Tunable Optical Nonlinear Magnetic Response
Bovino, F A; Sibilia, C; Giardina, M; Váró, G; Gergely, C
2011-01-01
We report on a strong and tunable magnetic optical nonlinear response of Bacteriorhodopsin (BR) under "off resonance" femtosecond (fs) pulse excitation, by detecting the polarization map of the noncollinear second harmonic signal of an oriented BR film, as a function of the input beam power. BR is a light-driven proton pump with a unique photochemistry initiated by the all trans retinal chromophore embedded in the protein. An elegant application of this photonic molecular machine has been recently found in the new area of optogenetics, where genetic expression of BR in brain cells conferred a light responsivity to the cells enabling thus specific stimulation of neurons. The observed strong tunable magnetic nonlinear response of BR might trigger promising applications in the emerging area of pairing optogenetics and functional magnetic resonance imaging susceptible to provide an unprecedented complete functional mapping of neural circuits.
Directory of Open Access Journals (Sweden)
Wei Khim Ng
2009-02-01
Full Text Available We construct nonlinear extensions of Dirac's relativistic electron equation that preserve its other desirable properties such as locality, separability, conservation of probability and Poincaré invariance. We determine the constraints that the nonlinear term must obey and classify the resultant non-polynomial nonlinearities in a double expansion in the degree of nonlinearity and number of derivatives. We give explicit examples of such nonlinear equations, studying their discrete symmetries and other properties. Motivated by some previously suggested applications we then consider nonlinear terms that simultaneously violate Lorentz covariance and again study various explicit examples. We contrast our equations and construction procedure with others in the literature and also show that our equations are not gauge equivalent to the linear Dirac equation. Finally we outline various physical applications for these equations.
Ionescu, Tudor C.; Scherpen, Jacquelien M. A.
We study the notion of cross Gramians for nonlinear gradient systems, using the characterization in terms of prolongation and gradient extension associated to the system. The cross Gramian is given for the variational system associated to the original nonlinear gradient system. We obtain linearization results that correspond to the notion of a cross Gramian for symmetric linear systems. Furthermore, first steps towards relations with the singular value functions of the nonlinear Hankel operator are studied and yield promising results.
Directory of Open Access Journals (Sweden)
W. L. Fouché
1983-03-01
Full Text Available In this article we discuss some aspects of nonlinear functional analysis. It included reviews of Banach’s contraction theorem, Schauder’s fixed point theorem, globalising techniques and applications of homotopy theory to nonlinear functional analysis. The author emphasises that fundamentally new ideas are required in order to achieve a better understanding of phenomena which contain both nonlinear and definite infinite dimensional features.
Nonlinear Electrodynamics and QED
2003-01-01
The limits of linear electrodynamics are reviewed, and possible directions of nonlinear extension are explored. The central theme is that the qualitative character of the empirical successes of quantum electrodynamics must be used as a guide for understanding the nature of the nonlinearity of electrodynamics at the subatomic level. Some established theories of nonlinear electrodynamics, namely, those of Mie, Born, and Infeld are presented in the language of the modern geometrical and topologi...
A Cauchy problem in nonlinear heat conduction
Energy Technology Data Exchange (ETDEWEB)
De Lillo, S [Istituto Nazionale di Fisica Nucleare, Sezione di Perugia, Perugia (Italy); Lupo, G [Dipartimento di Matematica e Informatica, Universita degli Studi di Perugia, Via Vanvitelli, 1, 06123 Perugia (Italy); Sanchini, G [Istituto Nazionale di Fisica Nucleare, Sezione di Perugia, Perugia (Italy)
2006-06-09
A Cauchy problem on the semiline for a nonlinear diffusion equation is considered, with a boundary condition corresponding to a prescribed thermal conductivity at the origin. The problem is mapped into a moving boundary problem for the linear heat equation with a Robin-type boundary condition. Such a problem is then reduced to a linear integral Volterra equation of II type which admits a unique solution.
Nonlinear programming with feedforward neural networks.
Energy Technology Data Exchange (ETDEWEB)
Reifman, J.
1999-06-02
We provide a practical and effective method for solving constrained optimization problems by successively training a multilayer feedforward neural network in a coupled neural-network/objective-function representation. Nonlinear programming problems are easily mapped into this representation which has a simpler and more transparent method of solution than optimization performed with Hopfield-like networks and poses very mild requirements on the functions appearing in the problem. Simulation results are illustrated and compared with an off-the-shelf optimization tool.
Kono, Mitsuo
2010-01-01
A nonlinearity is one of the most important notions in modern physics. A plasma is rich in nonlinearities and provides a variety of behaviors inherent to instabilities, coherent wave structures and turbulence. The book covers the basic concepts and mathematical methods, necessary to comprehend nonlinear problems widely encountered in contemporary plasmas, but also in other fields of physics and current research on self-organized structures and magnetized plasma turbulence. The analyses make use of strongly nonlinear models solved by analytical techniques backed by extensive simulations and available experiments. The text is written for senior undergraduates, graduate students, lecturers and researchers in laboratory, space and fusion plasmas.
Nonlinear magnetic metamaterials.
Shadrivov, Ilya V; Kozyrev, Alexander B; van der Weide, Daniel W; Kivshar, Yuri S
2008-12-08
We study experimentally nonlinear tunable magnetic metamaterials operating at microwave frequencies. We fabricate the nonlinear metamaterial composed of double split-ring resonators where a varactor diode is introduced into each resonator so that the magnetic resonance can be tuned dynamically by varying the input power. We demonstrate that at higher powers the transmission of the metamaterial becomes power-dependent and, as a result, such metamaterial can demonstrate various nonlinear properties. In particular, we study experimentally the power-dependent shift of the transmission band and demonstrate nonlinearity-induced enhancement (or suppression) of wave transmission. (c) 2008 Optical Society of America
Organic nonlinear optical materials
Umegaki, S.
1987-01-01
Recently, it became clear that organic compounds with delocalized pi electrons show a great nonlinear optical response. Especially, secondary nonlinear optical constants of more than 2 digits were often seen in the molecular level compared to the existing inorganic crystals such as LiNbO3. The crystallization was continuously tried. Organic nonlinear optical crystals have a new future as materials for use in the applied physics such as photomodulation, optical frequency transformation, opto-bistabilization, and phase conjugation optics. Organic nonlinear optical materials, e.g., urea, O2NC6H4NH2, I, II, are reviewed with 50 references.
Nonlinearity-reduced interferometer
Wu, Chien-ming
2007-12-01
Periodic nonlinearity is a systematic error limiting the accuracy of displacement measurements at the nanometer level. It results from many causes such as the frequency mixing, polarization mixing, polarization-frequency mixing, and the ghost reflections. An interferometer having accuracy in displacement measurement of less than one-nanometer is necessary in nanometrology. To meet the requirement, the periodic nonlinearity should be less than deep sub-nanometer. In this paper, a nonlinearity-reduced interferometry has been proposed. Both the linear- and straightness-interferometer were tested. The developed interferometer demonstrated of a residual nonlinearity less than 25 pm.
Nonlinear interpolation fractal classifier for multiple cardiac arrhythmias recognition
Energy Technology Data Exchange (ETDEWEB)
Lin, C.-H. [Department of Electrical Engineering, Kao-Yuan University, No. 1821, Jhongshan Rd., Lujhu Township, Kaohsiung County 821, Taiwan (China); Institute of Biomedical Engineering, National Cheng-Kung University, Tainan 70101, Taiwan (China)], E-mail: eechl53@cc.kyu.edu.tw; Du, Y.-C.; Chen Tainsong [Institute of Biomedical Engineering, National Cheng-Kung University, Tainan 70101, Taiwan (China)
2009-11-30
This paper proposes a method for cardiac arrhythmias recognition using the nonlinear interpolation fractal classifier. A typical electrocardiogram (ECG) consists of P-wave, QRS-complexes, and T-wave. Iterated function system (IFS) uses the nonlinear interpolation in the map and uses similarity maps to construct various data sequences including the fractal patterns of supraventricular ectopic beat, bundle branch ectopic beat, and ventricular ectopic beat. Grey relational analysis (GRA) is proposed to recognize normal heartbeat and cardiac arrhythmias. The nonlinear interpolation terms produce family functions with fractal dimension (FD), the so-called nonlinear interpolation function (NIF), and make fractal patterns more distinguishing between normal and ill subjects. The proposed QRS classifier is tested using the Massachusetts Institute of Technology-Beth Israel Hospital (MIT-BIH) arrhythmia database. Compared with other methods, the proposed hybrid methods demonstrate greater efficiency and higher accuracy in recognizing ECG signals.
Institute of Scientific and Technical Information of China (English)
LIN Xiangguo; LIANG Yong
2005-01-01
The processing of nonlinear data was one of hot topics in surveying and mapping field in recent years.As a result, many linear methods and nonlinear methods have been developed.But the methods for processing generalized nonlinear surveying and mapping data, especially for different data types and including unknown parameters with random or nonrandom, are seldom noticed.A new algorithm model is presented in this paper for processing nonlinear dynamic multiple-period and multiple-accuracy data derived from deformation monitoring network.
Denis Wood
2015-01-01
This is a description of an avant la lettre deep mapping project carried out by a geographer and a number of landscape architecture students in the early 1980s. Although humanists seem to take the “mapping” in deep mapping more metaphorically than cartographically, in this neighborhood mapping project, the mapmaking was taken literally, with the goal of producing an atlas of the neighborhood. In this, the neighborhood was construed as a transformer, turning the stuff of the world (gas, wate...
Narkiewicz, Wŀadysŀaw
1995-01-01
The book deals with certain algebraic and arithmetical questions concerning polynomial mappings in one or several variables. Algebraic properties of the ring Int(R) of polynomials mapping a given ring R into itself are presented in the first part, starting with classical results of Polya, Ostrowski and Skolem. The second part deals with fully invariant sets of polynomial mappings F in one or several variables, i.e. sets X satisfying F(X)=X . This includes in particular a study of cyclic points of such mappings in the case of rings of algebrai integers. The text contains several exercises and a list of open problems.
DEFF Research Database (Denmark)
Salovaara-Moring, Inka
2016-01-01
practice. In particular, mapping environmental damage, endangered species, and human-made disasters has become one focal point for environmental knowledge production. This type of digital map has been highlighted as a processual turn in critical cartography, whereas in related computational journalism...... of a geo-visualization within information mapping that enhances embodiment in the experience of the information. InfoAmazonia is defined as a digitally created map-space within which journalistic practice can be seen as dynamic, performative interactions between journalists, ecosystems, space, and species...
The theorem on existence of singular solutions to nonlinear equations
Directory of Open Access Journals (Sweden)
Prusinska А.
2005-01-01
Full Text Available The aim of this paper is to present some applications of pregularity theory to investigations of nonlinear multivalued mappings. The main result addresses to the problem of existence of solutions to nonlinear equations in the degenerate case when the linear part is singular at the considered initial point. We formulate conditions for existence of solutions of equation F(x = 0 when first p - 1 derivatives of F are singular.
Nonlinear optimization in electrical engineering with applications in Matlab
Bakr, Mohamed
2013-01-01
Nonlinear Optimization in Electrical Engineering with Applications in MATLAB® provides an introductory course on nonlinear optimization in electrical engineering, with a focus on applications such as the design of electric, microwave, and photonic circuits, wireless communications, and digital filter design. Basic concepts are introduced using a step-by-step approach and illustrated with MATLAB® codes that the reader can use and adapt. Topics covered include: classical optimization methods; one dimensional optimization; unconstrained and constrained optimization; global optimization; space map
Nonlinear Dynamic Analysis of the Whole Vehicle on Bumpy Road
Institute of Scientific and Technical Information of China (English)
王威; 李瑰贤; 宋玉玲
2010-01-01
Through the research into the characteristics of 7-DoF high dimensional nonlinear dynamics of a vehicle on bumpy road, the periodic movement and chaotic behavior of the vehicle were found.The methods of nonlinear frequency response analysis, global bifurcation, frequency chart and Poincaré maps were used simultaneously to derive strange super chaotic attractor.According to Lyapunov exponents calculated by Gram-Schmidt method, the unstable region was compartmentalized and the super chaotic characteristic of ...
Nonlinear characteristics of an autoparametric vibration system
Yan, Zhimiao; Taha, Haithem E.; Tan, Ting
2017-03-01
The nonlinear characteristics of an autoparametric vibration system are investigated. This system consists of a base structure and a cantilever beam with a tip mass. The dynamic equations for the system are derived using the extended Hamilton's principle. The method of multiple scales (MMS) is used to determine an approximate analytical solution of the nonlinear governing equations and, hence, analyze the stability and bifurcation of the system. Compared with the numerical simulation, the first-order MMS is not sufficient. A Lagrangian-based approach is proposed to perform a second-order analysis, which is applicable to a large class of nonlinear systems. The effects of the amplitude and frequency of the external force, damping and frequency of the attached cantilever beam, and the tip mass on the nonlinear responses of the autoparametric vibration system are determined. The results show that this system exhibits many interesting nonlinear phenomena including saturation, jumps, hysteresis and different kinds of bifurcations, such as saddle-node, supercritical pitchfork and subcritical pitchfork bifurcations. Power spectra, phase portraits and Poincare maps are employed to analyze the unstable behavior and the associated Hopf bifurcation and chaos. Depending on the application of such a system, its dynamical behaviors could be exploited or avoided.
Nonlinear fitness landscape of a molecular pathway.
Directory of Open Access Journals (Sweden)
Lilia Perfeito
2011-07-01
Full Text Available Genes are regulated because their expression involves a fitness cost to the organism. The production of proteins by transcription and translation is a well-known cost factor, but the enzymatic activity of the proteins produced can also reduce fitness, depending on the internal state and the environment of the cell. Here, we map the fitness costs of a key metabolic network, the lactose utilization pathway in Escherichia coli. We measure the growth of several regulatory lac operon mutants in different environments inducing expression of the lac genes. We find a strikingly nonlinear fitness landscape, which depends on the production rate and on the activity rate of the lac proteins. A simple fitness model of the lac pathway, based on elementary biophysical processes, predicts the growth rate of all observed strains. The nonlinearity of fitness is explained by a feedback loop: production and activity of the lac proteins reduce growth, but growth also affects the density of these molecules. This nonlinearity has important consequences for molecular function and evolution. It generates a cliff in the fitness landscape, beyond which populations cannot maintain growth. In viable populations, there is an expression barrier of the lac genes, which cannot be exceeded in any stationary growth process. Furthermore, the nonlinearity determines how the fitness of operon mutants depends on the inducer environment. We argue that fitness nonlinearities, expression barriers, and gene-environment interactions are generic features of fitness landscapes for metabolic pathways, and we discuss their implications for the evolution of regulation.
Nonlinear instability and chaos in plasma wave-wave interactions. II. Numerical methods and results
Energy Technology Data Exchange (ETDEWEB)
Kueny, C.S.; Morrison, P.J.
1995-05-01
In Part I of this work and Physics of Plasmas, June 1995, the behavior of linearly stable, integrable systems of waves in a simple plasma model was described using a Hamiltonian formulation. It was shown that explosive instability arises from nonlinear coupling between modes of positive and negative energy, with well-defined threshold amplitudes depending on the physical parameters. In this concluding paper, the nonintegrable case is treated numerically. Several sets of waves are considered, comprising systems of two and three degrees of freedom. The time evolution is modelled with an explicit symplectic integration algorithm derived using Lie algebraic methods. When initial wave amplitudes are large enough to support two-wave decay interactions, strongly chaotic motion destroys the separatrix bounding the stable region for explosive triplets. Phase space orbits then experience diffusive growth to amplitudes that are sufficient for explosive instability, thus effectively reducing the threshold amplitude. For initial amplitudes too small to drive decay instability, small perturbations might still grow to arbitrary size via Arnold diffusion. Numerical experiments do not show diffusion in this case, although the actual diffusion rate is probably underestimated due to the simplicity of the model.
Lasers for nonlinear microscopy.
Wise, Frank
2013-03-01
Various versions of nonlinear microscopy are revolutionizing the life sciences, almost all of which are made possible because of the development of ultrafast lasers. In this article, the main properties and technical features of short-pulse lasers used in nonlinear microscopy are summarized. Recent research results on fiber lasers that will impact future instruments are also discussed.
Eaton, D F
1991-07-19
The current state of materials development in nonlinear optics is summarized, and the promise of these materials is critically evaluated. Properties and important materials constants of current commercial materials and of new, promising, inorganic and organic molecular and polymeric materials with potential in second- and third-order nonlinear optical applications are presented.
Billings, S. A.
1988-03-01
Time and frequency domain identification methods for nonlinear systems are reviewed. Parametric methods, prediction error methods, structure detection, model validation, and experiment design are discussed. Identification of a liquid level system, a heat exchanger, and a turbocharge automotive diesel engine are illustrated. Rational models are introduced. Spectral analysis for nonlinear systems is treated. Recursive estimation is mentioned.
Ionescu, T. C.; Scherpen, J. M. A.; Korytowski, A; Malanowski, K; Mitkowski, W; Szymkat, M
2009-01-01
We study the notion of cross Gramians for nonlinear gradient systems, using the characterization in terms of prolongation and gradient extension associated to the system. The cross Gramian is given for the variational system associated to the original nonlinear gradient system. We obtain
DEFF Research Database (Denmark)
Clausen, Carl A. Balslev; Christiansen, Peter Leth; Torner, L.
1999-01-01
We show that with the quasi-phase-matching technique it is possible to fabricate stripes of nonlinearity that trap and guide light like waveguides. We investigate an array of such stripes and find that when the stripes are sufficiently narrow, the beam dynamics is governed by a quadratic nonlinear...
Controllability in nonlinear systems
Hirschorn, R. M.
1975-01-01
An explicit expression for the reachable set is obtained for a class of nonlinear systems. This class is described by a chain condition on the Lie algebra of vector fields associated with each nonlinear system. These ideas are used to obtain a generalization of a controllability result for linear systems in the case where multiplicative controls are present.
Menon, P. K. A.; Badgett, M. E.; Walker, R. A.
1992-01-01
Trajectory-control laws based on singular-perturbation theory and nonlinear dynamical modeling. Nonlinear maneuver autopilot commands flight-test trajectories of F-15 airplane. Underlying theory of controller enables separation of variables processed in fast and slow control loops, reducing amount of computation required.
Khan, Iftekhar; Morris, Stephen
2014-11-12
The performance of the Beta Binomial (BB) model is compared with several existing models for mapping the EORTC QLQ-C30 (QLQ-C30) on to the EQ-5D-3L using data from lung cancer trials. Data from 2 separate non small cell lung cancer clinical trials (TOPICAL and SOCCAR) are used to develop and validate the BB model. Comparisons with Linear, TOBIT, Quantile, Quadratic and CLAD models are carried out. The mean prediction error, R(2), proportion predicted outside the valid range, clinical interpretation of coefficients, model fit and estimation of Quality Adjusted Life Years (QALY) are reported and compared. Monte-Carlo simulation is also used. The Beta-Binomial regression model performed 'best' among all models. For TOPICAL and SOCCAR trials, respectively, residual mean square error (RMSE) was 0.09 and 0.11; R(2) was 0.75 and 0.71; observed vs. predicted means were 0.612 vs. 0.608 and 0.750 vs. 0.749. Mean difference in QALY's (observed vs. predicted) were 0.051 vs. 0.053 and 0.164 vs. 0.162 for TOPICAL and SOCCAR respectively. Models tested on independent data show simulated 95% confidence from the BB model containing the observed mean more often (77% and 59% for TOPICAL and SOCCAR respectively) compared to the other models. All algorithms over-predict at poorer health states but the BB model was relatively better, particularly for the SOCCAR data. The BB model may offer superior predictive properties amongst mapping algorithms considered and may be more useful when predicting EQ-5D-3L at poorer health states. We recommend the algorithm derived from the TOPICAL data due to better predictive properties and less uncertainty.
Expansive Mappings and Their Applications in Modular Space
Directory of Open Access Journals (Sweden)
A. Azizi
2014-01-01
Full Text Available Some fixed point theorems for ρ-expansive mappings in modular spaces are presented. As an application, two nonlinear integral equations are considered and the existence of their solutions is proved.
Nonlinear optics and photonics
He, Guang S
2015-01-01
This book provides a comprehensive presentation on most of the major topics in nonlinear optics and photonics, with equal emphasis on principles, experiments, techniques, and applications. It covers many major new topics including optical solitons, multi-photon effects, nonlinear photoelectric effects, fast and slow light , and Terahertz photonics. Chapters 1-10 present the fundamentals of modern nonlinear optics, and could be used as a textbook with problems provided at the end of each chapter. Chapters 11-17 cover the more advanced topics of techniques and applications of nonlinear optics and photonics, serving as a highly informative reference for researchers and experts working in related areas. There are also 16 pages of color photographs to illustrate the visual appearances of some typical nonlinear optical effects and phenomena. The book could be adopted as a textbook for both undergraduates and graduate students, and serve as a useful reference work for researchers and experts in the fields of physics...
