Sahadevan, R.; Prakash, P.
2017-01-01
We show how invariant subspace method can be extended to time fractional coupled nonlinear partial differential equations and construct their exact solutions. Effectiveness of the method has been illustrated through time fractional Hunter-Saxton equation, time fractional coupled nonlinear diffusion system, time fractional coupled Boussinesq equation and time fractional Whitman-Broer-Kaup system. Also we explain how maximal dimension of the time fractional coupled nonlinear partial differential equations can be estimated.
Directory of Open Access Journals (Sweden)
Khaled A. Gepreel
2016-07-01
Full Text Available In this paper, we improve the extended trial equation method to construct the exact solutions for nonlinear coupled system of partial differential equations in mathematical physics. We use the extended trial equation method to find some different types of exact solutions such as the Jacobi elliptic function solutions, soliton solutions, trigonometric function solutions and rational, exact solutions to the nonlinear coupled Schrodinger Boussinesq equations when the balance number is a positive integer. The performance of this method is reliable, effective and powerful for solving more complicated nonlinear partial differential equations in mathematical physics. The balance number of this method is not constant as we have in other methods. This method allows us to construct many new types of exact solutions. By using the Maple software package we show that all obtained solutions satisfy the original partial differential equations.
Directory of Open Access Journals (Sweden)
A. H. Bhrawy
2014-01-01
Full Text Available One of the most important advantages of collocation method is the possibility of dealing with nonlinear partial differential equations (PDEs as well as PDEs with variable coefficients. A numerical solution based on a Jacobi collocation method is extended to solve nonlinear coupled hyperbolic PDEs with variable coefficients subject to initial-boundary nonlocal conservation conditions. This approach, based on Jacobi polynomials and Gauss-Lobatto quadrature integration, reduces solving the nonlinear coupled hyperbolic PDEs with variable coefficients to a system of nonlinear ordinary differential equation which is far easier to solve. In fact, we deal with initial-boundary coupled hyperbolic PDEs with variable coefficients as well as initial-nonlocal conditions. Using triangular, soliton, and exponential-triangular solutions as exact solutions, the obtained results show that the proposed numerical algorithm is efficient and very accurate.
Sharma, Dinkar; Singh, Prince; Chauhan, Shubha
2016-01-01
In this paper, a combined form of the Laplace transform method with the homotopy perturbation method (HPTM) is applied to solve nonlinear systems of partial differential equations viz. the system of third order KdV Equations and the systems of coupled Burgers' equations in one- and two- dimensions. The nonlinear terms can be easily handled by the use of He's polynomials. The results shows that the HPTM is very efficient, simple and avoids the round-off errors. Four test examples are considered to illustrate the present scheme. Further the results are compared with Homotopy perturbation method (HPM) which shows that this method is a suitable method for solving systems of partial differential equations.
Directory of Open Access Journals (Sweden)
Fukang Yin
2013-01-01
Full Text Available This paper develops a modified variational iteration method coupled with the Legendre wavelets, which can be used for the efficient numerical solution of nonlinear partial differential equations (PDEs. The approximate solutions of PDEs are calculated in the form of a series whose components are computed by applying a recursive relation. Block pulse functions are used to calculate the Legendre wavelets coefficient matrices of the nonlinear terms. The main advantage of the new method is that it can avoid solving the nonlinear algebraic system and symbolic computation. Furthermore, the developed vector-matrix form makes it computationally efficient. The results show that the proposed method is very effective and easy to implement.
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.
Institute of Scientific and Technical Information of China (English)
WU YUE-XIANG; HUO YAN-MEI; WU YA-KUN
2012-01-01
The main purpose of this paper is to examine the existence of coupled solutions and coupled minimal-maximal solutions for a kind of nonlinear operator equations in partial ordered linear topology spaces by employing the semi-order method.Some new existence results are obtained.
Partial synchronization in networks of non-linearly coupled oscillators: The Deserter Hubs Model
Energy Technology Data Exchange (ETDEWEB)
Freitas, Celso, E-mail: cbnfreitas@gmail.com; Macau, Elbert, E-mail: elbert.macau@inpe.br [Associate Laboratory for Computing and Applied Mathematics - LAC, Brazilian National Institute for Space Research - INPE (Brazil); Pikovsky, Arkady, E-mail: pikovsky@uni-potsdam.de [Department of Physics and Astronomy, University of Potsdam, Germany and Department of Control Theory, Nizhni Novgorod State University, Gagarin Av. 23, 606950, Nizhni Novgorod (Russian Federation)
2015-04-15
We study the Deserter Hubs Model: a Kuramoto-like model of coupled identical phase oscillators on a network, where attractive and repulsive couplings are balanced dynamically due to nonlinearity of interactions. Under weak force, an oscillator tends to follow the phase of its neighbors, but if an oscillator is compelled to follow its peers by a sufficient large number of cohesive neighbors, then it actually starts to act in the opposite manner, i.e., in anti-phase with the majority. Analytic results yield that if the repulsion parameter is small enough in comparison with the degree of the maximum hub, then the full synchronization state is locally stable. Numerical experiments are performed to explore the model beyond this threshold, where the overall cohesion is lost. We report in detail partially synchronous dynamical regimes, like stationary phase-locking, multistability, periodic and chaotic states. Via statistical analysis of different network organizations like tree, scale-free, and random ones, we found a measure allowing one to predict relative abundance of partially synchronous stationary states in comparison to time-dependent ones.
Study of coupled nonlinear partial differential equations for finding exact analytical solutions.
Khan, Kamruzzaman; Akbar, M Ali; Koppelaar, H
2015-07-01
Exact solutions of nonlinear partial differential equations (NPDEs) are obtained via the enhanced (G'/G)-expansion method. The method is subsequently applied to find exact solutions of the Drinfel'd-Sokolov-Wilson (DSW) equation and the (2+1)-dimensional Painlevé integrable Burgers (PIB) equation. The efficiency of this method for finding these exact solutions is demonstrated. The method is effective and applicable for many other NPDEs in mathematical physics.
Indian Academy of Sciences (India)
M Lakshmanan; T Kanna
2001-11-01
Coupled nonlinear Schrödinger equations (CNLS) very often represent wave propagation in optical media such as multicore ﬁbers, photorefractive materials and so on. We consider speciﬁcally the pulse propagation in integrable CNLS equations (generalized Manakov systems). We point out that these systems possess novel exact soliton type pulses which are shape changing under collision leading to an intensity redistribution. The shape changes correspond to linear fractional transformations allowing for the possibility of construction of logic gates and Turing equivalent all optical computers in homogeneous bulk media as shown by Steiglitz recently. Special cases of such solitons correspond to the recently much discussed partially coherent stationary solitons (PCS). In this paper, we review critically the recent developments regarding the above properties with particular reference to 2-CNLS.
Energy Technology Data Exchange (ETDEWEB)
Moix, Pierre-Olivier; Ruchet, Claude [Studer Innotec, Sion (Switzerland)
2010-07-01
Partial AC-coupling: - It is feasible to make AC-coupling of some compatible elements without V/f droops. Standard elements available on the market were tested. - Optimum design for efficiency is a share of the solar modules between DC-coupling with a solar charger and AC-coupling with a grid inverter according to the load profile. - Partial AC-coupling is better in term of robustness; it is more reliable to have at least a part of the solar production connected directly to DC, or even only DC coupling. The presented concepts are not only theoretical but were implemented and tested on real products available on the market. Many tests have been done to find out the limits and problems that can occur with the use of grid connected and stand alone inverter together. Many combinations were tested and it was found robust enough to be used in the field with the precautions mentioned about microcycling. (orig.)
Generalized solutions of nonlinear partial differential equations
Rosinger, EE
1987-01-01
During the last few years, several fairly systematic nonlinear theories of generalized solutions of rather arbitrary nonlinear partial differential equations have emerged. The aim of this volume is to offer the reader a sufficiently detailed introduction to two of these recent nonlinear theories which have so far contributed most to the study of generalized solutions of nonlinear partial differential equations, bringing the reader to the level of ongoing research.The essence of the two nonlinear theories presented in this volume is the observation that much of the mathematics concernin
Numerical methods for nonlinear partial differential equations
Bartels, Sören
2015-01-01
The description of many interesting phenomena in science and engineering leads to infinite-dimensional minimization or evolution problems that define nonlinear partial differential equations. While the development and analysis of numerical methods for linear partial differential equations is nearly complete, only few results are available in the case of nonlinear equations. This monograph devises numerical methods for nonlinear model problems arising in the mathematical description of phase transitions, large bending problems, image processing, and inelastic material behavior. For each of these problems the underlying mathematical model is discussed, the essential analytical properties are explained, and the proposed numerical method is rigorously analyzed. The practicality of the algorithms is illustrated by means of short implementations.
First Integrals for Two Linearly Coupled Nonlinear Duffing Oscillators
Directory of Open Access Journals (Sweden)
R. Naz
2011-01-01
Full Text Available We investigate Noether and partial Noether operators of point type corresponding to a Lagrangian and a partial Lagrangian for a system of two linearly coupled nonlinear Duffing oscillators. Then, the first integrals with respect to Noether and partial Noether operators of point type are obtained explicitly by utilizing Noether and partial Noether theorems for the system under consideration. Moreover, if the partial Euler-Lagrange equations are independent of derivatives, then the partial Noether operators become Noether point symmetry generators for such equations. The difference arises in the gauge terms due to Lagrangians being different for respective approaches. This study points to new ways of constructing first integrals for nonlinear equations without regard to a Lagrangian. We have illustrated it here for nonlinear Duffing oscillators.
On invariant analysis of some time fractional nonlinear systems of partial differential equations. I
Singla, Komal; Gupta, R. K.
2016-10-01
An investigation of Lie point symmetries for systems of time fractional partial differential equations including Ito system, coupled Burgers equations, coupled Korteweg de Vries equations, Hirota-Satsuma coupled KdV equations, and coupled nonlinear Hirota equations has been done. Using the obtained symmetries, each one of the systems is reduced to the nonlinear system of fractional ordinary differential equations involving Erdélyi-Kober fractional differential operator depending on a parameter α.
Directory of Open Access Journals (Sweden)
Elsayed M.E. Zayed
2016-02-01
Full Text Available In this article, the modified extended tanh-function method is employed to solve fractional partial differential equations in the sense of the modified Riemann–Liouville derivative. Based on a nonlinear fractional complex transformation, certain fractional partial differential equations can be turned into nonlinear ordinary differential equations of integer orders. For illustrating the validity of this method, we apply it to four nonlinear equations namely, the space–time fractional generalized nonlinear Hirota–Satsuma coupled KdV equations, the space–time fractional nonlinear Whitham–Broer–Kaup equations, the space–time fractional nonlinear coupled Burgers equations and the space–time fractional nonlinear coupled mKdV equations.
Bifurcation and stability for a nonlinear parabolic partial differential equation
Chafee, N.
1973-01-01
Theorems are developed to support bifurcation and stability of nonlinear parabolic partial differential equations in the solution of the asymptotic behavior of functions with certain specified properties.
Interactive optomechanical coupling with nonlinear polaritonic systems
Bobrovska, N; Liew, T C H; Kyriienko, O
2016-01-01
We study a system of interacting matter quasiparticles strongly coupled to photons inside an optomechanical cavity. The resulting normal modes of the system are represented by hybrid polaritonic quasiparticles, which acquire effective nonlinearity. Its strength is influenced by the presence of the mechanical mode and depends on the resonance frequency of the cavity. This leads to an interactive type of optomechanical coupling, being distinct from the previously studied dispersive and dissipative couplings in optomechanical systems. The emergent interactive coupling is shown to generate effective optical nonlinearity terms of high order, being quartic in the polariton number. We consider particular systems of exciton-polaritons and dipolaritons, and show that the induced effective optical nonlinearity due to the interactive coupling can exceed in magnitude the strength of Kerr nonlinear terms, such as those arising from polariton-polariton interactions. As applications, we show that the higher order terms give...
Exact solutions for some nonlinear systems of partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Darwish, A.A. [Department of Mathematics, Faculty of Science, Helwan University (Egypt)], E-mail: profdarwish@yahoo.com; Ramady, A. [Department of Mathematics, Faculty of Science, Beni-Suef University (Egypt)], E-mail: aramady@yahoo.com
2009-04-30
A direct and unified algebraic method for constructing multiple travelling wave solutions of nonlinear systems of partial differential equations (PDEs) is used and implemented in a computer algebraic system. New solutions for some nonlinear partial differential equations (NLPDEs) are obtained. Graphs of the solutions are displayed.
Solution behaviors in coupled Schrödinger equations with full-modulated nonlinearities
Pınar, Zehra; Deliktaş, Ekin
2017-02-01
The nonlinear partial differential equations have an important role in real life problems. To obtain the exact solutions of the nonlinear partial differential equations, a number of approximate methods are known in the literature. In this work, a time- space modulated nonlinearities of coupled Schrödinger equations are considered. We provide a large class of Jacobi-elliptic solutions via the auxiliary equation method with sixth order nonlinearity and the Chebyshev approximation.
Techniques in Linear and Nonlinear Partial Differential Equations
1991-10-21
nonlinear partial differential equations , elliptic 15. NUMBER OF PAGES hyperbolic and parabolic. Variational methods. Vibration problems. Ordinary Five...NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS FINAL TECHNICAL REPORT PROFESSOR LOUIS NIRENBERG OCTOBER 21, 1991 NT)S CRA&I D FIC ,- U.S. ARMY RESEARCH OFFICE...Analysis and partial differential equations . ed. C. Sadowsky. Marcel Dekker (1990) 567-619. [7] Lin, Fanghua, Asymptotic behavior of area-minimizing
Exact solutions for nonlinear partial fractional differential equations
Institute of Scientific and Technical Information of China (English)
Khaled A.Gepreel; Saleh Omran
2012-01-01
In this article,we use the fractional complex transformation to convert nonlinear partial fractional differential equations to nonlinear ordinary differential equations.We use the improved (G’/G)-expansion function method to calculate the exact solutions to the time-and space-fractional derivative foam drainage equation and the time-and space-fractional derivative nonlinear KdV equation.This method is efficient and powerful for solving wide classes of nonlinear evolution fractional order equations.
Analytic solutions of a class of nonlinear partial differential equations
Institute of Scientific and Technical Information of China (English)
ZHANG Hong-qing; DING Qi
2008-01-01
An approach is presented for computing the adjoint operator vector of a class of nonlinear (that is,partial-nonlinear) operator matrices by using the properties of conjugate operators to generalize a previous method proposed by the author.A unified theory is then given to solve a class of nonlinear (partial-nonlinear and including all linear)and non-homogeneous differential equations with a mathematical mechanization method.In other words,a transformation is constructed by homogenization and triangulation,which reduces the original system to a simpler diagonal system.Applications are given to solve some elasticity equations.
Modified Homotopy Analysis Method for Nonlinear Fractional Partial Differential Equations
Directory of Open Access Journals (Sweden)
D. Ziane
2017-05-01
Full Text Available In this paper, a combined form of natural transform with homotopy analysis method is proposed to solve nonlinear fractional partial differential equations. This method is called the fractional homotopy analysis natural transform method (FHANTM. The FHANTM can easily be applied to many problems and is capable of reducing the size of computational work. The fractional derivative is described in the Caputo sense. The results show that the FHANTM is an appropriate method for solving nonlinear fractional partial differentia equation.
Approximate solution of a nonlinear partial differential equation
Vajta, M.
2007-01-01
Nonlinear partial differential equations (PDE) are notorious to solve. In only a limited number of cases can we find an analytic solution. In most cases, we can only apply some numerical scheme to simulate the process described by a nonlinear PDE. Therefore, approximate solutions are important for t
Auxiliary equation method for solving nonlinear partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Sirendaoreji,; Jiong, Sun
2003-03-31
By using the solutions of an auxiliary ordinary differential equation, a direct algebraic method is described to construct several kinds of exact travelling wave solutions for some nonlinear partial differential equations. By this method some physically important nonlinear equations are investigated and new exact travelling wave solutions are explicitly obtained with the aid of symbolic computation.
Logarithmic singularities of solutions to nonlinear partial differential equations
Tahara, Hidetoshi
2007-01-01
We construct a family of singular solutions to some nonlinear partial differential equations which have resonances in the sense of a paper due to T. Kobayashi. The leading term of a solution in our family contains a logarithm, possibly multiplied by a monomial. As an application, we study nonlinear wave equations with quadratic nonlinearities. The proof is by the reduction to a Fuchsian equation with singular coefficients.
Primordial fluctuations from nonlinear couplings
Calzetta, E A; Calzetta, Esteban A.; Gonorazky, Sonia
1997-01-01
We study the spectrum of primordial fluctuations in theories where the inflaton field is coupled to massless fields and/or to itself. Conformally invariant theories generically predict a scale invariant spectrum. Scales entering the theory through infrared divergences cause logarithmic corrections to the spectrum, tiltilng it towards the blue. We discuss in some detail wether these fluctuations are quantum or classical in nature.
Transition to Amplitude Death in Coupled System with Small Number of Nonlinear Oscillators
Institute of Scientific and Technical Information of China (English)
CHEN Hai-Ling; YANG Jun-Zhong
2009-01-01
In this work, we investigate the amplitude death in coupled system with small number of nonlinear oscillators. We show how the transitions to the partial and the complete amplitude deathes happen. We also show that the partial amplitude death can be found in globally coupled oscillators either.
Entropy and convexity for nonlinear partial differential equations.
Ball, John M; Chen, Gui-Qiang G
2013-12-28
Partial differential equations are ubiquitous in almost all applications of mathematics, where they provide a natural mathematical description of many phenomena involving change in physical, chemical, biological and social processes. The concept of entropy originated in thermodynamics and statistical physics during the nineteenth century to describe the heat exchanges that occur in the thermal processes in a thermodynamic system, while the original notion of convexity is for sets and functions in mathematics. Since then, entropy and convexity have become two of the most important concepts in mathematics. In particular, nonlinear methods via entropy and convexity have been playing an increasingly important role in the analysis of nonlinear partial differential equations in recent decades. This opening article of the Theme Issue is intended to provide an introduction to entropy, convexity and related nonlinear methods for the analysis of nonlinear partial differential equations. We also provide a brief discussion about the content and contributions of the papers that make up this Theme Issue.
Partially Linearizable Class of Nonlinear System with Uncertainty
Energy Technology Data Exchange (ETDEWEB)
Joo, Sung Jun [Samsung Electronics Coporation (Korea, Republic of); Seo, Jin H. [Seoul National University (Korea, Republic of)
1998-03-01
In this paper the problem of robust stabilizing control for nonlinear SISO systems in the presence of uncertainties is studied and we give some geometric conditions for this problem. We also show that if and only if the systems satisfy the proposed conditions it can be transformed into a partially linearized system with unknown parameter using the nominal transformation and nominal feedback linearizing controller. In this paper, we call the above considered class of nonlinear system as partially linearizable system. We design the robust controller which stabilizes the partially linearizable system. (author). 14 refs.
Coupled Oscillator Systems Having Partial PT Symmetry
Beygi, Alireza; Bender, Carl M
2015-01-01
This paper examines chains of $N$ coupled harmonic oscillators. In isolation, the $j$th oscillator ($1\\leq j\\leq N$) has the natural frequency $\\omega_j$ and is described by the Hamiltonian $\\frac{1}{2}p_j^2+\\frac{1}{2}\\omega_j^2x_j^2$. The oscillators are coupled adjacently with coupling constants that are purely imaginary; the coupling of the $j$th oscillator to the $(j+1)$st oscillator has the bilinear form $i\\gamma x_jx_{j+1}$ ($\\gamma$ real). The complex Hamiltonians for these systems exhibit {\\it partial} $\\mathcal{PT}$ symmetry; that is, they are invariant under $i\\to-i$ (time reversal), $x_j\\to-x_j$ ($j$ odd), and $x_j\\to x_j$ ($j$ even). [They are also invariant under $i\\to-i$, $x_j\\to x_j$ ($j$ odd), and $x_j\\to- x_j$ ($j$ even).] For all $N$ the quantum energy levels of these systems are calculated exactly and it is shown that the ground-state energy is real. When $\\omega_j=1$ for all $j$, the full spectrum consists of a real energy spectrum embedded in a complex one; the eigenfunctions correspondi...
Energy Technology Data Exchange (ETDEWEB)
Zhang Huiqun [College of Mathematical Science, Qingdao University, Qingdao, Shandong 266071 (China)], E-mail: hellozhq@yahoo.com.cn
2009-02-15
By using some exact solutions of an auxiliary ordinary differential equation, a direct algebraic method is described to construct the exact complex solutions for nonlinear partial differential equations. The method is implemented for the NLS equation, a new Hamiltonian amplitude equation, the coupled Schrodinger-KdV equations and the Hirota-Maccari equations. New exact complex solutions are obtained.
The coupled nonlinear dynamics of a lift system
Crespo, Rafael Sánchez; Kaczmarczyk, Stefan; Picton, Phil; Su, Huijuan
2014-12-01
Coupled lateral and longitudinal vibrations of suspension and compensating ropes in a high-rise lift system are often induced by the building motions due to wind or seismic excitations. When the frequencies of the building become near the natural frequencies of the ropes, large resonance motions of the system may result. This leads to adverse coupled dynamic phenomena involving nonplanar motions of the ropes, impact loads between the ropes and the shaft walls, as well as vertical vibrations of the car, counterweight and compensating sheave. Such an adverse dynamic behaviour of the system endangers the safety of the installation. This paper presents two mathematical models describing the nonlinear responses of a suspension/ compensating rope system coupled with the elevator car / compensating sheave motions. The models accommodate the nonlinear couplings between the lateral and longitudinal modes, with and without longitudinal inertia of the ropes. The partial differential nonlinear equations of motion are derived using Hamilton Principle. Then, the Galerkin method is used to discretise the equations of motion and to develop a nonlinear ordinary differential equation model. Approximate numerical solutions are determined and the behaviour of the system is analysed.