Lugiato, Luigi; Brambilla, Massimo
2015-01-01
Guiding graduate students and researchers through the complex world of laser physics and nonlinear optics, this book provides an in-depth exploration of the dynamics of lasers and other relevant optical systems, under the umbrella of a unitary spatio-temporal vision. Adopting a balanced approach, the book covers traditional as well as special topics in laser physics, quantum electronics and nonlinear optics, treating them from the viewpoint of nonlinear dynamical systems. These include laser emission, frequency generation, solitons, optically bistable systems, pulsations and chaos and optical pattern formation. It also provides a coherent and up-to-date treatment of the hierarchy of nonlinear optical models and of the rich variety of phenomena they describe, helping readers to understand the limits of validity of each model and the connections among the phenomena. It is ideal for graduate students and researchers in nonlinear optics, quantum electronics, laser physics and photonics.
L2-gain and passivity techniques in nonlinear control
van der Schaft, Arjan
2017-01-01
This standard text gives a unified treatment of passivity and L2-gain theory for nonlinear state space systems, preceded by a compact treatment of classical passivity and small-gain theorems for nonlinear input-output maps. The synthesis between passivity and L2-gain theory is provided by the theory of dissipative systems. Specifically, the small-gain and passivity theorems and their implications for nonlinear stability and stabilization are discussed from this standpoint. The connection between L2-gain and passivity via scattering is detailed. Feedback equivalence to a passive system and resulting stabilization strategies are discussed. The passivity concepts are enriched by a generalised Hamiltonian formalism, emphasising the close relations with physical modeling and control by interconnection, and leading to novel control methodologies going beyond passivity. The potential of L2-gain techniques in nonlinear control, including a theory of all-pass factorizations of nonlinear systems, and of parametrization...
Harbour, Denise
2002-01-01
Explains collection mapping for library media collections. Discusses purposes for creating collection maps, including helping with selection and weeding decisions, showing how the collection supports the curriculum, and making budget decisions; and methods of data collection, including evaluating a collaboratively taught unit with the classroom…
DEFF Research Database (Denmark)
Rasmussen, Lauge Baungaard
2006-01-01
The lecture note explains how to use the causal mapping method as well as the theoretical framework aoosciated to the method......The lecture note explains how to use the causal mapping method as well as the theoretical framework aoosciated to the method...
DEFF Research Database (Denmark)
Salovaara-Moring, Inka
of environmental knowledge production. It uses InfoAmazonia, the databased platform on Amazon rainforests, as an example of affective geo-visualization within information mapping that enhances embodiment in the experience of the information. Amazonia is defined as a digitally created affective (map)space within...
Travelling Wave Solutions in Nonlinear Diffusive and Dispersive Media
Bazeia, D; Raposo, and E.P.
1998-01-01
We investigate the presence of soliton solutions in some classes of nonlinear partial differential equations, namely generalized Korteweg-de Vries-Burgers, Korteveg-de Vries-Huxley, and Korteveg-de Vries-Burgers-Huxley equations, which combine effects of diffusion, dispersion, and nonlinearity. We emphasize the chiral behavior of the travelling solutions, whose velocities are determined by the parameters that define the equation. For some appropriate choices, we show that these equations can be mapped onto equations of motion of relativistic 1+1 dimensional phi^{4} and phi^{6} field theories of real scalar fields. We also study systems of two coupled nonlinear equations of the types mentioned.
Hamiltonian maps and normal forms for intense beams
Energy Technology Data Exchange (ETDEWEB)
Turchetti, G. [Dipartimento di Fisica Universita di Bologna and INFN, Bologna, Via Irnerio 46, 40126 (Italy)]. E-mail: turchetti@bo.infn.it
2006-06-01
The dynamics of a beam in a ring with a localized multipolar nonlinearity is described by a polynomial one turn map. The space charge forces act continuously along the ring, but their effect can be included by replacing the linear tune with the depressed tune which depends on the Courant Snyder invariant. This approximation allows to use the normal forms to compute the nonlinear invariants, the nonlinear tune and the islands geometric parameters when a low order resonance is approached.
Zweig, George
2016-05-01
An earlier paper characterizing the linear mechanical response of the organ of Corti [J. Acoust. Soc. Am. 138, 1102-1121 (2015)] is extended to the nonlinear domain. Assuming the existence of nonlinear oscillators nonlocally coupled through the pressure they help create, the oscillator equations are derived and examined when the stimuli are modulated tones and clicks. The nonlinearities are constrained by the requirements of oscillator stability and the invariance of zero crossings in the click response to changes in click amplitude. The nonlinear oscillator equations for tones are solved in terms of the fluid pressure that drives them, and its time derivative, presumably a proxy for forces created by outer hair cells. The pressure equation is reduced to quadrature, the integrand depending on the oscillators' responses. The resulting nonlocally coupled nonlinear equations for the pressure, and oscillator amplitudes and phases, are solved numerically in terms of the fluid pressure at the stapes. Methods for determining the nonlinear damping directly from measurements are described. Once the oscillators have been characterized from their tone and click responses, the mechanical response of the cochlea to natural sounds may be computed numerically. Signal processing inspired by cochlear mechanics opens up a new area of nonlocal nonlinear time-frequency analysis.
Nonlinear Preserver Problems on B(H)
Institute of Scientific and Technical Information of China (English)
Jian Lian CUI
2011-01-01
Let H be a complex Hilbert space of dimension greater than 2, and B(H) denote the Banach algebra of all bounded linear operators on H. For A, B ∈ B(H), define the binary relation A ≤* B by A*A = A*B and AA* = AB*. Then (B(H), "≤*") is a partially ordered set and the relation "≤*" is called the star order on B(H). Denote by Bs(H) the set of all self-adjoint operators in B(H). In this paper, we first characterize nonlinear continuous bijective maps on Bs (H) which preserve the star order in both directions. We characterize also additive maps (or linear maps) on B(H) (or nest algebras) which are multiplicative at some invertible operator.
Agrawal, Govind P
2001-01-01
The Optical Society of America (OSA) and SPIE - The International Society for Optical Engineering have awarded Govind Agrawal with an honorable mention for the Joseph W. Goodman Book Writing Award for his work on Nonlinear Fiber Optics, 3rd edition.Nonlinear Fiber Optics, 3rd Edition, provides a comprehensive and up-to-date account of the nonlinear phenomena occurring inside optical fibers. It retains most of the material that appeared in the first edition, with the exception of Chapter 6, which is now devoted to the polarization effects relevant for light propagation in optical
Will Nonlinear Backcalculation Help?
DEFF Research Database (Denmark)
Ullidtz, Per
2000-01-01
demonstrates, that treating the subgrade as a nonlinear elastic material, can result in more realistic moduli and a much better agreement between measured and calculated stresses and strains.The response of nonlinear elastic materials can be calculated using the Finite Element Method (FEM). A much simpler...... approach is to use the Method of Equivalent Thicknesses (MET), modified for a nonlinear subgrade. The paper includes an example where moduli backcalculated using FEM, linear elastic theory and MET are compared. Stresses and strains predicted by the three methods are also compared to measured values...
Nonlinear graphene metamaterial
Nikolaenko, Andrey E; Atmatzakis, Evangelos; Luo, Zhiqiang; Shen, Ze Xiang; De Angelis, Francesco; Boden, Stuart A; Di Fabrizio, Enzo; Zheludev, Nikolay I
2012-01-01
We demonstrate that the broadband nonlinear optical response of graphene can be resonantly enhanced by more than an order of magnitude through hybridization with a plasmonic metamaterial,while retaining an ultrafast nonlinear response time of ~1 ps. Transmission modulation close to ~1% is seen at a pump uence of ~0.03 mJ/cm^2 at the wavelength of ~1600 nm. This approach allows to engineer and enhance graphene's nonlinearity within a broad wavelength range enabling applications in optical switching, mode-locking and pulse shaping.
DEFF Research Database (Denmark)
Collin, Ib; Nielsen, Povl Holm; Larsen, Michael Holm
1998-01-01
To enhance the industrial applications of CALS, CALS Center Danmark has developed a cost efficient and transparent assessment, CALS Mapping, to uncover the potential of CALS - primarily dedicated to small and medium sized enterprises. The idea behind CALS Mapping is that the CALS State...... enterprise is, when applied in a given organisation modified with respect to the industry regarded, hence irrelevant measure parameters are eliminated to avoid redundancy. This assessment of CALS Mapping, quantify the CALS potential of an organisation with the purpose of providing decision support to the top...
How Wigner functions transform under symplectic maps
Energy Technology Data Exchange (ETDEWEB)
Dragt, A.J. [Univ. of Maryland, College Park, MD (United States). Center for Theoretical Physics; Habib, S. [Los Alamos National Lab., NM (United States). Theoretical Div.
1998-05-16
It is shown that, while Wigner and Liouville functions transform in an identical way under linear symplectic maps, in general they do not transform identically for nonlinear symplectic maps. Instead there are quantum corrections whose {Dirac_h} {r_arrow} 0 limit may be very complicated. Examples of the behavior of Wigner functions in the {Dirac_h} {r_arrow} 0 limit are given in order to examine to what extent the corresponding Liouville densities are recovered.
Random Feature Maps for Dot Product Kernels
Kar, Purushottam; Karnick, Harish
2012-01-01
Approximating non-linear kernels using feature maps has gained a lot of interest in recent years due to applications in reducing training and testing times of SVM classifiers and other kernel based learning algorithms. We extend this line of work and present low distortion embeddings for dot product kernels into linear Euclidean spaces. We base our results on a classical result in harmonic analysis characterizing all dot product kernels and use it to define randomized feature maps into explic...
How Wigner functions transform under symplectic maps
Energy Technology Data Exchange (ETDEWEB)
Dragt, A.J. [Univ. of Maryland, College Park, MD (United States). Center for Theoretical Physics; Habib, S. [Los Alamos National Lab., NM (United States). Theoretical Div.
1998-05-16
It is shown that, while Wigner and Liouville functions transform in an identical way under linear symplectic maps, in general they do not transform identically for nonlinear symplectic maps. Instead there are quantum corrections whose {Dirac_h} {r_arrow} 0 limit may be very complicated. Examples of the behavior of Wigner functions in the {Dirac_h} {r_arrow} 0 limit are given in order to examine to what extent the corresponding Liouville densities are recovered.
The Universal α-Family of Maps
Edelman, Mark
2013-03-01
We modified the way in which the Universal Map is obtained in the regular dynamics to derive the Universal α-Family of Maps depending on a single parameter α > 0 which is the order of the fractional derivative in the nonlinear fractional differential equation describing a system experiencing periodic kicks. We show that many well-known regular maps, like integer n- dimensional (area/volume preserving for n > 1) quadratic maps (including for n = 1 the Logistic Map which is not measure preserving) and n-dimensional (volume preserving for n > 2) standard maps (including the non-measure preserving Circle Map and the area preserving Standard Map), can be considered as particular forms of the Universal α-Family of Maps. In the case of the fractional α corresponding maps, which are maps with memory, demonstrate various types of attractors including cascade of bifurcation types trajectories. Maps with memory can be applied for modeling biological systems and circuit elements with memory.
Institute of Scientific and Technical Information of China (English)
李峰; 卞贺; 郑经堂; 胡燕
2012-01-01
Titanium dioxide (TiO2) is of strong UV absorption and catalytic performance. As a kind of cheap and environment friendly photocatalyst, the TiC>2 particles (especially its nanoparticles) have been considered as potential materials in some fields, such as sewage treatment, air purification and solar cells. Based on the experimental results, RE doping TiO2 was found to enhance the activity of TiO2 for some organic pollutant photodegradations. In order to select proper catalyzer, structure-activity/property relationship for RE-doped TiO2 must be further researched. As a effective data mining method, Nonlinear mapping genetic algorithm was propitious to classification and optimum control, which was firstly used to study the structure-effective relationship of RE-doped TiO2 photocatalysts in this paper. Rare-earth (RE)-doped TiO2 photocatalysts were prepared by doping samarium ions into TiO2 nanoparticles in a sol-gel process. The samples were characterized using X-ray diffraction (XRD). Their photocatalytic activities were evaluated by photodegradation of methyl orange (MO) in water under UV light irradiation. Finally, nonlinear mapping analysis based on XRD parameters was carried out. It was demonstrated that the RE-doped TiO2 photocatalysts had the smaller grain sizes. And the higher the doping concentration, the smaller the grain size. When the doping concentration was 0.05 mol%, it had the highest activity with the sequence of catalytic reactivity Eu > Y> Ce. It was also demonstrated that nonlinear mapping results had a good coincidence with the experimental ones. Nonlinear mapping genetic algorithm maybe a good way to to solve the structure-effective relationship of RE-doped TiO2 photocatalysts. Data mining can help us to develop effective photocatalysts and should gain new respect and application.%TiO2具有很好的紫外吸收和高催化活性.作为一种廉价和环境友好的光催化剂,纳米TiO2在废水处理、空气净化和太阳能电池等方面
Multipolar nonlinear nanophotonics
Smirnova, Daria
2016-01-01
Nonlinear nanophotonics is a rapidly developing field with many useful applications for a design of nonlinear nanoantennas, light sources, nanolasers, sensors, and ultrafast miniature metadevices. A tight confinement of the local electromagnetic fields in resonant photonic nanostructures can boost nonlinear optical effects, thus offering versatile opportunities for subwavelength control of light. To achieve the desired functionalities, it is essential to gain flexible control over the near- and far-field properties of nanostructures. Thus, both modal and multipolar analyses are widely exploited for engineering nonlinear scattering from resonant nanoscale elements, in particular for enhancing the near-field interaction, tailoring the far-field multipolar interference, and optimization of the radiation directionality. Here, we review the recent advances in this recently emerged research field ranging from metallic structures exhibiting localized plasmonic resonances to hybrid metal-dielectric and all-dielectric...
Solitons in nonlinear lattices
Kartashov, Yaroslav V; Torner, Lluis
2010-01-01
This article offers a comprehensive survey of results obtained for solitons and complex nonlinear wave patterns supported by purely nonlinear lattices (NLs), which represent a spatially periodic modulation of the local strength and sign of the nonlinearity, and their combinations with linear lattices. A majority of the results obtained, thus far, in this field and reviewed in this article are theoretical. Nevertheless, relevant experimental settings are surveyed too, with emphasis on perspectives for implementation of the theoretical predictions in the experiment. Physical systems discussed in the review belong to the realms of nonlinear optics (including artificial optical media, such as photonic crystals, and plasmonics) and Bose-Einstein condensation (BEC). The solitons are considered in one, two, and three dimensions (1D, 2D, and 3D). Basic properties of the solitons presented in the review are their existence, stability, and mobility. Although the field is still far from completion, general conclusions c...
Directory of Open Access Journals (Sweden)
Shakeeb Bin Hasan
2014-12-01
Full Text Available Contrary to traditional optical elements, plasmonic antennas made from nanostructured metals permit the localization of electromagnetic fields on length scales much smaller than the wavelength of light. This results in huge amplitudes for the electromagnetic field close to the antenna being conducive for the observation of nonlinear effects already at moderate pump powers. Thus, these antennas exhibit a promising potential to achieve optical frequency conversion and all-optical control of light at the nano-scale. This opens unprecedented opportunities for ultrafast nonlinear spectroscopy, sensing devices, on-chip optical frequency conversion, nonlinear optical metamaterials, and novel photon sources. Here, we review some of the recent advances in exploiting the potential of plasmonic antennas to realize robust nonlinear applications.
Leburn, Christopher; Reid, Derryck
2013-01-01
The field of ultrafast nonlinear optics is broad and multidisciplinary, and encompasses areas concerned with both the generation and measurement of ultrashort pulses of light, as well as those concerned with the applications of such pulses. Ultrashort pulses are extreme events – both in terms of their durations, and also the high peak powers which their short durations can facilitate. These extreme properties make them powerful experiment tools. On one hand, their ultrashort durations facilitate the probing and manipulation of matter on incredibly short timescales. On the other, their ultrashort durations can facilitate high peak powers which can drive highly nonlinear light-matter interaction processes. Ultrafast Nonlinear Optics covers a complete range of topics, both applied and fundamental in nature, within the area of ultrafast nonlinear optics. Chapters 1 to 4 are concerned with the generation and measurement of ultrashort pulses. Chapters 5 to 7 are concerned with fundamental applications of ultrasho...
DEFF Research Database (Denmark)
Nguyen-Duy, Khiem
and remains the prime source of energy in non-terrestrial applications such as those in sky-explorers. However, a renewable energy source is expensive, bulky, and its performance is weather dependent, which make testing of downstream converters very difficult. As a result, a nonlinear source emulator (NSE......) is a good solution to solve the problems associated with the use of real nonlinear sources in testing phases. However, a recent technical survey conducted during this work shows that most existing NSEs have only been concerned with simulating nonlinear systems in terrestrial applications. Furthermore......, their dynamic performance were not fast enough in order to imitate how a real nonlinear energy source would react under extreme conditions and operation modes. Particularly, a system in the sky can experience a step change of sunlight irradiation. Moreover, operation modes may include load step between nominal...
Introduction to nonlinear science
Nicolis, G
1995-01-01
One of the most unexpected results in science in recent years is that quite ordinary systems obeying simple laws can give rise to complex, nonlinear or chaotic, behavior. In this book, the author presents a unified treatment of the concepts and tools needed to analyze nonlinear phenomena and to outline some representative applications drawn from the physical, engineering, and biological sciences. Some of the interesting topics covered include: dynamical systems with a finite number of degrees of freedom, linear stability analysis of fixed points, nonlinear behavior of fixed points, bifurcation analysis, spatially distributed systems, broken symmetries, pattern formation, and chaotic dynamics. The author makes a special effort to provide a logical connection between ordinary dynamical systems and spatially extended systems, and to balance the emphasis on chaotic behavior and more classical nonlinear behavior. He also develops a statistical approach to complex systems and compares it to traditional deterministi...
Nonlinear magnetoinductive transmission lines
Lazarides, Nikos; Tsironis, G P
2011-01-01
Power transmission in one-dimensional nonlinear magnetic metamaterials driven at one end is investigated numerically and analytically in a wide frequency range. The nonlinear magnetic metamaterials are composed of varactor-loaded split-ring resonators which are coupled magnetically through their mutual inductances, forming thus a magnetoiductive transmission line. In the linear limit, significant power transmission along the array only appears for frequencies inside the linear magnetoinductive wave band. We present analytical, closed form solutions for the magnetoinductive waves transmitting the power in this regime, and their discrete frequency dispersion. When nonlinearity is important, more frequency bands with significant power transmission along the array may appear. In the equivalent circuit picture, the nonlinear magnetoiductive transmission line driven at one end by a relatively weak electromotive force, can be modeled by coupled resistive-inductive-capacitive (RLC) circuits with voltage-dependent cap...
Optimization under Nonlinear Constraints
1982-01-01
In this paper a timesaving method is proposed for maximizing likelihood functions when the parameter space is subject to nonlinear constraints, expressible as second order polynomials. The suggested approach is especially attractive when dealing with systems with many parameters.
Nonlinearity in nanomechanical cantilevers
DEFF Research Database (Denmark)
Villanueva Torrijo, Luis Guillermo; Karabalin, R. B.; Matheny, M. H.
2013-01-01
Euler-Bernoulli beam theory is widely used to successfully predict the linear dynamics of micro-and nanocantilever beams. However, its capacity to characterize the nonlinear dynamics of these devices has not yet been rigorously assessed, despite its use in nanoelectromechanical systems development....... These findings underscore the delicate balance between inertial and geometric nonlinear effects in the fundamental mode, and strongly motivate further work to develop theories beyond the Euler-Bernoulli approximation. DOI: 10.1103/PhysRevB.87.024304....... In this article, we report the first highly controlled measurements of the nonlinear response of nanomechanical cantilevers using an ultralinear detection system. This is performed for an extensive range of devices to probe the validity of Euler-Bernoulli theory in the nonlinear regime. We find that its...
Nonlinear Stokes Mueller Polarimetry
Samim, Masood; Barzda, Virginijus
2015-01-01
The Stokes Mueller polarimetry is generalized to include nonlinear optical processes such as second- and third-harmonic generation, sum- and difference-frequency generations. The overall algebraic form of the polarimetry is preserved, where the incoming and outgoing radiations are represented by column vectors and the intervening medium is represented by a matrix. Expressions for the generalized nonlinear Stokes vector and the Mueller matrix are provided in terms of coherency and correlation matrices, expanded by higher-dimensional analogues of Pauli matrices. In all cases, the outgoing radiation is represented by the conventional $4\\times 1$ Stokes vector, while dimensions of the incoming radiation Stokes vector and Mueller matrix depend on the order of the process being examined. In addition, relation between nonlinear susceptibilities and the measured Mueller matrices are explicitly provided. Finally, the approach of combining linear and nonlinear optical elements is discussed within the context of polarim...