The coupled nonlinear dynamics of a lift system
Energy Technology Data Exchange (ETDEWEB)
Crespo, Rafael Sánchez, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk; Kaczmarczyk, Stefan, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk; Picton, Phil, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk; Su, Huijuan, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk [The University of Northampton, School of Science and Technology, Avenue Campus, St George' s Avenue, Northampton (United Kingdom)
2014-12-10
Coupled lateral and longitudinal vibrations of suspension and compensating ropes in a high-rise lift system are often induced by the building motions due to wind or seismic excitations. When the frequencies of the building become near the natural frequencies of the ropes, large resonance motions of the system may result. This leads to adverse coupled dynamic phenomena involving nonplanar motions of the ropes, impact loads between the ropes and the shaft walls, as well as vertical vibrations of the car, counterweight and compensating sheave. Such an adverse dynamic behaviour of the system endangers the safety of the installation. This paper presents two mathematical models describing the nonlinear responses of a suspension/ compensating rope system coupled with the elevator car / compensating sheave motions. The models accommodate the nonlinear couplings between the lateral and longitudinal modes, with and without longitudinal inertia of the ropes. The partial differential nonlinear equations of motion are derived using Hamilton Principle. Then, the Galerkin method is used to discretise the equations of motion and to develop a nonlinear ordinary differential equation model. Approximate numerical solutions are determined and the behaviour of the system is analysed.
Scalable nonlinear iterative methods for partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Cai, X-C
2000-10-29
We conducted a six-month investigation of the design, analysis, and software implementation of a class of singularity-insensitive, scalable, parallel nonlinear iterative methods for the numerical solution of nonlinear partial differential equations. The solutions of nonlinear PDEs are often nonsmooth and have local singularities, such as sharp fronts. Traditional nonlinear iterative methods, such as Newton-like methods, are capable of reducing the global smooth nonlinearities at a nearly quadratic convergence rate but may become very slow once the local singularities appear somewhere in the computational domain. Even with global strategies such as line search or trust region the methods often stagnate at local minima of {parallel}F{parallel}, especially for problems with unbalanced nonlinearities, because the methods do not have built-in machinery to deal with the unbalanced nonlinearities. To find the same solution u* of F(u) = 0, we solve, instead, an equivalent nonlinearly preconditioned system G(F(u*)) = 0 whose nonlinearities are more balanced. In this project, we proposed and studied a nonlinear additive Schwarz based parallel nonlinear preconditioner and showed numerically that the new method converges well even for some difficult problems, such as high Reynolds number flows, when a traditional inexact Newton method fails.
Residual models for nonlinear partial differential equations
Directory of Open Access Journals (Sweden)
Garry Pantelis
2005-11-01
Full Text Available Residual terms that appear in nonlinear PDEs that are constructed to generate filtered representations of the variables of the fully resolved system are examined by way of a consistency condition. It is shown that certain commonly used empirical gradient models for the residuals fail the test of consistency and therefore cannot be validated as approximations in any reliable sense. An alternate method is presented for computing the residuals. These residual models are independent of free or artificial parameters and there direct link with the functional form of the system of PDEs which describe the fully resolved system are established.
Soliton solution for nonlinear partial differential equations by cosine-function method
Energy Technology Data Exchange (ETDEWEB)
Ali, A.H.A. [Mathematics Department, Faculty of Science, Menoufia University, Shebein El-Koom (Egypt); Soliman, A.A. [Department of Mathematics, Faculty of Education (AL-Arish), Suez Canal University, AL-Arish 45111 (Egypt)], E-mail: asoliman_99@yahoo.com; Raslan, K.R. [Mathematics Department, Faculty of Science, Al-Azhar University, Nasr-City, Cairo (Egypt)
2007-08-20
In this Letter, we established a traveling wave solution by using Cosine-function algorithm for nonlinear partial differential equations. The method is used to obtain the exact solutions for five different types of nonlinear partial differential equations such as, general equal width wave equation (GEWE), general regularized long wave equation (GRLW), general Korteweg-de Vries equation (GKdV), general improved Korteweg-de Vries equation (GIKdV), and Coupled equal width wave equations (CEWE), which are the important soliton equations.
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...
Multiwave nonlinear couplings in elastic structures
Directory of Open Access Journals (Sweden)
2006-01-01
Full Text Available This short contribution considers the essentials of nonlinear wave properties in typical mechanical systems such as an infinite straight bar, a circular ring, and a flat plate. It is found that nonlinear resonance is experienced in all the systems exhibiting continuous and discrete spectra, respectively. Multiwave interactions and the stability of coupled modes with respect to small perturbations are discussed. The emphasis is placed on mechanical phenomena, for example, stress amplification, although some analogies with some nonlinear optical systems are also obvious. The nonlinear resonance coupling in a plate within the Kirchhoff-Love approximation is selected as a two-dimensional example exhibiting a rich range of resonant wave phenomena. This is originally examined by use of Whitham's averaged Lagrangian method. In particular, the existence of three basic resonant triads between longitudinal, shear, and bending modes is shown. Some of these necessarily enter cascade wave processes related to the instability of some mode components of the triad under small perturbations.
REDUCTION OF NONLINEAR PARTIAL DIFFERENTIAL EQUATION AND EXACT SOLUTIONS
Institute of Scientific and Technical Information of China (English)
YeCaier; PanZuliang
2003-01-01
Nonlinear partial differetial equation(NLPDE)is converted into ordinary differential equation(ODE)via a new ansatz.Using undetermined function method,the ODE obtained above is replaced by a set of algebraic equations which are solved out with the aid of Mathematica.The exact solutions and solitary solutions of NLPDE are obtained.
Exact periodic wave solutions for some nonlinear partial differential equations
Energy Technology Data Exchange (ETDEWEB)
El-Wakil, S.A. [Theoretical Physics Research Group, Department of Physics, Faculty of Science, Mansoura University, Mansoura 35516 (Egypt); Elgarayhi, A. [Theoretical Physics Research Group, Department of Physics, Faculty of Science, Mansoura University, Mansoura 35516 (Egypt)]. E-mail: elgarayhi@yahoo.com; Elhanbaly, A. [Theoretical Physics Research Group, Department of Physics, Faculty of Science, Mansoura University, Mansoura 35516 (Egypt)
2006-08-15
The periodic wave solutions for some nonlinear partial differential equations, including generalized Klein-Gordon equation, Kadomtsev-Petviashvili (KP) equation and Boussinesq equations, are obtained by using the solutions of Jacobi elliptic equation. Under limit conditions, exact solitary wave solutions, shock wave solutions and triangular periodic wave solutions have been recovered.
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.
Advances in nonlinear partial differential equations and stochastics
Kawashima, S
1998-01-01
In the past two decades, there has been great progress in the theory of nonlinear partial differential equations. This book describes the progress, focusing on interesting topics in gas dynamics, fluid dynamics, elastodynamics etc. It contains ten articles, each of which discusses a very recent result obtained by the author. Some of these articles review related results.
Large Time Asymptotics for Solutions of Nonlinear Partial Differential Equations
Sachdev, PL
2010-01-01
A large number of physical phenomena are modeled by nonlinear partial differential equations, subject to appropriate initial/boundary conditions. This title presents the constructive mathematical techniques. It deals with the asymptotic methods which include self-similarity, balancing argument, and matched asymptotic expansions
Optimal Variational Asymptotic Method for Nonlinear Fractional Partial Differential Equations.
Baranwal, Vipul K; Pandey, Ram K; Singh, Om P
2014-01-01
We propose optimal variational asymptotic method to solve time fractional nonlinear partial differential equations. In the proposed method, an arbitrary number of auxiliary parameters γ 0, γ 1, γ 2,… and auxiliary functions H 0(x), H 1(x), H 2(x),… are introduced in the correction functional of the standard variational iteration method. The optimal values of these parameters are obtained by minimizing the square residual error. To test the method, we apply it to solve two important classes of nonlinear partial differential equations: (1) the fractional advection-diffusion equation with nonlinear source term and (2) the fractional Swift-Hohenberg equation. Only few iterations are required to achieve fairly accurate solutions of both the first and second problems.
Nonlinearly Coupled Superconducting Lumped Element Resonators
Collodo, Michele C.; Potočnik, Anton; Rubio Abadal, Antonio; Mondal, Mintu; Oppliger, Markus; Wallraff, Andreas
We study SQUID-mediated tunable coupling between two superconducting on-chip resonators in the microwave frequency range. In this circuit QED implementation, we employ lumped-element type resonators, which consist of Nb thin film structured into interdigitated finger shunt capacitors and meander inductors. A SQUID, functioning as flux dependent and intrinsically nonlinear inductor, is placed as a coupling element together with an interdigitated capacitor between the two resonators (cf. A. Baust et al., Phys Rev. B 91 014515 (2015)). We perform a spectroscopic measurement in a dilution refrigerator and find the linear photon hopping rate between the resonators to be widely tunable as well as suppressible for an appropriate choice of parameters, which is made possible due to the interplay of inductively and capacitively mediated coupling. Vanishing linear coupling promotes nonlinear effects ranging from onsite- to cross-Kerr interaction. A dominating cross-Kerr interaction related to this configuration is notable, as it induces a unique quantum state. In the course of analog quantum simulations, such elementary building blocks can serve as a precursor for more complex geometries and thus pave the way to a number of novel quantum phases of light
Self-organized quasiperiodicity in oscillator ensembles with global nonlinear coupling.
Rosenblum, Michael; Pikovsky, Arkady
2007-02-09
We describe a transition from fully synchronous periodic oscillations to partially synchronous quasiperiodic dynamics in ensembles of identical oscillators with all-to-all coupling that nonlinearly depends on the generalized order parameters. We present an analytically solvable model that predicts a regime where the mean field does not entrain individual oscillators, but has a frequency incommensurate to theirs. The self-organized onset of quasiperiodicity is illustrated with Landau-Stuart oscillators and a Josephson junction array with a nonlinear coupling.
He-Laplace Method for Linear and Nonlinear Partial Differential Equations
Directory of Open Access Journals (Sweden)
Hradyesh Kumar Mishra
2012-01-01
Full Text Available A new treatment for homotopy perturbation method is introduced. The new treatment is called He-Laplace method which is the coupling of the Laplace transform and the homotopy perturbation method using He’s polynomials. The nonlinear terms can be easily handled by the use of He’s polynomials. The method is implemented on linear and nonlinear partial differential equations. It is found that the proposed scheme provides the solution without any discretization or restrictive assumptions and avoids the round-off errors.
Painlevé analysis for nonlinear partial differential equations
Musette, M
1998-01-01
The Painlevé analysis introduced by Weiss, Tabor and Carnevale (WTC) in 1983 for nonlinear partial differential equations (PDE's) is an extension of the method initiated by Painlevé and Gambier at the beginning of this century for the classification of algebraic nonlinear differential equations (ODE's) without movable critical points. In these lectures we explain the WTC method in its invariant version introduced by Conte in 1989 and its application to solitonic equations in order to find algorithmically their associated so-called ``integrable'' equations but they are generically no more valid for equations modelising physical phenomema. Belonging to this second class, some equations called ``partially integrable'' sometimes keep remnants of integrability. In that case, the singularity analysis may also be useful for building closed form analytic solutions, which necessarily % Conte agree with the singularity structure of the equations. We display the privileged role played by the Riccati equation and syste...
Nonlinear partial differential equations for scientists and engineers
Debnath, Lokenath
1997-01-01
"An exceptionally complete overview. There are numerous examples and the emphasis is on applications to almost all areas of science and engineering. There is truly something for everyone here. This reviewer feels that it is a very hard act to follow, and recommends it strongly. [This book] is a jewel." ---Applied Mechanics Review (Review of First Edition) This expanded and revised second edition is a comprehensive and systematic treatment of linear and nonlinear partial differential equations and their varied applications. Building upon the successful material of the first book, this edition contains updated modern examples and applications from areas of fluid dynamics, gas dynamics, plasma physics, nonlinear dynamics, quantum mechanics, nonlinear optics, acoustics, and wave propagation. Methods and properties of solutions are presented, along with their physical significance, making the book more useful for a diverse readership. Topics and key features: * Thorough coverage of derivation and methods of soluti...
Extended Trial Equation Method for Nonlinear Partial Differential Equations
Gepreel, Khaled A.; Nofal, Taher A.
2015-04-01
The main objective of this paper is to use the extended trial equation method to construct a series of some new solutions for some nonlinear partial differential equations (PDEs) in mathematical physics. We will construct the solutions in many different functions such as hyperbolic function solutions, trigonometric function solutions, Jacobi elliptic function solutions, and rational functional solutions for the nonlinear PDEs when the balance number is a real number via the Zhiber-Shabat nonlinear differential equation. The balance number of this method is not constant as we shown in other methods, but it is changed by changing the trial equation derivative definition. This method allowed us to construct many new types of solutions. It is shown by using the Maple software package that all obtained solutions satisfy the original PDEs.
Nonclassical Symmetries for Nonlinear Partial Differential Equations via Compatibility
Institute of Scientific and Technical Information of China (English)
Mostafa F. El-Sabbagh; Ahmad T. Ali
2011-01-01
The determining equations for the nonclassical symmetry reductions of nonlinear partial differential equations with arbitrary order can be obtained by requiring the compatibility between the original equations and the invariant surface conditions. The （2＋1）-dimensional shallow water wave equation, Boussinesq equation, and the dispersive wave equations in shallow water serve as examples i11ustrating how compatibility leads quickly and easily to the determining equations for their nonclassical symmetries.
Kernel Partial Least Squares for Nonlinear Regression and Discrimination
Rosipal, Roman; Clancy, Daniel (Technical Monitor)
2002-01-01
This paper summarizes recent results on applying the method of partial least squares (PLS) in a reproducing kernel Hilbert space (RKHS). A previously proposed kernel PLS regression model was proven to be competitive with other regularized regression methods in RKHS. The family of nonlinear kernel-based PLS models is extended by considering the kernel PLS method for discrimination. Theoretical and experimental results on a two-class discrimination problem indicate usefulness of the method.
Symposium on Nonlinear Semigroups, Partial Differential Equations and Attractors
Zachary, Woodford
1987-01-01
The original idea of the organizers of the Washington Symposium was to span a fairly narrow range of topics on some recent techniques developed for the investigation of nonlinear partial differential equations and discuss these in a forum of experts. It soon became clear, however, that the dynamical systems approach interfaced significantly with many important branches of applied mathematics. As a consequence, the scope of this resulting proceedings volume is an enlarged one with coverage of a wider range of research topics.
Partial Synchronization in a System of Coupled Logistic Maps
DEFF Research Database (Denmark)
Taborov, A. V.; Maistrenko, Y. L.; Mosekilde, Erik
2000-01-01
Clustering (or partial synchronization) in a system of globally coupled chaotic oscillators is studied by means of a model of three coupled logistic maps. For this model we determine the regions in parameter space where total and partial synchronization take place, examine the bifurcations through...
Partial synchronization in a system of coupled logistic maps
DEFF Research Database (Denmark)
Taborov, A.V.; Maistrenko, Y.L; Mosekilde, Erik
1999-01-01
The phenomenon of clustering (or partial synchronization) in a system of globqally coupled chaotic oscillators is studied by means of a model of three coupled logistic maps. We determine the regions in parameter space where total and partial synchronization take place, examine the bifurcations...
Directory of Open Access Journals (Sweden)
Imran Talib
2015-12-01
Full Text Available In this article, study the existence of solutions for the second-order nonlinear coupled system of ordinary differential equations $$\\displaylines{ u''(t=f(t,v(t,\\quad t\\in [0,1],\\cr v''(t=g(t,u(t,\\quad t\\in [0,1], }$$ with nonlinear coupled boundary conditions $$\\displaylines{ \\phi(u(0,v(0,u(1,v(1,u'(0,v'(0=(0,0, \\cr \\psi(u(0,v(0,u(1,v(1,u'(1,v'(1=(0,0, }$$ where $f,g:[0,1]\\times \\mathbb{R}\\to \\mathbb{R}$ and $\\phi,\\psi:\\mathbb{R}^6\\to \\mathbb{R}^2$ are continuous functions. Our main tools are coupled lower and upper solutions, Arzela-Ascoli theorem, and Schauder's fixed point theorem.
Experimental observation of partial amplitude death in coupled chaotic oscillators
Institute of Scientific and Technical Information of China (English)
Liu Wei-Qing; Yang Jun-Zhong; Xiao Jing-Hua
2006-01-01
The dynamics of coupled Lorenz circuits is investigated experimentally. The partial amplitude death reported in Phys. Rev. E 72, 057201 (2005) is verified by physical experiments with electronic circuits. With the increase of coupling constant, the coupled circuits undergo the transition from the breakdown of both the reflection symmetry and the translational symmetry to the partial amplitude death. Its stability is also confirmed by analysing the effects of noise.
Nonlinear evolution operators and semigroups applications to partial differential equations
Pavel, Nicolae H
1987-01-01
This research monograph deals with nonlinear evolution operators and semigroups generated by dissipative (accretive), possibly multivalued operators, as well as with the application of this theory to partial differential equations. It shows that a large class of PDE's can be studied via the semigroup approach. This theory is not available otherwise in the self-contained form provided by these Notes and moreover a considerable part of the results, proofs and methods are not to be found in other books. The exponential formula of Crandall and Liggett, some simple estimates due to Kobayashi and others, the characterization of compact semigroups due to Brézis, the proof of a fundamental property due to Ursescu and the author and some applications to PDE are of particular interest. Assuming only basic knowledge of functional analysis, the book will be of interest to researchers and graduate students in nonlinear analysis and PDE, and to mathematical physicists.
On a Nonlinear Partial Integro-Differential Equation
Abergel, Frederic
2009-01-01
Consistently fitting vanilla option surfaces is an important issue when it comes to modelling in finance. Local volatility models introduced by Dupire in 1994 are widely used to price and manage the risks of structured products. However, the inconsistencies observed between the dynamics of the smile in those models and in real markets motivate researches for stochastic volatility modelling. Combining both those ideas to form Local and Stochastic Volatility models is of interest for practitioners. In this paper, we study the calibration of the vanillas in those models. This problem can be written as a nonlinear and nonlocal partial differential equation, for which we prove short-time existence of solutions.
Exact travelling wave solutions of nonlinear partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Soliman, A.A. [Department of Mathematics, Faculty of Education (AL-Arish) Suez Canal University, AL-Arish 45111 (Egypt)]. E-mail: asoliman_99@yahoo.com; Abdou, M.A. [Theoretical Research Group, Department of Physics, Faculty of Science, Mansoura University, Mansoura 35516 (Egypt)]. E-mail: m_abdou_eg@yahoo.com
2007-04-15
An extended Fan-sub equation method is developed for searching exact travelling wave solutions of nonlinear partial differential equations. The key idea of this method is to take full advantage of the general elliptic equation, involving five parameters, which has more new solutions and whose degeneracies can lead to special sub equation involving three parameters. As an illustration of the extended Fan method, more new solutions are obtained for three models namely, generalized KdV, Drinfeld-Sokolov system and RLW equation.
Approximation on computing partial sum of nonlinear differential eigenvalue problems
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
In computing the electronic structure and energy band in a system of multi-particles, quite a large number of problems are referred to the acquisition of obtaining the partial sum of densities and energies using the “first principle”. In the conventional method, the so-called self-consistency approach is limited to a small scale because of high computing complexity. In this paper, the problem of computing the partial sum for a class of nonlinear differential eigenvalue equations is changed into the constrained functional minimization. By space decomposition and perturbation method, a secondary approximating formula for the minimal is provided. It is shown that this formula is more precise and its quantity of computation can be reduced significantly
Applications of Elliptic Equation to Nonlinear Coupled Systems
Institute of Scientific and Technical Information of China (English)
FUZun-Tao; LIUShi-Da; LIUShi-Kuo
2003-01-01
The elliptic equation is taken as a transformation and applied to solve nonlinear coupled systems. It is shown that this method is more powerful to give more kinds of solutions, such as rational solutions, solitary wave solutions, periodic wave solutions and so on, so this method can be taken as a unified method in solving nonlinear coupled systems.
Applications of Elliptic Equation to Nonlinear Coupled Systems
Institute of Scientific and Technical Information of China (English)
FU Zun-Tao; LIU Shi-Da; LIU Shi-Kuo
2003-01-01
The elliptic equation is taken as a transformation and applied to solve nonlinear coupled systems. Itis shown that this method is more powerful to give more kinds of solutions, such as rational solutions, solitary wavesolutions, periodic wave solutions and so on, so this method can be taken as a unified method in solving nonlinear coupled systems.
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.
Nonlinear Super Integrable Couplings of Super Classical-Boussinesq Hierarchy
Directory of Open Access Journals (Sweden)
Xiuzhi Xing
2014-01-01
Full Text Available Nonlinear integrable couplings of super classical-Boussinesq hierarchy based upon an enlarged matrix Lie super algebra were constructed. Then, its super Hamiltonian structures were established by using super trace identity. As its reduction, nonlinear integrable couplings of the classical integrable hierarchy were obtained.
Nonlinear interaction of meta-atoms through optical coupling
Energy Technology Data Exchange (ETDEWEB)
Slobozhanyuk, A. P.; Kapitanova, P. V.; Filonov, D. S.; Belov, P. A. [National Research University of Information Technologies, Mechanics and Optics (ITMO), St. Petersburg 197101 (Russian Federation); Powell, D. A. [Nonlinear Physics Centre and Centre for Ultrahigh-bandwidth Devices for Optical Systems (CUDOS), Australian National University, Canberra, ACT 0200 (Australia); Shadrivov, I. V.; Kivshar, Yu. S. [National Research University of Information Technologies, Mechanics and Optics (ITMO), St. Petersburg 197101 (Russian Federation); Nonlinear Physics Centre and Centre for Ultrahigh-bandwidth Devices for Optical Systems (CUDOS), Australian National University, Canberra, ACT 0200 (Australia); Lapine, M., E-mail: mlapine@physics.usyd.edu.au [National Research University of Information Technologies, Mechanics and Optics (ITMO), St. Petersburg 197101 (Russian Federation); Centre for Ultrahigh-bandwidth Devices for Optical Systems (CUDOS), School of Physics, University of Sydney, New South Wales 2006 (Australia); McPhedran, R. C. [Centre for Ultrahigh-bandwidth Devices for Optical Systems (CUDOS), School of Physics, University of Sydney, New South Wales 2006 (Australia)
2014-01-06
We propose and experimentally demonstrate a multi-frequency nonlinear coupling mechanism between split-ring resonators. We engineer the coupling between two microwave resonators through optical interaction, whilst suppressing the direct electromagnetic coupling. This allows for a power-dependent interaction between the otherwise independent resonators, opening interesting opportunities to address applications in signal processing, filtering, directional coupling, and electromagnetic compatibility.
On Unique Ergodicity in Nonlinear Stochastic Partial Differential Equations
Glatt-Holtz, Nathan; Mattingly, Jonathan C.; Richards, Geordie
2017-02-01
We illustrate how the notion of asymptotic coupling provides a flexible and intuitive framework for proving the uniqueness of invariant measures for a variety of stochastic partial differential equations whose deterministic counterpart possesses a finite number of determining modes. Examples exhibiting parabolic and hyperbolic structure are studied in detail. In the later situation we also present a simple framework for establishing the existence of invariant measures when the usual approach relying on the Krylov-Bogolyubov procedure and compactness fails.
On Unique Ergodicity in Nonlinear Stochastic Partial Differential Equations
Glatt-Holtz, Nathan; Mattingly, Jonathan C.; Richards, Geordie
2016-08-01
We illustrate how the notion of asymptotic coupling provides a flexible and intuitive framework for proving the uniqueness of invariant measures for a variety of stochastic partial differential equations whose deterministic counterpart possesses a finite number of determining modes. Examples exhibiting parabolic and hyperbolic structure are studied in detail. In the later situation we also present a simple framework for establishing the existence of invariant measures when the usual approach relying on the Krylov-Bogolyubov procedure and compactness fails.
Analytical Evaluation of the Nonlinear Vibration of Coupled Oscillator Systems
DEFF Research Database (Denmark)
Bayat, M.; Shahidi, M.; Barari, Amin
2011-01-01
We consider periodic solutions for nonlinear free vibration of conservative, coupled mass-spring systems with linear and nonlinear stiffnesses. Two practical cases of these systems are explained and introduced. An analytical technique called energy balance method (EBM) was applied to calculate ap...... accuracy which is valid for a wide range of vibration amplitudes as indicated in the presented examples.......We consider periodic solutions for nonlinear free vibration of conservative, coupled mass-spring systems with linear and nonlinear stiffnesses. Two practical cases of these systems are explained and introduced. An analytical technique called energy balance method (EBM) was applied to calculate...
Directory of Open Access Journals (Sweden)
Yusuf Pandir
2013-01-01
Full Text Available We firstly give some new functions called generalized hyperbolic functions. By the using of the generalized hyperbolic functions, new kinds of transformations are defined to discover the exact approximate solutions of nonlinear partial differential equations. Based on the generalized hyperbolic function transformation of the generalized KdV equation and the coupled equal width wave equations (CEWE, we find new exact solutions of two equations and analyze the properties of them by taking different parameter values of the generalized hyperbolic functions. We think that these solutions are very important to explain some physical phenomena.
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
In this paper, an extended method is proposed for constructing new forms ofexact travelling wave solutions to nonlinear partial differential equations by making a more general transformation. For illustration, we apply the method to the asymmetric Nizhnik-Novikov-Vesselov equation and the coupled Drinfel'd-Sokolov-Wilson equation and successfully cover the previously known travelling wave solutions found by Chen's method [Y. Chen, et al. Chaos, Solitons and Fractals 22 (2004) 675; Y. Chen, et al. Int. J. Mod. Phys. C 4 (2004) 595].
Huang, Qing; Wang, Li-Zhen; Zuo, Su-Li
2016-02-01
In this paper, a consistent Riccati expansion method is developed to solve nonlinear fractional partial differential equations involving Jumarie's modified Riemann-Liouville derivative. The efficiency and power of this approach are demonstrated by applying it successfully to some important fractional differential equations, namely, the time fractional Burgers, fractional Sawada-Kotera, and fractional coupled mKdV equation. A variety of new exact solutions to these equations under study are constructed. Supported by the National Natural Science Foundation of China under Grant Nos. 11101332, 11201371, 11371293 and the Natural Science Foundation of Shaanxi Province under Grant No. 2015JM1037
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.
Dynamic nonlinear thermal optical effects in coupled ring resonators
Directory of Open Access Journals (Sweden)
Chenguang Huang
2012-09-01
Full Text Available We investigate the dynamic nonlinear thermal optical effects in a photonic system of two coupled ring resonators. A bus waveguide is used to couple light in and out of one of the coupled resonators. Based on the coupling from the bus to the resonator, the coupling between the resonators and the intrinsic loss of each individual resonator, the system transmission spectrum can be classified by three different categories: coupled-resonator-induced absorption, coupled-resonator-induced transparency and over coupled resonance splitting. Dynamic thermal optical effects due to linear absorption have been analyzed for each category as a function of the input power. The heat power in each resonator determines the thermal dynamics in this coupled resonator system. Multiple “shark fins” and power competition between resonators can be foreseen. Also, the nonlinear absorption induced thermal effects have been discussed.
DIFFERENCE METHODS FOR A NON-LINEAR ELLIPTIC SYSTEM OF PARTIAL DIFFERENTIAL EQUATIONS,
DIFFERENCE EQUATIONS, ITERATIONS), (*ITERATIONS, DIFFERENCE EQUATIONS), (* PARTIAL DIFFERENTIAL EQUATIONS , BOUNDARY VALUE PROBLEMS), EQUATIONS, FUNCTIONS(MATHEMATICS), SEQUENCES(MATHEMATICS), NONLINEAR DIFFERENTIAL EQUATIONS
Inertial Force Coupling to Nonlinear Aeroelasticity of Flexible Wing Aircraft
Nguyen, Nhan T.; Ting, Eric
2016-01-01
This paper investigates the inertial force effect on nonlinear aeroelasticity of flexible wing aircraft. The geometric are nonlinearity due to rotational and tension stiffening. The effect of large bending deflection will also be investigated. Flutter analysis will be conducted for a truss-braced wing aircraft concept with tension stiffening and inertial force coupling.
Exact Travelling Wave Solutions to a Coupled Nonlinear Evolution Equation[
Institute of Scientific and Technical Information of China (English)
HUANGDing-Jiang; ZHANGHong-Qing
2004-01-01
By using an improved hyperbola function method, several types of exact travelling wave solutions to a coupled nonlinear evolution equation are obtained, which include kink-shaped soliton solutions, bell-shaped soliton solutions, envelop solitary wave solutions, and new solitary waves. The method can be applied to other nonlinear evolution equations in mathematical physics.
Exact Travelling Wave Solutions to a Coupled Nonlinear Evolution Equation
Institute of Scientific and Technical Information of China (English)
HUANG Ding-Jiang; ZHANG Hong-Qing
2004-01-01
By using an improved hyperbola function method, several types of exact travelling wave solutions to a coupled nonlinear evolution equation are obtained, which include kink-shaped soliton solutions, bell-shaped soliton solutions, envelop solitary wave solutions, and new solitary waves. The method can be applied to other nonlinear evolution equations in mathematical physics.
Multistability in nonlinearly coupled ring of Duffing systems
Jaros, P.; Kapitaniak, T.; Perlikowski, P.
2016-11-01
In this paper we consider dynamics of three unidirectionally coupled Duffing oscillators with nonlinear coupling function in the form of third degree polynomial. We focus on the influence of the coupling on the occurrence of different bifurcation's scenarios. The stability of equilibria, using Routh-Hurwitz criterion, is investigated. Moreover, we check how coefficients of the nonlinear coupling influence an appearance of different types of periodic solutions. The stable periodic solutions are computed using path-following. Finally, we show the two parameters' bifurcation diagrams with marked areas where one can observe the coexistence of solutions.
Nonlinear spin wave coupling in adjacent magnonic crystals
Energy Technology Data Exchange (ETDEWEB)
Sadovnikov, A. V., E-mail: sadovnikovav@gmail.com; Nikitov, S. A. [Laboratory “Metamaterials,” Saratov State University, Saratov 410012 (Russian Federation); Kotel' nikov Institute of Radioengineering and Electronics, Russian Academy of Sciences, Moscow 125009 (Russian Federation); Beginin, E. N.; Morozova, M. A.; Sharaevskii, Yu. P.; Grishin, S. V.; Sheshukova, S. E. [Laboratory “Metamaterials,” Saratov State University, Saratov 410012 (Russian Federation)
2016-07-25
We have experimentally studied the coupling of spin waves in the adjacent magnonic crystals. Space- and time-resolved Brillouin light-scattering spectroscopy is used to demonstrate the frequency and intensity dependent spin-wave energy exchange between the side-coupled magnonic crystals. The experiments and the numerical simulation of spin wave propagation in the coupled periodic structures show that the nonlinear phase shift of spin wave in the adjacent magnonic crystals leads to the nonlinear switching regime at the frequencies near the forbidden magnonic gap. The proposed side-coupled magnonic crystals represent a significant advance towards the all-magnonic signal processing in the integrated magnonic circuits.
Thermally induced nonlinear mode coupling in high power fiber amplifiers
DEFF Research Database (Denmark)
Johansen, Mette Marie; Hansen, Kristian Rymann; Alkeskjold, Thomas T.;
2013-01-01
Thermally induced nonlinear mode coupling leads to transverse mode instability (TMI) in high power fiber amplifiers. A numerical model including altering mode profiles from thermal effects and waveguide perturbations predicts a TMI threshold of ~200W.......Thermally induced nonlinear mode coupling leads to transverse mode instability (TMI) in high power fiber amplifiers. A numerical model including altering mode profiles from thermal effects and waveguide perturbations predicts a TMI threshold of ~200W....
Entanglement Dynamics of Quantum Oscillators Nonlinearly Coupled to Thermal Environments
Voje, Aurora; Croy, Alexander; Isacsson, Andreas
2014-01-01
We study the asymptotic entanglement of two quantum harmonic oscillators nonlinearly coupled to an environment. Coupling to independent baths and a common bath are investigated. Numerical results obtained using the Wangsness-Bloch-Redfield method are supplemented by analytical results in the rotating wave approximation. The asymptotic negativity as function of temperature, initial squeezing and coupling strength, is compared to results for systems with linear system-reservoir coupling. We fin...
Diagnosing nonlinearities in the local and remote responses to partial Amazon deforestation
Badger, Andrew M.; Dirmeyer, Paul A.
2016-08-01
Using a set of fully coupled climate model simulations, the response to partial deforestation over the Amazon due to agricultural expansion has been analyzed. Three variations of 50% deforestation (all of western half, all of eastern half, and half of each grid box) were compared with total deforestation to determine the degree and character of nonlinearity of the climate response to partial deforestation. A metric is developed to quantify the degree and distribution of nonlinearity in the response, applicable to any variable. The metric also quantifies whether the response is saturating or accelerating, meaning significantly either more or less than 50% of the simulated response to total deforestation is attained at 50% deforestation. The spatial structure of the atmospheric response to Amazon deforestation reveals large areas across the tropics that exhibit a significant nonlinear component, particularly for temperature and geopotential height. Over the domain between 45°S and 45°N across all longitudes, 50% deforestation generally provides less than half of the total response to deforestation over oceans, indicating the marine portion of climate system is somewhat resilient to progressive deforestation. However, over continents there are both accelerating and saturating responses to 50% Amazon deforestation, and the response is different depending on whether the eastern or western half of Amazonia is deforested or half of the forest is removed uniformly across the region.
Coupling of spatially partially coherent beams into planar waveguides.
Partanen, Henri; Tervo, Jani; Turunen, Jari
2015-03-23
The second-order coherence theory of partially spatially coherent light and the overlap integral method are applied to study the end-coupling of stationary multimode light beams into planar waveguides. A method is presented for the determination of the cross-spectral density function of the guided field. Examples are given on the effects of spatial coherence, lateral shift, angular tilt, and defocusing of the incident beam on the coupling efficiency, spatial coherence, and propagation characteristics of the guided field.
Nonlinear Analysis of a Cross-Coupled Quadrature Harmonic Oscillator
DEFF Research Database (Denmark)
Djurhuus, Torsten; Krozer, Viktor; Vidkjær, Jens;
2004-01-01
We derive the dynamic equations governing the cross-coupled quadrature oscillator leading to an expression for the trade-off between signal quadrature and close-in phase noise. The theory shows that nonlinearity in the coupling transconductance results in AM-PM noise close to the carrier, which...
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.
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.
Energy Technology Data Exchange (ETDEWEB)
Zhao Xiqiang [Department of Mathematics, Ocean University of China, Qingdao Shandong 266071 (China)] e-mail: zhaodss@yahoo.com.cn; Wang Limin [Shandong University of Technology, Zibo Shandong 255049 (China); Sun Weijun [Shandong University of Technology, Zibo Shandong 255049 (China)
2006-04-01
In this letter, a new method, called the repeated homogeneous balance method, is proposed for seeking the traveling wave solutions of nonlinear partial differential equations. The Burgers-KdV equation is chosen to illustrate our method. It has been confirmed that more traveling wave solutions of nonlinear partial differential equations can be effectively obtained by using the repeated homogeneous balance method.
Recent topics in non-linear partial differential equations 4
Mimura, M
1989-01-01
This fourth volume concerns the theory and applications of nonlinear PDEs in mathematical physics, reaction-diffusion theory, biomathematics, and in other applied sciences. Twelve papers present recent work in analysis, computational analysis of nonlinear PDEs and their applications.
Sampled-Data Fuzzy Control for Nonlinear Coupled Parabolic PDE-ODE Systems.
Wang, Zi-Peng; Wu, Huai-Ning; Li, Han-Xiong
2017-09-01
In this paper, a sampled-data fuzzy control problem is addressed for a class of nonlinear coupled systems, which are described by a parabolic partial differential equation (PDE) and an ordinary differential equation (ODE). Initially, the nonlinear coupled system is accurately represented by the Takagi-Sugeno (T-S) fuzzy coupled parabolic PDE-ODE model. Then, based on the T-S fuzzy model, a novel time-dependent Lyapunov functional is used to design a sampled-data fuzzy controller such that the closed-loop coupled system is exponentially stable, where the sampled-data fuzzy controller consists of the ODE state feedback and the PDE static output feedback under spatially averaged measurements. The stabilization condition is presented in terms of a set of linear matrix inequalities. Finally, simulation results on the control of a hypersonic rocket car are given to illustrate the effectiveness of the proposed design method.
Coupled parametric processes in binary nonlinear photonic structures
Saygin, M Yu
2016-01-01
We study parametric interactions in a new type of nonlinear photonic structures, which is realized in the vicinity of a pair of nonlinear crystals. In this kind of structure, which we call binary, multiple nonlinear optical processes can be implemented simultaneously, owing to multiple phase-matching conditions, fulfilled separately in the constituent crystals. The coupling between the nonlinear processes by means of modes sharing similar frequency is attained by the spatially-broadband nature of the parametric fields. We investigate the spatial properties of the fields generated in the binary structure constructed from periodically poled crystals for the two examples: 1) single parametric down-conversion, and 2) coupled parametric down-conversion and up-conversion processes. The efficacy of the fields' generation in these examples is analyzed through comparison with the cases of traditional single periodically poled crystal and aperiodic photonic structure, respectively. It has been shown that the relative s...
Entanglement dynamics of quantum oscillators nonlinearly coupled to thermal environments
Voje, Aurora; Croy, Alexander; Isacsson, Andreas
2015-07-01
We study the asymptotic entanglement of two quantum harmonic oscillators nonlinearly coupled to an environment. Coupling to independent baths and a common bath are investigated. Numerical results obtained using the Wangsness-Bloch-Redfield method are supplemented by analytical results in the rotating wave approximation. The asymptotic negativity as function of temperature, initial squeezing, and coupling strength, is compared to results for systems with linear system-reservoir coupling. We find that, due to the parity-conserving nature of the coupling, the asymptotic entanglement is considerably more robust than for the linearly damped cases. In contrast to linearly damped systems, the asymptotic behavior of entanglement is similar for the two bath configurations in the nonlinearly damped case. This is due to the two-phonon system-bath exchange causing a suppression of information exchange between the oscillators via the bath in the common-bath configuration at low temperatures.
Matter coupling in partially constrained vielbein formulation of massive gravity
Energy Technology Data Exchange (ETDEWEB)
Felice, Antonio De [Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502 (Japan); Gümrükçüoğlu, A. Emir [School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD (United Kingdom); Heisenberg, Lavinia [Institute for Theoretical Studies, ETH Zurich,Clausiusstrasse 47, 8092 Zurich (Switzerland); Mukohyama, Shinji [Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502 (Japan); Kavli Institute for the Physics and Mathematics of the Universe,Todai Institutes for Advanced Study, University of Tokyo (WPI),5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8583 (Japan)
2016-01-04
We consider a linear effective vielbein matter coupling without introducing the Boulware-Deser ghost in ghost-free massive gravity. This is achieved in the partially constrained vielbein formulation. We first introduce the formalism and prove the absence of ghost at all scales. As next we investigate the cosmological application of this coupling in this new formulation. We show that even if the background evolution accords with the metric formulation, the perturbations display important different features in the partially constrained vielbein formulation. We study the cosmological perturbations of the two branches of solutions separately. The tensor perturbations coincide with those in the metric formulation. Concerning the vector and scalar perturbations, the requirement of absence of ghost and gradient instabilities yields slightly different allowed parameter space.
Matter coupling in partially constrained vielbein formulation of massive gravity
De Felice, Antonio; Heisenberg, Lavinia; Mukohyama, Shinji
2015-01-01
We consider a consistent linear effective vielbein matter coupling without introducing the Boulware-Deser ghost in ghost-free massive gravity. This is achieved in the partially constrained vielbein formulation. We first introduce the formalism and prove the absence of ghost at all scales. As next we investigate the cosmological application of this coupling in this new formulation. We show that even if the background evolution accords with the metric formulation, the perturbations display important different features in the partially constrained vielbein formulation. We study the cosmological perturbations of the two branches of solutions separately. The tensor perturbations coincide with those in the metric formulation. Concerning the vector and scalar perturbations, the requirement of absence of ghost and gradient instabilities yields slightly different allowed parameter space.
Matter coupling in partially constrained vielbein formulation of massive gravity
De Felice, Antonio; Gümrükçüoğlu, A. Emir; Heisenberg, Lavinia; Mukohyama, Shinji
2016-01-01
We consider a linear effective vielbein matter coupling without introducing the Boulware-Deser ghost in ghost-free massive gravity. This is achieved in the partially constrained vielbein formulation. We first introduce the formalism and prove the absence of ghost at all scales. As next we investigate the cosmological application of this coupling in this new formulation. We show that even if the background evolution accords with the metric formulation, the perturbations display important different features in the partially constrained vielbein formulation. We study the cosmological perturbations of the two branches of solutions separately. The tensor perturbations coincide with those in the metric formulation. Concerning the vector and scalar perturbations, the requirement of absence of ghost and gradient instabilities yields slightly different allowed parameter space.
A Coupled Analysis of Nonlinear Sloshing and Ship Motion
Institute of Scientific and Technical Information of China (English)
Shuo Huang; Wenyang Duan; Hao Zhang
2012-01-01
Nonlinear interactions among incident wave,tank-sloshing and floating body coupling motion are investigated.The fully nonlinear sloshing and body-surface nonlinear free surface hydrodynamics is simulated using a Non-Uniform Rational B-Spline (NURBS) higher-order panel method in time domain based on the potential theory.A robust and stable improved iterative procedure (Yan and Ma,2007) for floating bodies is used for calculating the time derivative of velocity potential and floating body motion.An energy dissipation condition based on linear theory adopted by Huang (2011) is developed to consider flow viscosity effects of sloshing flow in nonlinear model.A two-dimensional tank model test was performed to identify its validity.The present nonlinear coupling sway motion results are subsequently compared with the corresponding Rognebakke and Faltinsen (2003)'s experimental results,showing fair agreement.Thus,the numerical approach presented in this paper is expected to be very efficient and realistic in evaluating the coupling effects of nonlinear sloshing and body motion.
Asymptotic analysis of a coupled nonlinear parabolic system
Institute of Scientific and Technical Information of China (English)
Lan QIAO; Sining ZHENG
2008-01-01
This paper deals with asymptotic analysis of a parabolic system with inner absorptions and coupled nonlinear boundary fluxes. Three simultaneous blow-up rates are established under different dominations of nonlinearities, and simply represented in a characteristic algebraic system introduced for the problem. In particular, it is observed that two of the multiple blow-up rates are absorption-related. This is substantially different from those for nonlinear parabolic problems with absorptions in all the previous literature, where the blow-up rates were known as absorption-independent. The results of the paper rely on the scaling method with a complete classification for the nonlinear parameters of the model. The first example of absorption-related blow-up rates was recently proposed by the authors for a coupled parabolic system with mixed type nonlinearities. The present paper shows that the newly observed phenomena of absorption-related blow-up rates should be due to the coupling mechanism, rather than the mixed type nonlinearities.
Non-linear partially massless symmetry in an SO(1,5) continuation of conformal gravity
Apolo, Luis
2016-01-01
We construct a non-linear theory of interacting spin-2 fields that is invariant under the partially massless (PM) symmetry to all orders. This theory is based on the SO(1,5) group, in analogy with the SO(2,4) formulation of conformal gravity, but has a quadratic spectrum free of ghost instabilities. The action contains a vector field associated to a local SO(2) symmetry which is manifest in the vielbein formulation of the theory. We show that, in a perturbative expansion, the SO(2) symmetry transmutes into the PM transformations of a massive spin-2 field. In this context, the vector field is crucial to circumvent earlier obstructions to an order-by-order construction of PM symmetry. Although the non-linear theory lacks enough first class constraints to remove all helicity-0 modes from the spectrum, the PM transformations survive to all orders. The absence of ghosts and strong coupling effects at the non-linear level are not addressed here.
ON THE PARTIAL EQUIASYMPTOTIC STABILITY OF NONLINEAR TIME-VARYING DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
JianJigui; JiangMinghui; ShenYanjun
2005-01-01
In this paper, the problem of partial equiasymptotic stability for nonlinear time-varying differential equations are analyzed. A sufficient condition of partial stability and a set of sufficient conditions of partial equiasymptotic stability are given. Some of these conditions allow the derivative of Lyapunov function to be positive. Finally, several numerical examples are also given to illustrate the main results.