1992-01-01
The work plan for the implementation of the Convention on Long-Range Transboundary Air Pollution under the UN Economic Commission for Europe (UN ECE) includes the production of maps of critical loads, critical levels, and exceedances as a basis for developing potential abatement strategies for sulphur and nitrogen. This Vademecum is designed to provide guidance to those responsible for calculating and mapping critical loads, critical levels, and exceedances on a national or regional scale. Th...
Adaptive and Nonlinear Control
1992-02-29
in [22], we also applied the concept of zero dynamics to the problem of exact linearization of a nonlinear control system by dynamic feedback. Exact ...nonlinear systems, although it was well-known that the conditions for exact linearization are very stringent and consequently do not apply to a broad...29th IEEE Conference n Decision and Control, Invited Paper delivered by Dr. Gilliam. Exact Linearization of Zero Dynamics, 29th IEEE Conference on
Nonlinear Optics and Turbulence
1992-10-01
currently at Queen Mary College, London Patrick Dunne, (Ph.D., 1987, M.I.T., Hydrodynamic Stability, Nonlinear Waves), 1987-1988. Alecsander Dyachenko...U I I I U I I 3 9 3 V. BIOGRAPHIES A. FACULTY BRUCE BAYLY, 31, Ph.D. 1986, Princeton University. Postdoctoral visiting member 1986-88 at Courant...Caputo, A. C. Newell, and M. Shelley , "Nonlinear Wave Propagation Through a Random Medium and Soliton Tunneling", Integrable Systems and
Online Exhibits & Concept Maps
Douma, M.
2009-12-01
Presenting the complexity of geosciences to the public via the Internet poses a number of challenges. For example, utilizing various - and sometimes redundant - Web 2.0 tools can quickly devour limited time. Do you tweet? Do you write press releases? Do you create an exhibit or concept map? The presentation will provide participants with a context for utilizing Web 2.0 tools by briefly highlighting methods of online scientific communication across several dimensions. It will address issues of: * breadth and depth (e.g. from narrow topics to well-rounded views), * presentation methods (e.g. from text to multimedia, from momentary to enduring), * sources and audiences (e.g. for experts or for the public, content developed by producers to that developed by users), * content display (e.g. from linear to non-linear, from instructive to entertaining), * barriers to entry (e.g. from an incumbent advantage to neophyte accessible, from amateur to professional), * cost and reach (e.g. from cheap to expensive), and * impact (e.g. the amount learned, from anonymity to brand awareness). Against this backdrop, the presentation will provide an overview of two methods of online information dissemination, exhibits and concept maps, using the WebExhibits online museum (www.webexhibits.org) and SpicyNodes information visualization tool (www.spicynodes.org) as examples, with tips on how geoscientists can use either to communicate their science. Richly interactive online exhibits can serve to engage a large audience, appeal to visitors with multiple learning styles, prompt exploration and discovery, and present a topic’s breadth and depth. WebExhibits, which was among the first online museums, delivers interactive information, virtual experiments, and hands-on activities to the public. While large, multidisciplinary exhibits on topics like “Color Vision and Art” or “Calendars Through the Ages” require teams of scholars, user interface experts, professional writers and editors
Yang, Qianli; Pitkow, Xaq
2015-03-01
Most interesting natural sensory stimuli are encoded in the brain in a form that can only be decoded nonlinearly. But despite being a core function of the brain, nonlinear population codes are rarely studied and poorly understood. Interestingly, the few existing models of nonlinear codes are inconsistent with known architectural features of the brain. In particular, these codes have information content that scales with the size of the cortical population, even if that violates the data processing inequality by exceeding the amount of information entering the sensory system. Here we provide a valid theory of nonlinear population codes by generalizing recent work on information-limiting correlations in linear population codes. Although these generalized, nonlinear information-limiting correlations bound the performance of any decoder, they also make decoding more robust to suboptimal computation, allowing many suboptimal decoders to achieve nearly the same efficiency as an optimal decoder. Although these correlations are extremely difficult to measure directly, particularly for nonlinear codes, we provide a simple, practical test by which one can use choice-related activity in small populations of neurons to determine whether decoding is suboptimal or optimal and limited by correlated noise. We conclude by describing an example computation in the vestibular system where this theory applies. QY and XP was supported by a grant from the McNair foundation.
Nonlinear Multiantenna Detection Methods
Directory of Open Access Journals (Sweden)
Chen Sheng
2004-01-01
Full Text Available A nonlinear detection technique designed for multiple-antenna assisted receivers employed in space-division multiple-access systems is investigated. We derive the optimal solution of the nonlinear spatial-processing assisted receiver for binary phase shift keying signalling, which we refer to as the Bayesian detector. It is shown that this optimal Bayesian receiver significantly outperforms the standard linear beamforming assisted receiver in terms of a reduced bit error rate, at the expense of an increased complexity, while the achievable system capacity is substantially enhanced with the advent of employing nonlinear detection. Specifically, when the spatial separation expressed in terms of the angle of arrival between the desired and interfering signals is below a certain threshold, a linear beamformer would fail to separate them, while a nonlinear detection assisted receiver is still capable of performing adequately. The adaptive implementation of the optimal Bayesian detector can be realized using a radial basis function network. Two techniques are presented for constructing block-data-based adaptive nonlinear multiple-antenna assisted receivers. One of them is based on the relevance vector machine invoked for classification, while the other on the orthogonal forward selection procedure combined with the Fisher ratio class-separability measure. A recursive sample-by-sample adaptation procedure is also proposed for training nonlinear detectors based on an amalgam of enhanced -means clustering techniques and the recursive least squares algorithm.
Nonlinear systems in medicine.
Higgins, John P
2002-01-01
Many achievements in medicine have come from applying linear theory to problems. Most current methods of data analysis use linear models, which are based on proportionality between two variables and/or relationships described by linear differential equations. However, nonlinear behavior commonly occurs within human systems due to their complex dynamic nature; this cannot be described adequately by linear models. Nonlinear thinking has grown among physiologists and physicians over the past century, and non-linear system theories are beginning to be applied to assist in interpreting, explaining, and predicting biological phenomena. Chaos theory describes elements manifesting behavior that is extremely sensitive to initial conditions, does not repeat itself and yet is deterministic. Complexity theory goes one step beyond chaos and is attempting to explain complex behavior that emerges within dynamic nonlinear systems. Nonlinear modeling still has not been able to explain all of the complexity present in human systems, and further models still need to be refined and developed. However, nonlinear modeling is helping to explain some system behaviors that linear systems cannot and thus will augment our understanding of the nature of complex dynamic systems within the human body in health and in disease states.
Handbook of nonlinear optical crystals
Dmitriev, Valentin G; Nikogosyan, David N
1991-01-01
This Handbook of Nonlinear Optical Crystals provides a complete description of the properties and applications of nonlinear crystals In addition, it presents the most important equations for calculating the main parameters of nonlinear frequency converters This comprehensive reference work will be of great value to all scientists and engineers working in nonlinear optics, quantum electronics and laser physics
EXISTENCE AND UNIQUENESS OF SOLUTIONS TO A NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
The initial value problem of a nonlinear fractional differential equation is discussed in this paper. Using the nonlinear alternative of Leray-Schauder type and the contraction mapping principle,we obtain the existence and uniqueness of solutions to the fractional differential equation,which extend some results of the previous papers.
NONLOCAL INITIAL PROBLEM FOR NONLINEAR NONAUTONOMOUS DIFFERENTIAL EQUATIONS IN A BANACH SPACE
Institute of Scientific and Technical Information of China (English)
M.I.Gil＇
2004-01-01
The nonlocal initial problem for nonlinear nonautonomous evolution equations in a Banach space is considered. It is assumed that the nonlinearities have the local Lipschitz properties. The existence and uniqueness of mild solutions are proved. Applications to integro-differential equations are discussed. The main tool in the paper is the normalizing mapping (the generalized norm).
Nonlinear Approaches in Engineering Applications
Jazar, Reza
2012-01-01
Nonlinear Approaches in Engineering Applications focuses on nonlinear phenomena that are common in the engineering field. The nonlinear approaches described in this book provide a sound theoretical base and practical tools to design and analyze engineering systems with high efficiency and accuracy and with less energy and downtime. Presented here are nonlinear approaches in areas such as dynamic systems, optimal control and approaches in nonlinear dynamics and acoustics. Coverage encompasses a wide range of applications and fields including mathematical modeling and nonlinear behavior as applied to microresonators, nanotechnologies, nonlinear behavior in soil erosion,nonlinear population dynamics, and optimization in reducing vibration and noise as well as vibration in triple-walled carbon nanotubes. This book also: Provides a complete introduction to nonlinear behavior of systems and the advantages of nonlinearity as a tool for solving engineering problems Includes applications and examples drawn from the el...
A Simulation Platform for Localization and Mapping
DEFF Research Database (Denmark)
Sejerøe, Thomas Hanefeld; Poulsen, Niels Kjølstad; Ravn, Ole
2006-01-01
In this paper we present a simulation platform for evaluate methods for simultaneous location and mapping. The platform is based on The Kalmtool 3 toolbox which is a set of MATLAB tools for state estimation for nonlinear systems. The toolbox contains functions for extended Kalman filtering as wel...
Visualization of neural networks using saliency maps
DEFF Research Database (Denmark)
Mørch, Niels J.S.; Kjems, Ulrik; Hansen, Lars Kai
1995-01-01
The saliency map is proposed as a new method for understanding and visualizing the nonlinearities embedded in feedforward neural networks, with emphasis on the ill-posed case, where the dimensionality of the input-field by far exceeds the number of examples. Several levels of approximations...
Feedback Control of Chaos in Delay Maps
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
In this paper, we discuss feedback control of a class of delay chaotic maps. Our aim is to drive the chaoticmaps to its initially unstable fixed points by using linear and nonlinear state feedback control. The control is achievedby using small, bounded perturbations. Some numerical simulations are given to demonstrate the effectiveness of theproposed control method.
Simultanuous Location and Mapping - A Simulation Platform
DEFF Research Database (Denmark)
Sejerøe, Thomas Hanefeld; Ravn, Ole; Poulsen, Niels Kjølstad
2005-01-01
In this paper we present a simulation platform for evaluate methods for simultaneous location and mapping. The platfor is based on The KALMTOOL 2 toolbox which is a set of MATLAB tools for state estimation for nonlinear systems. The toolbox contains functions for extended Kalman filtering as well...
On intrinsic nonlinear particle motion in compact synchrotrons
Hwang, Kyung Ryun
Due to the low energy and small curvature characteristics of compact synchrotrons, there can be unexpected features that were not present or negligible in high energy accelerators. Nonlinear kinetics, fringe field effect, and space charge effect are those features which become important for low energy and small curvature accelerators. Nonlinear kinematics can limit the dynamics aperture for compact machine even if it consists of all linear elements. The contribution of the nonlinear kinematics on nonlinear optics parameters are first derived. As the dipole bending radius become smaller, the dipole fringe field effect become stronger. Calculation of the Lie map generator and corresponding mapping equation of dipole fringe field is presented. It is found that the higher order nonlinear potential is inverse proportional to powers of fringe field extent and correction to focusing and low order nonlinear potential is proportional to powers of fringe field extent. The fringe field also found to cause large closed orbit deviation for compact synchrotrons. The 2:1 and 4:1 space charge resonances are known to cause beam loss, emittance growth and halo formation for low energy high intensity beams. By numerical simulations, we observe a higher order 6:2 space charge resonance, which can successfully be understood by the concatenation of 2:1 and 4:1 resonances via canonical perturbation. We also develop an explicit symplectic tracking method for compact electrostatic storage rings and explore the feasibility of electric dipole moment (EDM) measurements.
Directory of Open Access Journals (Sweden)
Denis Wood
2015-08-01
Full Text Available This is a description of an avant la lettre deep mapping project carried out by a geographer and a number of landscape architecture students in the early 1980s. Although humanists seem to take the “mapping” in deep mapping more metaphorically than cartographically, in this neighborhood mapping project, the mapmaking was taken literally, with the goal of producing an atlas of the neighborhood. In this, the neighborhood was construed as a transformer, turning the stuff of the world (gas, water, electricity into the stuff of individual lives (sidewalk graffiti, wind chimes, barking dogs, and vice versa. Maps in the central transformer section of the atlas were to have charted this process in action, as in one showing the route of an individual newspaper into the neighborhood, then through the neighborhood to a home, and finally, as trash, out of the neighborhood in a garbage truck; though few of these had been completed when the project concluded in 1986. Resurrected in 1998 in an episode on Ira Glass’ This American Life, the atlas was finally published, as Everything Sings: Maps for a Narrative Atlas, in 2010 (and an expanded edition in 2013.
Exact solutions for some nonlinear partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Peng, Yan-Ze
2003-08-11
Exact solutions to some nonlinear partial differential equations, including (2+1)-dimensional breaking soliton equation, sine-Gordon equation and double sine-Gordon equation, are studied by means of the mapping method proposed by the author recently. Many new results are presented. A simple review of the method is finally given.
Applied Nonlinear Dynamics Analytical, Computational, and Experimental Methods
Nayfeh, Ali H
1995-01-01
A unified and coherent treatment of analytical, computational and experimental techniques of nonlinear dynamics with numerous illustrative applications. Features a discourse on geometric concepts such as Poincaré maps. Discusses chaos, stability and bifurcation analysis for systems of differential and algebraic equations. Includes scores of examples to facilitate understanding.
Innovation as a Nonlinear Process and the Scientometric Perspective
Leydesdorff, L.; Rotolo, D.; de Nooy, W.; Archambault, E.; Gingras, Y.; Larivière, V.
2012-01-01
The process of innovation follows non-linear patterns across the domains of science, technology, and the economy. Novel bibliometric mapping techniques can be used to investigate and represent distinctive, but complementary perspectives on the innovation process (e.g., "demand" and "supply") as well
Intracellular water diffusion probed by femtosecond nonlinear CARS microscopy
Potma, E.O; de Boeij, W.P.; Wiersma, D. A.; Elsaesser, T; Mukamel, S; Murnane, MM; Scherer, NF
2001-01-01
We report on a nonlinear coherent anti-Stokes Raman microscope system based on a high repetition rate femtosecond cavity-dumped visible optical parametric oscillator. This microscope enables real-time mapping of water concentration gradients in single living cells at high spatial resolution.
Nonlinear Contractive Conditions for Coupled Cone Fixed Point Theorems
Directory of Open Access Journals (Sweden)
Du Wei-Shih
2010-01-01
Full Text Available We establish some new coupled fixed point theorems for various types of nonlinear contractive maps in the setting of quasiordered cone metric spaces which not only obtain several coupled fixed point theorems announced by many authors but also generalize them under weaker assumptions.
PowerPoint and Concept Maps: A Great Double Act
Simon, Jon
2015-01-01
This article explores how concept maps can provide a useful addition to PowerPoint slides to convey interconnections of knowledge and help students see how knowledge is often non-linear. While most accounting educators are familiar with PowerPoint, they are likely to be less familiar with concept maps and this article shows how the tool can be…
The Organization of Multimedia Information in Electronic Map
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
On the basis of an electronic map-based hypermedia data model (EMBHDM),this paper makes a study on the technologies of nonlinear storage,organization,management and browsing of information as well as organization of data on the basis of the relationship between multimedia information of electronic maps.
Completely generalized multivalued nonlinear quasi-variational inclusions
Directory of Open Access Journals (Sweden)
Zeqing Liu
2002-01-01
Full Text Available We introduce and study a new class of completely generalized multivalued nonlinear quasi-variational inclusions. Using the resolvent operator technique for maximal monotone mappings, we suggest two kinds of iterative algorithms for solving the completely generalized multivalued nonlinear quasi-variational inclusions. We establish both four existence theorems of solutions for the class of completely generalized multivalued nonlinear quasi-variational inclusions involving strongly monotone, relaxed Lipschitz, and generalized pseudocontractive mappings, and obtain a few convergence results of iterative sequences generated by the algorithms. The results presented in this paper extend, improve, and unify a lot of results due to Adly, Huang, Jou-Yao, Kazmi, Noor, Noor-Al-Said, Noor-Noor, Noor-Noor-Rassias, Shim-Kang-Huang-Cho, Siddiqi-Ansari, Verma, Yao, and Zhang.
Nonlinear Excitations in Inflationary Power Spectra
Miranda, Vinicius; He, Chen; Motohashi, Hayato
2016-01-01
We develop methods to calculate the curvature power spectrum in models where features in the inflaton potential nonlinearly excite modes and generate high frequency features in the spectrum. The first nontrivial effect of excitations generating further excitations arises at third order in deviations from slow roll. If these further excitations are contemporaneous, the series can be resummed, showing the exponential sensitivity of the curvature spectrum to potential features. More generally, this exponential approximation provides a power spectrum template which nonlinearly obeys relations between excitation coefficients and whose parameters may be appropriately adjusted. For a large sharp step in the potential, it greatly improves the analytic power spectrum template and its dependence on potential parameters. For axionic oscillations in the potential, it corrects the mapping between the potential and the amplitude, phase and zero point of the curvature oscillations, which might otherwise cause erroneous infe...
Energy Technology Data Exchange (ETDEWEB)
Davis, C.G.
1990-01-01
The advent of nonlinear pulsation theory really coincides with the development of the large computers after the second world war. Christy and Stobbie were the first to make use of finite difference techniques on computers to model the bumps'' observed in the classical Cepheid light and velocity curves, the so-called Hertzsprung'' sequence. Following this work a more sophisticated analysis of the light and velocity curves from the models was made by Simon and Davis using Fourier techniques. Recently a simpler amplitude equation formalism has been developed that helps explain this resonance mechanism. The determination of Population I Cepheid masses by nonlinear methods will be discussed. For the lower mass objects, such as RR Lyrae and BL Her. stars, we find general agreement using evolutionary masses and nonlinear pulsation theory. An apparent difficulty of nonlinear pulsation theory occurs in the understanding of double'' mode pulsation, which will also be discussed. Recent studies in nonlinear pulsation theory have dealt with the question of mode selection, period doubling and the trends towards chaotic behavior such as is observed in the transition from W Virginis to RV Tauri-like stars. 10 refs., 1 fig., 2 tabs.
DEFF Research Database (Denmark)
Minder, Bettina; Laursen, Linda Nhu; Lassen, Astrid Heidemann
2014-01-01
. Conceptual clustering is used to analyse and order information according to concepts or variables from within the data. The cognitive maps identified are validated through the comments of some of the same experts. The study presents three cognitive maps and respective world-views explaining how the design...... and innovation field are related and under which dimensions they differ. The paper draws preliminary conclusions on the implications of the different world- views on the innovation process. With the growing importance of the design approach in innovation e.g. design thinking, a clear conception...
DEFF Research Database (Denmark)
Minder, Bettina; Laursen, Linda Nhu; Lassen, Astrid Heidemann
2014-01-01
. Conceptual clustering is used to analyse and order information according to concepts or variables from within the data. The cognitive maps identified are validated through the comments of some of the same experts. The study presents three cognitive maps and respective world-views explaining how the design...... and innovation field are related and under which dimensions they differ. The paper draws preliminary conclusions on the implications of the different world- views on the innovation process. With the growing importance of the design approach in innovation e.g. design thinking, a clear conception...
Nonlinear inverse modeling of sensor based on back-propagation fuzzy logical system
Institute of Scientific and Technical Information of China (English)
Li Jun; Liu Junhua
2007-01-01
Objective To correct the nonlinear error of sensor output, a new approach to sensor inverse modeling based on Back-Propagation Fuzzy Logical System (BP FS) is presented. Methods The BP FS is a computationally efficient nonlinear universal approximator, which is capable of implementing complex nonlinear mapping from its input pattern space to the output with fast convergence speed. Results The neuro-fuzzy hybrid system, i.e. BP FS, is then applied to construct nonlinear inverse model of pressure sensor. The experimental results show that the proposed inverse modeling method automatically compensates the associated nonlinear error in pressure estimation, and thus the performance of pressure sensor is significantly improved. Conclusion The proposed method can be widely used in nonlinearity correction of various kinds of sensors to compensate the effects of nonlinearity and temperature on sensor output.
Integrable vs Nonintegrable Geodesic Soliton Behavior
Fringer, O B
1999-01-01
We study confined solutions of certain evolutionary partial differential equations (pde) in 1+1 space-time. The pde we study are Lie-Poisson Hamiltonian systems for quadratic Hamiltonians defined on the dual of the Lie algebra of vector fields on the real line. These systems are also Euler-Poincare equations for geodesic motion on the diffeomorphism group in the sense of the Arnold program for ideal fluids, but where the kinetic energy metric is different from the L2 norm of the velocity. These pde possess a finite-dimensional invariant manifold of particle-like (measure-valued) solutions we call ``pulsons.'' We solve the particle dynamics of the two-pulson interaction analytically as a canonical Hamiltonian system for geodesic motion with two degrees of freedom and a conserved momentum. The result of this two-pulson interaction for rear-end collisions is elastic scattering with a phase shift, as occurs with solitons. In contrast, head-on antisymmetric collisons of pulsons tend to form singularities.