UV Nano Lights - Nonlinear Quantum Dot-Plasmon Coupling
2016-06-20
AFRL-AFOSR-JP-TR-2016-0072 UV Nano-Lights - Nonlinear Quantum Dot-Plasmon Coupling Eric Waclawik QUEENSLAND UNIVERSITY OF TECHNOLOGY Final Report 06...Final 3. DATES COVERED (From - To) 03 Feb 2014 to 02 Feb 2016 4. TITLE AND SUBTITLE UV Nano-Lights - Nonlinear Quantum Dot-Plasmon Coupling 5a...CONTRACT NUMBER 5b. GRANT NUMBER FA2386-14-1-4056 5c. PROGRAM ELEMENT NUMBER 61102F 6. AUTHOR(S) Eric Waclawik 5d. PROJECT NUMBER 5e. TASK NUMBER 5f
Nonlinear magnetoplasmons in strongly coupled Yukawa plasmas
Bonitz, M; Ott, T; Kaehlert, H; Hartmann, P
2010-01-01
The existence of plasma oscillations at multiples of the magnetoplasmon frequency in a strongly coupled two-dimensional magnetized Yukawa plasma is reported, based on extensive molecular dynamics simulations. These modes are the analogues of Bernstein modes which are renormalized by strong interparticle correlations. Their properties are theoretically explained by a dielectric function incorporating the combined effect of a magnetic field, strong correlations and finite temperature.
An effective analytic approach for solving nonlinear fractional partial differential equations
Ma, Junchi; Zhang, Xiaolong; Liang, Songxin
2016-08-01
Nonlinear fractional differential equations are widely used for modelling problems in applied mathematics. A new analytic approach with two parameters c1 and c2 is first proposed for solving nonlinear fractional partial differential equations. These parameters are used to improve the accuracy of the resulting series approximations. It turns out that much more accurate series approximations are obtained by choosing proper values of c1 and c2. To demonstrate the applicability and effectiveness of the new method, two typical fractional partial differential equations, the nonlinear gas dynamics equation and the nonlinear KdV-Burgers equation, are solved.
The numerical dynamic for highly nonlinear partial differential equations
Lafon, A.; Yee, H. C.
1992-01-01
Problems associated with the numerical computation of highly nonlinear equations in computational fluid dynamics are set forth and analyzed in terms of the potential ranges of spurious behaviors. A reaction-convection equation with a nonlinear source term is employed to evaluate the effects related to spatial and temporal discretizations. The discretization of the source term is described according to several methods, and the various techniques are shown to have a significant effect on the stability of the spurious solutions. Traditional linearized stability analyses cannot provide the level of confidence required for accurate fluid dynamics computations, and the incorporation of nonlinear analysis is proposed. Nonlinear analysis based on nonlinear dynamical systems complements the conventional linear approach and is valuable in the analysis of hypersonic aerodynamics and combustion phenomena.
Nonlinear Characteristics of an Intense Laser Pulse Propagating in Partially Stripped Plasmas
Institute of Scientific and Technical Information of China (English)
HU Qiang-Lin; LIU Shi-Bing; CHEN Tao; JIANG Yi-Jian
2005-01-01
The nonlinear optic characteristics of an intense laser pulse propagating in partially stripped plasmas are investigated analytically. The phase and group velocity of the laser pulse propagation as well as the three general expressions governing the nonlinear optic behavior, based on the photon number conservation, are obtained by considering the partially stripped plasma as a nonlinear optic medium. The numerical result shows that the presence of the bound electrons in partially stripped plasma can significantly change the propagating property of the intense laser pulse.
Switching field of partially exchange-coupled particles
Energy Technology Data Exchange (ETDEWEB)
Oliva, M.I. [Facultad de Matematica Astronomia y Fisica, Universidad Nacional de Cordoba, 5000 Cordoba (Argentina); Secyt - UNC (Argentina); Bertorello, H.R. [Facultad de Matematica Astronomia y Fisica, Universidad Nacional de Cordoba, 5000 Cordoba (Argentina); CONICET (Argentina); Bercoff, P.G. [Facultad de Matematica Astronomia y Fisica, Universidad Nacional de Cordoba, 5000 Cordoba (Argentina) and CONICET (Argentina)]. E-mail: bercoff@famaf.unc.edu.ar
2004-12-31
The magnetization reversal of partially exchange-coupled particles is studied in detail. The starting point is the observation of a complicated phenomenology in the irreversible susceptibility and FORC distribution functions of Ba hexaferrite samples obtained by means of different sintering conditions. Several peaks in the first-order reversal curve (FORC) distribution functions were identified and associated with clusters with different number of particles. The switching fields of these clusters were related to an effective anisotropy constant Keff that depends on the number of particles in the cluster. Keff is linked to the exchange-coupled volume between two neighboring particles and as a weighted mean between the anisotropy constants of the coupled and uncoupled volumes. By using the modified Brown's equation {alpha}ex=0.322 is obtained.In order to interpret these results, the switching field of a two-particle system with partial exchange coupling is studied. It is assumed that the spins reorientation across the contact plane between the particles is like a Bloch wall. The energy of the system is written in terms of the fraction of volume affected by exchange coupling and the switching fields for both particles are calculated. At small interaction volume fraction each particle inverts its magnetization independently from the other. As the fraction of exchange-coupled volume increases, cooperative effects appear and the two particles invert their magnetization in a cooperative way.The proposed model allows to interpret for the first time the empirical factor {alpha}ex in terms of physical arguments and also explain the details observed in the FORC distribution function.
Oscillation criteria for a class of nonlinear partial differential equations
Directory of Open Access Journals (Sweden)
Robert Marik
2002-03-01
Full Text Available This paper presents sufficient conditions on the function $c(x$ to ensure that every solution of partial differential equation $$ sum_{i=1}^{n}{partial over partial x_i} Phi_{p}({partial u over partial x_i}+B(x,u=0, quad Phi_p(u:=|u|^{p-1}mathop{ m sgn} u. quad p>1 $$ is weakly oscillatory, i.e. has zero outside of every ball in $mathbb{R}^n$. The main tool is modified Riccati technique developed for Schrodinger operator by Noussair and Swanson [11].
The coupling of non-linear supersymmetry to supergravity
Energy Technology Data Exchange (ETDEWEB)
Antoniadis, Ignatios [Sorbonne Universites, UPMC Paris 6, LPTHE, UMR CNRS 7589, Paris (France); University of Bern, Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, Bern (Switzerland); Markou, Chrysoula [Sorbonne Universites, UPMC Paris 6, LPTHE, UMR CNRS 7589, Paris (France)
2015-12-15
We study the coupling of non-linear supersymmetry to supergravity. The goldstino nilpotent superfield of global supersymmetry coupled to supergravity is described by a geometric action of the chiral curvature superfield R subject to the constraint (R - λ){sup 2} = 0 with an appropriate constant λ. This constraint can be found as the decoupling limit of the scalar partner of the goldstino in a class of f(R) supergravity theories. (orig.)
The coupling of non-linear supersymmetry to supergravity
Energy Technology Data Exchange (ETDEWEB)
Antoniadis, Ignatios, E-mail: antoniad@lpthe.jussieu.fr [LPTHE, UMR CNRS 7589, Sorbonne Universités, UPMC Paris 6, 75005, Paris (France); Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, Sidlestrasse 5, 3012, Bern (Switzerland); Markou, Chrysoula, E-mail: chrysoula@lpthe.jussieu.fr [LPTHE, UMR CNRS 7589, Sorbonne Universités, UPMC Paris 6, 75005, Paris (France)
2015-12-09
We study the coupling of non-linear supersymmetry to supergravity. The goldstino nilpotent superfield of global supersymmetry coupled to supergravity is described by a geometric action of the chiral curvature superfield R subject to the constraint (R-λ){sup 2}=0 with an appropriate constant λ. This constraint can be found as the decoupling limit of the scalar partner of the goldstino in a class of f(R) supergravity theories.
Nonlinear Integrable Couplings of Levi Hierarchy and WKI Hierarchy
Directory of Open Access Journals (Sweden)
Zhengduo Shan
2014-01-01
Full Text Available With the help of the known Lie algebra, a type of new 8-dimensional matrix Lie algebra is constructed in the paper. By using the 8-dimensional matrix Lie algebra, the nonlinear integrable couplings of the Levi hierarchy and the Wadati-Konno-Ichikawa (WKI hierarchy are worked out, which are different from the linear integrable couplings. Based on the variational identity, the Hamiltonian structures of the above hierarchies are derived.
Nonlinear Integrable Couplings of Levi Hierarchy and WKI Hierarchy
Zhengduo Shan; Hongwei Yang; Baoshu Yin
2014-01-01
With the help of the known Lie algebra, a type of new 8-dimensional matrix Lie algebra is constructed in the paper. By using the 8-dimensional matrix Lie algebra, the nonlinear integrable couplings of the Levi hierarchy and the Wadati-Konno-Ichikawa (WKI) hierarchy are worked out, which are different from the linear integrable couplings. Based on the variational identity, the Hamiltonian structures of the above hierarchies are derived.
Projective synchronization of chaotic systems with bidirectional nonlinear coupling
Indian Academy of Sciences (India)
Mohammada Ali Khan; Swarup Poria
2013-09-01
This paper presents a new scheme for constructing bidirectional nonlinear coupled chaotic systems which synchronize projectively. Conditions necessary for projective synchronization (PS) of two bidirectionally coupled chaotic systems are derived using Lyapunov stability theory. The proposed PS scheme is discussed by taking as examples the so-called unified chaotic model, the Lorenz–Stenflo system and the nonautonomous chaotic Van der Pol oscillator. Numerical simulation results are presented to show the efficiency of the proposed synchronization scheme.
Dilaton black holes coupled to nonlinear electrodynamic field
Sheykhi, A
2015-01-01
The theory of nonlinear electrodynamics has got a lot of attentions in recent years. It was shown that Born-Infeld nonlinear electrodynamics is not the only modification of the linear Maxwell's field which keeps the electric field of a charged point particle finite at the origin, and other type of nonlinear Lagrangian such as exponential and logarithmic nonlinear electrodynamics can play the same role. In this paper, we generalize the study on the exponential nonlinear electrodynamics by adding a scalar dilaton field to the action. By suitably choosing the coupling of the matter field to the dilaton field, we vary the action and obtain the corresponding field equations. Then, by making a proper ansatz, we construct a new class of charged dilaton black hole solutions coupled to the exponential nonlinear electrodynamics field in the presence of two Liouville-type potentials for the dilaton field. Due to the presence of the dilaton field, the asymptotic behavior of these solutions are neither flat nor (A)dS. In ...
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.
On the recovering of a coupled nonlinear Schroedinger potential
Energy Technology Data Exchange (ETDEWEB)
Corona, Gulmaro Corona [Area de Analisis Matematico y sus Aplicaciones, Universidad Autonoma Metropolitana, Atzcapotzalco, DF (Mexico)]. E-mail: ccg@hp9000a1.uam.mx
2000-04-28
We establish a priori conditions for a Gel'fand-Levitan (GL) integral using some results of the Fredholm theory. As consequence, we obtain a recovering formula for the potential of the coupled nonlinear Schroedinger equations. The remarkable fact is that the recovering formula is given in terms of the solutions of a classical GL-integral equation. (author)
Nonlinear Observers for Gyro Calibration Coupled with a Nonlinear Control Algorithm
Thienel, Julie; Sanner, Robert M.
2003-01-01
Nonlinear observers for gyro calibration are presented. The first observer estimates a constant gyro bias. The second observer estimates scale factor errors. The third observer estimates the gyro alignment for three orthogonal gyros. The observers are then combined. The convergence properties of all three observers, and the combined observers, are discussed. Additionally, all three observers are coupled with a nonlinear control algorithm. The stability of each of the resulting closed loop systems is analyzed. Simulated test results are presented for each system.
Boundary control of nonlinear coupled heat systems using backstepping
Bendevis, Paul
2016-10-20
A state feedback boundary controller is designed for a 2D coupled PDE system modelling heat transfer in a membrane distillation system for water desalination. Fluid is separated into two compartments with nonlinear coupling at a membrane boundary. The controller sets the temperature on one boundary in order to track a temperature difference across the membrane boundary. The control objective is achieved by an extension of backstepping methods to these coupled equations. Stability of the target system via Lyapunov like methods, and the invertibility of the integral transformation are used to show the stability of the tracking error.
A higher order lattice BGK model for simulating some nonlinear partial differential equations
Institute of Scientific and Technical Information of China (English)
LAI HuiLin; MA ChangFeng
2009-01-01
In this paper, we consider a one-dimensional nonlinear partial differential equation that has the form ut + αuux+βunux-γuxx+δuxxx= F(U). A higher order lattice Bhatnager-Gross-Krook (BGK) model with an amending-function is proposed. With the Chapman-Enskog expansion, different kinds of nonlinear partial differential equations are recovered correctly from the continuous Boltzmann equation. The numerical results show that this method is very effective.
A higher order lattice BGK model for simulating some nonlinear partial differential equations
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
In this paper, we consider a one-dimensional nonlinear partial differential equation that has the form ut + αuux + βunux - γuxx + δuxxx = F(u). A higher order lattice Bhatnager-Gross-Krook (BGK) model with an amending-function is proposed. With the Chapman-Enskog expansion, different kinds of nonlinear partial differential equations are recovered correctly from the continuous Boltzmann equation. The numerical results show that this method is very effective.
Analytic continuation of solutions of some nonlinear convolution partial differential equations
Directory of Open Access Journals (Sweden)
Hidetoshi Tahara
2015-01-01
Full Text Available The paper considers a problem of analytic continuation of solutions of some nonlinear convolution partial differential equations which naturally appear in the summability theory of formal solutions of nonlinear partial differential equations. Under a suitable assumption it is proved that any local holomorphic solution has an analytic extension to a certain sector and its extension has exponential growth when the variable goes to infinity in the sector.
A unified lattice Boltzmann model for some nonlinear partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Chai Zhenhua [State Key Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan 430074 (China); Shi Baochang [Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074 (China)], E-mail: sbchust@126.com; Zheng Lin [Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074 (China)
2008-05-15
In this paper, a unified and novel lattice Boltzmann model is proposed for solving nonlinear partial differential equation that has the form DU{sub t} + {alpha}UU{sub x} + {beta}U{sup n}U{sub x} - {gamma}U{sub xx} + {delta} U{sub xxx} = F(x,t). Numerical results agree well with the analytical solutions and results derived by existing literature, which indicates the present model is satisfactory and efficient on solving nonlinear partial differential equations.
Nonlinear simulations of the convection-pulsation coupling
Gastine, T
2011-01-01
In cold Cepheids close to the red edge of the classical instability strip, a strong coupling between the stellar pulsations and the surface convective motions occurs. This coupling is by now poorly described by 1-D models of convection, the so-called "time-dependent convection models" (TDC). The intrinsic weakness of such models comes from the large number of unconstrained free parameters entering in the description of turbulent convection. A way to overcome these limits is to compute two-dimensional direct simulations (DNS), in which all the nonlinearities are correctly solved. Two-dimensional DNS of the convection-pulsation coupling are presented here. In an appropriate parameter regime, convective motions can actually quench the radial pulsations of the star, as suspected in Cepheids close to the red edge of the instability strip. These nonlinear simulations can also be used to determine the limits and the relevance of the TDC models.
Applications of algebraic method to exactly solve some nonlinear partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Darwish, A.A. [Department of Mathematics, Faculty of Science, Helwan University (Egypt)]. E-mail: profdarwish@yahoo.com; Ramady, A. [Department of Mathematics, Faculty of Science, Beni-Suef University (Egypt)]. E-mail: aramady@yahoo.com
2007-08-15
A direct and unified algebraic method for constructing multiple travelling wave solutions of nonlinear evolution equations is used and implemented in a computer algebraic system. New solutions for some nonlinear partial differential equations (NLPDE's) are obtained. Graphs of the solutions are displayed.
Geometric nonlinear formulation for thermal-rigid-flexible coupling system
Fan, Wei; Liu, Jin-Yang
2013-10-01
This paper develops geometric nonlinear hybrid formulation for flexible multibody system with large deformation considering thermal effect. Different from the conventional formulation, the heat flux is the function of the rotational angle and the elastic deformation, therefore, the coupling among the temperature, the large overall motion and the elastic deformation should be taken into account. Firstly, based on nonlinear strain-displacement relationship, variational dynamic equations and heat conduction equations for a flexible beam are derived by using virtual work approach, and then, Lagrange dynamics equations and heat conduction equations of the first kind of the flexible multibody system are obtained by leading into the vectors of Lagrange multiplier associated with kinematic and temperature constraint equations. This formulation is used to simulate the thermal included hub-beam system. Comparison of the response between the coupled system and the uncoupled system has revealed the thermal chattering phenomenon. Then, the key parameters for stability, including the moment of inertia of the central body, the incident angle, the damping ratio and the response time ratio, are analyzed. This formulation is also used to simulate a three-link system applied with heat flux. Comparison of the results obtained by the proposed formulation with those obtained by the approximate nonlinear model and the linear model shows the significance of considering all the nonlinear terms in the strain in case of large deformation. At last, applicability of the approximate nonlinear model and the linear model are clarified in detail.
Solving Nonlinear Partial Differential Equations with Maple and Mathematica
Shingareva, Inna K
2011-01-01
The emphasis of the book is given in how to construct different types of solutions (exact, approximate analytical, numerical, graphical) of numerous nonlinear PDEs correctly, easily, and quickly. The reader can learn a wide variety of techniques and solve numerous nonlinear PDEs included and many other differential equations, simplifying and transforming the equations and solutions, arbitrary functions and parameters, presented in the book). Numerous comparisons and relationships between various types of solutions, different methods and approaches are provided, the results obtained in Maple an
Nonlinear coupled dynamics analysis of a truss spar platform
Li, Cheng-xi; Zhang, Jun
2016-12-01
Accurate prediction of the offshore structure motion response and associate mooring line tension is important in both technical applications and scientific research. In our study, a truss spar platform, operated in Gulf of Mexico, is numerically simulated and analyzed by an in-house numerical code `COUPLE'. Both the platform motion responses and associated mooring line tension are calculated and investigated through a time domain nonlinear coupled dynamic analysis. Satisfactory agreement between the simulation and corresponding field measurements is in general reached, indicating that the numerical code can be used to conduct the time-domain analysis of a truss spar interacting with its mooring and riser system. Based on the comparison between linear and nonlinear results, the relative importance of nonlinearity in predicting the platform motion response and mooring line tensions is assessed and presented. Through the coupled and quasi-static analysis, the importance of the dynamic coupling effect between the platform hull and the mooring/riser system in predicting the mooring line tension and platform motions is quantified. These results may provide essential information pertaining to facilitate the numerical simulation and design of the large scale offshore structures.
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.
Nonlinear partial differential equations: Integrability, geometry and related topics
Krasil'shchik, Joseph; Rubtsov, Volodya
2017-03-01
Geometry and Differential Equations became inextricably entwined during the last one hundred fifty years after S. Lie and F. Klein's fundamental insights. The two subjects go hand in hand and they mutually enrich each other, especially after the "Soliton Revolution" and the glorious streak of Symplectic and Poisson Geometry methods in the context of Integrability and Solvability problems for Non-linear Differential Equations.
Non-Linearity in Wide Dynamic Range CMOS Image Sensors Utilizing a Partial Charge Transfer Technique
Directory of Open Access Journals (Sweden)
Izhal Abdul Halin
2009-11-01
Full Text Available The partial charge transfer technique can expand the dynamic range of a CMOS image sensor by synthesizing two types of signal, namely the long and short accumulation time signals. However the short accumulation time signal obtained from partial transfer operation suffers of non-linearity with respect to the incident light. In this paper, an analysis of the non-linearity in partial charge transfer technique has been carried, and the relationship between dynamic range and the non-linearity is studied. The results show that the non-linearity is caused by two factors, namely the current diffusion, which has an exponential relation with the potential barrier, and the initial condition of photodiodes in which it shows that the error in the high illumination region increases as the ratio of the long to the short accumulation time raises. Moreover, the increment of the saturation level of photodiodes also increases the error in the high illumination region.
Non-Linearity in Wide Dynamic Range CMOS Image Sensors Utilizing a Partial Charge Transfer Technique
Shafie, Suhaidi; Kawahito, Shoji; Halin, Izhal Abdul; Hasan, Wan Zuha Wan
2009-01-01
The partial charge transfer technique can expand the dynamic range of a CMOS image sensor by synthesizing two types of signal, namely the long and short accumulation time signals. However the short accumulation time signal obtained from partial transfer operation suffers of non-linearity with respect to the incident light. In this paper, an analysis of the non-linearity in partial charge transfer technique has been carried, and the relationship between dynamic range and the non-linearity is studied. The results show that the non-linearity is caused by two factors, namely the current diffusion, which has an exponential relation with the potential barrier, and the initial condition of photodiodes in which it shows that the error in the high illumination region increases as the ratio of the long to the short accumulation time raises. Moreover, the increment of the saturation level of photodiodes also increases the error in the high illumination region. PMID:22303133
Institute of Scientific and Technical Information of China (English)
Ronghua Huan; Lincong Chen; Weiliang Jin; Weiqiu Zhu
2009-01-01
An optimal vibration control strategy for partially observable nonlinear quasi Hamil-tonian systems with actuator saturation is proposed. First, a controlled partially observable non-linear system is converted into a completely observable linear control system of finite dimension based on the theorem due to Charalambous and Elliott. Then the partially averaged Ito stochas-tic differential equations and dynamical programming equation associated with the completely observable linear system are derived by using the stochastic averaging method and stochastic dynamical programming principle, respectively. The optimal control law is obtained from solving the final dynamical programming equation. The results show that the proposed control strategy has high control effectiveness and control efficiency.