Algebraic non-integrability of magnetic billiards
Bialy, Misha; Mironov, Andrey E.
2016-11-01
We consider billiard ball motion in a convex domain of the Euclidean plane bounded by a piece-wise smooth curve under the action of a constant magnetic field. We show that if there exists a first integral polynomial in the velocities of the magnetic billiard flow, then every smooth piece γ of the boundary must be algebraic, and either is a circle or satisfies very strong restrictions. In particular, it follows that any non-circular magnetic Birkhoff billiard is not algebraically integrable for all but finitely many values of the magnitude of the magnetic field. Moreover, a magnetic billiard in ellipse is not algebraically integrable for all values of the magnitude of the magnetic field. We conjecture that the circle is the only integrable magnetic billiard, not only in the algebraic sense, but also for a broader meaning of integrability. We also introduce what we call outer magnetic billiards. As an application of our method, we prove analogous results on algebraically integrable outer magnetic billiards.
Hierarchical Gompertzian growth maps with application in astrophysics
De Martino, S
2010-01-01
The Gompertz model describes the growth in time of the size of significant quantities associated to a large number of systems, taking into account nonlinearity features by a linear equation satisfied by a nonlinear function of the size. Following this scheme, we introduce a class of hierarchical maps which describe discrete sequences of intermediate characteristic scales. We find the general solutions of the maps, which account for a rich set of possible phenomena. Eventually, we provide an important application, by showing that a map belonging to the class so introduced generates all the observed astrophysical length and mass scales.
Nonlinear elastic waves in materials
Rushchitsky, Jeremiah J
2014-01-01
The main goal of the book is a coherent treatment of the theory of propagation in materials of nonlinearly elastic waves of displacements, which corresponds to one modern line of development of the nonlinear theory of elastic waves. The book is divided on five basic parts: the necessary information on waves and materials; the necessary information on nonlinear theory of elasticity and elastic materials; analysis of one-dimensional nonlinear elastic waves of displacement – longitudinal, vertically and horizontally polarized transverse plane nonlinear elastic waves of displacement; analysis of one-dimensional nonlinear elastic waves of displacement – cylindrical and torsional nonlinear elastic waves of displacement; analysis of two-dimensional nonlinear elastic waves of displacement – Rayleigh and Love nonlinear elastic surface waves. The book is addressed first of all to people working in solid mechanics – from the students at an advanced undergraduate and graduate level to the scientists, professional...
Nonlinear Methods in Riemannian and Kählerian Geometry
Jost, Jürgen
1991-01-01
In this book, I present an expanded version of the contents of my lectures at a Seminar of the DMV (Deutsche Mathematiker Vereinigung) in Düsseldorf, June, 1986. The title "Nonlinear methods in complex geometry" already indicates a combination of techniques from nonlinear partial differential equations and geometric concepts. In older geometric investigations, usually the local aspects attracted more attention than the global ones as differential geometry in its foundations provides approximations of local phenomena through infinitesimal or differential constructions. Here, all equations are linear. If one wants to consider global aspects, however, usually the presence of curvature Ieads to a nonlinearity in the equations. The simplest case is the one of geodesics which are described by a system of second ordernonlinear ODE; their linearizations are the Jacobi fields. More recently, nonlinear PDE played a more and more pro~inent röle in geometry. Let us Iist some of the most important ones: - harmonic maps ...
Nonlinear Dynamic Force Spectroscopy
Björnham, Oscar
2016-01-01
Dynamic force spectroscopy (DFS) is an experimental technique that is commonly used to assess information of the strength, energy landscape, and lifetime of noncovalent bio-molecular interactions. DFS traditionally requires an applied force that increases linearly with time so that the bio-complex under investigation is exposed to a constant loading rate. However, tethers or polymers can modulate the applied force in a nonlinear regime. For example, bacterial adhesion pili and polymers with worm-like chain properties are examples of structures that show nonlinear force responses. In these situations, the theory for traditional DFS cannot be readily applied. In this work we expand the theory for DFS to also include nonlinear external forces while still maintaining compatibility with the linear DFS theory. To validate the theory we modeled a bio-complex expressed on a stiff, an elastic and a worm-like chain polymer, using Monte Carlo methods, and assessed the corresponding rupture force spectra. It was found th...
Nonlinear optomechanical paddle nanocavities
Kaviani, Hamidreza; Wu, Marcelo; Ghobadi, Roohollah; Barclay, Paul E
2014-01-01
A photonic crystal optomechanical system combining strong nonlinear optomechanical coupling, low effective mass and large optical mode spacing is introduced. This nanoscale "paddle nanocavity" device supports mechanical resonances with effective mass of 300--600 fg which couple nonlinearly to co-localized optical modes with a quadratic optomechanical coupling coefficient $g^{(2)} > 2\\pi\\times400$ MHz/nm$^2$, and a two phonon to single photon optomechanical coupling rate $\\Delta \\omega_0 > 2\\pi\\times 16$ Hz. This coupling relies on strong phonon-photon interactions in a structure whose optical mode spectrum is highly non--degenerate. Simulations indicate that nonlinear optomechanical readout of thermally driven motion in these devices should be observable for T $> 50 $ mK, and that measurement of phonon shot noise is achievable.
Nonlinear dynamics of structures
Oller, Sergio
2014-01-01
This book lays the foundation of knowledge that will allow a better understanding of nonlinear phenomena that occur in structural dynamics. This work is intended for graduate engineering students who want to expand their knowledge on the dynamic behavior of structures, specifically in the nonlinear field, by presenting the basis of dynamic balance in non‐linear behavior structures due to the material and kinematics mechanical effects. Particularly, this publication shows the solution of the equation of dynamic equilibrium for structure with nonlinear time‐independent materials (plasticity, damage and frequencies evolution), as well as those time dependent non‐linear behavior materials (viscoelasticity and viscoplasticity). The convergence conditions for the non‐linear dynamic structure solution are studied, and the theoretical concepts and its programming algorithms are presented.
Nonlinear Photonic Crystal Fibers
DEFF Research Database (Denmark)
Hansen, Kim Per
2004-01-01
, leading to reduced mode confinement and dispersion flexibility. In this thesis, we treat the nonlinear photonic crystal fiber – a special sub-class of photonic crystal fibers, the core of which has a diameter comparable to the wavelength of the light guided in the fiber. The small core results in a large...... nonlinear coefficient and in various applications, it is therefore possible to reduce the required fiber lengths quite dramatically, leading to increased stability and efficiency. Furthermore, it is possible to design these fibers with zero-dispersion at previously unreachable wavelengths, paving the way...... for completely new applications, especially in and near the visible wavelength region. One such application is supercontinuum generation. Supercontinuum generation is extreme broadening of pulses in a nonlinear medium (in this case a small-core fiber), and depending on the dispersion of the fiber, it is possible...
Schmidt, Bruno E; Ernotte, Guilmot; Clerici, Matteo; Morandotti, Roberto; Ibrahim, Heide; Legare, Francois
2016-01-01
In the framework of linear optics, light fields do not interact with each other in a medium. Yet, when their field amplitude becomes comparable to the electron binding energies of matter, the nonlinear motion of these electrons emits new dipole radiation whose amplitude, frequency and phase differ from the incoming fields. Such high fields are typically achieved with ultra-short, femtosecond (1fs = 10-15 sec.) laser pulses containing very broad frequency spectra. Here, the matter not only couples incoming and outgoing fields but also causes different spectral components to interact and mix through a convolution process. In this contribution, we describe how frequency domain nonlinear optics overcomes the shortcomings arising from this convolution in conventional time domain nonlinear optics1. We generate light fields with previously inaccessible properties because the uncontrolled coupling of amplitudes and phases is turned off. For example, arbitrary phase functions are transferred linearly to the second har...
Nonlinear optomechanics with graphene
Shaffer, Airlia; Patil, Yogesh Sharad; Cheung, Hil F. H.; Wang, Ke; Vengalattore, Mukund
2016-05-01
To date, studies of cavity optomechanics have been limited to exploiting the linear interactions between the light and mechanics. However, investigations of quantum signal transduction, quantum enhanced metrology and manybody physics with optomechanics each require strong, nonlinear interactions. Graphene nanomembranes are an exciting prospect for realizing such studies due to their inherently nonlinear nature and low mass. We fabricate large graphene nanomembranes and study their mechanical and optical properties. By using dark ground imaging techniques, we correlate their eigenmode shapes with the measured dissipation. We study their hysteretic response present even at low driving amplitudes, and their nonlinear dissipation. Finally, we discuss ongoing efforts to use these resonators for studies of quantum optomechanics and force sensing. This work is supported by the DARPA QuASAR program through a Grant from the ARO.
Nonlinear Analysis of Buckling
Directory of Open Access Journals (Sweden)
Psotný Martin
2014-06-01
Full Text Available The stability analysis of slender web loaded in compression was presented. To solve this problem, a specialized computer program based on FEM was created. The nonlinear finite element method equations were derived from the variational principle of minimum of potential energy. To obtain the nonlinear equilibrium paths, the Newton-Raphson iteration algorithm was used. Corresponding levels of the total potential energy were defined. The peculiarities of the effects of the initial imperfections were investigated. Special attention was focused on the influence of imperfections on the post-critical buckling mode. The stable and unstable paths of the nonlinear solution were separated. Obtained results were compared with those gained using ANSYS system.
Nonlinear Metamaterials for Holography
Almeida, Euclides; Prior, Yehiam
2015-01-01
A hologram is an optical element storing phase and possibly amplitude information enabling the reconstruction of a three dimensional image of an object by illumination and scattering of a coherent beam of light, and the image is generated at the same wavelength as the input laser beam. In recent years it was shown that information can be stored in nanometric antennas giving rise to ultrathin components. Here we demonstrate nonlinear multi-layer metamaterial holograms where by the nonlinear process of Third Harmonic Generation, a background free image is formed at a new frequency which is the third harmonic of the illuminating beam. Using e-beam lithography of multilayer plasmonic nanoantennas, we fabricate polarization-sensitive nonlinear elements such as blazed gratings, lenses and other computer-generated holograms. These holograms are analyzed and prospects for future device applications are discussed.
Multidimensional nonlinear descriptive analysis
Nishisato, Shizuhiko
2006-01-01
Quantification of categorical, or non-numerical, data is a problem that scientists face across a wide range of disciplines. Exploring data analysis in various areas of research, such as the social sciences and biology, Multidimensional Nonlinear Descriptive Analysis presents methods for analyzing categorical data that are not necessarily sampled randomly from a normal population and often involve nonlinear relations. This reference not only provides an overview of multidimensional nonlinear descriptive analysis (MUNDA) of discrete data, it also offers new results in a variety of fields. The first part of the book covers conceptual and technical preliminaries needed to understand the data analysis in subsequent chapters. The next two parts contain applications of MUNDA to diverse data types, with each chapter devoted to one type of categorical data, a brief historical comment, and basic skills peculiar to the data types. The final part examines several problems and then concludes with suggestions for futu...
Nonlinear airship aeroelasticity
Bessert, N.; Frederich, O.
2005-12-01
The aeroelastic derivatives for today's aircraft are calculated in the concept phase using a standard procedure. This scheme has to be extended for large airships, due to various nonlinearities in structural and aerodynamic behaviour. In general, the structural model of an airship is physically as well as geometrically nonlinear. The main sources of nonlinearity are large deformations and the nonlinear material behaviour of membranes. The aerodynamic solution is also included in the nonlinear problem, because the deformed airship influences the surrounding flow. Due to these nonlinearities, the aeroelastic problem for airships can only be solved by an iterative procedure. As one possibility, the coupled aerodynamic and structural dynamic problem was handled using linked standard solvers. On the structural side, the Finite-Element program package ABAQUS was extended with an interface to the aerodynamic solver VSAERO. VSAERO is based on the aerodynamic panel method using potential flow theory. The equilibrium of the internal structural and the external aerodynamic forces leads to the structural response and a trimmed flight state for the specified flight conditions (e.g. speed, altitude). The application of small perturbations around a trimmed state produces reaction forces and moments. These constraint forces are then transferred into translational and rotational acceleration fields by performing an inertia relief analysis of the disturbed structural model. The change between the trimmed flight state and the disturbed one yields the respective aeroelastic derivatives. By including the calculated derivatives in the linearised equation of motion system, it is possible to judge the stability and controllability of the investigated airship.
DEFF Research Database (Denmark)
Dehlholm, Christian; Brockhoff, Per B.; Bredie, Wender Laurentius Petrus
2012-01-01
Projective Mapping (Risvik et.al., 1994) and its Napping (Pagès, 2003) variations have become increasingly popular in the sensory field for rapid collection of spontaneous product perceptions. It has been applied in variations which sometimes are caused by the purpose of the analysis and sometime...
Crippen, Kent J.; Curtright, Robert D.; Brooks, David W.
2000-01-01
The abstract nature of the mole and its applications to problem solving make learning the concept difficult for students, and teaching the concept challenging for teachers. Presents activities that use concept maps and graphing calculators as tools for solving mole problems. (ASK)
DEFF Research Database (Denmark)
Salovaara-Moring, Inka
looks at computer-assisted cartography as part of environmental knowledge production. It uses InfoAmazonia, the databased platform on Amazon rainforests, as an example of affective geo-visualization within information mapping that enhances embodiment in the experience of the information. Amazonia...
Nonlinear dynamics from lasers to butterflies
Ball, R
2003-01-01
This book is an inspirational introduction to modern research directions and scholarship in nonlinear dynamics, and will also be a valuable reference for researchers in the field. With the scholarly level aimed at the beginning graduate student, the book will have broad appeal to those with an undergraduate background in mathematical or physical sciences.In addition to pedagogical and new material, each chapter reviews the current state of the area and discusses classic and open problems in engaging, surprisingly non-technical ways. The contributors are Brian Davies (bifurcations in maps), Nal
Unraveling flow patterns through nonlinear manifold learning.
Tauro, Flavia; Grimaldi, Salvatore; Porfiri, Maurizio
2014-01-01
From climatology to biofluidics, the characterization of complex flows relies on computationally expensive kinematic and kinetic measurements. In addition, such big data are difficult to handle in real time, thereby hampering advancements in the area of flow control and distributed sensing. Here, we propose a novel framework for unsupervised characterization of flow patterns through nonlinear manifold learning. Specifically, we apply the isometric feature mapping (Isomap) to experimental video data of the wake past a circular cylinder from steady to turbulent flows. Without direct velocity measurements, we show that manifold topology is intrinsically related to flow regime and that Isomap global coordinates can unravel salient flow features.
Unraveling flow patterns through nonlinear manifold learning.
Directory of Open Access Journals (Sweden)
Flavia Tauro
Full Text Available From climatology to biofluidics, the characterization of complex flows relies on computationally expensive kinematic and kinetic measurements. In addition, such big data are difficult to handle in real time, thereby hampering advancements in the area of flow control and distributed sensing. Here, we propose a novel framework for unsupervised characterization of flow patterns through nonlinear manifold learning. Specifically, we apply the isometric feature mapping (Isomap to experimental video data of the wake past a circular cylinder from steady to turbulent flows. Without direct velocity measurements, we show that manifold topology is intrinsically related to flow regime and that Isomap global coordinates can unravel salient flow features.
Agrawal, Govind
2012-01-01
Since the 4e appeared, a fast evolution of the field has occurred. The 5e of this classic work provides an up-to-date account of the nonlinear phenomena occurring inside optical fibers, the basis of all our telecommunications infastructure as well as being used in the medical field. Reflecting the big developments in research, this new edition includes major new content: slow light effects, which offers a reduction in noise and power consumption and more ordered network traffic-stimulated Brillouin scattering; vectorial treatment of highly nonlinear fibers; and a brand new chapter o
Fundamentals of nonlinear optics
Powers, Peter E
2011-01-01
Peter Powers's rigorous but simple description of a difficult field keeps the reader's attention throughout. … All chapters contain a list of references and large numbers of practice examples to be worked through. … By carefully working through the proposed problems, students will develop a sound understanding of the fundamental principles and applications. … the book serves perfectly for an introductory-level course for second- and third-order nonlinear optical phenomena. The author's writing style is refreshing and original. I expect that Fundamentals of Nonlinear Optics will fast become pop
Tunable nonlinear graphene metasurfaces
Smirnova, Daria A; Kivshar, Yuri S; Khanikaev, Alexander B
2015-01-01
We introduce the concept of nonlinear graphene metasurfaces employing the controllable interaction between a graphene layer and a planar metamaterial. Such hybrid metasurfaces support two types of subradiant resonant modes, asymmetric modes of structured metamaterial elements ("metamolecules") and graphene plasmons exhibiting strong mutual coupling and avoided dispersion crossing. High tunability of graphene plasmons facilitates strong interaction between the subradiant modes, modifying the spectral position and lifetime of the associated Fano resonances. We demonstrate that strong resonant interaction, combined with the subwavelength localization of plasmons, leads to the enhanced nonlinear response and high efficiency of the second-harmonic generation.
Nonlinear effects in optical fibers
Ferreira, Mario F
2011-01-01
Cutting-edge coverage of nonlinear phenomena occurring inside optical fibers Nonlinear fiber optics is a specialized part of fiber optics dealing with optical nonlinearities and their applications. As fiber-optic communication systems have become more advanced and complex, the nonlinear effects in optical fibers have increased in importance, as they adversely affect system performance. Paradoxically, the same nonlinear phenomena also offer the promise of addressing the bandwidth bottleneck for signal processing for future ultra-high speed optical networks. Nonlinear Effects in Optical Fiber
Auto-identifying Diagnostic Symptom of Nonlinear Vibration
Institute of Scientific and Technical Information of China (English)
无
2003-01-01
The technology of diagnostic symptom identification of nonlinear vibration is based on a database of a diagnostic case. This paper defines the periodic degree, quasi-periodic degree, and chaotic degree of a Poincare map, an iterated map, and adopts the image-identification theory, so the three states of periodic, quasi-periodic, and chaotic running states of a machine can be distinguished. It also defines the variable identity, rotating angle and spread degree. The database of diagnostic case is expressed by means of an access database. The diagnostic symptoms are identified using the difference between the Poincare maps of samples and the fault-case. Finally, we demonstrate an identification system of a nonlinear vibration diagnostic symptom of large rotating machinery.
Polynomial approximation of Poincare maps for Hamiltonian system
Froeschle, Claude; Petit, Jean-Marc
1992-01-01
Different methods are proposed and tested for transforming a non-linear differential system, and more particularly a Hamiltonian one, into a map without integrating the whole orbit as in the well-known Poincare return map technique. We construct piecewise polynomial maps by coarse-graining the phase-space surface of section into parallelograms and using either only values of the Poincare maps at the vertices or also the gradient information at the nearest neighbors to define a polynomial approximation within each cell. The numerical experiments are in good agreement with both the real symplectic and Poincare maps.
Nonlinear elliptic systems with exponential nonlinearities
Directory of Open Access Journals (Sweden)
Said El Manouni
2002-12-01
Full Text Available In this paper we investigate the existence of solutions for {gather*} -mathop{m div}( a(| abla u | ^N| abla u |^{N-2}u = f(x,u,v quad mbox{in } Omega -mathop{m div}(a(| abla v| ^N| abla v |^{N-2}v = g(x,u,v quad mbox{in } Omega u(x = v(x = 0 quad mbox{on }partial Omega. end{gather*} Where $Omega$ is a bounded domain in ${mathbb{R}}^N$, $Ngeq 2$, $f$ and $g$ are nonlinearities having an exponential growth on $Omega$ and $a$ is a continuous function satisfying some conditions which ensure the existence of solutions.
Nonlinearity and disorder: Classification and stability of nonlinear impurity modes
DEFF Research Database (Denmark)
Sukhorukov, Andrey A.; Kivshar, Yuri S.; Bang, Ole
2001-01-01
We study the effects produced by competition of two physical mechanisms of energy localization in inhomogeneous nonlinear systems. As an example, we analyze spatially localized modes supported by a nonlinear impurity in the generalized nonlinear Schrödinger equation and describe three types of no...
Generalized Nonlinear Yule Models
Lansky, Petr; Polito, Federico; Sacerdote, Laura
2016-10-01
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.
Ritz, Christian; Parmigiani, Giovanni
2009-01-01
R is a rapidly evolving lingua franca of graphical display and statistical analysis of experiments from the applied sciences. This book provides a coherent treatment of nonlinear regression with R by means of examples from a diversity of applied sciences such as biology, chemistry, engineering, medicine and toxicology.
Gorban, A. N.; Karlin, I.V.
2003-01-01
Nonlinear kinetic equations are reviewed for a wide audience of specialists and postgraduate students in physics, mathematical physics, material science, chemical engineering and interdisciplinary research. Contents: The Boltzmann equation, Phenomenology and Quasi-chemical representation of the Boltzmann equation, Kinetic models, Discrete velocity models, Direct simulation, Lattice Gas and Lattice Boltzmann models, Minimal Boltzmann models for flows at low Knudsen number, Other kinetic equati...
Intramolecular and nonlinear dynamics
Energy Technology Data Exchange (ETDEWEB)
Davis, M.J. [Argonne National Laboratory, IL (United States)
1993-12-01
Research in this program focuses on three interconnected areas. The first involves the study of intramolecular dynamics, particularly of highly excited systems. The second area involves the use of nonlinear dynamics as a tool for the study of molecular dynamics and complex kinetics. The third area is the study of the classical/quantum correspondence for highly excited systems, particularly systems exhibiting classical chaos.
DEFF Research Database (Denmark)
Jørgensen, Michael Finn
1995-01-01
It is generally very difficult to solve nonlinear systems, and such systems often possess chaotic solutions. In the rare event that a system is completely solvable, it is said to integrable. Such systems never have chaotic solutions. Using the Inverse Scattering Transform Method (ISTM) two...
Nonlinear phased array imaging
Croxford, Anthony J.; Cheng, Jingwei; Potter, Jack N.
2016-04-01
A technique is presented for imaging acoustic nonlinearity within a specimen using ultrasonic phased arrays. Acoustic nonlinearity is measured by evaluating the difference in energy of the transmission bandwidth within the diffuse field produced through different focusing modes. The two different modes being classical beam forming, where delays are applied to different element of a phased array to physically focus the energy at a single location (parallel firing) and focusing in post processing, whereby one element at a time is fired and a focused image produced in post processing (sequential firing). Although these two approaches are linearly equivalent the difference in physical displacement within the specimen leads to differences in nonlinear effects. These differences are localized to the areas where the amplitude is different, essentially confining the differences to the focal point. Direct measurement at the focal point are however difficult to make. In order to measure this the diffuse field is used. It is a statistical property of the diffuse field that it represents the total energy in the system. If the energy in the diffuse field for both the sequential and parallel firing case is measured then the difference between these, within the input signal bandwidth, is largely due to differences at the focal spot. This difference therefore gives a localized measurement of where energy is moving out of the transmission bandwidth due to nonlinear effects. This technique is used to image fatigue cracks and other damage types undetectable with conventional linear ultrasonic measurements.
Generalized Nonlinear Yule Models
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.
Trirefringence in nonlinear metamaterials
De Lorenci, Vitorio A
2012-01-01
We study the propagation of electromagnetic waves in the limit of geometrical optics for a class of nearly transparent nonlinear uniaxial metamaterials for which their permittivity tensors present a negative principal component. Their permeability are assumed positive and dependent on the electric field. We show that light waves experience triple refraction -- trirefringence. Additionally to the ordinary wave, two extraordinary waves propagate in such media.
Borghi, M.; Castellan, C.; Signorini, S.; Trenti, A.; Pavesi, L.
2017-09-01
Silicon photonics is a technology based on fabricating integrated optical circuits by using the same paradigms as the dominant electronics industry. After twenty years of fervid development, silicon photonics is entering the market with low cost, high performance and mass-manufacturable optical devices. Until now, most silicon photonic devices have been based on linear optical effects, despite the many phenomenologies associated with nonlinear optics in both bulk materials and integrated waveguides. Silicon and silicon-based materials have strong optical nonlinearities which are enhanced in integrated devices by the small cross-section of the high-index contrast silicon waveguides or photonic crystals. Here the photons are made to strongly interact with the medium where they propagate. This is the central argument of nonlinear silicon photonics. It is the aim of this review to describe the state-of-the-art in the field. Starting from the basic nonlinearities in a silicon waveguide or in optical resonator geometries, many phenomena and applications are described—including frequency generation, frequency conversion, frequency-comb generation, supercontinuum generation, soliton formation, temporal imaging and time lensing, Raman lasing, and comb spectroscopy. Emerging quantum photonics applications, such as entangled photon sources, heralded single-photon sources and integrated quantum photonic circuits are also addressed at the end of this review.
Nonlinear fibre optics overview
DEFF Research Database (Denmark)
Travers, J. C.; Frosz, Michael Henoch; Dudley, J. M.
2010-01-01
, provides a background to the associated nonlinear optical processes, treats the generation mechanisms from continuous wave to femtosecond pulse pump regimes and highlights the diverse applications. A full discussion of numerical methods and comprehensive computer code are also provided, enabling readers...
Tsia, Kevin K.; Jalali, Bahram
2010-05-01
An intriguing optical property of silicon is that it exhibits a large third-order optical nonlinearity, with orders-ofmagnitude larger than that of silica glass in the telecommunication band. This allows efficient nonlinear optical interaction at relatively low power levels in a small footprint. Indeed, we have witnessed a stunning progress in harnessing the Raman and Kerr effects in silicon as the mechanisms for enabling chip-scale optical amplification, lasing, and wavelength conversion - functions that until recently were perceived to be beyond the reach of silicon. With all the continuous efforts developing novel techniques, nonlinear silicon photonics is expected to be able to reach even beyond the prior achievements. Instead of providing a comprehensive overview of this field, this manuscript highlights a number of new branches of nonlinear silicon photonics, which have not been fully recognized in the past. In particular, they are two-photon photovoltaic effect, mid-wave infrared (MWIR) silicon photonics, broadband Raman effects, inverse Raman scattering, and periodically-poled silicon (PePSi). These novel effects and techniques could create a new paradigm for silicon photonics and extend its utility beyond the traditionally anticipated applications.
Leitao, J C; Gerlach, M; Altmann, E G
2016-01-01
One of the most celebrated findings in complex systems in the last decade is that different indexes y (e.g., patents) scale nonlinearly with the population~x of the cities in which they appear, i.e., $y\\sim x^\\beta, \\beta \
Nonlinear Gravitational Lagrangians revisited
Magnano, Guido
2016-01-01
The Legendre transformation method, applied in 1987 to deal with purely metric gravitational Lagrangians with nonlinear dependence on the Ricci tensor, is extended to metric-affine models and is shown to provide a concise and insightful comparison of the dynamical content of the two variational frameworks.
Nonlinearities in Microwave Superconductivity
Ledenyov, Dimitri O.; Ledenyov, Viktor O.
2012-01-01
The research is focused on the modeling of nonlinear properties of High Temperature Superconducting (HTS) thin films, using Bardeen, Cooper, Schrieffer and Lumped Element Circuit theories, with purpose to enhance microwave power handling capabilities of microwave filters and optimize design of microwave circuits in micro- and nano- electronics.
Nonlinear tsunami generation mechanism
Directory of Open Access Journals (Sweden)
M. A. Nosov
2001-01-01
Full Text Available The nonlinear mechanism of long gravitational surface water wave generation by high-frequency bottom oscillations in a water layer of constant depth is investigated analytically. The connection between the surface wave amplitude and the parameters of bottom oscillations and source length is investigated.
DEFF Research Database (Denmark)
Mosekilde, Erik
Through a significant number of detailed and realistic examples this book illustrates how the insights gained over the past couple of decades in the fields of nonlinear dynamics and chaos theory can be applied in practice. Aomng the topics considered are microbiological reaction systems, ecological...
Terahertz semiconductor nonlinear optics
DEFF Research Database (Denmark)
Turchinovich, Dmitry; Hvam, Jørn Märcher; Hoffmann, Matthias
2013-01-01
nonlinearity in doped semiconductors originates from the near-instantaneous heating of free electrons in the ponderomotive potential created by electric field of the THz pulse, leading to ultrafast increase of electron effective mass by intervalley scattering. Modification of effective mass in turn leads...
Nonlinear Optical Terahertz Technology Project
National Aeronautics and Space Administration — Our approach is based on high-Q optical WGM resonators made with a nonlinear crystal. Such resonators have been demonstrated to dramatically enhance nonlinear...
Phase retrieval using nonlinear diversity.
Lu, Chien-Hung; Barsi, Christopher; Williams, Matthew O; Kutz, J Nathan; Fleischer, Jason W
2013-04-01
We extend the Gerchberg-Saxton algorithm to phase retrieval in a nonlinear system. Using a tunable photorefractive crystal, we experimentally demonstrate the noninterferometric technique by reconstructing an unknown phase object from optical intensity measurements taken at different nonlinear strengths.
Strong nonlinear oscillators analytical solutions
Cveticanin, Livija
2017-01-01
This book outlines an analytical solution procedure of the pure nonlinear oscillator system, offering a solution for free and forced vibrations of the one-degree-of-freedom strong nonlinear system with constant and time variable parameter. Includes exercises.
DEFF Research Database (Denmark)
Thuesen, Christian Langhoff; Koch, Christian
2011-01-01
By adopting a theoretical framework from strategic niche management research (SNM) this paper presents an analysis of the innovation system of the Danish Construction industry. The analysis shows a multifaceted landscape of innovation around an existing regime, built around existing ways of working...... and developed over generations. The regime is challenged from various niches and the socio-technical landscape through trends as globalization. Three niches (Lean Construction, BIM and System Deliveries) are subject to a detailed analysis showing partly incompatible rationales and various degrees of innovation...... potential. The paper further discusses how existing policymaking operates in a number of tensions one being between government and governance. Based on the concepts from SNM the paper introduces an innovation map in order to support the development of meta-governance policymaking. By mapping some...
DEFF Research Database (Denmark)
Gilje, Øystein; Frølunde, Lisbeth; Lindstrand, Fredrik
2010-01-01
This chapter concerns mapping patterns in regards to how young filmmakers (age 15 – 20) in the Scandinavian countries learn about filmmaking. To uncover the patterns, we present portraits of four young filmmakers who participated in the Scandinavian research project Making a filmmaker. The focus ...... is on their learning practices and how they create ‘learning paths’ in relation to resources in diverse learning contexts, whether formal, non-formal and informal contexts.......This chapter concerns mapping patterns in regards to how young filmmakers (age 15 – 20) in the Scandinavian countries learn about filmmaking. To uncover the patterns, we present portraits of four young filmmakers who participated in the Scandinavian research project Making a filmmaker. The focus...
2014-03-27
errors found using the polynomial response surrogate (LS PRM ) overlaid on the data from the space-mapped (SM) surrogate...nonlinear space-mapped surrogate responses, with the least-squares PRM surrogate response plotted for comparison . . . . . . . . . . . . . . . . . 65 42...Percent error comparison between the least-squares space-mapping and the PRM surrogate models derived from samples in the second dataset
Nonlinear Forecasting With Many Predictors Using Kernel Ridge Regression
DEFF Research Database (Denmark)
Exterkate, Peter; Groenen, Patrick J.F.; Heij, Christiaan
This paper puts forward kernel ridge regression as an approach for forecasting with many predictors that are related nonlinearly to the target variable. In kernel ridge regression, the observed predictor variables are mapped nonlinearly into a high-dimensional space, where estimation of the predi......This paper puts forward kernel ridge regression as an approach for forecasting with many predictors that are related nonlinearly to the target variable. In kernel ridge regression, the observed predictor variables are mapped nonlinearly into a high-dimensional space, where estimation...... of the predictive regression model is based on a shrinkage estimator to avoid overfitting. We extend the kernel ridge regression methodology to enable its use for economic time-series forecasting, by including lags of the dependent variable or other individual variables as predictors, as typically desired...... in macroeconomic and financial applications. Monte Carlo simulations as well as an empirical application to various key measures of real economic activity confirm that kernel ridge regression can produce more accurate forecasts than traditional linear and nonlinear methods for dealing with many predictors based...
Analytical exact solution of the non-linear Schroedinger equation
Energy Technology Data Exchange (ETDEWEB)
Martins, Alisson Xavier; Rocha Filho, Tarcisio Marciano da [Universidade de Brasilia (UnB), DF (Brazil). Inst. de Fisica. Grupo de Fisica e Matematica
2011-07-01
Full text: In this work we present how to classify and obtain analytical solutions of the Schroedinger equation with a generic non-linearity in 1+1 dimensions. Our approach is based on the determination of Lie symmetry transformation mapping solutions into solutions, and non-classical symmetry transformations, mapping a given solution into itself. From these symmetries it is then possible to reduce the equation to a system of ordinary differential equations which can then be solved using standard methods. The generic non-linearity is handled by considering it as an additional unknown in the determining equations for the symmetry transformations. This results in an over-determined system of non-linear partial differential equations. Its solution can then be determined in some cases by reducing it to the so called involutive (triangular) form, and then solved. This reduction is very tedious and can only performed using a computer algebra system. Once the determining system is solved, we obtain the explicit form for the non-linearity admitting a Lie or non-classical symmetry. The analytical solutions are then derived by solving the reduced ordinary differential equations. The non-linear determining system for the non-classical symmetry transformations and Lie symmetry generators are obtaining using the computer algebra package SADE (symmetry analysis of differential equations), developed at our group. (author)
Cubication of Conservative Nonlinear Oscillators
Belendez, Augusto; Alvarez, Mariela L.; Fernandez, Elena; Pascual, Immaculada
2009-01-01
A cubication procedure of the nonlinear differential equation for conservative nonlinear oscillators is analysed and discussed. This scheme is based on the Chebyshev series expansion of the restoring force, and this allows us to approximate the original nonlinear differential equation by a Duffing equation in which the coefficients for the linear…
Terahertz Nonlinear Optics in Semiconductors
DEFF Research Database (Denmark)
Turchinovich, Dmitry; Hvam, Jørn Märcher; Hoffmann, Matthias C.
2013-01-01
We demonstrate the nonlinear optical effects – selfphase modulation and saturable absorption of a single-cycle THz pulse in a semiconductor. Resulting from THz-induced modulation of Drude plasma, these nonlinear optical effects, in particular, lead to self-shortening and nonlinear spectral...
Fault Detection for Nonlinear Systems
DEFF Research Database (Denmark)
Stoustrup, Jakob; Niemann, H.H.
1998-01-01
The paper describes a general method for designing fault detection and isolation (FDI) systems for nonlinear processes. For a rich class of nonlinear systems, a nonlinear FDI system can be designed using convex optimization procedures. The proposed method is a natural extension of methods based...
Nonlinear Disorder Mapping Through Three-Wave Mixing
Pasquazi, Alessia; Stivala, Salvatore; Morandotti, Roberto; Assanto, Gaetano; 10.1109/JPHOT.2009.2039866
2012-01-01
We implement a simple and powerful approach to characterize the domain distribution in the bulk of quadratic ferroelectric crystals via far-field second-harmonic spectroscopy. The approach is demonstrated in a lithium tantalate sample with periodic electric field poling and random mark-to-space ratio.
Visualization of Nonlinear Classification Models in Neuroimaging - Signed Sensitivity Maps
DEFF Research Database (Denmark)
Rasmussen, Peter Mondrup; Schmah, Tanya; Madsen, Kristoffer Hougaard
2012-01-01
Classification models are becoming increasing popular tools in the analysis of neuroimaging data sets. Besides obtaining good prediction accuracy, a competing goal is to interpret how the classifier works. From a neuroscientific perspective, we are interested in the brain pattern reflecting...
Quasiconformal space mappings a collection of surveys, 1960–1990
1992-01-01
This volume is a collection of surveys on function theory in euclidean n-dimensional spaces centered around the theme of quasiconformal space mappings. These surveys cover or are related to several topics including inequalities for conformal invariants and extremal length, distortion theorems, L(p)-theory of quasiconformal maps, nonlinear potential theory, variational calculus, value distribution theory of quasiregular maps, topological properties of discrete open mappings, the action of quasiconformal maps in special classes of domains, and global injectivity theorems. The present volume is the first collection of surveys on Quasiconformal Space Mappings since the origin of the theory in 1960 and this collection provides in compact form access to a wide spectrum of recent results due to well-known specialists. CONTENTS: G.D. Anderson, M.K. Vamanamurthy, M. Vuorinen: Conformal invariants, quasiconformal maps and special functions.- F.W. Gehring: Topics in quasiconformal mappings.- T.Iwaniec: L(p)-theory of qu...
Nonlinear electrostatic drift Kelvin-Helmholtz instability
Sharma, Avadhesh C.; Srivastava, Krishna M.
1993-01-01
Nonlinear analysis of electrostatic drift Kelvin-Helmholtz instability is performed. It is shown that the analysis leads to the propagation of the weakly nonlinear dispersive waves, and the nonlinear behavior is governed by the nonlinear Burger's equation.
Optothermal nonlinearity of silica aerogel
Braidotti, Maria Chiara; Fleming, Adam; Samuels, Michiel C; Di Falco, Andrea; Conti, Claudio
2016-01-01
We report on the characterization of silica aerogel thermal optical nonlinearity, obtained by z-scan technique. The results show that typical silica aerogels have nonlinear optical coefficient similar to that of glass $(\\simeq 10^{-12} $m$^2/$W), with negligible optical nonlinear absorption. The non\\-li\\-near coefficient can be increased to values in the range of $10^{-10} $m$^2/$W by embedding an absorbing dye in the aerogel. This value is one order of magnitude higher than that observed in the pure dye and in typical highly nonlinear materials like liquid crystals.
Essentials of nonlinear optics
Murti, Y V G S
2014-01-01
Current literature on Nonlinear Optics varies widely in terms of content, style, and coverage of specific topics, relative emphasis of areas and the depth of treatment. While most of these books are excellent resources for the researchers, there is a strong need for books appropriate for presenting the subject at the undergraduate or postgraduate levels in Universities. The need for such a book to serve as a textbook at the level of the bachelors and masters courses was felt by the authors while teaching courses on nonlinear optics to students of both science and engineering during the past two decades. This book has emerged from an attempt to address the requirement of presenting the subject at college level. A one-semester course covering the essentials can effectively be designed based on this.
Nonlinear metamaterials for holography
Almeida, Euclides; Bitton, Ora; Prior, Yehiam
2016-08-01
A hologram is an optical element storing phase and possibly amplitude information enabling the reconstruction of a three-dimensional image of an object by illumination and scattering of a coherent beam of light, and the image is generated at the same wavelength as the input laser beam. In recent years, it was shown that information can be stored in nanometric antennas giving rise to ultrathin components. Here we demonstrate nonlinear multilayer metamaterial holograms. A background free image is formed at a new frequency--the third harmonic of the illuminating beam. Using e-beam lithography of multilayer plasmonic nanoantennas, we fabricate polarization-sensitive nonlinear elements such as blazed gratings, lenses and other computer-generated holograms. These holograms are analysed and prospects for future device applications are discussed.
Nonlinear metamaterials for holography
Almeida, Euclides; Bitton, Ora
2016-01-01
A hologram is an optical element storing phase and possibly amplitude information enabling the reconstruction of a three-dimensional image of an object by illumination and scattering of a coherent beam of light, and the image is generated at the same wavelength as the input laser beam. In recent years, it was shown that information can be stored in nanometric antennas giving rise to ultrathin components. Here we demonstrate nonlinear multilayer metamaterial holograms. A background free image is formed at a new frequency—the third harmonic of the illuminating beam. Using e-beam lithography of multilayer plasmonic nanoantennas, we fabricate polarization-sensitive nonlinear elements such as blazed gratings, lenses and other computer-generated holograms. These holograms are analysed and prospects for future device applications are discussed. PMID:27545581
Van Leeuwen, Peter Jan; Reich, Sebastian
2015-01-01
This book contains two review articles on nonlinear data assimilation that deal with closely related topics but were written and can be read independently. Both contributions focus on so-called particle filters. The first contribution by Jan van Leeuwen focuses on the potential of proposal densities. It discusses the issues with present-day particle filters and explorers new ideas for proposal densities to solve them, converging to particle filters that work well in systems of any dimension, closing the contribution with a high-dimensional example. The second contribution by Cheng and Reich discusses a unified framework for ensemble-transform particle filters. This allows one to bridge successful ensemble Kalman filters with fully nonlinear particle filters, and allows a proper introduction of localization in particle filters, which has been lacking up to now.
Nonlinearity without Superluminality
Kent, A
2002-01-01
Quantum theory is compatible with special relativity. In particular, though measurements on entangled systems are correlated in a way that cannot be reproduced by local hidden variables, they cannot be used for superluminal signalling. As Gisin and Polchinski first pointed out, this is not true for general nonlinear modifications of the Schroedinger equation. Excluding superluminal signalling has thus been taken to rule out most nonlinear versions of quantum theory. The no superluminal signalling constraint has also been used for alternative derivations of the optimal fidelities attainable for imperfect quantum cloning and other operations. These results apply to theories satisfying the rule that their predictions for widely separated and slowly moving entangled systems can be approximated by non-relativistic equations of motion with respect to a preferred time coordinate. This paper describes a natural way in which this rule might fail to hold. In particular, it is shown that quantum readout devices which di...