Modified extended tanh-function method for solving nonlinear partial differential equations
Energy Technology Data Exchange (ETDEWEB)
El-Wakil, S.A. [Department of Physics, Faculty of Science, Theoretical Research Group, Mansoura University, 35516 Mansoura (Egypt); Abdou, M.A. [Department of Physics, Faculty of Science, Theoretical Research Group, Mansoura University, 35516 Mansoura (Egypt)]. E-mail: m_abdou_eg@yahoo.com
2007-03-15
Based on computerized symbolic computation, modified extended tanh-method for constructing multiple travelling wave solutions of nonlinear evolution equations is presented and implemented in a computer algebraic system. Applying this method, with the aid of Maple, we consider some nonlinear evolution equations in mathematical physics such as the nonlinear partial differential equation, nonlinear Fisher-type equation, ZK-BBM equation, generalized Burgers-Fisher equation and Drinfeld-Sokolov system. As a result, we can successfully recover the previously known solitary wave solutions that had been found by the extended tanh-function method and other more sophisticated methods.
Investigation of the nonlinear dynamics of a partially cracked plate
Energy Technology Data Exchange (ETDEWEB)
Israr, A [School of Engineering and Physical Sciences, Heriot Watt University - Dubai Campus, Block 2, Dubai International Academic City, P O Box 294345, Dubai (United Arab Emirates); Atepor, L, E-mail: a.israr@hw.ac.u, E-mail: katepor@yahoo.co [Department of Mechanical Engineering, James Watt South Building, University of Glasgow, Glasgow, G12 8QQ Scotland (United Kingdom)
2009-08-01
In this paper the nonlinear vibration of an aircraft panel structure modelled as an isotropic cracked plate and subjected to transverse harmonic excitation is considered for studying the dynamic response, both analytically and experimentally. A crack is arbitrarily located at the centre of the plate, consisting of a continuous line. This mathematical model is in the form of Duffing equation with a cubic nonlinear term. The perturbation method of multiple scales is used to solve the algebraic equation, and then investigated with the results of the direct integration within Mathematica{sup TM} and finite element analysis in ABAQUS for the first mode only. In addition, experimental measurements are also carried out to verify the dependence of the cracked plate's fundamental mode shape and resonance frequency on the vibration displacement amplitude. An extermely close agreement between these results is observed.
Multistable internal resonance in electroelastic crystals with nonlinearly coupled modes
Kirkendall, Christopher R.; Kwon, Jae W.
2016-03-01
Nonlinear modal interactions have recently become the focus of intense research in micro- and nanoscale resonators for their use to improve oscillator performance and probe the frontiers of fundamental physics. However, our understanding of modal coupling is largely restricted to clamped-clamped beams, and lacking in systems with both geometric and material nonlinearities. Here we report multistable energy transfer between internally resonant modes of an electroelastic crystal plate and use a mixed analytical-numerical approach to provide new insight into these complex interactions. Our results reveal a rich bifurcation structure marked by nested regions of multistability. Even the simple case of two coupled modes generates a host of topologically distinct dynamics over the parameter space, ranging from the usual Duffing bistability to complex multistable behaviour and quasiperiodic motion.
New Exact Solutions for New Model Nonlinear Partial Differential Equation
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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.
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M. R.Odekunle
2014-08-01
Full Text Available Tau method which is an economized polynomial technique for solving ordinary and partial differential equations with smooth solutions is modified in this paper for easy computation, accuracy and speed. The modification is based on the systematic use of „Catalan polynomial‟ in collocation tau method and the linearizing the nonlinear part by the use of Adomian‟s polynomial to approximate the solution of 2-dimentional Nonlinear Partial differential equation. The method involves the direct use of Catalan Polynomial in the solution of linearizedPartial differential Equation without first rewriting them in terms of other known functions as commonly practiced. The linearization process was done through adopting the Adomian Polynomial technique. The results obtained are quite comparable with the standard collocation tau methods for nonlinear partial differential equations.
Calculus of variations and nonlinear partial differential equations
Marcellini, Paolo
2008-01-01
This volume provides the texts of lectures given by L. Ambrosio, L. Caffarelli, M. Crandall, L.C. Evans, N. Fusco at the Summer course held in Cetraro (Italy) in 2005. These are introductory reports on current research by world leaders in the fields of calculus of variations and partial differential equations. The topics discussed are transport equations for nonsmooth vector fields, homogenization, viscosity methods for the infinite Laplacian, weak KAM theory and geometrical aspects of symmetrization. A historical overview of all CIME courses on the calculus of variations and partial differential equations is contributed by Elvira Mascolo.
Mean Square Synchronization of Stochastic Nonlinear Delayed Coupled Complex Networks
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Chengrong Xie
2013-01-01
Full Text Available We investigate the problem of adaptive mean square synchronization for nonlinear delayed coupled complex networks with stochastic perturbation. Based on the LaSalle invariance principle and the properties of the Weiner process, the controller and adaptive laws are designed to ensure achieving stochastic synchronization and topology identification of complex networks. Sufficient conditions are given to ensure the complex networks to be mean square synchronization. Furthermore, numerical simulations are also given to demonstrate the effectiveness of the proposed scheme.
Global solution for coupled nonlinear Klein-Gordon system
Institute of Scientific and Technical Information of China (English)
GAN Zai-hui; ZHANG Jian
2007-01-01
The global solution for a coupled nonlinear Klein-Gordon system in twodimensional space was studied.First,a sharp threshold of blowup and global existenoe for the system was obtained by constructing a type of cross-constrained variational problem and establishing so-called cross-invariant manifolds of the evolution flow.Then the result of how small the initial data for which the solution exists globally was proved by using the scaling argument.
Complex spatiotemporal behavior in a chain of one-way nonlinearly coupled elements
DEFF Research Database (Denmark)
Gaididei, Yuri Borisovich; Berkemer, Rainer; Gorria, C.;
2011-01-01
The dynamics of asymmetrically coupled nonlinear elements is considered. It is shown that there are two distinctive regimes of oscillatory behavior of one-way nonlinearly coupled elements depending on the relaxation time and the strength of the coupling. In the subcritical regime when...... nonlinear model....
A nonlinear discrete integrable coupling system and its infinite conservation laws
Institute of Scientific and Technical Information of China (English)
Yu Fa-Jun
2012-01-01
We construct a nonlinear integrable coupling of discrete soliton hierarchy,and establish the infinite conservation laws (CLs) for the nonlinear integrable coupling of the lattice hierarchy.As an explicit application of the method proposed in the paper,the infinite conservation laws of the nonlinear integrable coupling of the Volterra lattice hierarchy are presented.
Differential geometry techniques for sets of nonlinear partial differential equations
Estabrook, Frank B.
1990-01-01
An attempt is made to show that the Cartan theory of partial differential equations can be a useful technique for applied mathematics. Techniques for finding consistent subfamilies of solutions that are generically rich and well-posed and for introducing potentials or other usefully consistent auxiliary fields are introduced. An extended sample calculation involving the Korteweg-de Vries equation is given.
Nonlinear Programming Approach to Optimal Scaling of Partially Ordered Categories
Nishisato, Shizuhiko; Arri, P. S.
1975-01-01
A modified technique of separable programming was used to maximize the squared correlation ratio of weighted responses to partially ordered categories. The technique employs a polygonal approximation to each single-variable function by choosing mesh points around the initial approximation supplied by Nishisato's method. Numerical examples were…
Fitting and forecasting non-linear coupled dark energy
Casas, Santiago; Baldi, Marco; Pettorino, Valeria; Vollmer, Adrian
2015-01-01
We consider cosmological models in which dark matter feels a fifth force mediated by the dark energy scalar field, also known as coupled dark energy. Our interest resides in estimating forecasts for future surveys like Euclid when we take into account non-linear effects, relying on new fitting functions that reproduce the non-linear matter power spectrum obtained from N-body simulations. We obtain fitting functions for models in which the dark matter-dark energy coupling is constant. Their validity is demonstrated for all available simulations in the redshift range $z=0-1.6$ and wave modes below $k=10 \\text{h/Mpc}$. These fitting formulas can be used to test the predictions of the model in the non-linear regime without the need for additional computing-intensive N-body simulations. We then use these fitting functions to perform forecasts on the constraining power that future galaxy-redshift surveys like Euclid will have on the coupling parameter, using the Fisher matrix method for galaxy clustering (GC) and w...
Experiments on oscillator ensemble with global nonlinear coupling
Rosenblum, Michael; Temirbayev, Amirkhan; Zhanabaev, Zeinulla; Tarasov, Stanislav; Ponomarenko, Vladimir
2012-02-01
We experimentally analyze collective dynamics of a population of 20 electronic Wien-bridge limit-cycle oscillators with a linear or nonlinear phase-shifting unit in the global feedback loop. With linear unit we observe, with increase of the coupling strength, a standard Kuramoto-like transition to a fully synchronous state; the threshold of the transition depends on the phase shift. In case of nonlinear global coupling we first observe a transition to a state when approximately half of the population forms a synchronous cluster. With further increase of the coupling strength we observe destruction of this cluster and formation of a self-organized quasiperiodic state, predicted in [M. Rosenblum and A. Pikovsky, PRL, 98, 064101 (2007)]. In this state, frequencies of all oscillators are smaller than the frequency of the mean field, so that the oscillators are not locked to the mean field they create and their dynamics is quasiperiodic. The transition is characterized by a non-monotonic dependence of the order parameter on the coupling strength. We demonstrate a good correspondence between theory and experiment.
Adaptive synchronization of two nonlinearly coupled complex dynamical networks with delayed coupling
Zheng, Song; Wang, Shuguo; Dong, Gaogao; Bi, Qinsheng
2012-01-01
This paper investigates the adaptive synchronization between two nonlinearly delay-coupled complex networks with the bidirectional actions and nonidentical topological structures. Based on LaSalle's invariance principle, some criteria for the synchronization between two coupled complex networks are achieved via adaptive control. To validate the proposed methods, the unified chaotic system as the nodes of the networks are analyzed in detail, and numerical simulations are given to illustrate the theoretical results.
Light-enhanced electron-phonon coupling from nonlinear electron-phonon coupling
Sentef, M. A.
2017-05-01
We investigate an exact nonequilibrium solution of a two-site electron-phonon model, where an infrared-active phonon that is nonlinearly coupled to the electrons is driven by a laser field. The time-resolved electronic spectrum shows coherence-incoherence spectral weight transfer, a clear signature of light-enhanced electron-phonon coupling. The present study is motivated by recent evidence for enhanced electron-phonon coupling in pump-probe terahertz and angle-resolved photoemission spectroscopy in bilayer graphene when driven near resonance with an infrared-active phonon mode [E. Pomarico et al., Phys. Rev. B 95, 024304 (2017), 10.1103/PhysRevB.95.024304], and by a theoretical study suggesting that transient electronic attraction arises from nonlinear electron-phonon coupling [D. M. Kennes et al., Nat. Phys. 13, 479 (2017), 10.1038/nphys4024]. We show that a linear scaling of light-enhanced electron-phonon coupling with the pump field intensity emerges, in accordance with a time-nonlocal self-energy based on a mean-field decoupling using quasiclassical phonon coherent states. Finally, we demonstrate that this leads to enhanced double occupancies in accordance with an effective electron-electron attraction. Our results suggest that materials with strong phonon nonlinearities provide an ideal playground to achieve light-enhanced electron-phonon coupling and possibly light-induced superconductivity.
PARTIAL STABILIZATION OF A CLASS OF CONTINUOUS NONLINEAR CONTROL SYSTEMS WITH SEPARATED VARIABLES
Institute of Scientific and Technical Information of China (English)
Jigui JIAN; Xiaoxin LIAO
2005-01-01
In this paper, the partial stabilization problem for a class of nonlinear continuous control systems with separated variables is investigated. Several stabilizing controllers are constructed based on the partial stability theory of Lyapunov and the property of M-matrix, and some of these stabilizing controllers are only related to partial state variables. The controllers constructed here are shown to guarantee partial asymptotic stability of the closed-loop systems and these sufficient conditions may give some instructions to actual engineering application. A example is also given to illustrate the design method.
Directory of Open Access Journals (Sweden)
Jun Shuai
2013-11-01
Full Text Available A new approach using optimization technique for constructing low-dimensional dynamical systems of nonlinear partial differential equations (PDEs is presented. After the spatial basis functions of the nonlinear PDEs are chosen, spatial basis functions expansions combined with weighted residual methods are used for time/space separation and truncation to obtain a high-dimensional dynamical system. Secondly, modes of lower-dimensional dynamical systems are obtained by linear combination from the modes of the high-dimensional dynamical systems (ordinary differential equations of nonlinear PDEs. An error function for matrix of the linear combination coefficients is derived, and a simple algorithm to determine the optimal combination matrix is also introduced. A numerical example shows that the optimal dynamical system can use much smaller number of modes to capture the dynamics of nonlinear partial differential equations.
Higher-order spectra for identification of nonlinear modal coupling
Hickey, Daryl; Worden, Keith; Platten, Michael F.; Wright, Jan R.; Cooper, Jonathan E.
2009-05-01
Over the past four decades considerable work has been done in the area of power spectrum estimation. The information contained within the power spectrum relates to a signal's autocorrelation or 'second-order statistics'. The power spectrum provides a complete statistical description of a Gaussian process; however, a problem with this information is that it is phase blind. This problem is addressed if one turns to a system's frequency response function (FRF). The FRF graphs the magnitude and phase of the frequency response of a system; in order to do this it requires information regarding the frequency content of the input and output signals. Situations arise in science and engineering whereby signal analysts are required to look beyond second-order statistics and analyse a signal's higher-order statistics (HOS). HOS or spectra give information on a signal's deviation from Gaussianity and consequently are a good indicator function for the presence of nonlinearity within a system. One of the main problems in nonlinear system identification is that of high modal density. Many modelling schemes involve making some expansion of the nonlinear restoring force in terms of polynomial or other basis terms. If more than one degree-of-freedom is involved this becomes a multivariate problem and the number of candidate terms in the expansion grows explosively with the order of nonlinearity and the number of degrees-of-freedom. This paper attempts to use HOS to detect and qualify nonlinear behaviour for a number of symmetrical and asymmetrical systems over a range of degrees-of-freedom. In doing so the paper also attempts to show that HOS are a more sensitive tool than the FRF in detecting nonlinearity. Furthermore, the object of this paper is to try and identify which modes couple in a nonlinear manner in order to reduce the number of candidate coupling terms, for a model, as much as possible. The bispectrum method has previously been applied to simple low-DOF systems with high
Coupling nonlinear Stokes and Darcy flow using mortar finite elements
Ervin, Vincent J.
2011-11-01
We study a system composed of a nonlinear Stokes flow in one subdomain coupled with a nonlinear porous medium flow in another subdomain. Special attention is paid to the mathematical consequence of the shear-dependent fluid viscosity for the Stokes flow and the velocity-dependent effective viscosity for the Darcy flow. Motivated by the physical setting, we consider the case where only flow rates are specified on the inflow and outflow boundaries in both subdomains. We recast the coupled Stokes-Darcy system as a reduced matching problem on the interface using a mortar space approach. We prove a number of properties of the nonlinear interface operator associated with the reduced problem, which directly yield the existence, uniqueness and regularity of a variational solution to the system. We further propose and analyze a numerical algorithm based on mortar finite elements for the interface problem and conforming finite elements for the subdomain problems. Optimal a priori error estimates are established for the interface and subdomain problems, and a number of compatibility conditions for the finite element spaces used are discussed. Numerical simulations are presented to illustrate the algorithm and to compare two treatments of the defective boundary conditions. © 2010 Published by Elsevier B.V. on behalf of IMACS.
Passivation and control of partially known SISO nonlinear systems via dynamic neural networks
Reyes-Reyes J.; yu W.; Poznyak A. S.
2000-01-01
In this paper, an adaptive technique is suggested to provide the passivity property for a class of partially known SISO nonlinear systems. A simple Dynamic Neural Network (DNN), containing only two neurons and without any hidden-layers, is used to identify the unknown nonlinear system. By means of a Lyapunov-like analysis the new learning law for this DNN, guarantying both successful identification and passivation effects, is derived. Based on this adaptive DNN model, an adaptive feedback con...
A Maple Package for the Painlevé Test of Nonlinear Partial Differential Equations
Institute of Scientific and Technical Information of China (English)
徐桂琼; 李志斌
2003-01-01
A Maple package, named PLtest, is presented to study whether or not nonlinear partial differential equations the standard WTC algorithm and the Kruskal simplification algorithm. Therefore, we not only study whether the given PDEs pass the test or not, but also obtain its truncated expansion form related to some integrability properties. Several well-known nonlinear models with physical interests illustrate the effectiveness of this package.
Analysis of boundary layer flow over a porous nonlinearly stretching sheet with partial slip at
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Swati Mukhopadhyay
2013-12-01
Full Text Available The boundary layer flow of a viscous incompressible fluid toward a porous nonlinearly stretching sheet is considered in this analysis. Velocity slip is considered instead of no-slip condition at the boundary. Similarity transformations are used to convert the partial differential equation corresponding to the momentum equation into nonlinear ordinary differential equation. Numerical solution of this equation is obtained by shooting method. It is found that the horizontal velocity decreases with increasing slip parameter.
Nonlinear electrodynamics coupled to teleparallel theory of gravity
Institute of Scientific and Technical Information of China (English)
Gamal G. L. Nashed
2011-01-01
Using nonlinear electrodynamics coupled to teleparallel theory of gravity, regular charged spherically symmetric solutions are obtained. The nonlinear theory is reduced to the Maxwell one in the weak limit and the solutions correspond to charged spacetimes. One of the obtained solutions contains an arbitrary function which we call general solution since we can generate from it the other solutions. The metric associated with these spacetimes is the same, i.e., regular charged static spherically symmetric black hole. In calculating the energy content of the general solution using the gravitational energy-momentum within the framework of the teleparallel geometry, we find that the resulting form depends on the arbitrary function. Using the regularized expression of the gravitational energy-momentum we obtain the value of energy.
Nonlinear localized flatband modes with spin-orbit coupling
Gligorić, G; Hadžievski, Lj; Flach, S; Malomed, B
2016-01-01
We report the coexistence and properties of stable compact localized states (CLSs) and discrete solitons (DSs) for nonlinear spinor waves on a flatband network with spin-orbit coupling (SOC). The system can be implemented by means of a binary Bose-Einstein condensate loaded in the corresponding optical lattice. In the linear limit, the SOC opens a minigap between flat and dispersive bands in the system's bandgap structure, and preserves the existence of CLSs at the flatband frequency, simultaneously lowering their symmetry. Adding onsite cubic nonlinearity, the CLSs persist and remain available in an exact analytical form, with frequencies which are smoothly tuned into the minigap. Inside of the minigap, the CLS and DS families are stable in narrow areas adjacent to the FB. Deep inside the semi-infinite gap, both the CLSs and DSs are stable too.
Rotating Dilaton Black Strings Coupled to Exponential Nonlinear Electrodynamics
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Ahmad Sheykhi
2014-01-01
Full Text Available We construct a new class of charged rotating black string solutions coupled to dilaton and exponential nonlinear electrodynamic fields with cylindrical or toroidal horizons in the presence of a Liouville-type potential for the dilaton field. Due to the presence of the dilaton field, the asymptotic behaviors of these solutions are neither flat nor (AdS. We analyze the physical properties of the solutions in detail. We compute the conserved and thermodynamic quantities of the solutions and verify the first law of thermodynamics on the black string horizon. When the nonlinear parameter β2 goes to infinity, our results reduce to those of black string solutions in Einstein-Maxwell-dilaton gravity.
Unconventional Hamilton-type variational principles for nonlinear coupled thermoelastodynamics
Institute of Scientific and Technical Information of China (English)
罗恩; 邝君尚; 黄伟江; 罗志国
2002-01-01
According to the basic idea of classical yin-yang complementarity and modem dual-com plementarity, in a simple and unified new way proposed by Luo, the unconventional Hamilton-type vari ational principles for geometrically nonlinear coupled thermoelastodynamics can be established system atically. The new unconventional Hamilton-type variational principle can fully characterize the initia boundary-value problem of this dynamics. In this paper, an important integral relation is given, which can be considered as the expression of the generalized principle of virtual work for geometrically nonlin ear coupled thermodynamics. Based on this relation, it is possible not only to obtain the principle of vir tual work in geometrically nonlinear coupled thermodynamics, but also to derive systematically the complementary functionals for eight-field, six-field, four-field and two-field unconventional Hamilton type variational principles by the generalized Legendre transformations given in this paper. Further more, with this approach, the intrinsic relationship among various principles can be explained clearly.
Instability of coupled geostrophic density fronts and its nonlinear evolution
Scherer, Emilie; Zeitlin, Vladimir
Instability of coupled density fronts, and its fully nonlinear evolution are studied within the idealized reduced-gravity rotating shallow-water model. By using the collocation method, we benchmark the classical stability results on zero potential vorticity (PV) fronts and generalize them to non-zero PV fronts. In both cases, we find a series of instability zones intertwined with the stability regions along the along-front wavenumber axis, the most unstable modes being long wave. We then study the nonlinear evolution of the unstable modes with the help of a high-resolution well-balanced finite-volume numerical scheme by initializing it with the unstable modes found from the linear stability analysis. The most unstable long-wave mode evolves as follows: after a couple of inertial periods, the coupled fronts are pinched at some location and a series of weakly connected co-rotating elliptic anticyclonic vortices is formed, thus totally changing the character of the flow. The characteristics of these vortices are close to known rodon lens solutions. The shorter-wave unstable modes from the next instability zones are strongly concentrated in the frontal regions, have sharp gradients, and are saturated owing to dissipation without qualitatively changing the flow pattern.
Nonlinear grid error effects on numerical solution of partial differential equations
Dey, S. K.
1980-01-01
Finite difference solutions of nonlinear partial differential equations require discretizations and consequently grid errors are generated. These errors strongly affect stability and convergence properties of difference models. Previously such errors were analyzed by linearizing the difference equations for solutions. Properties of mappings of decadence were used to analyze nonlinear instabilities. Such an analysis is directly affected by initial/boundary conditions. An algorithm was developed, applied to nonlinear Burgers equations, and verified computationally. A preliminary test shows that Navier-Stokes equations may be treated similarly.
Passivation and control of partially known SISO nonlinear systems via dynamic neural networks
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Reyes-Reyes J.