Monte Carlo and nonlinearities
Dauchet, Jérémi; Blanco, Stéphane; Caliot, Cyril; Charon, Julien; Coustet, Christophe; Hafi, Mouna El; Eymet, Vincent; Farges, Olivier; Forest, Vincent; Fournier, Richard; Galtier, Mathieu; Gautrais, Jacques; Khuong, Anaïs; Pelissier, Lionel; Piaud, Benjamin; Roger, Maxime; Terrée, Guillaume; Weitz, Sebastian
2016-01-01
The Monte Carlo method is widely used to numerically predict systems behaviour. However, its powerful incremental design assumes a strong premise which has severely limited application so far: the estimation process must combine linearly over dimensions. Here we show that this premise can be alleviated by projecting nonlinearities on a polynomial basis and increasing the configuration-space dimension. Considering phytoplankton growth in light-limited environments, radiative transfer in planetary atmospheres, electromagnetic scattering by particles and concentrated-solar-power-plant productions, we prove the real world usability of this advance on four test-cases that were so far regarded as impracticable by Monte Carlo approaches. We also illustrate an outstanding feature of our method when applied to sharp problems with interacting particles: handling rare events is now straightforward. Overall, our extension preserves the features that made the method popular: addressing nonlinearities does not compromise o...
Nonlinear Photonics 2014: introduction.
Akhmediev, N; Kartashov, Yaroslav
2015-01-12
International Conference "Nonlinear Photonics-2014" took place in Barcelona, Spain on July 27-31, 2014. It was a part of the "Advanced Photonics Congress" which is becoming a traditional notable event in the world of photonics. The current focus issue of Optics Express contains contributions from the participants of the Conference and the Congress. The articles in this focus issue by no means represent the total number of the congress contributions (around 400). However, it demonstrates wide range of topics covered at the event. The next conference of this series is to be held in 2016 in Australia, which is the home of many researchers working in the field of photonics in general and nonlinear photonics in particular.
Nonlinear fractional relaxation
Indian Academy of Sciences (India)
A Tofighi
2012-04-01
We deﬁne a nonlinear model for fractional relaxation phenomena. We use -expansion method to analyse this model. By studying the fundamental solutions of this model we ﬁnd that when → 0 the model exhibits a fast decay rate and when → ∞ the model exhibits a power-law decay. By analysing the frequency response we ﬁnd a logarithmic enhancement for the relative ratio of susceptibility.
Controllability of nonlinear systems.
Sussmann, H. J.; Jurdjevic, V.
1972-01-01
Discussion of the controllability of nonlinear systems described by the equation dx/dt - F(x,u). Concepts formulated by Chow (1939) and Lobry (1970) are applied to establish criteria for F and its derivatives to obtain qualitative information on sets which can be obtained from x which denotes a variable of state in an arbitrary, real, analytical manifold. It is shown that controllability implies strong accessibility for a large class of manifolds including Euclidean spaces.-
Stochastic Nonlinear Aeroelasticity
2009-01-01
STOCHASTIC NONLINEAR AEROELASTICITY 5a. CONTRACT NUMBER In- house 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 0601102 6. AUTHOR(S) Philip S...ABSTRACT This report documents the culmination of in- house work in the area of uncertainty quantification and probabilistic techniques for... coff U∞ cs ea lw cw Figure 6: Wing and store geometry (left), wing box structural model (middle), flutter distribution (right
2007-03-01
IEEE Transactions on Automatic Control , AC- 48, pp. 1712-1723, (2003). [14] C.I. Byrnes, A. Isidori...Nonlinear internal models for output regulation,” IEEE Transactions on Automatic Control , AC-49, pp. 2244-2247, (2004). [15] C.I. Byrnes, F. Celani, A...approach,” IEEE Transactions on Automatic Control , 48 (Dec. 2003), 2172–2190. 2. C. I. Byrnes, “Differential Forms and Dynamical Systems,” to appear
Filamentation with nonlinear Bessel vortices.
Jukna, V; Milián, C; Xie, C; Itina, T; Dudley, J; Courvoisier, F; Couairon, A
2014-10-20
We present a new type of ring-shaped filaments featured by stationary nonlinear high-order Bessel solutions to the laser beam propagation equation. Two different regimes are identified by direct numerical simulations of the nonlinear propagation of axicon focused Gaussian beams carrying helicity in a Kerr medium with multiphoton absorption: the stable nonlinear propagation regime corresponds to a slow beam reshaping into one of the stationary nonlinear high-order Bessel solutions, called nonlinear Bessel vortices. The region of existence of nonlinear Bessel vortices is found semi-analytically. The influence of the Kerr nonlinearity and nonlinear losses on the beam shape is presented. Direct numerical simulations highlight the role of attractors played by nonlinear Bessel vortices in the stable propagation regime. Large input powers or small cone angles lead to the unstable propagation regime where nonlinear Bessel vortices break up into an helical multiple filament pattern or a more irregular structure. Nonlinear Bessel vortices are shown to be sufficiently intense to generate a ring-shaped filamentary ionized channel in the medium which is foreseen as opening the way to novel applications in laser material processing of transparent dielectrics.
Strongly nonlinear oscillators analytical solutions
Cveticanin, Livija
2014-01-01
This book provides the presentation of the motion of pure nonlinear oscillatory systems and various solution procedures which give the approximate solutions of the strong nonlinear oscillator equations. The book presents the original author’s method for the analytical solution procedure of the pure nonlinear oscillator system. After an introduction, the physical explanation of the pure nonlinearity and of the pure nonlinear oscillator is given. The analytical solution for free and forced vibrations of the one-degree-of-freedom strong nonlinear system with constant and time variable parameter is considered. Special attention is given to the one and two mass oscillatory systems with two-degrees-of-freedom. The criteria for the deterministic chaos in ideal and non-ideal pure nonlinear oscillators are derived analytically. The method for suppressing chaos is developed. Important problems are discussed in didactic exercises. The book is self-consistent and suitable as a textbook for students and also for profess...
Quantum well nonlinear microcavities
Oudar, J. L.; Kuszelewicz, R.; Sfez, B.; Pellat, D.; Azoulay, R.
We report on recent progress in reducing the power threshold of all-optical bistable quantum well vertical microcavities. Significant improvements are achieved through an increase of the cavity finesse, together with a reduction of the device active layer thickness. A critical intensity of 5 μW/μm 2 has been observed on a microcavity of finesse 250, with a nonlinear medium of only 18 GaAs quantum wells of 10 nm thickness. Further improvements of the Bragg mirror quality resulted in a finesse of 700 and a power-lifetime product of 15 fJ/μm 2. Microresonator pixellation allows to obtain 2-dimensional arrays. A thermally-induced alloy-mixing technique is described, which produced a 110 meV carrier confinement energy, together with a refractive index change of -.012, averaged over the 2.6 μm nonlinear medium thickness. The resulting electrical and optical confinement is shown to improve the nonlinear characteristics, by limiting lateral carrier diffusion and light diffraction.
WEIERSTRASS REPRESENTATION FOR SURFACES WITH PRESCRIBED NORMAL GAUSS MAP AND GAUSS CURVATURE IN H3
Institute of Scientific and Technical Information of China (English)
SHI SHUGUO
2004-01-01
The author obtains a Weierstrass representation for surfaces with prescribed normal Gauss map and Gauss curvature in H3. A differential equation about the hyperbolic Gauss map is also obtained, which characterizes the relation among the hyperbolic Gauss map, the normal Gauss map and Gauss curvature. The author discusses the harmonicity of the normal Gauss map and the hyperbolic Gauss map from surface with constant Gauss curvature in H3 to S2 with certain altered conformal metric.Finally, the author considers the surface whose normal Gauss map is conformal and derives a completely nonlinear differential equation of second order which graph must satisfy.
Institute of Scientific and Technical Information of China (English)
赵方平; 魏庆朝
2014-01-01
研究了需求和市场价格确定情形下非一体化供应链库存与物流运输联合优化的问题，建立了数学模型，考虑了供应链非一体化运输成本由供应商和零售商分别承担的情况，并以秦皇岛市福州茶叶有限公司及其零售商为例进行了参数灵敏度分析，最终得出结论。零售商承担运输成本具有稳定性和优越性，并且可实现供应链整体收益最优，将增加的收益合理分配给供应商和零售商，可实现双方利润最大化，促进供应链的协调发展。%In this paper, we studied the problem of the joint optimization of the non-integrative supply chain inventory and logistics transportation under determined demand and market price, built the corresponding mathematical model, considered the scenarios where the non-integrative supply chain transportation cost was borne by the supplier and by the retailer respectively, then through a case study, reached the conclusion that the retailer-borne transportation cost was more stable and superior and conductive to the coordinated development of the supply chain.
An Integrated Map of Soybean Physical Map and Genetic Map
Institute of Scientific and Technical Information of China (English)
QI Zhaoming; LI Hui; WU Qiong; SUN Yanan; LIU Chunyan; HU Guohua; CHEN Qingshan
2009-01-01
Soybean is a major crop in the world, and it is a main source of plant proteins and oil. A lot of soybean genetic maps and physical maps have been constructed, but there are no integrated map between soybean physical map and genetic map. In this study, soybean genome sequence data, released by JGI (US Department of Energy's Joint Genome Institute), had been downloaded. With the software Blast 2.2.16, a total of 161 super sequences were mapped on the soybean public genetic map to construct an integrated map. The length of these super sequences accounted for 73.08% of all the genome sequence. This integrated map could be used for gene cloning, gene mining, and comparative genome of legume.
OPEN PROBLEM: Some nonlinear challenges in biology
Mosconi, Francesco; Julou, Thomas; Desprat, Nicolas; Sinha, Deepak Kumar; Allemand, Jean-François; Croquette, Vincent; Bensimon, David
2008-08-01
Driven by a deluge of data, biology is undergoing a transition to a more quantitative science. Making sense of the data, building new models, asking the right questions and designing smart experiments to answer them are becoming ever more relevant. In this endeavour, nonlinear approaches can play a fundamental role. The biochemical reactions that underlie life are very often nonlinear. The functional features exhibited by biological systems at all levels (from the activity of an enzyme to the organization of a colony of ants, via the development of an organism or a functional module like the one responsible for chemotaxis in bacteria) are dynamically robust. They are often unaffected by order of magnitude variations in the dynamical parameters, in the number or concentrations of actors (molecules, cells, organisms) or external inputs (food, temperature, pH, etc). This type of structural robustness is also a common feature of nonlinear systems, exemplified by the fundamental role played by dynamical fixed points and attractors and by the use of generic equations (logistic map, Fisher-Kolmogorov equation, the Stefan problem, etc.) in the study of a plethora of nonlinear phenomena. However, biological systems differ from these examples in two important ways: the intrinsic stochasticity arising from the often very small number of actors and the role played by evolution. On an evolutionary time scale, nothing in biology is frozen. The systems observed today have evolved from solutions adopted in the past and they will have to adapt in response to future conditions. The evolvability of biological system uniquely characterizes them and is central to biology. As the great biologist T Dobzhansky once wrote: 'nothing in biology makes sense except in the light of evolution'.
Unit 02 - Maps and Map Analysis
Unit 55, CC in GIS; Rhind, David
1990-01-01
This unit explores the map analysis roots of GIS. It discusses cartography and its relationship to GIS, including topics such as map types and characteristics, the concept of scale, map projections, applications of maps, computer-assisted cartography and geographic data display and analysis.
PERIODIC SOLUTIONS IN ONE-DIMENSIONAL COUPLED MAP LATTICES
Institute of Scientific and Technical Information of China (English)
郑永爱; 刘曾荣
2003-01-01
It is proven that the existence of nonlinear solutions with time period in one-dimensional coupled map lattice with nearest neighbor coupling. This is a class of systemswhose behavior can be regarded as infinite array of coupled oscillators. A method forestimating the critical coupling strength below which these solutions with time period persistis given. For some particular nonlinear solutions with time period, exponential decay inspace is proved.
Nonlinear scattering in plasmonic nanostructures
Chu, Shi-Wei
2016-09-01
Nonlinear phenomena provide novel light manipulation capabilities and innovative applications. Recently, we discovered nonlinear saturation on single-particle scattering of gold nanospheres by continuous-wave laser excitation and innovatively applied to improve microscopic resolution down to λ/8. However, the nonlinearity was limited to the green-orange plasmonic band of gold nanosphere, and the underlying mechanism has not yet been fully understood. In this work, we demonstrated that nonlinear scattering exists for various material/geometry combinations, thus expanding the applicable wavelength range. For near-infrared, gold nanorod is used, while for blue-violet, silver nanospheres are adopted. In terms of mechanism, the nonlinearity may originate from interband/intraband absorption, hot electron, or hot lattice, which are spectrally mixed in the case of gold nanosphere. For gold nanorod and silver nanosphere, nonlinear scattering occurs at plasmonic resonances, which are spectrally far from interband/intraband absorptions, so they are excluded. We found that the nonlinear index is much larger than possible contributions from hot electrons in literature. Therefore, we conclude that hot lattice is the major mechanism. In addition, we propose that similar to z-scan, which is the standard method to characterize nonlinearity of a thin sample, laser scanning microscopy should be adopted as the standard method to characterize nonlinearity from a nanostructure. Our work not only provides the physical mechanism of the nonlinear scattering, but also paves the way toward multi-color superresolution imaging based on non-bleaching plasmonic scattering.
Discrete nonlinear Schrodinger equations with arbitrarily high-order nonlinearities
DEFF Research Database (Denmark)
Khare, A.; Rasmussen, Kim Ø; Salerno, M.
2006-01-01
A class of discrete nonlinear Schrodinger equations with arbitrarily high-order nonlinearities is introduced. These equations are derived from the same Hamiltonian using different Poisson brackets and include as particular cases the saturable discrete nonlinear Schrodinger equation and the Ablowi......-Ladik equation. As a common property, these equations possess three kinds of exact analytical stationary solutions for which the Peierls-Nabarro barrier is zero. Several properties of these solutions, including stability, discrete breathers, and moving solutions, are investigated....
Dichromatic nonlinear eigenmodes in slab waveguide with chi(2) nonlinearity.
Darmanyan, S A; Nevière, M
2001-03-01
The existence of purely nonlinear eigenmodes in a waveguiding structure composed of a slab with quadratic nonlinearity surrounded by (non)linear claddings is reported. Modes having bright and dark solitonlike shapes and consisting of two mutually locked harmonics are identified. Asymmetrical modes are shown to exist in symmetrical environments. Constraints for the existence of the modes are derived in terms of parameters of guiding structure materials.
DEFF Research Database (Denmark)
Carruth, Susan
2015-01-01
Resilience theory is a growing discipline with great relevance for the discipline of planning, particularly in fields like energy planning that face great uncertainty and rapidly transforming contexts. Building on the work of the Stockholm Resilience Centre, this paper begins by outlining...... the relationship between resilience and energy planning, suggesting that planning in, and with, time is a core necessity in this domain. It then reviews four examples of graphically mapping with time, highlighting some of the key challenges, before tentatively proposing a graphical language to be employed...... by planners when aiming to construct resilient energy plans. It concludes that a graphical language has the potential to be a significant tool, flexibly facilitating cross-disciplinary communication and decision-making, while emphasising that its role is to support imaginative, resilient planning rather than...
DEFF Research Database (Denmark)
Carruth, Susan
2015-01-01
Resilience theory is a growing discipline with great relevance for the discipline of planning, particularly in fields like energy planning that face great uncertainty and rapidly transforming contexts. Building on the work of the Stockholm Resilience Centre, this paper begins by outlining...... the relationship between resilience and energy planning, suggesting that planning in, and with, time is a core necessity in this domain. It then reviews four examples of graphically mapping with time, highlighting some of the key challenges, before tentatively proposing a graphical language to be employed...... by planners when aiming to construct resilient energy plans. It concludes that a graphical language has the potential to be a significant tool, flexibly facilitating cross-disciplinary communication and decision-making, while emphasising that its role is to support imaginative, resilient planning rather than...
Bernoulli Embedding Model and Its Application in Texture Mapping
Institute of Scientific and Technical Information of China (English)
Hong-Xin Zhang; Ying Tang; Hui Zhao; Hu-Jun Bao
2006-01-01
A novel texture mapping technique is proposed based on nonlinear dimension reduction, called Bernoulli logistic embedding (BLE). Our probabilistic embedding model builds texture mapping with minimal shearing effects. A log-likelihood function, related to the Bregman distance, is used to measure the similarity between two related matrices defined over the spaces before and after embedding. Low-dimensional embeddings can then be obtained through minimizing this function by a fast block relaxation algorithm. To achieve better quality of texture mapping, the embedded results are adopted as initial values for mapping enhancement by stretch-minimizing. Our method can be applied to both complex mesh surfaces and dense point clouds.
Deep subspace mapping in hyperspectral imaging
Wadströmer, Niclas; Gustafsson, David; Perersson, Henrik; Bergström, David
2016-10-01
We propose a novel Deep learning approach using autoencoders to map spectral bands to a space of lower dimensionality while preserving the information that makes it possible to discriminate different materials. Deep learning is a relatively new pattern recognition approach which has given promising result in many applications. In Deep learning a hierarchical representation of increasing level of abstraction of the features is learned. Autoencoder is an important unsupervised technique frequently used in Deep learning for extracting important properties of the data. The learned latent representation is a non-linear mapping of the original data which potentially preserve the discrimination capacity.
Random Feature Maps for Dot Product Kernels
Kar, Purushottam
2012-01-01
Approximating non-linear kernels using feature maps has gained a lot of interest in recent years due to applications in reducing training and testing times of SVM classifiers and other kernel based learning algorithms. We extend this line of work and present low distortion embeddings for dot product kernels into linear Euclidean spaces. We base our results on a classical result in harmonic analysis characterizing all dot product kernels and use it to define randomized feature maps into explicit low dimensional Euclidean spaces in which the native dot product provides an approximation to the dot product kernel with high confidence.
Nonlinear Schrodinger equation with chaotic, random, and nonperiodic nonlinearity
Cardoso, W B; Avelar, A T; Bazeia, D; Hussein, M S
2009-01-01
In this paper we deal with a nonlinear Schr\\"{o}dinger equation with chaotic, random, and nonperiodic cubic nonlinearity. Our goal is to study the soliton evolution, with the strength of the nonlinearity perturbed in the space and time coordinates and to check its robustness under these conditions. Comparing with a real system, the perturbation can be related to, e.g., impurities in crystalline structures, or coupling to a thermal reservoir which, on the average, enhances the nonlinearity. We also discuss the relevance of such random perturbations to the dynamics of Bose-Einstein Condensates and their collective excitations and transport.
Double symbolic joint entropy in nonlinear dynamic complexity analysis
Yao, Wenpo; Wang, Jun
2017-07-01
Symbolizations, the base of symbolic dynamic analysis, are classified as global static and local dynamic approaches which are combined by joint entropy in our works for nonlinear dynamic complexity analysis. Two global static methods, symbolic transformations of Wessel N. symbolic entropy and base-scale entropy, and two local ones, namely symbolizations of permutation and differential entropy, constitute four double symbolic joint entropies that have accurate complexity detections in chaotic models, logistic and Henon map series. In nonlinear dynamical analysis of different kinds of heart rate variability, heartbeats of healthy young have higher complexity than those of the healthy elderly, and congestive heart failure (CHF) patients are lowest in heartbeats' joint entropy values. Each individual symbolic entropy is improved by double symbolic joint entropy among which the combination of base-scale and differential symbolizations have best complexity analysis. Test results prove that double symbolic joint entropy is feasible in nonlinear dynamic complexity analysis.
Nonlinear pulse propagation: a time-transformation approach.
Xiao, Yuzhe; Agrawal, Govind P; Maywar, Drew N
2012-04-01
We present a time-transformation approach for studying the propagation of optical pulses inside a nonlinear medium. Unlike the conventional way of solving for the slowly varying amplitude of an optical pulse, our new approach maps directly the input electric field to the output one, without making the slowly varying envelope approximation. Conceptually, the time-transformation approach shows that the effect of propagation through a nonlinear medium is to change the relative spacing and duration of various temporal slices of the pulse. These temporal changes manifest as self-phase modulation in the spectral domain and self-steepening in the temporal domain. Our approach agrees with the generalized nonlinear Schrödinger equation for 100 fs pulses and the finite-difference time-domain solution of Maxwell's equations for two-cycle pulses, while producing results 20 and 50 times faster, respectively.
Nonlinear Statistical Process Monitoring and Fault Detection Using Kernel ICA
Institute of Scientific and Technical Information of China (English)
ZHANG Xi; YAN Wei-wu; ZHAO Xu; SHAO Hui-he
2007-01-01
A novel nonlinear process monitoring and fault detection method based on kernel independent component analysis (ICA) is proposed. The kernel ICA method is a two-phase algorithm: whitened kernel principal component (KPCA) plus ICA. KPCA spheres data and makes the data structure become as linearly separable as possible by virtue of an implicit nonlinear mapping determined by kernel. ICA seeks the projection directions in the KPCA whitened space, making the distribution of the projected data as non-gaussian as possible. The application to the fluid catalytic cracking unit (FCCU) simulated process indicates that the proposed process monitoring method based on kernel ICA can effectively capture the nonlinear relationship in process variables. Its performance significantly outperforms monitoring method based on ICA or KPCA.