2000-01-01
Full Text Available In this paper, an adaptive technique is suggested to provide the passivity property for a class of partially known SISO nonlinear systems. A simple Dynamic Neural Network (DNN, containing only two neurons and without any hidden-layers, is used to identify the unknown nonlinear system. By means of a Lyapunov-like analysis the new learning law for this DNN, guarantying both successful identification and passivation effects, is derived. Based on this adaptive DNN model, an adaptive feedback controller, serving for wide class of nonlinear systems with an a priori incomplete model description, is designed. Two typical examples illustrate the effectiveness of the suggested approach.
Variational iteration method for solving non-linear partial differential equations
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Hemeda, A.A. [Department of Mathematics, Faculty of Science, University of Tanta, Tanta (Egypt)], E-mail: aahemeda@yahoo.com
2009-02-15
In this paper, we shall use the variational iteration method to solve some problems of non-linear partial differential equations (PDEs) such as the combined KdV-MKdV equation and Camassa-Holm equation. The variational iteration method is superior than the other non-linear methods, such as the perturbation methods where this method does not depend on small parameters, such that it can fined wide application in non-linear problems without linearization or small perturbation. In this method, the problems are initially approximated with possible unknowns, then a correction functional is constructed by a general Lagrange multiplier, which can be identified optimally via the variational theory.
Modeling Solution of Nonlinear Dispersive Partial Differential Equations using the Marker Method
Energy Technology Data Exchange (ETDEWEB)
Jerome L.V. Lewandowski
2005-01-25
A new method for the solution of nonlinear dispersive partial differential equations is described. The marker method relies on the definition of a convective field associated with the underlying partial differential equation; the information about the approximate solution is associated with the response of an ensemble of markers to this convective field. Some key aspects of the method, such as the selection of the shape function and the initial loading, are discussed in some details.
Periodic Partial Extinction Regime in Acoustically Coupled Fuel Droplet Combustion
Plascencia Quiroz, Miguel; Bennewitz, John; Vargas, Andres; Sim, Hyung Sub; Smith, Owen; Karagozian, Ann
2016-11-01
This experimental study investigates the response of burning liquid fuel droplets exposed to standing acoustic waves, extending prior studies quantifying mean and temporal flame response to moderate acoustic excitation. This investigation explores alternative fuels exposed to a range of acoustic forcing conditions (frequencies and amplitudes), with a focus on ethanol and JP-8. Three fundamental flame regimes are observed: sustained oscillatory combustion, periodic partial extinction and reignition (PPER), and full extinction. Phase-locked OH* chemiluminescence imaging and local temporal pressure measurements allow quantification of the combustion-acoustic coupling through the local Rayleigh index G. As expected, PPER produces negative G values, despite having clear flame oscillations. PPER is observed to occur at low-frequency, high amplitude excitation, where the acoustic time scales are large compared with kinetic/reaction times scales for diffusion-limited combustion processes. These quantitative differences in behavior are determined to depend on localized fluid mechanical strain created by the acoustic excitation as well as reaction kinetics. Supported by AFOSR Grant FA9550-15-1-0339.
Nonlinear thermoelectric properties of molecular junctions with vibrational coupling
DEFF Research Database (Denmark)
Leijnse, Martin Christian; Wegewijs, M. R.; Flensberg, Karsten
2010-01-01
We present a detailed study of the nonlinear thermoelectric properties of a molecular junction, represented by a dissipative Anderson-Holstein model. A single-orbital level with strong Coulomb interaction is coupled to a localized vibrational mode and we account for both electron and phonon...... exchange with both electrodes, investigating how these contribute to the heat and charge transports. We calculate the efficiency and power output of the device operated as a heat to electric power converter in the regime of weak tunnel coupling and phonon exchange rate and identify the optimal operating...... conditions, which are found to be qualitatively changed by the presence of the vibrational mode. Based on this study of a generic model system, we discuss the desirable properties of molecular junctions for thermoelectric applications....
Nonlinear partial least squares with Hellinger distance for nonlinear process monitoring
Harrou, Fouzi
2017-02-16
This paper proposes an efficient data-based anomaly detection method that can be used for monitoring nonlinear processes. The proposed method merges advantages of nonlinear projection to latent structures (NLPLS) modeling and those of Hellinger distance (HD) metric to identify abnormal changes in highly correlated multivariate data. Specifically, the HD is used to quantify the dissimilarity between current NLPLS-based residual and reference probability distributions. The performances of the developed anomaly detection using NLPLS-based HD technique is illustrated using simulated plug flow reactor data.
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.
Institute of Scientific and Technical Information of China (English)
WANG Peng-Zhou; ZHANG Shun-Li
2008-01-01
We present basic theory of variable separation for (1 + 1)-dimensional nonlinear evolution equations with mixed partial derivatives. As an application, we classify equations uxt = A(u, ux)uxxx + B(u, ux) that admits derivative-dependent functional separable solutions (DDFSSs) and illustrate how to construct those DDFSSs with some examples.
Banks, H. T.; Kunisch, K.
1982-01-01
Approximation results from linear semigroup theory are used to develop a general framework for convergence of approximation schemes in parameter estimation and optimal control problems for nonlinear partial differential equations. These ideas are used to establish theoretical convergence results for parameter identification using modal (eigenfunction) approximation techniques. Results from numerical investigations of these schemes for both hyperbolic and parabolic systems are given.
Nonlinear perturbations of systems of partial differential equations with constant coefficients
Directory of Open Access Journals (Sweden)
Carmen J. Vanegas
2000-01-01
Full Text Available In this article, we show the existence of solutions to boundary-value problems, consisting of nonlinear systems of partial differential equations with constant coefficients. For this purpose, we use the right inverse of an associated operator and a fix point argument. As illustrations, we apply this method to Helmholtz equations and to second order systems of elliptic equations.
Special Conditional Similarity Reduction Solutions for Two Nonlinear Partial Differential Equations
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
We present a method of special conditional similarity reduction solutions for nonlinear partial differential equations. As concrete examples of its application, we apply this method to the (2+1)-dimensional modified Broer-Kaup equations and the variable coefficient KdV-mKdV equation, which have extensive physics backgrounds, and obtain abundant exact solutions derived from some reduction equations.
A Class of Traveling Wave Solutions to Some Nonlinear Partial Differential Equations
Institute of Scientific and Technical Information of China (English)
BAI Cheng-Lin
2003-01-01
For the Noyes-Fields equations, two-dimensional hyperbolic equations of conversation laws, and theBurgers-KdV equation, a class of traveling wave solutions has been obtained by constructing appropriate functiontransformations. The main idea of solving the equations is that nonlinear partial differential equations are changed intosolving algebraic equations. This method has a wide-rangingpracticability.
A Class of Traveling Wave Solutions to Some Nonlinear Partial Differential Equations
Institute of Scientific and Technical Information of China (English)
BAICheng-Lin
2003-01-01
For the Noyes-Fields equations, two-dimenslonal hyperbolic equations of conversation laww and the Burgers-KdV equation, a class of travellng wave solutions has been obtained by constructhag appropriate function transformations. The main idea of solving the equations is that nonlinear partial differential equations are changed into solving algebraic equations. This method has a wide-ranging practicability.
Picone's identity for a system of first-order nonlinear partial differential equations
Directory of Open Access Journals (Sweden)
Jaroslav Jaros
2013-06-01
Full Text Available We established a Picone identity for systems of nonlinear partial differential equations of first-order. With the help of this formula, we obtain qualitative results such as an integral inequality of Wirtinger type and the existence of zeros for the first components of solutions in a given bounded domain.
Application of homotopy-perturbation to non-linear partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Cveticanin, L. [Faculty of Technical Sciences, 21000 Novi Sad, Trg D. Obradovica 6 (Serbia)], E-mail: cveticanin@uns.ns.ac.yu
2009-04-15
In this paper He's homotopy perturbation method has been adopted for solving non-linear partial differential equations. An approximate solution of the differential equation which describes the longitudinal vibration of a beam is obtained. The solution is compared with that found using the variational iteration method introduced by He. The difference between the two solutions is negligible.
Energy Technology Data Exchange (ETDEWEB)
Zhou Yubin; Wang Mingliang; Miao Tiande
2004-03-15
The periodic wave solutions for a class of nonlinear partial differential equations, including the Davey-Stewartson equations and the generalized Zakharov equations, are obtained by using the F-expansion method, which can be regarded as an overall generalization of the Jacobi elliptic function expansion method recently proposed. In the limit cases the solitary wave solutions of the equations are also obtained.
Directory of Open Access Journals (Sweden)
Yusuf Pandir
2012-01-01
Full Text Available We obtain the classification of exact solutions, including soliton, rational, and elliptic solutions, to the one-dimensional general improved Camassa Holm KP equation and KdV equation by the complete discrimination system for polynomial method. In discussion, we propose a more general trial equation method for nonlinear partial differential equations with generalized evolution.
Directory of Open Access Journals (Sweden)
Abaker. A. Hassaballa.
2015-10-01
Full Text Available - In recent years, many more of the numerical methods were used to solve a wide range of mathematical, physical, and engineering problems linear and nonlinear. This paper applies the homotopy perturbation method (HPM to find exact solution of partial differential equation with the Dirichlet and Neumann boundary conditions.
Directory of Open Access Journals (Sweden)
Qi Song
2013-01-01
Full Text Available This paper proposes a partial refactorization for faster nonlinear analysis based on sparse matrix solution, which is nowadays the default solution choice in finite element analysis and can solve finite element models up to millions degrees of freedom. Among various fill-in’s reducing strategies for sparse matrix solution, the graph partition is in general the best in terms of resultant fill-ins and floating-point operations and furthermore produces a particular graph of sparse matrix that prevents local change of entries from wide spreading in factorization. Based on this feature, an explicit partial triangular refactorization with local change is efficiently constructed with limited additional storage requirement in row-sparse storage scheme. The partial refactorization of the changed stiffness matrix inherits a big percentage of the original factor and is carried out only on partial factor entries. The proposed method provides a new possibility for faster nonlinear analysis and is mainly suitable for material nonlinear problems and optimization problems. Compared to full factorization, it can significantly reduce the factorization time and can make nonlinear analysis more efficient.
On the average uncertainty for systems with nonlinear coupling
Nelson, Kenric P.; Umarov, Sabir R.; Kon, Mark A.
2017-02-01
The increased uncertainty and complexity of nonlinear systems have motivated investigators to consider generalized approaches to defining an entropy function. New insights are achieved by defining the average uncertainty in the probability domain as a transformation of entropy functions. The Shannon entropy when transformed to the probability domain is the weighted geometric mean of the probabilities. For the exponential and Gaussian distributions, we show that the weighted geometric mean of the distribution is equal to the density of the distribution at the location plus the scale (i.e. at the width of the distribution). The average uncertainty is generalized via the weighted generalized mean, in which the moment is a function of the nonlinear source. Both the Rényi and Tsallis entropies transform to this definition of the generalized average uncertainty in the probability domain. For the generalized Pareto and Student's t-distributions, which are the maximum entropy distributions for these generalized entropies, the appropriate weighted generalized mean also equals the density of the distribution at the location plus scale. A coupled entropy function is proposed, which is equal to the normalized Tsallis entropy divided by one plus the coupling.
Experiments on oscillator ensembles with global nonlinear coupling
Temirbayev, Amirkhan A.; Zhanabaev, Zeinulla Zh.; Tarasov, Stanislav B.; Ponomarenko, Vladimir I.; Rosenblum, Michael
2012-01-01
We experimentally analyze collective dynamics of a population of 20 electronic Wien-bridge limit-cycle oscillators with a nonlinear phase-shifting unit in the global feedback loop. With an increase in the coupling strength we first observe formation and then destruction of a synchronous cluster, so that the dependence of the order parameter on the coupling strength is not monotonic. After destruction of the cluster the ensemble remains nevertheless coherent, i.e., it exhibits an oscillatory collective mode (mean field). We show that the system is now in a self-organized quasiperiodic state, predicted in Rosenblum and Pikovsky [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.98.064101 98, 064101 (2007)]. In this state, frequencies of all oscillators are smaller than the frequency of the mean field, so that the oscillators are not locked to the mean field they create and their dynamics is quasiperiodic. Without a nonlinear phase-shifting unit, the system exhibits a standard Kuramoto-like transition to a fully synchronous state. We demonstrate a good correspondence between the experiment and previously developed theory. We also propose a simple measure which characterizes the macroscopic incoherence-coherence transition in a finite-size ensemble.
Fokas, A. S.; De Lillo, S.
2014-03-01
So-called inverse scattering provides a powerful method for analyzing the initial value problem for a large class of nonlinear evolution partial differential equations which are called integrable. In the late 1990s, the first author, motivated by inverse scattering, introduced a new method for analyzing boundary value problems. This method provides a unified treatment for linear, linearizable and integrable nonlinear partial differential equations. Here, this method, which is often referred to as the unified transform, is illustrated for the following concrete cases: the heat equation on the half-line; the nonlinear Schrödinger equation on the half-line; Burger's equation on the half-line; and Burger's equation on a moving boundary.
Tang, Chen; Lu, Wenjing; Chen, Song; Zhang, Zhen; Li, Botao; Wang, Wenping; Han, Lin
2007-10-20
We extend and refine previous work [Appl. Opt. 46, 2907 (2007)]. Combining the coupled nonlinear partial differential equations (PDEs) denoising model with the ordinary differential equations enhancement method, we propose the new denoising and enhancing model for electronic speckle pattern interferometry (ESPI) fringe patterns. Meanwhile, we propose the backpropagation neural networks (BPNN) method to obtain unwrapped phase values based on a skeleton map instead of traditional interpolations. We test the introduced methods on the computer-simulated speckle ESPI fringe patterns and experimentally obtained fringe pattern, respectively. The experimental results show that the coupled nonlinear PDEs denoising model is capable of effectively removing noise, and the unwrapped phase values obtained by the BPNN method are much more accurate than those obtained by the well-known traditional interpolation. In addition, the accuracy of the BPNN method is adjustable by changing the parameters of networks such as the number of neurons.
Stochastic optimal control of partially observable nonlinear quasi-integrable Hamiltonian systems
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
The stochastic optimal control of partially observable nonlinear quasi-integrable Hamiltonian systems is investigated. First, the stochastic optimal control problem of a partially observable nonlinear quasi-integrable Hamiltonian system is converted into that of a completely observable linear system based on a theorem due to Charalambous and Elliot. Then, the converted stochastic optimal control problem is solved by applying the stochastic averaging method and the stochastic dynamical programming principle. The response of the controlled quasi Hamiltonian system is predicted by solving the averaged Fokker-Planck-Kolmogorov equation and the Riccati equation for the estimated error of system states. As an example to illustrate the procedure and effectiveness of the proposed method, the stochastic optimal control problem of a partially observable two-degree-of-freedom quasi-integrable Hamiltonian system is worked out in detail.
Coupled Nonlinear Schr\\"{o}dinger equation and Toda equation (the Root of Integrability)
Hisakado, Masato
1997-01-01
We consider the relation between the discrete coupled nonlinear Schr\\"{o}dinger equation and Toda equation. Introducing complex times we can show the intergability of the discrete coupled nonlinear Schr\\"{o}dinger equation. In the same way we can show the integrability in coupled case of dark and bright equations. Using this method we obtain several integrable equations.
Nonlinear Spline Kernel-based Partial Least Squares Regression Method and Its Application
Institute of Scientific and Technical Information of China (English)
JIA Jin-ming; WEN Xiang-jun
2008-01-01
Inspired by the traditional Wold's nonlinear PLS algorithm comprises of NIPALS approach and a spline inner function model,a novel nonlinear partial least squares algorithm based on spline kernel(named SK-PLS)is proposed for nonlinear modeling in the presence of multicollinearity.Based on the iuner-product kernel spanned by the spline basis functions with infinite numher of nodes,this method firstly maps the input data into a high dimensional feature space,and then calculates a linear PLS model with reformed NIPALS procedure in the feature space and gives a unified framework of traditional PLS"kernel"algorithms in consequence.The linear PLS in the feature space corresponds to a nonlinear PLS in the original input (primal)space.The good approximating property of spline kernel function enhances the generalization ability of the novel model,and two numerical experiments are given to illustrate the feasibility of the proposed method.
Lenci, Stefano; Rega, Giuseppe
2016-06-01
The nonlinear free oscillations of a straight planar Timoshenko beam are investigated analytically by means of the asymptotic development method. Attention is focused for the first time, to the best of our knowledge, on the nonlinear coupling between the axial and the transversal oscillations of the beam, which are decoupled in the linear regime. The existence of coupled and uncoupled motion is discussed. Furthermore, the softening versus hardening nature of the backbone curves is investigated in depth. The results are summarized by means of behaviour charts that illustrate the different possible classes of motion in the parameter space. New, and partially unexpected, phenomena, such as the changing of the nonlinear behaviour from softening to hardening by adding/removing the axial vibrations, are highlighted.
Coupled nonlinear aeroelasticity and flight dynamics of fully flexible aircraft
Su, Weihua
This dissertation introduces an approach to effectively model and analyze the coupled nonlinear aeroelasticity and flight dynamics of highly flexible aircraft. A reduced-order, nonlinear, strain-based finite element framework is used, which is capable of assessing the fundamental impact of structural nonlinear effects in preliminary vehicle design and control synthesis. The cross-sectional stiffness and inertia properties of the wings are calculated along the wing span, and then incorporated into the one-dimensional nonlinear beam formulation. Finite-state unsteady subsonic aerodynamics is used to compute airloads along lifting surfaces. Flight dynamic equations are then introduced to complete the aeroelastic/flight dynamic system equations of motion. Instead of merely considering the flexibility of the wings, the current work allows all members of the vehicle to be flexible. Due to their characteristics of being slender structures, the wings, tail, and fuselage of highly flexible aircraft can be modeled as beams undergoing three dimensional displacements and rotations. New kinematic relationships are developed to handle the split beam systems, such that fully flexible vehicles can be effectively modeled within the existing framework. Different aircraft configurations are modeled and studied, including Single-Wing, Joined-Wing, Blended-Wing-Body, and Flying-Wing configurations. The Lagrange Multiplier Method is applied to model the nodal displacement constraints at the joint locations. Based on the proposed models, roll response and stability studies are conducted on fully flexible and rigidized models. The impacts of the flexibility of different vehicle members on flutter with rigid body motion constraints, flutter in free flight condition, and roll maneuver performance are presented. Also, the static stability of the compressive member of the Joined-Wing configuration is studied. A spatially-distributed discrete gust model is incorporated into the time simulation
Institute of Scientific and Technical Information of China (English)
2008-01-01
Using functional derivative technique in quantum field theory, the algebraic dy-namics approach for solution of ordinary differential evolution equations was gen-eralized to treat partial differential evolution equations. The partial differential evo-lution equations were lifted to the corresponding functional partial differential equations in functional space by introducing the time translation operator. The functional partial differential evolution equations were solved by algebraic dynam-ics. The algebraic dynamics solutions are analytical in Taylor series in terms of both initial functions and time. Based on the exact analytical solutions, a new nu-merical algorithm—algebraic dynamics algorithm was proposed for partial differ-ential evolution equations. The difficulty of and the way out for the algorithm were discussed. The application of the approach to and computer numerical experi-ments on the nonlinear Burgers equation and meteorological advection equation indicate that the algebraic dynamics approach and algebraic dynamics algorithm are effective to the solution of nonlinear partial differential evolution equations both analytically and numerically.
Institute of Scientific and Technical Information of China (English)
WANG Shundin; ZHANG Hua
2008-01-01
Using functional derivative technique In quantum field theory,the algebraic dy-namics approach for solution of ordinary differential evolution equations was gen-eralized to treat partial differential evolution equations.The partial differential evo-lution equations were lifted to the corresponding functional partial differential equations in functional space by Introducing the time translation operator.The functional partial differential evolution equations were solved by algebraic dynam-ics.The algebraic dynamics solutions are analytical In Taylor series In terms of both initial functions and time.Based on the exact analytical solutions,a new nu-merical algorithm-algebraic dynamics algorithm was proposed for partial differ-ential evolution equations.The difficulty of and the way out for the algorithm were discussed.The application of the approach to and computer numerical experi-ments on the nonlinear Burgers equation and meteorological advection equation indicate that the algebraic dynamics approach and algebraic dynamics algorithm are effective to the solution of nonlinear partial differential evolution equations both analytically and numerically.
Yang, T C
2014-02-01
This paper applies the mode coupling equation to calculate the mode-coupling matrix for nonlinear internal waves appearing as a train of solitons. The calculation is applied to an individual soliton up to second order expansion in sound speed perturbation in the Dyson series. The expansion is valid so long as the fractional sound speed change due to a single soliton, integrated over range and depth, times the wavenumber is smaller than unity. Scattering between the solitons are included by coupling the mode coupling matrices between the solitons. Acoustic fields calculated using this mode-coupling matrix formulation are compared with that obtained using a parabolic equation (PE) code. The results agree very well in terms of the depth integrated acoustic energy at the receivers for moving solitary internal waves. The advantages of using the proposed approach are: (1) The effects of mode coupling can be studied as a function of range and time as the solitons travel along the propagation path, and (2) it allows speedy calculations of sound propagation through a packet or packets of solitons saving orders of magnitude computations compared with the PE code. The mode coupling theory is applied to at-sea data to illustrate the underlying physics.
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
In this paper, we study the regularity of solutions of nonlinear stochastic partial differential equations (SPDEs) with multiplicative noises in the framework of Hilbert scales. Then we apply our abstract result to several typical nonlinear SPDEs such as stochastic Burgers and Ginzburg-Landau equations on the real line, stochastic 2D Navier-Stokes equations (SNSEs) in the whole space and a stochastic tamed 3D Navier-Stokes equation in the whole space, and obtain the existence of their smooth solutions respectively. In particular, we also get the existence of local smooth solutions for 3D SNSEs.
Exact solutions of some nonlinear partial differential equations using functional variable method
Indian Academy of Sciences (India)
A Nazarzadeh; M Eslami; M Mirzazadeh
2013-08-01
The functional variable method is a powerful solution method for obtaining exact solutions of some nonlinear partial differential equations. In this paper, the functional variable method is used to establish exact solutions of the generalized forms of Klein–Gordon equation, the (2 + 1)-dimensional Camassa–Holm Kadomtsev–Petviashvili equation and the higher-order nonlinear Schrödinger equation. By using this useful method, we found some exact solutions of the above-mentioned equations. The obtained solutions include solitary wave solutions, periodic wave solutions and combined formal solutions. It is shown that the proposed method is effective and general.
Grothaus, Martin
2012-01-01
In this paper a length-conserving numerical scheme for a nonlinear fourth order system of partial differential algebraic equations arising in technical textile industry is studied. Applying a semidiscretization in time, the resulting sequence of nonlinear elliptic systems with algebraic constraint is reformulated as constrained optimization problems in a Hilbert space setting that admit a solution at each time level. Stability and convergence of the scheme are proved. The numerical realization is performed by projected gradient methods on finite element spaces which determine the computational effort and approximation quality of the algorithm. Simulation results are presented and discussed in view of the application of an elastic inextensible fiber motion.
Energy Technology Data Exchange (ETDEWEB)
Ravi Kanth, A.S.V. [Applied Mathematics Division, School of Science and Humanities, V.I.T. University, Vellore-632 014, Tamil Nadu (India)], E-mail: asvravikanth@yahoo.com; Aruna, K. [Applied Mathematics Division, School of Science and Humanities, V.I.T. University, Vellore-632 014, Tamil Nadu (India)
2008-11-17
In this Letter, we propose a reliable algorithm to develop exact and approximate solutions for the linear and non-linear systems of partial differential equations. The approach rest mainly on two-dimensional differential transform method which is one of the approximate methods. The method can easily be applied to many linear and non-linear problems and is capable of reducing the size of computational work. Exact solutions can also be achieved by the known forms of the series solutions. Several illustrative examples are given to demonstrate the effectiveness of the present method.
Simple equation method for nonlinear partial differential equations and its applications
Directory of Open Access Journals (Sweden)
Taher A. Nofal
2016-04-01
Full Text Available In this article, we focus on the exact solution of the some nonlinear partial differential equations (NLPDEs such as, Kodomtsev–Petviashvili (KP equation, the (2 + 1-dimensional breaking soliton equation and the modified generalized Vakhnenko equation by using the simple equation method. In the simple equation method the trial condition is the Bernoulli equation or the Riccati equation. It has been shown that the method provides a powerful mathematical tool for solving nonlinear wave equations in mathematical physics and engineering problems.
Elementary Superconductivity in Nonlinear Electrodynamics Coupled to Gravity
Dymnikova, Irina
2015-01-01
Source-free equations of nonlinear electrodynamics minimally coupled to gravity admit regular axially symmetric asymptotically Kerr-Newman solutions which describe charged rotating black holes and electromagnetic spinning solitons (lumps). Asymptotic analysis of solutions shows, for both black holes and solitons, the existence of de Sitter vacuum interior which has the properties of a perfect conductor and ideal diamagnetic and displays superconducting behaviour which can be responsible for practically unlimited life time of an object. Superconducting current flows on the equatorial ring replacing the Kerr ring singularity of the Kerr-Newman geometry. Interior de Sitter vacuum supplies the electron with the finite positive electromagnetic mass related the interior de Sitter vacuum of the electroweak scale and to breaking of space-time symmetry, which allows to explain the mass-square differences for neutrino and the appearance of the minimal length scale in the annihilation reaction $e^{+}e^{-}\\rightarrow\\gam...
Nonlinear Dynamic Reliability of Coupled Stay Cables and Bridge Tower
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
Nonlinear vibration can cause serious problems in long span cable-stayed bridges. When the internal resonance threshold is reached between the excitation frequency and natural frequency,large amplitudes occur in the cable. Based on the current situation of lacking corresponding constraint criteria, a model was presented for analyzing the dynamic reliability of coupling oscillation between the cable and tower in a cable-stayed bridge. First of all, in the case of cable sag, the d'Alembert principle is applied to studying the nonlinear dynamic behavior of the structure, and resonance failure interval of parametric oscillation is calculated accordingly. Then the dynamic reliability model is set up using the JC method. An application of this model has been developed for the preliminary design of one cable-stayed bridge located on Hai River in Tianjin, and time histories analysis as well as reliability indexes have been obtained. When frequency ratio between the cable and tower is approaching 1∶2, the reliability index is 0.98, indicating high failure probability. And this is consistent with theoretical derivation and experimental results in reference. This model, which is capable of computing the reliability index of resonance failure, provides theoretical basis for the establishment of corresponding rule.
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.
Fem Formulation of Coupled Partial Differential Equations for Heat Transfer
Ameer Ahamad, N.; Soudagar, Manzoor Elahi M.; Kamangar, Sarfaraz; Anjum Badruddin, Irfan
2017-08-01
Heat Transfer in any field plays an important role for transfer of energy from one region to another region. The heat transfer in porous medium can be simulated with the help of two partial differential equations. These equations need an alternate and relatively easy method due to complexity of the phenomenon involved. This article is dedicated to discuss the finite element formulation of heat transfer in porous medium in Cartesian coordinates. A triangular element is considered to discretize the governing partial differential equations and matrix equations are developed for 3 nodes of element. Iterative approach is used for the two sets of matrix equations involved representing two partial differential equations.
Kannan, Rohit; Tangirala, Arun K.
2014-06-01
Identification of directional influences in multivariate systems is of prime importance in several applications of engineering and sciences such as plant topology reconstruction, fault detection and diagnosis, and neurosciences. A spectrum of related directionality measures, ranging from linear measures such as partial directed coherence (PDC) to nonlinear measures such as transfer entropy, have emerged over the past two decades. The PDC-based technique is simple and effective, but being a linear directionality measure has limited applicability. On the other hand, transfer entropy, despite being a robust nonlinear measure, is computationally intensive and practically implementable only for bivariate processes. The objective of this work is to develop a nonlinear directionality measure, termed as KPDC, that possesses the simplicity of PDC but is still applicable to nonlinear processes. The technique is founded on a nonlinear measure called correntropy, a recently proposed generalized correlation measure. The proposed method is equivalent to constructing PDC in a kernel space where the PDC is estimated using a vector autoregressive model built on correntropy. A consistent estimator of the KPDC is developed and important theoretical results are established. A permutation scheme combined with the sequential Bonferroni procedure is proposed for testing hypothesis on absence of causality. It is demonstrated through several case studies that the proposed methodology effectively detects Granger causality in nonlinear processes.
Ming, Yi; Li, Hui-Min; Ding, Ze-Jun
2016-03-01
Thermal rectification and negative differential thermal conductance were realized in harmonic chains in this work. We used the generalized Caldeira-Leggett model to study the heat flow. In contrast to most previous studies considering only the linear system-bath coupling, we considered the nonlinear system-bath coupling based on recent experiment [Eichler et al., Nat. Nanotech. 6, 339 (2011)]. When the linear coupling constant is weak, the multiphonon processes induced by the nonlinear coupling allow more phonons transport across the system-bath interface and hence the heat current is enhanced. Consequently, thermal rectification and negative differential thermal conductance are achieved when the nonlinear couplings are asymmetric. However, when the linear coupling constant is strong, the umklapp processes dominate the multiphonon processes. Nonlinear coupling suppresses the heat current. Thermal rectification is also achieved. But the direction of rectification is reversed compared to the results of weak linear coupling constant.
Ming, Yi; Li, Hui-Min; Ding, Ze-Jun
2016-03-01
Thermal rectification and negative differential thermal conductance were realized in harmonic chains in this work. We used the generalized Caldeira-Leggett model to study the heat flow. In contrast to most previous studies considering only the linear system-bath coupling, we considered the nonlinear system-bath coupling based on recent experiment [Eichler et al., Nat. Nanotech. 6, 339 (2011), 10.1038/nnano.2011.71]. When the linear coupling constant is weak, the multiphonon processes induced by the nonlinear coupling allow more phonons transport across the system-bath interface and hence the heat current is enhanced. Consequently, thermal rectification and negative differential thermal conductance are achieved when the nonlinear couplings are asymmetric. However, when the linear coupling constant is strong, the umklapp processes dominate the multiphonon processes. Nonlinear coupling suppresses the heat current. Thermal rectification is also achieved. But the direction of rectification is reversed compared to the results of weak linear coupling constant.
Directory of Open Access Journals (Sweden)
Jialin Wang
2013-01-01
Full Text Available This paper is concerned with partial regularity to nonlinear subelliptic systems with Dini continuous coefficients under quadratic controllable growth conditions in the Heisenberg group ℍn. Based on a generalization of the technique of -harmonic approximation introduced by Duzaar and Steffen, partial regularity to the sub-elliptic system is established in the Heisenberg group. Our result is optimal in the sense that in the case of Hölder continuous coefficients we establish the optimal Hölder exponent for the horizontal gradients of the weak solution on its regular set.
On stochastic optimal control of partially observable nonlinear quasi Hamiltonian systems
Institute of Scientific and Technical Information of China (English)
朱位秋; 应祖光
2004-01-01
A stochastic optimal control strategy for partially observable nonlinear quasi Hamiltonian systems is proposed.The optimal control forces consist of two parts. The first part is determined by the conditions under which the stochastic optimal control problem of a partially observable nonlinear system is converted into that of a completely observable linear system. The second part is determined by solving the dynamical programming equation derived by applying the stochastic averaging method and stochastic dynamical programming principle to the completely observable linear control system. The response of the optimally controlled quasi Hamiltonian system is predicted by solving the averaged Fokker-Planck-Kolmogorov equation associated with the optimally controlled completely observable linear system and solving the Riccati equation for the estimated error of system states. An example is given to illustrate the procedure and effectiveness of the proposed control strategy.
Institute of Scientific and Technical Information of China (English)
朱位秋; 应祖光
2004-01-01
A stochastic optimal control strategy for partially observable nonlinear quasi Hamiltonian systems is proposed. The optimal control forces consist of two parts. The first part is determined by the conditions under which the stochastic optimal control problem of a partially observable nonlinear system is converted into that of a completely observable linear system. The second part is determined by solving the dynamical programming equation derived by applying the stochastic averaging method and stochastic dynamical programming principle to the completely observable linear control system. The response of the optimally controlled quasi Hamiltonian system is predicted by solving the averaged Fokker-Planck-Kolmogorov equation associated with the optimally controlled completely observable linear system and solving the Riccati equation for the estimated error of system states. An example is given to illustrate the procedure and effectiveness of the proposed control strategy.
Coupled-Channels Partial-Wave Analysis of Kaon Photoproduction
Scholten, Olaf
2010-01-01
The K-matrix formalism is offering a very realistic approach to arrive at a description of meson-nucleon scattering that obeys unitarity since it takes into account the full coupled channels dynamics. Some examples of the importance of coupled channels effects are presented for photo-induced reactio
Coupled-Channels Partial-Wave Analysis of Kaon Photoproduction
Scholten, O.
2008-01-01
The K-matrix formalism is offering a very realistic approach to arrive at a description of meson-nucleon scattering that obeys unitarity since it takes into account the full coupled channels dynamics. Some examples of the importance of coupled channels effects are presented for photo-induced reactio
Institute of Scientific and Technical Information of China (English)
2009-01-01
The paper is concerned with a stochastic optimal control problem in which the controlled system is described by a fully coupled nonlinear forward-backward stochastic differential equation driven by a Brownian motion.It is required that all admissible control processes are adapted to a given subfiltration of the filtration generated by the underlying Brownian motion.For this type of partial information control,one sufficient(a verification theorem) and one necessary conditions of optimality are proved.The control domain need to be convex and the forward diffusion coefficient of the system can contain the control variable.
Institute of Scientific and Technical Information of China (English)
MENG QingXin
2009-01-01
The paper is concerned with a stochastic optimal control problem in which the controlled system is described by a fully coupled nonlinear forward-backward stochastic differential equation driven by a Brownian motion. It is required that all admissible control processes are adapted to a given subfiltration of the filtration generated by the underlying Brownian motion. For this type of partial information control, one sufficient (a verification theorem) and one necessary conditions of optimality are proved. The control domain need to be convex and the forward diffusion coefficient of the system can contain the control variable.
Directory of Open Access Journals (Sweden)
Manish Jain
2014-01-01
Full Text Available The object of this paper is to establish the existence and uniqueness of coupled fixed points under a (φ, ψ-contractive condition for mixed monotone operators in the setup of partially ordered metric spaces. Presented work generalizes the recent results of Berinde (2011, 2012 and weakens the contractive conditions involved in the well-known results of Bhaskar and Lakshmikantham (2006, and Luong and Thuan (2011. The effectiveness of our work is validated with the help of a suitable example. As an application, we give a result of existence and uniqueness for the solutions of a class of nonlinear integral equations.
An ansatz for solving nonlinear partial differential equations in mathematical physics.
Akbar, M Ali; Ali, Norhashidah Hj Mohd
2016-01-01
In this article, we introduce an ansatz involving exact traveling wave solutions to nonlinear partial differential equations. To obtain wave solutions using direct method, the choice of an appropriate ansatz is of great importance. We apply this ansatz to examine new and further general traveling wave solutions to the (1+1)-dimensional modified Benjamin-Bona-Mahony equation. Abundant traveling wave solutions are derived including solitons, singular solitons, periodic solutions and general solitary wave solutions. The solutions emphasize the nobility of this ansatz in providing distinct solutions to various tangible phenomena in nonlinear science and engineering. The ansatz could be more efficient tool to deal with higher dimensional nonlinear evolution equations which frequently arise in many real world physical problems.
Directory of Open Access Journals (Sweden)
Veyis Turut
2013-01-01
Full Text Available Two tecHniques were implemented, the Adomian decomposition method (ADM and multivariate Padé approximation (MPA, for solving nonlinear partial differential equations of fractional order. The fractional derivatives are described in Caputo sense. First, the fractional differential equation has been solved and converted to power series by Adomian decomposition method (ADM, then power series solution of fractional differential equation was put into multivariate Padé series. Finally, numerical results were compared and presented in tables and figures.
Energy Technology Data Exchange (ETDEWEB)
Zhang, Sheng [Department of Mathematics, Bohai University, Jinzhou 121000 (China)]. E-mail: zhshaeng@yahoo.com.cn; Xia, Tiecheng [Department of Mathematics, Bohai University, Jinzhou 121000 (China); Department of Mathematics, Shanghai University, Shanghai 200444 (China)
2007-04-09
In this Letter, a generalized new auxiliary equation method is proposed for constructing more general exact solutions of nonlinear partial differential equations. With the aid of symbolic computation, we choose the combined KdV-mKdV equation and the (2+1)-dimensional asymmetric Nizhnik-Novikov-Vesselov equations to illustrate the validity and advantages of the method. As a result, many new and more general exact solutions are obtained.
Homotopy perturbation method for nonlinear partial differential equations of fractional order
Energy Technology Data Exchange (ETDEWEB)
Momani, Shaher [Department of Mathematics and Physics, Qatar University (Qatar)]. E-mail: shahermm@yahoo.com; Odibat, Zaid [Prince Abdullah Bin Ghazi Faculty of Science and IT, Al-Balqa' Applied University, Salt (Jordan)]. E-mail: odibat@bau.edu.jo
2007-06-11
The aim of this Letter is to present an efficient and reliable treatment of the homotopy perturbation method (HPM) for nonlinear partial differential equations with fractional time derivative. The fractional derivative is described in the Caputo sense. The modified algorithm provides approximate solutions in the form of convergent series with easily computable components. The obtained results are in good agreement with the existing ones in open literature and it is shown that the technique introduced here is robust, efficient and easy to implement.
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.
An ansatz for solving nonlinear partial differential equations in mathematical physics
Akbar, M. Ali; Ali, Norhashidah Hj Mohd
2016-01-01
In this article, we introduce an ansatz involving exact traveling wave solutions to nonlinear partial differential equations. To obtain wave solutions using direct method, the choice of an appropriate ansatz is of great importance. We apply this ansatz to examine new and further general traveling wave solutions to the (1+1)-dimensional modified Benjamin–Bona–Mahony equation. Abundant traveling wave solutions are derived including solitons, singular solitons, periodic solutions and general sol...
Mattei, P.-O.; Ponçot, R.; Pachebat, M.; Côte, R.
2016-07-01
In order to control the sound radiation by a structure, one aims to control vibration of radiating modes of vibration using "Energy Pumping" also named "Targeted Energy Transfer". This principle is here applied to a simplified model of a double leaf panel. This model is made of two beams coupled by a spring. One of the beams is connected to a nonlinear absorber. This nonlinear absorber is made of a 3D-printed support on which is clamped a buckled thin small beam with a small mass fixed at its centre having two equilibrium positions. The experiments showed that, once attached onto a vibrating system to be controlled, under forced excitation of the primary system, the light bistable oscillator allows a reduction of structural vibration up to 10 dB for significant amplitude and frequency range around the first two vibration modes of the system.
Constructive role of sensors nonlinearities in the acquisition of partially polarized speckle images
Energy Technology Data Exchange (ETDEWEB)
Delahaies, Agnes; Rousseau, David; Chapeau-Blondeau, Francois [Laboratoire d' Ingenierie des Systemes Automatises (LISA), Universite d' Angers, 62 avenue Notre Dame du Lac, 49000 Angers (France); Gindre, Denis, E-mail: david.rousseau@univ-angers.f [Laboratoire des Proprietes Optiques des Materiaux et Applications (POMA), Universite d' Angers, 2 boulevard Lavoisier, 49000 Angers (France)
2010-02-01
We study the impact of the level of the speckle noise on data acquisition in a partially polarized coherent imaging system with the presence of a nonlinearity in the imaging sensor characteristic. In perfectly linear acquisition conditions, due to the essentially multiplicative action of the speckle, the image contrast is unchanged as the speckle noise level increases, and so it has no impact on the quality of the acquired images. On the contrary, in nonlinear conditions the acquisition is affected by the speckle noise level. However, this effect of the speckle is not always detrimental. We show that, in definite nonlinear conditions, there is usually an optimal level of the speckle noise that leads to a maximum quality of the acquired images. We theoretically analyze such nonlinear regimes with partially polarized speckled images. We specifically exhibit the existence of an optimal speckle noise level in the interesting case of images realized only by a depolarization contrast. Illustrations are given with a simple 1-bit hard limiter and binary images. Then, we propose and discuss as perspectives an experimental optical setup to confront theory and experiment.
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.
Nonlinear Super Integrable Couplings of Super Dirac Hierarchy and Its Super Hamiltonian Structures
Institute of Scientific and Technical Information of China (English)
尤福财
2012-01-01
We construct nonlinear super integrable couplings of the super integrable Dirac hierarchy based on an enlarged matrix Lie superalgebra. Then its super Hamiltonian structure is furnished by super trace identity. As its reduction, we gain the nonlinear integrable couplings of the classical integrable Dirac hierarchy.
Enhanced continuous-variable entanglement by a pair of nonlinearly coupled waveguides
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
We seek to analyze a three-level cascade laser with a pair of nonlinearly coupled waveguides inside the cavity. Applying the pertinent master equation, we investigate the squeezing and entanglement properties intracavity produced by our system. It is shown that with the help of nonlinearly coupled waveguides highly squeezed as well as macroscopic entangled light with high intensity can be achieved.
Inversion of geothermal heat flux in a thermomechanically coupled nonlinear Stokes ice sheet model
Zhu, Hongyu; Petra, Noemi; Stadler, Georg; Isaac, Tobin; Hughes, Thomas J. R.; Ghattas, Omar
2016-07-01
We address the inverse problem of inferring the basal geothermal heat flux from surface velocity observations using a steady-state thermomechanically coupled nonlinear Stokes ice flow model. This is a challenging inverse problem since the map from basal heat flux to surface velocity observables is indirect: the heat flux is a boundary condition for the thermal advection-diffusion equation, which couples to the nonlinear Stokes ice flow equations; together they determine the surface ice flow velocity. This multiphysics inverse problem is formulated as a nonlinear least-squares optimization problem with a cost functional that includes the data misfit between surface velocity observations and model predictions. A Tikhonov regularization term is added to render the problem well posed. We derive adjoint-based gradient and Hessian expressions for the resulting partial differential equation (PDE)-constrained optimization problem and propose an inexact Newton method for its solution. As a consequence of the Petrov-Galerkin discretization of the energy equation, we show that discretization and differentiation do not commute; that is, the order in which we discretize the cost functional and differentiate it affects the correctness of the gradient. Using two- and three-dimensional model problems, we study the prospects for and limitations of the inference of the geothermal heat flux field from surface velocity observations. The results show that the reconstruction improves as the noise level in the observations decreases and that short-wavelength variations in the geothermal heat flux are difficult to recover. We analyze the ill-posedness of the inverse problem as a function of the number of observations by examining the spectrum of the Hessian of the cost functional. Motivated by the popularity of operator-split or staggered solvers for forward multiphysics problems - i.e., those that drop two-way coupling terms to yield a one-way coupled forward Jacobian - we study the
Liu, Chuangye; Nguyen, Nghiem V.; Wang, Zhi-Qiang
2016-10-01
In this paper, we investigate the orbital stability of solitary-wave solutions for an m-coupled nonlinear Schrödinger system i /∂ ∂ t u j + /∂ 2 ∂ x 2 u j + ∑ i = 1 m b i j |" separators=" u i | 2 u j = 0 , j = 1 , … , m , where m ≥ 2, uj are complex-valued functions of (x, t) ∈ ℝ2, bjj ∈ ℝ, j = 1, 2, …, m, and bij, i ≠ j are positive coupling constants satisfying bij = bji. It will be shown that spatially synchronized solitary-wave solutions of the m-coupled nonlinear Schrödinger system exist and are orbitally stable. Here, by synchronized solutions we mean solutions in which the components are proportional to one another. Our results completely settle the question on the existence and stability of synchronized solitary waves for the m-coupled system while only partial results were known in the literature for the cases of m ≥ 3 heretofore. Furthermore, the conditions imposed on the symmetric matrix B = (bij) satisfied here are both sufficient and necessary for the m-coupled nonlinear Schrödinger system to admit synchronized ground-state solutions.
UV Nano-Lights: Nonlinear Quantum Dot-Plasmon Coupling
2014-08-01
method is also applicable to bare nanoparticles in polar solvents. 15. SUBJECT TERMS Quantum Dots, Nonlinear Optical Materials , Energy...TERMS Quantum Dots, Nonlinear Optical Materials , Energy Conservation, Up-conversion 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT
Nonlinear Coherent Directional Coupler: Coupled Mode Theory and BPM Simulation
National Research Council Canada - National Science Library
Kumbhakar, Dharmadas
2012-01-01
.... The coupling lengths derived from this simulation are compared with coupled mode theories. BPM results for the critical power follow the trend of the coupled mode theories, but it lies in between two coupled mode theories...