ON NONLINEAR STABILITY IN NONPARALLEL BOUNDARY LAYER FLOW
Institute of Scientific and Technical Information of China (English)
TANG Deng-bin; WANG Wei-zhi
2004-01-01
The nonlinear stability problem in nonparallel boundary layer flow for two-dimensional disturbances was studied by using a newly presented method called Parabolic Stability Equations (PSE). A series of new modes generated by the nonlinear interaction of disturbance waves were tabulately analyzed, and the Mean Flow Distortion (MFD) was numerically given. The computational techniques developed, including the higher-order spectral method and the more effective algebraic mapping, increased greatly the numerical accuracy and the rate of convergence. With the predictor-corrector approach in the marching procedure, the normalization condition was satisfied, and the stability of numerical calculation could be ensured. With different initial amplitudes, the nonlinear stability of disturbance wave was studied. The results of examples show good agreement with the data given by the DNS using the full Navier-Stokes equations.
Nonlinear transformation on the transfer entropy of financial time series
Wu, Zhenyu; Shang, Pengjian
2017-09-01
Transfer entropy (TE) now is widely used in the data mining and economic field. However, TE itself demands that time series intend to be stationary and meet Markov condition. Naturally, we are interested in investigating the effect of the nonlinear transformation of the two series on the TE. Therefore, the paper is designed to study the TE of five nonlinear ;volatile; transformations based on the data which are generated by the linear modeling and the logistic maps modeling, as well as the dataset that come from financial markets. With only one of the TE of nonlinear transformations fluctuating around the TE of original series, the TE of others all have increased with different degrees.
Stolz, A; Markey, L; Francs, G Colas des; Bouhelier, A
2013-01-01
We introduce strongly-coupled optical gap antennas to interface optical radiation with current-carrying electrons at the nanoscale. The transducer relies on the nonlinear optical and electrical properties of an optical antenna operating in the tunneling regime. We discuss the underlying physical mechanisms controlling the conversion and demonstrate that a two-wire optical antenna can provide advanced optoelectronic functionalities beyond tailoring the electromagnetic response of a single emitter. Interfacing an electronic command layer with a nanoscale optical device may thus be facilitated by the optical rectennas discussed here.
Nonlinear surface electromagnetic phenomena
Ponath, H-E
1991-01-01
In recent years the physics of electromagnetic surface phenomena has developed rapidly, evolving into technologies for communications and industry, such as fiber and integrated optics. The variety of phenomena based on electromagnetism at surfaces is rich and this book was written with the aim of summarizing the available knowledge in selected areas of the field. The book contains reviews written by solid state and optical physicists on the nonlinear interaction of electromagnetic waves at and with surfaces and films. Both the physical phenomena and some potential applications are
Nonlinear electrodynamics with birefringence
Kruglov, S I
2015-01-01
A new model of nonlinear electrodynamics with three parameters is suggested. The phenomena of vacuum birefringence takes place when there is the external constant magnetic field. We calculate the indices of refraction for two polarizations of electromagnetic waves, parallel and perpendicular to the magnetic induction field. From the Bir\\'{e}fringence Magn\\'{e}tique du Vide (BMV) experiment one of the coefficients, $\\gamma\\approx 10^{-20}$ T$^{-2}$, was estimated. The canonical, symmetrical Belinfante energy-momentum tensors and dilatation current were obtained. The dilatation symmetry and the dual symmetry are broken in the model considered.
Wu Zhuo Qun; Li Hui Lai; Zhao Jun Ning
2001-01-01
Nonlinear diffusion equations, an important class of parabolic equations, come from a variety of diffusion phenomena which appear widely in nature. They are suggested as mathematical models of physical problems in many fields, such as filtration, phase transition, biochemistry and dynamics of biological groups. In many cases, the equations possess degeneracy or singularity. The appearance of degeneracy or singularity makes the study more involved and challenging. Many new ideas and methods have been developed to overcome the special difficulties caused by the degeneracy and singularity, which
Nonlinear dynamics in psychology
Directory of Open Access Journals (Sweden)
Stephen J. Guastello
2001-01-01
Full Text Available This article provides a survey of the applications of nonlinear dynamical systems theory to substantive problems encountered in the full scope of psychological science. Applications are organized into three topical areas – cognitive science, social and organizational psychology, and personality and clinical psychology. Both theoretical and empirical studies are considered with an emphasis on works that capture the broadest scope of issues that are of substantive interest to psychological theory. A budding literature on the implications of NDS principles in professional practice is reported also.
2009-11-18
analytic semigroup T(t) ~ eAl is exponentially stable (Notice that it is also a contraction semigroup ). 3. Be 3(U, Z) and P e £(W, 2) are bounded. 4. Ce...quite often in practice, .4 is self-adjoint. We also note that, since we assume (—A) is sectorial, we work with the semigroup exp(.4f) rather than...Uniform Output Regulation of Nonlinear Sys- tems: A convergent Dynamics Approach, Birkhauser, Boston, 2006. 23 135] A. Pazy, Semigroups of Linear
Directory of Open Access Journals (Sweden)
DJAIRO G. DEFIGUEIREDO
2000-12-01
Full Text Available In this paper we treat the question of the existence of solutions of boundary value problems for systems of nonlinear elliptic equations of the form - deltau = f (x, u, v,Ñu,Ñv, - deltav = g(x, u, v, Ñu, Ñv, in omega, We discuss several classes of such systems using both variational and topological methods. The notion of criticality takes into consideration the coupling, which plays important roles in both a priori estimates for the solutions and Palais-Smale conditions for the associated functional in the variational case.
Infinite invariant densities due to intermittency in a nonlinear oscillator
Meyer, Philipp; Kantz, Holger
2017-08-01
Dynamical intermittency is known to generate anomalous statistical behavior of dynamical systems, a prominent example being the Pomeau-Manneville map. We present a nonlinear oscillator, i.e., a physical model in continuous time, whose properties in terms of weak ergodity breaking and aging have a one-to-one correspondence to the properties of the Pomeau-Manneville map. So for both systems in a wide range of parameters no physical invariant density exists. We show how this regime can be characterized quantitatively using the techniques of infinite invariant densities and the Thaler-Dynkin limit theorem. We see how expectation values exhibit aging in terms of scaling in time.
Nonlinear evolution of drift instabilities
Energy Technology Data Exchange (ETDEWEB)
Lee, W.W.; Krommes, J.A.; Oberman, C.R.; Smith, R.A.
1984-01-01
The nonlinear evolution of collisionless drift instabilities in a shear-free magnetic field has been studied by means of gyrokinetic particle simulation as well as numerical integration of model mode-coupling equations. The purpose of the investigation is to identify relevant nonlinear mechanisms responsible for the steady-state drift wave fluctuations. It is found that the saturation of the instability is mainly caused by the nonlinear E x B convection of the resonant electrons and their associated velocity space nonlinearity. The latter also induces energy exchange between the competing modes, which, in turn, gives rise to enhanced diffusion. The nonlinear E x B convection of the ions, which contributes to the nonlinear frequency shift, is also an important ingredient for the saturation.
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.
Nonlinear solar cycle forecasting: theory and perspectives
Directory of Open Access Journals (Sweden)
A. L. Baranovski
2008-02-01
Full Text Available In this paper we develop a modern approach to solar cycle forecasting, based on the mathematical theory of nonlinear dynamics. We start from the design of a static curve fitting model for the experimental yearly sunspot number series, over a time scale of 306 years, starting from year 1700 and we establish a least-squares optimal pulse shape of a solar cycle. The cycle-to-cycle evolution of the parameters of the cycle shape displays different patterns, such as a Gleissberg cycle and a strong anomaly in the cycle evolution during the Dalton minimum. In a second step, we extract a chaotic mapping for the successive values of one of the key model parameters – the rate of the exponential growth-decrease of the solar activity during the n-th cycle. We examine piece-wise linear techniques for the approximation of the derived mapping and we provide its probabilistic analysis: calculation of the invariant distribution and autocorrelation function. We find analytical relationships for the sunspot maxima and minima, as well as their occurrence times, as functions of chaotic values of the above parameter. Based on a Lyapunov spectrum analysis of the embedded mapping, we finally establish a horizon of predictability for the method, which allows us to give the most probable forecasting of the upcoming solar cycle 24, with an expected peak height of 93±21 occurring in 2011/2012.
Astra, Egon; Olsson, Samuel L I; Eliasson, Henrik; Andrekson, Peter A
2017-06-12
We present an investigation of dispersion map optimization for two-span single-channel 28 GBaud QPSK transmission systems with phase-sensitive amplifiers (PSAs). In experiments, when the PSA link is operated in a highly nonlinear regime, a 1.4 dB error vector magnitude (EVM) improvement is achieved compared to a one-span optimized dispersion map link due to improved nonlinearity mitigation. The two-span optimized dispersion map of a PSA link differs from the optimized dispersion map of a dispersion managed phase-insensitive amplifier (PIA) link. Simulations show that the performance of the two-span dispersion map optimized PSA link does not improve by residual dispersion optimization. Further, by using the two-span optimized dispersion maps repeatedly in a long-haul PSA link instead of one-span optimized maps, the maximum transmission reach can be improved 1.5 times.
Topics on nonlinear generalized functions
Colombeau, J F
2011-01-01
The aim of this paper is to give the text of a recent introduction to nonlinear generalized functions exposed in my talk in the congress gf2011, which was asked by several participants. Three representative topics were presented: two recalls "Nonlinear generalized functions and their connections with distribution theory", "Examples of applications", and a recent development: "Locally convex topologies and compactness: a functional analysis of nonlinear generalized functions".
Nonlinear Ultrasonic Phased Array Imaging
Potter, J. N.; Croxford, A. J.; Wilcox, P. D.
2014-10-01
This Letter reports a technique for the imaging of acoustic nonlinearity. By contrasting the energy of the diffuse field produced through the focusing of an ultrasonic array by delayed parallel element transmission with that produced by postprocessing of sequential transmission data, acoustic nonlinearity local to the focal point is measured. Spatially isolated wave distortion is inferred without requiring interrogation of the wave at the inspection point, thereby allowing nonlinear imaging through depth.
Nonlinear ultrasonic phased array imaging
Potter, J N; Croxford, A.J.; Wilcox, P. D.
2014-01-01
This Letter reports a technique for the imaging of acoustic nonlinearity. By contrasting the energy of the diffuse field produced through the focusing of an ultrasonic array by delayed parallel element transmission with that produced by postprocessing of sequential transmission data, acoustic nonlinearity local to the focal point is measured. Spatially isolated wave distortion is inferred without requiring interrogation of the wave at the inspection point, thereby allowing nonlinear imaging t...
Research on Nonlinear Dynamical Systems.
1983-01-10
investigated fundamental aspects of functional differential equations, including qualitative questions (stability, nonlinear oscillations ), in 142,45,47,52...Bifurcation in the Duffing equation with several parameters, II. Proc. of the Royal Society of Edinburgh, Series A, 79A (1977), pp.317-326. 1I.J (with ;Ibtoas...Lecture Notes in Mathematics, Vol. 730 (1979). [54] Nonlinear oscillations in equations with delays. Proc. at A.M.S. 10th Summer Seminar on Nonlinear
Nonlinear ultrasonic phased array imaging.
Potter, J N; Croxford, A J; Wilcox, P D
2014-10-03
This Letter reports a technique for the imaging of acoustic nonlinearity. By contrasting the energy of the diffuse field produced through the focusing of an ultrasonic array by delayed parallel element transmission with that produced by postprocessing of sequential transmission data, acoustic nonlinearity local to the focal point is measured. Spatially isolated wave distortion is inferred without requiring interrogation of the wave at the inspection point, thereby allowing nonlinear imaging through depth.
Remote Atmospheric Nonlinear Optical Magnetometry
2014-04-28
Boyd , Nonlinear Optics (Elsevier, Burlington, MA, 2008). [13] M. Scully and S. Zubairy, Quantum Optics (Cambridge U. Press, Cambridge, UK, 1997...Naval Research Laboratory Washington, DC 20375-5320 NRL/MR/6703--14-9548 Remote Atmospheric Nonlinear Optical Magnetometry PhilliP SPrangle...b. ABSTRACT c. THIS PAGE 18. NUMBER OF PAGES 17. LIMITATION OF ABSTRACT Remote Atmospheric Nonlinear Optical Magnetometry Phillip Sprangle, Luke
Applications of nonlinear fiber optics
Agrawal, Govind
2008-01-01
* The only book describing applications of nonlinear fiber optics * Two new chapters on the latest developments: highly nonlinear fibers and quantum applications* Coverage of biomedical applications* Problems provided at the end of each chapterThe development of new highly nonlinear fibers - referred to as microstructured fibers, holey fibers and photonic crystal fibers - is the next generation technology for all-optical signal processing and biomedical applications. This new edition has been thoroughly updated to incorporate these key technology developments.The bo
Linearization of conservative nonlinear oscillators
Energy Technology Data Exchange (ETDEWEB)
Belendez, A; Alvarez, M L [Departamento de Fisica, IngenierIa de Sistemas y TeorIa de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Fernandez, E; Pascual, I [Departamento de Optica, FarmacologIa y AnatomIa, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)], E-mail: a.belendez@ua.es
2009-03-11
A linearization method of the nonlinear differential equation for conservative nonlinear oscillators is analysed and discussed. This scheme is based on the Chebyshev series expansion of the restoring force which allows us to obtain a frequency-amplitude relation which is valid not only for small but also for large amplitudes and, sometimes, for the complete range of oscillation amplitudes. Some conservative nonlinear oscillators are analysed to illustrate the usefulness and effectiveness of the technique.
From spiking neuron models to linear-nonlinear models.
Directory of Open Access Journals (Sweden)
Srdjan Ostojic
Full Text Available Neurons transform time-varying inputs into action potentials emitted stochastically at a time dependent rate. The mapping from current input to output firing rate is often represented with the help of phenomenological models such as the linear-nonlinear (LN cascade, in which the output firing rate is estimated by applying to the input successively a linear temporal filter and a static non-linear transformation. These simplified models leave out the biophysical details of action potential generation. It is not a priori clear to which extent the input-output mapping of biophysically more realistic, spiking neuron models can be reduced to a simple linear-nonlinear cascade. Here we investigate this question for the leaky integrate-and-fire (LIF, exponential integrate-and-fire (EIF and conductance-based Wang-Buzsáki models in presence of background synaptic activity. We exploit available analytic results for these models to determine the corresponding linear filter and static non-linearity in a parameter-free form. We show that the obtained functions are identical to the linear filter and static non-linearity determined using standard reverse correlation analysis. We then quantitatively compare the output of the corresponding linear-nonlinear cascade with numerical simulations of spiking neurons, systematically varying the parameters of input signal and background noise. We find that the LN cascade provides accurate estimates of the firing rates of spiking neurons in most of parameter space. For the EIF and Wang-Buzsáki models, we show that the LN cascade can be reduced to a firing rate model, the timescale of which we determine analytically. Finally we introduce an adaptive timescale rate model in which the timescale of the linear filter depends on the instantaneous firing rate. This model leads to highly accurate estimates of instantaneous firing rates.
On the nonlinear design of industrial arc spring dampers
DEFF Research Database (Denmark)
Lahriri, Said; Santos, Ilmar; Hartmann, Henning
2011-01-01
The objective of this paper is to present a numerical approach for analyzing parameter excited vibrations on a gas compressor, induced by the nonlinear characteristic of the arc spring feature of certain designs of squeeze film dampers, SFDs. The behavior of the journal is studied in preparation...... acting on the SFD are presented. It is worth mentioning, that the maps and diagrams can be used as design guidance....
Chaos and Nonlinear Dynamics in a Quantum Artificial Economy
Gonçalves, Carlos Pedro
2012-01-01
Chaos and nonlinear economic dynamics are addressed for a quantum coupled map lattice model of an artificial economy, with quantized supply and demand equilibrium conditions. The measure theoretic properties and the patterns that emerge in both the economic business volume dynamics' diagrams as well as in the quantum mean field averages are addressed and conclusions are drawn in regards to the application of quantum chaos theory to address signatures of chaotic dynamics in relevant discrete economic state variables.
New Exact Solutions for New Model Nonlinear Partial Differential Equation
Directory of Open Access Journals (Sweden)
A. Maher
2013-01-01
Full Text Available In this paper we propose a new form of Padé-II equation, namely, a combined Padé-II and modified Padé-II equation. The mapping method is a promising method to solve nonlinear evaluation equations. Therefore, we apply it, to solve the combined Padé-II and modified Padé-II equation. Exact travelling wave solutions are obtained and expressed in terms of hyperbolic functions, trigonometric functions, rational functions, and elliptic functions.
On the nonlinear design of industrial arc spring dampers
DEFF Research Database (Denmark)
Lahriri, Said; Santos, Ilmar; Hartmann, Henning
2011-01-01
The objective of this paper is to present a numerical approach for analyzing parameter excited vibrations on a gas compressor, induced by the nonlinear characteristic of the arc spring feature of certain designs of squeeze film dampers, SFDs. The behavior of the journal is studied in preparation...... acting on the SFD are presented. It is worth mentioning, that the maps and diagrams can be used as design guidance....
Problems in nonlinear resistive MHD
Energy Technology Data Exchange (ETDEWEB)
Turnbull, A.D.; Strait, E.J.; La Haye, R.J.; Chu, M.S.; Miller, R.L. [General Atomics, San Diego, CA (United States)
1998-12-31
Two experimentally relevant problems can relatively easily be tackled by nonlinear MHD codes. Both problems require plasma rotation in addition to the nonlinear mode coupling and full geometry already incorporated into the codes, but no additional physics seems to be crucial. These problems discussed here are: (1) nonlinear coupling and interaction of multiple MHD modes near the B limit and (2) nonlinear coupling of the m/n = 1/1 sawtooth mode with higher n gongs and development of seed islands outside q = 1.
Asymptotics for dissipative nonlinear equations
Hayashi, Nakao; Kaikina, Elena I; Shishmarev, Ilya A
2006-01-01
Many of problems of the natural sciences lead to nonlinear partial differential equations. However, only a few of them have succeeded in being solved explicitly. Therefore different methods of qualitative analysis such as the asymptotic methods play a very important role. This is the first book in the world literature giving a systematic development of a general asymptotic theory for nonlinear partial differential equations with dissipation. Many typical well-known equations are considered as examples, such as: nonlinear heat equation, KdVB equation, nonlinear damped wave equation, Landau-Ginzburg equation, Sobolev type equations, systems of equations of Boussinesq, Navier-Stokes and others.
Focus issue introduction: nonlinear optics.
Boulanger, Benoît; Cundiff, Steven T; Gauthier, Daniel J; Karlsson, Magnus; Lu, Yan-Qing; Norwood, Robert A; Skryabin, Dmitry; Taira, Takunori
2011-11-07
It is now fifty years since the original observation of second harmonic generation ushered in the field of nonlinear optics, close on the heels of the invention of the laser. This feature issue celebrates this anniversary with papers that span the range from new nonlinear optical materials, through the increasingly novel methods that have been developed for phase matching, to emerging areas such as nonlinear metamaterials and plasmonic enhancement of optical properties. It is clear that the next fifty years of nonlinear optics will witness a proliferation of new applications with increasing technological impact.
Nonlocal homogenization for nonlinear metamaterials
Gorlach, Maxim A; Lapine, Mikhail; Kivshar, Yuri S; Belov, Pavel A
2016-01-01
We present a consistent theoretical approach for calculating effective nonlinear susceptibilities of metamaterials taking into account both frequency and spatial dispersion. Employing the discrete dipole model, we demonstrate that effects of spatial dispersion become especially pronounced in the vicinity of effective permittivity resonance where nonlinear susceptibilities reach their maxima. In that case spatial dispersion may enable simultaneous generation of two harmonic signals with the same frequency and polarization but different wave vectors. We also prove that the derived expressions for nonlinear susceptibilities transform into the known form when spatial dispersion effects are negligible. In addition to revealing new physical phenomena, our results provide useful theoretical tools for analysing resonant nonlinear metamaterials.
Nonlinear Peltier effect in semiconductors
Zebarjadi, Mona; Esfarjani, Keivan; Shakouri, Ali
2007-09-01
Nonlinear Peltier coefficient of a doped InGaAs semiconductor is calculated numerically using the Monte Carlo technique. The Peltier coefficient is also obtained analytically for single parabolic band semiconductors assuming a shifted Fermi-Dirac electronic distribution under an applied bias. Analytical results are in agreement with numerical simulations. Key material parameters affecting the nonlinear behavior are doping concentration, effective mass, and electron-phonon coupling. Current density thresholds at which nonlinear behavior is observable are extracted from numerical data. It is shown that the nonlinear Peltier effect can be used to enhance cooling of thin film microrefrigerator devices especially at low temperatures.
Nonlinearities in Behavioral Macroeconomics.
Gomes, Orlando
2017-07-01
This article undertakes a journey across the literature on behavioral macroeconomics, with attention concentrated on the nonlinearities that the behavioral approach typically suggests or implies. The emphasis is placed on thinking the macro economy as a living organism, composed of many interacting parts, each one having a will of its own, which is in sharp contrast with the mechanism of the orthodox view (well represented by the neoclassical or new Keynesian dynamic stochastic general equilibrium - DSGE - model). The paper advocates that a thorough understanding of individual behavior in collective contexts is the only possible avenue to further explore macroeconomic phenomena and the often observed 'anomalies' that the benchmark DSGE macro framework is unable to explain or justify. After a reflection on the role of behavioral traits as a fundamental component of a new way of thinking the economy, the article proceeds with a debate on some of the most relevant frameworks in the literature that somehow link macro behavior and nonlinearities; covered subjects include macro models with disequilibrium rules, agent-based models that highlight interaction and complexity, evolutionary switching frameworks, and inattention based decision problems. These subjects have, as a fundamental point in common, the use of behavioral elements to transform existing interpretations of the economic reality, making it more evident how irregular fluctuations emerge and unfold on the aggregate.
Improved nonlinear prediction method
Adenan, Nur Hamiza; Md Noorani, Mohd Salmi
2014-06-01
The analysis and prediction of time series data have been addressed by researchers. Many techniques have been developed to be applied in various areas, such as weather forecasting, financial markets and hydrological phenomena involving data that are contaminated by noise. Therefore, various techniques to improve the method have been introduced to analyze and predict time series data. In respect of the importance of analysis and the accuracy of the prediction result, a study was undertaken to test the effectiveness of the improved nonlinear prediction method for data that contain noise. The improved nonlinear prediction method involves the formation of composite serial data based on the successive differences of the time series. Then, the phase space reconstruction was performed on the composite data (one-dimensional) to reconstruct a number of space dimensions. Finally the local linear approximation method was employed to make a prediction based on the phase space. This improved method was tested with data series Logistics that contain 0%, 5%, 10%, 20% and 30% of noise. The results show that by using the improved method, the predictions were found to be in close agreement with the observed ones. The correlation coefficient was close to one when the improved method was applied on data with up to 10% noise. Thus, an improvement to analyze data with noise without involving any noise reduction method was introduced to predict the time series data.
An integrable Poisson map generated from the eigenvalue problem of the Lotka-Volterra hierarchy
Energy Technology Data Exchange (ETDEWEB)
Wu Yongtang [Department of Computer Science, Hong Kong Baptist University, Kowloon Tong, Hong Kong (China); Wang Hongye [Department of Mathematics, Zhengzhou University, Henan (China); Du Dianlou [Department of Mathematics, Zhengzhou University, Henan (China)]. E-mail: ddl@zzu.edu.cn
2002-05-03
A 3x3 discrete eigenvalue problem associated with the Lotka-Volterra hierarchy is studied and the corresponding nonlinearized one, an integrable Poisson map with a Lie-Poisson structure, is also presented. Moreover, a 2x2 nonlinearized eigenvalue problem, which also begets the Lotka-Volterra hierarchy, is proved to be a reduction of the Poisson map on the leaves of the symplectic foliation. (author)
Nonlinear Response of Strong Nonlinear System Arisen in Polymer Cushion
Directory of Open Access Journals (Sweden)
Jun Wang
2013-01-01
Full Text Available A dynamic model is proposed for a polymer foam-based nonlinear cushioning system. An accurate analytical solution for the nonlinear free vibration of the system is derived by applying He's variational iteration method, and conditions for resonance are obtained, which should be avoided in the cushioning design.
A machine learning approach to nonlinear modal analysis
Worden, K.; Green, P. L.
2017-02-01
Although linear modal analysis has proved itself to be the method of choice for the analysis of linear dynamic structures, its extension to nonlinear structures has proved to be a problem. A number of competing viewpoints on nonlinear modal analysis have emerged, each of which preserves a subset of the properties of the original linear theory. From the geometrical point of view, one can argue that the invariant manifold approach of Shaw and Pierre is the most natural generalisation. However, the Shaw-Pierre approach is rather demanding technically, depending as it does on the analytical construction of a mapping between spaces, which maps physical coordinates into invariant manifolds spanned by independent subsets of variables. The objective of the current paper is to demonstrate a data-based approach motivated by Shaw-Pierre method which exploits the idea of statistical independence to optimise a parametric form of the mapping. The approach can also be regarded as a generalisation of the Principal Orthogonal Decomposition (POD). A machine learning approach to inversion of the modal transformation is presented, based on the use of Gaussian processes, and this is equivalent to a nonlinear form of modal superposition. However, it is shown that issues can arise if the forward transformation is a polynomial and can thus have a multi-valued inverse. The overall approach is demonstrated using a number of case studies based on both simulated and experimental data.
Glass, Tom
2016-01-01
When students generate mind maps, or concept maps, the maps are usually on paper, computer screens, or a blackboard. Human Mind Maps require few resources and little preparation. The main requirements are space where students can move around and a little creativity and imagination. Mind maps can be used for a variety of purposes, and Human Mind…
Discrete Integrable Systems and Poisson Algebras From Cluster Maps
Fordy, Allan P.; Hone, Andrew
2014-01-01
We consider nonlinear recurrences generated from cluster mutations applied to quivers that have the property of being cluster mutation-periodic with period 1. Such quivers were completely classified by Fordy and Marsh, who characterised them in terms of the skew-symmetric matrix that defines the quiver. The associated nonlinear recurrences are equivalent to birational maps, and we explain how these maps can be endowed with an invariant Poisson bracket and/or presymplectic structure. Upon applying the algebraic entropy test, we are led to a series of conjectures which imply that the entropy of the cluster maps can be determined from their tropical analogues, which leads to a sharp classification result. Only four special families of these maps should have zero entropy. These families are examined in detail, with many explicit examples given, and we show how they lead to discrete dynamics that is integrable in the Liouville-Arnold sense.
The approximate weak inertial manifolds of a class of nonlinear hyperbolic dynamical systems
Institute of Scientific and Technical Information of China (English)
赵怡
1996-01-01
Some concepts about approximate and semi-approximate weak inertial manifolds are introduced and the existence of global attractor and semi-approximate weak inertial manifolds is obtained for a class of nonlinear hyperbolic dynamical systems by means of some topologically homeomorphic mappings and techniques. Using these results, the existence of approximate weak inertial manifolds is also presented for a kind of nonlinear hyperbolic system arising from relativistic quantum mechanics. The regularization problem is proposed finally.
BLIND IDENTIFICATION OF A CLASS OF NONLINEAR SYSTEMS WITH CYCLOSTATIONARY INPUT
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
This letter deals with blind identification of nonlinear discrete Hammerstein system under the input signal that is cyclostationary.The first-order moment of the specific input as well as the inverse nonlinear mapping of the Hammerstein model are combined to establish a relationship between the system output and the system parameters,which implies an approach to identifying the system blindly.Simulation results demonstrate the effectiveness of this approach to blind identification of a class of nonUnear systems.
The Nonlinear Interaction of Two-Crossed Focussed Ultrasonic Beams in the Presence of Turbulence
1988-06-10
in water or any fluid medium can be obtained by the vibration of a solid body in the fluid, such as the vibration of a vocal chord or guitar string . In... physical phenomenon due to the nonlinearity of sound arises from the interaction of two sound beams. Nonlinear acoustic theory predictions by Westervelt in...known experimental data for the turbulent velocity field. Goals of this research include mapping out the turbulence and studying the physical
Spatial 3-D nonlinear calibration technique for PSD
Guo, Lifeng; Zhang, Guoxiong; Zheng, Qi; Gong, Qiang; Liu, Wenyao
2006-11-01
A 3-D nonlinear calibration technique for Position sensitive detector (PSD) in long distance laser collimating measurement is proposed. An automatic calibration system was developed to measure the nonlinearity of a 2-D PSD in 3-D space. It is mainly composed of a high accurate 2-D motorized translational stage, a high precision distance measuring device, and a computer-based data acquisition and control system. With the aid of the calibration system, the nonlinear characteristic of 2-D PSD is checked in a long collimating distance up to 78 meters. The calibration experiment was carried out for a series of distance, e.g. every 15 meters. The results showed that the nonlinearity of 2-D PSD is different evidently when the PSD element is at different distance from the laser head. One calculating method is defined to evaluate the nonlinear errors. The spatial 3-D mapping relationship between the actual displacements of the incident light and the coordinates of 2-D PSD outputs is established using a multilayer feedforward neural network.
Nonlinear aeroelastic analysis of airfoils: bifurcation and chaos
Lee, B. H. K.; Price, S. J.; Wong, Y. S.
1999-04-01
Different types of structural and aerodynamic nonlinearities commonly encountered in aeronautical engineering are discussed. The equations of motion of a two-dimensional airfoil oscillating in pitch and plunge are derived for a structural nonlinearity using subsonic aerodynamics theory. Three classical nonlinearities, namely, cubic, freeplay and hysteresis are investigated in some detail. The governing equations are reduced to a set of ordinary differential equations suitable for numerical simulations and analytical investigation of the system stability. The onset of Hopf-bifurcation, and amplitudes and frequencies of limit cycle oscillations are investigated, with examples given for a cubic hardening spring. For various geometries of the freeplay, bifurcations and chaos are discussed via the phase plane, Poincaré maps, and Lyapunov spectrum. The route to chaos is investigated from bifurcation diagrams, and for the freeplay nonlinearity it is shown that frequency doubling is the most commonly observed route. Examples of aerodynamic nonlinearities arising from transonic flow and dynamic stall are discussed, and special attention is paid to numerical simulation results for dynamic stall using a time-synthesized method for the unsteady aerodynamics. The assumption of uniform flow is usually not met in practice since perturbations in velocities are encountered in flight. Longitudinal atmospheric turbulence is introduced to show its effect on both the flutter boundary and the onset of Hopf-bifurcation for a cubic restoring force.
Nonlinear Evolution of Ferroelectric Domains
Institute of Scientific and Technical Information of China (English)
WeiLU; Dai－NingFANG; 等
1997-01-01
The nonlinear evolution of ferroelectric domains is investigated in the paper and amodel is proposed which can be applied to numerical computation.Numerical results show that the model can accurately predict some nonlinear behavior and consist with those experimental results.
Nonlinear Electrodynamics and black holes
Breton, N; Breton, Nora; Garcia-Salcedo, Ricardo
2007-01-01
It is addressed the issue of black holes with nonlinear electromagnetic field, focussing mainly in the Born-Infeld case. The main features of these systems are described, for instance, geodesics, energy conditions, thermodynamics and isolated horizon aspects. Also are revised some black hole solutions of alternative nonlinear electrodynamics and its inconveniences.
Space curves, anholonomy and nonlinearity
Indian Academy of Sciences (India)
Radha Balakrishnan
2005-04-01
Using classical differential geometry, we discuss the phenomenon of anholonomy that gets associated with a static and a moving curve. We obtain the expressions for the respective geometric phases in the two cases and interpret them. We show that there is a close connection between anholonomy and nonlinearity in a wide class of nonlinear systems.
Balancing for unstable nonlinear systems
Scherpen, J.M.A.
1993-01-01
A previously obtained method of balancing for stable nonlinear systems is extended to unstable nonlinear systems. The similarity invariants obtained by the concept of LQG balancing for an unstable linear system can also be obtained by considering a past and future energy function of the system. By c
Nonlinear diffusion and superconducting hysteresis
Energy Technology Data Exchange (ETDEWEB)
Mayergoyz, I.D. [Univ. of Maryland, College Park, MD (United States)
1996-12-31
Nonlinear diffusion of electromagnetic fields in superconductors with ideal and gradual resistive transitions is studied. Analytical results obtained for linear and nonlinear polarizations of electromagnetic fields are reported. These results lead to various extensions of the critical state model for superconducting hysteresis.
U.S. Geological Survey, Department of the Interior — ShakeMap is a product of the USGS Earthquake Hazards Program in conjunction with the regional seismic networks. ShakeMaps provide near-real-time maps of ground...
Whitmore, Paul M.
1988-01-01
Reviews the history of cartography. Describes the contributions of Strabo and Ptolemy in early maps. Identifies the work of Gerhard Mercator as the most important advancement in mapping. Discusses present mapping standards from history. (CW)
National Aeronautics and Space Administration — The Lunar Map Catalog includes various maps of the moon's surface, including Apollo landing sites; earthside, farside, and polar charts; photography index maps; zone...
Energy Technology Data Exchange (ETDEWEB)
Lallart, Mickael; Guyomar, Daniel, E-mail: mickael.lallart@insa-lyon.fr [LGEF, INSA-Lyon, Universite de Lyon, 8 rue de la Physique, F-69621 (France)
2011-10-29
The proliferation of wearable and left-behind devices has raised the issue of powering such systems. While primary batteries have been widely used in order to address this issue, recent trends have focused on energy harvesting products that feature high reliability and low maintenance issues. Among all the ambient sources available for energy harvesting, vibrations and heat have been of significant interest among the research community for small-scale devices. However, the conversion abilities of materials are still limited when dealing with systems featuring small dimensions. The purpose of this paper is to presents an up-to-date view of nonlinear approaches for increasing the efficiency of electromechanical and electrocaloric conversion mechanisms. From the modeling of the operation principles of the different architectures, a comparative analysis will be exposed, emphasizing the advantages and drawbacks of the presented concepts, in terms of maximal output power (under constant vibration magnitude or taking into account the damping effect), load independence, and implementation easiness.
Fainberg, B D
2015-01-01
Purely organic materials with negative and near-zero dielectric permittivity can be easily fabricated. Here we develop a theory of nonlinear non-steady-state organic plasmonics with strong laser pulses. The bistability response of the electron-vibrational model of organic materials in the condensed phase has been demonstrated. Non-steady-state organic plasmonics enable us to obtain near-zero dielectric permittivity during a short time. We have proposed to use non-steady-state organic plasmonics for the enhancement of intersite dipolar energy-transfer interaction in the quantum dot wire that influences on electron transport through nanojunctions. Such interactions can compensate Coulomb repulsions for particular conditions. We propose the exciton control of Coulomb blocking in the quantum dot wire based on the non-steady-state near-zero dielectric permittivity of the organic host medium.
2016-01-01
This volume brings together four lecture courses on modern aspects of water waves. The intention, through the lectures, is to present quite a range of mathematical ideas, primarily to show what is possible and what, currently, is of particular interest. Water waves of large amplitude can only be fully understood in terms of nonlinear effects, linear theory being not adequate for their description. Taking advantage of insights from physical observation, experimental evidence and numerical simulations, classical and modern mathematical approaches can be used to gain insight into their dynamics. The book presents several avenues and offers a wide range of material of current interest. Due to the interdisciplinary nature of the subject, the book should be of interest to mathematicians (pure and applied), physicists and engineers. The lectures provide a useful source for those who want to begin to investigate how mathematics can be used to improve our understanding of water wave phenomena. In addition, some of the...
Nonlinear estimation and classification
Hansen, Mark; Holmes, Christopher; Mallick, Bani; Yu, Bin
2003-01-01
Researchers in many disciplines face the formidable task of analyzing massive amounts of high-dimensional and highly-structured data This is due in part to recent advances in data collection and computing technologies As a result, fundamental statistical research is being undertaken in a variety of different fields Driven by the complexity of these new problems, and fueled by the explosion of available computer power, highly adaptive, non-linear procedures are now essential components of modern "data analysis," a term that we liberally interpret to include speech and pattern recognition, classification, data compression and signal processing The development of new, flexible methods combines advances from many sources, including approximation theory, numerical analysis, machine learning, signal processing and statistics The proposed workshop intends to bring together eminent experts from these fields in order to exchange ideas and forge directions for the future
Nonlinear transmission sputtering
Bitensky, I. S.; Sigmund, P.
1996-05-01
General expressions have been derived for the nonlinear yield of transmission sputtering for an incident polyatomic ion under the assumption that the molecule breaks up on entering the target and that sputter yields are enhanced due to proximity of atomic trajectories. Special attention is given to the case of negligible Coulomb explosion where projectile atoms penetrate independently. For weakly overlapping trajectories, the yield enhancement factor of a polyatomic molecule can be expressed by that of a diatom, amended with a correction for triple correlations if necessary. This expression is in good agreement with recent experimental findings on phenylalanine targets. Pertinent results on multiple scattering of atomic ions are reviewed and applied to independently-moving fragment atoms. The merits of measurements at variable layer thickness in addition to variable projectile energy are mentioned.
Perspectives on Nonlinear Filtering
Law, Kody
2015-01-07
The solution to the problem of nonlinear filtering may be given either as an estimate of the signal (and ideally some measure of concentration), or as a full posterior distribution. Similarly, one may evaluate the fidelity of the filter either by its ability to track the signal or its proximity to the posterior filtering distribution. Hence, the field enjoys a lively symbiosis between probability and control theory, and there are plenty of applications which benefit from algorithmic advances, from signal processing, to econometrics, to large-scale ocean, atmosphere, and climate modeling. This talk will survey some recent theoretical results involving accurate signal tracking with noise-free (degenerate) dynamics in high-dimensions (infinite, in principle, but say d between 103 and 108 , depending on the size of your application and your computer), and high-fidelity approximations of the filtering distribution in low dimensions (say d between 1 and several 10s).
Nonlinear rotordynamics analysis
Day, W. B.; Zalik, R. A.
1986-01-01
Three analytic consequences of the nonlinear Jeffcott equations are examined. The primary application of these analyses is directed toward understanding the excessive vibrations recorded in the Liquid Oxygen (LOX) pump of the Space Shuttle Main Engine (SSME) during hot firing ground testing. The first task is to provide bounds on the coefficients of the equations which delimit the two cases of numerical solution as a circle or an annulus. The second task examines the mathematical generalization to multiple forcing functions, which includes the special problems of mass imbalance, side force, rubbing, and combination of these forces. Finally, stability and boundedness of the steady-state solutions is discussed and related to the corresponding linear problem.
Studying the nonlinearity in Sonic IR NDE
Yu, Qiuye; Obeidat, Omar; Han, Xiaoyan
2017-02-01
Sonic IR Imaging combines pulsed ultrasound excitation and infrared imaging to detect defects in materials. The sound pulse causes rubbing due to non--unison motion between faces of defects, and infrared sensors image the temperature map over the target to identify defects. It works in various materials, including metal/metal alloy, ceramics, and composite materials. Its biggest advantage is that it's a fast, wide area NDE technique. It takes only a fraction of a second or a few seconds, depending on the thermal properties of the target, for one test over a few square feet. However, due to the nonlinearity in the coupling between the ultrasound transducer and the target, the repeatability has been an issue, which affects its application. In this paper, we present our study on this issue in Sonic IR.
Symmetries in Non-Linear Mechanics
Aldaya, Victor; López-Ruiz, Francisco F; Cossío, Francisco
2014-01-01
In this paper we exploit the use of symmetries of a physical system so as to characterize the corresponding solution manifold by means of Noether invariants. This constitutes a necessary preliminary step towards the correct quantisation in non-linear cases, where the success of Canonical Quantisation is not guaranteed in general. To achieve this task "point symmetries" of the Lagrangian are generally not enough, and the notion of contact transformations is in order. The use of the Poincar\\'e-Cartan form permits finding both the symplectic structure on the solution manifold, through the Hamilton-Jacobi transformation, and the required symmetries, realized as Hamiltonian vector fields, associated with functions on the solution manifold (thus constituting an inverse of the Noether Theorem), lifted back to the evolution space through the inverse of this Hamilton-Jacobi mapping. In this framework, solutions and symmetries are somehow identified and this correspondence is also kept at a perturbative level. We prese...
Nonlinear system modeling based on experimental data
Energy Technology Data Exchange (ETDEWEB)
PAEZ,THOMAS L.; HUNTER,NORMAN F.
2000-02-02
The canonical variate analysis technique is used in this investigation, along with a data transformation algorithm, to identify a system in a transform space. The transformation algorithm involves the preprocessing of measured excitation/response data with a zero-memory-nonlinear transform, specifically, the Rosenblatt transform. This transform approximately maps the measured excitation and response data from its own space into the space of uncorrelated, standard normal random variates. Following this transform, it is appropriate to model the excitation/response relation as linear since Gaussian inputs excite Gaussian responses in linear structures. The linear model is identified in the transform space using the canonical variate analysis approach, and system responses in the original space are predicted using inverse Rosenblatt transformation. An example is presented.
Mapping with the Masses: Google Map Maker
Pfund, J.
2008-12-01
After some 15,000 years of map making, which saw the innovations of cardinal directions, map projections for a spherical earth, and GIS analysis, many parts of the world still appear as the "Dark Continent" on modern maps. Google Map Maker intends to shine a light on these areas by tapping into the power of the GeoWeb. Google Map Maker is a website which allows you to collaborate with others on one unified map to add, edit, locate, describe, and moderate map features, such as roads, cities, businesses, parks, schools and more, for certain regions of the world using Google Maps imagery. In this session, we will show some examples of how people are mapping with this powerful tool as well as what they are doing with the data. With Google Map Maker, you can become a citizen cartographer and join the global network of users helping to improve the quality of maps and local information in your region of interest. You are invited to map the world with us!