Nonlinear Debye screening in strongly-coupled plasmas
Sarmah, D; Tessarotto, M
2006-01-01
An ubiquitous property of plasmas is the so-called Debye shielding of the electrostatic potential. Important aspects of Debye screening concern, in particular, the investigation of non-linear charge screening effects taking place in strongly-coupled plasmas, that imply a reduction of the effective charge characterizing the Debye-H\\"{u}ckel potential. These effects are particularly relevant in dusty plasmas which are characterized by high-Z particles. The investigation of the effective interactions of these particles has attracted interest in recent years especially for numerical simulations. In this work we intend to analyze the consistency of the traditional mathematical model for the Debye screening. In particular, we intend to prove that the 3D Poisson equation involved in the DH model does not admit strong solutions. For this purpose a modified model is proposed which takes into account the effect of local plasma sheath (i.e., the local domain near test particles where the plasma must be considered discre...
Fast Simulation of Nonlinear Circuits with an Algorithm of Partial Matrix Elimination (PME)
Institute of Scientific and Technical Information of China (English)
CAI Xingjian; MAO Junfa; YANG Xiaoping; LI Zhengfan
2001-01-01
In this paper a theorem is proven thatthe contribution of any linear circuit elements to theadmittance matrix [Y] in the modified nodal admit-tance (MNA) equation of circuit analysis is invariantwith time.Based on this theorem a fast time-domainalgorithm of partial matrix elimination (PME) is de-veloped for simulation of high-speed nonlinear circuitswith interconnects.In PME the matrix [Y] is ar-ranged to consist of two submatrices.The lower sub-matrix that contains entries from only linear circuit el-ements is partially triangulated by Gauss eliminationfor the first-time-step transient analysis.At the fol-lowing time steps of transient analysis,Gauss elimina-tion is needed only for the upper submatrix containingcontributions of nonlinear circuit devices.Efficiencyanalysis of PME is given in detail,showing that it canaccelerate circuit simulation by a factor of at least 2.5for linear or lightly nonlinear circuits without employ-ing any numerical approximation.Moreover,PME isuseful for circuits debugging.
Nonlinear plasmonic dispersion and coupling analysis in the symmetric graphene sheets waveguide
Jiang, Xiangqian; Yuan, Haiming; Sun, Xiudong
2016-12-01
We study the nonlinear dispersion and coupling properties of the graphene-bounded dielectric slab waveguide at near-THz/THz frequency range, and then reveal the mechanism of symmetry breaking in nonlinear graphene waveguide. We analyze the influence of field intensity and chemical potential on dispersion relation, and find that the nonlinearity of graphene affects strongly the dispersion relation. As the chemical potential decreases, the dispersion properties change significantly. Antisymmetric and asymmetric branches disappear and only symmetric one remains. A nonlinear coupled mode theory is established to describe the dispersion relations and its variation, which agrees with the numerical results well. Using the nonlinear couple model we reveal the reason of occurrence of asymmetric mode in the nonlinear waveguide.
Filimonov, M. Yu.
2016-12-01
An analytical method for representation of solutions of nonlinear partial differential equations in the form of special series with recurrently computed coefficients is presented. The coefficients recurrent obtaining from linear differential equations is achieved by specificity of the considered equations. It turns out that due to the functional arbitrariness which possibly is contained in special series, one can prove global convergence of the constructed series to solution of considered nonlinear partial differential equations.
Noether, Partial Noether Operators and First Integrals for the Coupled Lane-Emden System
Muatjetjeja, Ben; Khalique, Chaudry
2010-01-01
Systems of Lane-Emden equations arise in the modelling of several physical phenomena, such as pattern formation, population evolution and chemical reactions. In this paper we construct Noether and partial Noether operators corresponding to a Lagrangian and a partial Lagrangian for a coupled Lane-Emden system. Then the first integrals with respect to Noether and partial Noether operators are obtained for the Lane-Emden system under consideration. We show that the first integrals for both the N...
Lu, Bin
2012-06-01
In this Letter, the fractional derivatives in the sense of modified Riemann-Liouville derivative and the Bäcklund transformation of fractional Riccati equation are employed for constructing the exact solutions of nonlinear fractional partial differential equations. The power of this manageable method is presented by applying it to several examples. This approach can also be applied to other nonlinear fractional differential equations.
Integrable nonlinear evolution partial differential equations in 4 + 2 and 3 + 1 dimensions.
Fokas, A S
2006-05-19
The derivation and solution of integrable nonlinear evolution partial differential equations in three spatial dimensions has been the holy grail in the field of integrability since the late 1970s. The celebrated Korteweg-de Vries and nonlinear Schrödinger equations, as well as the Kadomtsev-Petviashvili (KP) and Davey-Stewartson (DS) equations, are prototypical examples of integrable evolution equations in one and two spatial dimensions, respectively. Do there exist integrable analogs of these equations in three spatial dimensions? In what follows, I present a positive answer to this question. In particular, I first present integrable generalizations of the KP and DS equations, which are formulated in four spatial dimensions and which have the novelty that they involve complex time. I then impose the requirement of real time, which implies a reduction to three spatial dimensions. I also present a method of solution.
Directory of Open Access Journals (Sweden)
Ji Juan-Juan
2017-01-01
Full Text Available A table lookup method for solving nonlinear fractional partial differential equations (fPDEs is proposed in this paper. Looking up the corresponding tables, we can quickly obtain the exact analytical solutions of fPDEs by using this method. To illustrate the validity of the method, we apply it to construct the exact analytical solutions of four nonlinear fPDEs, namely, the time fractional simplified MCH equation, the space-time fractional combined KdV-mKdV equation, the (2+1-dimensional time fractional Zoomeron equation, and the space-time fractional ZKBBM equation. As a result, many new types of exact analytical solutions are obtained including triangular periodic solution, hyperbolic function solution, singular solution, multiple solitary wave solution, and Jacobi elliptic function solution.
Directory of Open Access Journals (Sweden)
S. S. Motsa
2014-01-01
Full Text Available This paper presents a new application of the homotopy analysis method (HAM for solving evolution equations described in terms of nonlinear partial differential equations (PDEs. The new approach, termed bivariate spectral homotopy analysis method (BISHAM, is based on the use of bivariate Lagrange interpolation in the so-called rule of solution expression of the HAM algorithm. The applicability of the new approach has been demonstrated by application on several examples of nonlinear evolution PDEs, namely, Fisher’s, Burgers-Fisher’s, Burger-Huxley’s, and Fitzhugh-Nagumo’s equations. Comparison with known exact results from literature has been used to confirm accuracy and effectiveness of the proposed method.
Directory of Open Access Journals (Sweden)
Yang Zhang
2013-01-01
Full Text Available We introduce a continuum modeling method to approximate a class of large wireless networks by nonlinear partial differential equations (PDEs. This method is based on the convergence of a sequence of underlying Markov chains of the network indexed by N, the number of nodes in the network. As N goes to infinity, the sequence converges to a continuum limit, which is the solution of a certain nonlinear PDE. We first describe PDE models for networks with uniformly located nodes and then generalize to networks with nonuniformly located, and possibly mobile, nodes. Based on the PDE models, we develop a method to control the transmissions in nonuniform networks so that the continuum limit is invariant under perturbations in node locations. This enables the networks to maintain stable global characteristics in the presence of varying node locations.
Partial and total actuator faults accommodation for input-affine nonlinear process plants.
Mihankhah, Amin; Salmasi, Farzad R; Salahshoor, Karim
2013-05-01
In this paper, a new fault-tolerant control system is proposed for input-affine nonlinear plants based on Model Reference Adaptive System (MRAS) structure. The proposed method has the capability to accommodate both partial and total actuator failures along with bounded external disturbances. In this methodology, the conventional MRAS control law is modified by augmenting two compensating terms. One of these terms is added to eliminate the nonlinear dynamic, while the other is reinforced to compensate the distractive effects of the total actuator faults and external disturbances. In addition, no Fault Detection and Diagnosis (FDD) unit is needed in the proposed method. Moreover, the control structure has good robustness capability against the parameter variation. The performance of this scheme is evaluated using a CSTR system and the results were satisfactory.
Nonlinear propagation of coupled electromagnetic waves in a circular cylindrical waveguide
Valovik, D. V.; Smol'kin, E. Yu.
2017-08-01
The problem of the propagation of coupled surface electromagnetic waves in a two-layer cylindrical circular waveguide filled with an inhomogeneous nonlinear medium is considered. A nonlinear coupled TE-TM wave is characterized by two (independent) frequencies ωe and ωm and two propagation constants {\\widehat γ _e} and {\\widehat γ _m}. The physical problem reduces to a nonlinear two-parameter eigenvalue problem for a system of nonlinear ordinary differential equations. The existence of eigenvalues ({\\widehat γ _e}, {\\widehat γ _m}) in proven and intervals of their localization are determined.
Coupled Particle Transport and Pattern Formation in a Nonlinear Leaky-Box Model
Barghouty, A. F.; El-Nemr, K. W.; Baird, J. K.
2009-01-01
Effects of particle-particle coupling on particle characteristics in nonlinear leaky-box type descriptions of the acceleration and transport of energetic particles in space plasmas are examined in the framework of a simple two-particle model based on the Fokker-Planck equation in momentum space. In this model, the two particles are assumed coupled via a common nonlinear source term. In analogy with a prototypical mathematical system of diffusion-driven instability, this work demonstrates that steady-state patterns with strong dependence on the magnetic turbulence but a rather weak one on the coupled particles attributes can emerge in solutions of a nonlinearly coupled leaky-box model. The insight gained from this simple model may be of wider use and significance to nonlinearly coupled leaky-box type descriptions in general.
Intrinsic Nonlinearities and Layout Impacts of 100 V Integrated Power MOSFETs in Partial SOI Process
DEFF Research Database (Denmark)
Fan, Lin; Knott, Arnold; Jørgensen, Ivan Harald Holger
Parasitic capacitances of power semiconductors are a part of the key design parameters of state-of-the-art very high frequency (VHF) power supplies. In this poster, four 100 V integrated power MOSFETs with different layout structures are designed, implemented, and analyzed in a 0.18 ȝm partial...... Silicon-on-Insulator (SOI) process with a die area 2.31 mm2. A small-signal model of power MOSFETs is proposed to systematically analyze the nonlinear parasitic capacitances in different transistor states: off-state, sub-threshold region, and on-state in the linear region. 3D plots are used to summarize...
Institute of Scientific and Technical Information of China (English)
FAN En-Gui
2001-01-01
Two new applications of homogeneous balance (HB) method are presented.It is shown that HB methodcan be extended to search for the Backlund transformations and similarity reductions of nonlinear partial differentialequations.The close relations among the HB method,Weiss-Tabor-Carnevale method and Clarkson-Kruskal directreduction method are also found.KdV-MKdV equation is considered as an illustrative example,and its one kind of Backlund transformation,three kinds of similarity reductions and several kinds of travelling wave solutions are obtained by using extended HB method.
Calatroni, Luca
2013-08-01
We present directional operator splitting schemes for the numerical solution of a fourth-order, nonlinear partial differential evolution equation which arises in image processing. This equation constitutes the H -1-gradient flow of the total variation and represents a prototype of higher-order equations of similar type which are popular in imaging for denoising, deblurring and inpainting problems. The efficient numerical solution of this equation is very challenging due to the stiffness of most numerical schemes. We show that the combination of directional splitting schemes with implicit time-stepping provides a stable and computationally cheap numerical realisation of the equation.
Directory of Open Access Journals (Sweden)
Abdon Atangana
2014-01-01
Full Text Available A novel approach is proposed to deal with a class of nonlinear partial equations including integer and noninteger order derivative. This class of equations cannot be handled with any other commonly used analytical technique. The proposed method is based on the multi-Laplace transform. We solved as an example some complicated equations. Three illustrative examples are presented to confirm the applicability of the proposed method. We have presented in detail the stability, the convergence and the uniqueness analysis of some examples.
Instability and dynamics of two nonlinearly coupled laser beams in a plasma
Shukla, P K; Marklund, M; Stenflo, L; Kourakis, I; Parviainen, M; Dieckmann, M E
2006-01-01
We investigate the nonlinear interaction between two laser beams in a plasma in the weakly nonlinear and relativistic regime. The evolution of the laser beams is governed by two nonlinear Schroedinger equations that are coupled with the slow plasma density response. We study the growth rates of the Raman forward and backward scattering instabilities as well of the Brillouin and self-focusing/modulational instabilities. The nonlinear evolution of the instabilities is investigated by means of direct simulations of the time-dependent system of nonlinear equations.
Numerical approximation on computing partial sum of nonlinear Schroedinger eigenvalue problems
Institute of Scientific and Technical Information of China (English)
JiachangSUN; DingshengWANG; 等
2001-01-01
In computing electronic structure and energy band in the system of multiparticles,quite a large number of problems are to obtain the partial sum of the densities and energies by using “First principle”。In the ordinary method,the so-called self-consistency approach,the procedure is limited to a small scale because of its high computing complexity.In this paper,the problem of computing the partial sum for a class of nonlinear Schroedinger eigenvalue equations is changed into the constrained functional minimization.By space decompostion and Rayleigh-Schroedinger method,one approximating formula for the minimal is provided.The numerical experiments show that this formula is more precise and its quantity of computation is smaller.
Exact travelling wave solutions for a class of nonlinear partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Xie Fuding E-mail: xiefd@sohu.com; Gao Xiaoshan
2004-03-01
In this paper, the tanh-method is improved by means of a proper rational transformation based upon a coupled projective Riccati equations. The ansatz can be applied to find more and new exact solutions of the partial differential equations with the aid of symbolic computation system, Maple. We choose an example, which includes phi{sup 4} equation, Klein-Gordon equation, Duffing equation, Landau-Ginburg-Higgs equation and Sine-Gordon equation, to illustrate the method.
Semiclassical mode-coupling factorizations of coherent nonlinear optical response
Jansen, TL; Mukamel, S
2003-01-01
The identification of relevant collective coordinates is crucial for the interpretation of coherent nonlinear spectroscopies of complex molecules and liquids. Using an h expansion of Liouville space generating functions, we show how to factorize multitime nonlinear response functions into products o
Energy Technology Data Exchange (ETDEWEB)
Mvogo, Alain, E-mail: mvogal_2009@yahoo.fr [Laboratory of Biophysics, Department of Physics, Faculty of Science, University of Yaounde I (Cameroon); Ben-Bolie, G.H., E-mail: gbenbolie@yahoo.fr [Laboratory of Nuclear Physics, Department of Physics, Faculty of Science, University of Yaounde I (Cameroon); Centre d' Excellence Africain en Technologies de l' Information et de la Communication, University of Yaounde I, P.O. Box 812, Yaounde (Cameroon); Kofané, T.C., E-mail: tckofane@yahoo.com [Laboratory of Mechanics, Department of Physics, Faculty of Science, University of Yaounde I (Cameroon); Centre d' Excellence Africain en Technologies de l' Information et de la Communication, University of Yaounde I, P.O. Box 812, Yaounde (Cameroon); The Abdus Salam International Center for Theoretical Physics, P.O. Box 586, Strada Costiera 11, I-34014 Trieste (Italy)
2014-07-04
An improved quantum model for exciton–phonon dynamics in an α-helix is investigated taking into account the interspine coupling and the influence of power-law long-range exciton–exciton interactions. Having constructed the model Hamiltonian, we derive the lattice equations and employ the Fourier transforms to go in continuum space showing that the long-range interactions (LRI) lead to a nonlocal integral term in the equations of motion. Indeed, the non-locality originating from the LRI results in the dynamic equations with space derivatives of fractional order. New theoretical frameworks are derived, such that: fractional generalization of coupled Zakharov equations, coupled nonlinear fractional Schrödinger equations, coupled fractional Ginzburg–Landau equations, coupled Hilbert–Zakharov equations, coupled nonlinear Hilbert–Ginzburg–Landau equations, coupled nonlinear Schrödinger equations and coupled nonlinear Hilbert–Schrödinger equations. Through the F-expansion method, we derive a set of exact Jacobian solutions of coupled nonlinear Schrödinger equations. These solutions include Jacobian periodic solutions as well as bright and dark soliton which are important in the process of energy transport in the molecule. We also discuss of the impact of LRI on the energy transport in the molecule.
Existence of least energy solutions to coupled elliptic systems with critical nonlinearities
Directory of Open Access Journals (Sweden)
Gong-Ming Wei
2008-04-01
Full Text Available In this paper we study the existence of nontrivial solutions of elliptic systems with critical nonlinearities and subcritical nonlinear coupling interactions, under Dirichlet or Neumann boundary conditions. These equations are motivated from solitary waves of nonlinear Schrodinger systems in physics. Using minimax theorem and by estimates on the least energy, we prove the existence of nonstandard least energy solutions, i.e. solutions with least energy and each component is nontrivial.
New Exact Solutions for a Class of Nonlinear Coupled Differential Equations
Institute of Scientific and Technical Information of China (English)
ZHAO Hong; GUO Jun; BAI Cheng-Lin; HAN Ji-Guang
2005-01-01
More new exact solutions for a class of nonlinear coupled differential equations are obtained by using a direct and efficient hyperbola function transform method based on the idea of the extended homogeneous balance method.
On the importance of nonlinear couplings in large-scale neutrino streams
Dupuy, Hélène
2015-01-01
We propose a procedure to evaluate the impact of nonlinear couplings on the evolution of massive neutrino streams in the context of large-scale structure growth. Such streams can be described by general nonlinear conservation equations, derived from a multiple-flow perspective, which generalize the conservation equations of non-relativistic pressureless fluids. The relevance of the nonlinear couplings is quantified with the help of the eikonal approximation applied to the subhorizon limit of this system. It highlights the role played by the relative displacements of different cosmic streams and it specifies, for each flow, the spatial scales at which the growth of structure is affected by nonlinear couplings. We found that, at redshift zero, such couplings can be significant for wavenumbers as small as $k=0.2\\,h$/Mpc for most of the neutrino streams.
Nonlinear coupling of left and right handed circularly polarized dispersive Alfvén wave
Energy Technology Data Exchange (ETDEWEB)
Sharma, R. P., E-mail: rpsharma@ces.iitd.ac.in; Sharma, Swati, E-mail: swati.sharma704@gmail.com; Gaur, Nidhi, E-mail: nidhiphysics@gmail.com [Centre for Energy Studies, Indian Institute of Technology Delhi, New Delhi 110016 (India)
2014-07-15
The nonlinear phenomena are of prominent interests in understanding the particle acceleration and transportation in the interplanetary space. The ponderomotive nonlinearity causing the filamentation of the parallel propagating circularly polarized dispersive Alfvén wave having a finite frequency may be one of the mechanisms that contribute to the heating of the plasmas. The contribution will be different of the left (L) handed mode, the right (R) handed mode, and the mix mode. The contribution also depends upon the finite frequency of the circularly polarized waves. In the present paper, we have investigated the effect of the nonlinear coupling of the L and R circularly polarized dispersive Alfvén wave on the localized structures formation and the respective power spectra. The dynamical equations are derived in the presence of the ponderomotive nonlinearity of the L and R pumps and then studied semi-analytically as well as numerically. The ponderomotive nonlinearity accounts for the nonlinear coupling between both the modes. In the presence of the adiabatic response of the density fluctuations, the nonlinear dynamical equations satisfy the modified nonlinear Schrödinger equation. The equations thus obtained are solved in solar wind regime to study the coupling effect on localization and the power spectra. The effect of coupling is also studied on Faraday rotation and ellipticity of the wave caused due to the difference in the localization of the left and the right modes with the distance of propagation.
EXISTENCE OF TIME PERIODIC SOLUTIONS FOR A DAMPED GENERALIZED COUPLED NONLINEAR WAVE EQUATIONS
Institute of Scientific and Technical Information of China (English)
房少梅; 郭柏灵
2003-01-01
The time periodic solution problem of damped generalized coupled nonlinear wave equations with periodic boundary condition was studied. By using the Galerkin method to construct the approximating sequence of time periodic solutions, a priori estimate and Laray-Schauder fixed point theorem to prove the convergence of the approximate solutions, the existence of time periodic solutions for a damped generalized coupled nonlinear wave equations can be obtained.
Matsuda, Nobuyuki; Kato, Takumi; Harada, Ken-Ichi; Takesue, Hiroki; Kuramochi, Eiichi; Taniyama, Hideaki; Notomi, Masaya
2011-10-10
We demonstrate highly enhanced optical nonlinearity in a coupled-resonator optical waveguide (CROW) in a four-wave mixing experiment. Using a CROW consisting of 200 coupled resonators based on width-modulated photonic crystal nanocavities in a line defect, we obtained an effective nonlinear constant exceeding 10,000 /W/m, thanks to slow light propagation combined with a strong spatial confinement of light achieved by the wavelength-sized cavities.
Report from LHC MD 1399: Effect of linear coupling on nonlinear observables in the LHC.
Maclean, Ewen Hamish; Giovannozzi, Massimo; Persson, Tobias Hakan Bjorn; Tomas Garcia, Rogelio; CERN. Geneva. ATS Department
2017-01-01
Simulation work during Run 1 established that linear coupling had a large impact on nonlinear observables such as detuning with amplitude and dynamic aperture. Linear coupling is generally taken to be the largest single source of uncertainty in the modelling of the LHC’s nonlinear single particle dynamics. ThisMD sought to verify that such behaviour, to this point only observed in simulation, translated into the real machine.
Mode coupling in partial reflections from the ionosphere at vertical incidence.
Connolly, D. J.; Tanenbaum, B. S.
1972-01-01
The effect of mode coupling has been calculated for radio waves partially reflected from the lower ionosphere at vertical incidence. Calculations were made for parameters appropriate to the partial reflection experiments (Belrose, 1970). The four reflection coefficients (two direct and two coupled) are calculated for a plane discontinuity using a matrix perturbation analysis. The ratios of coupled to direct reflection coefficients are calculated for a general one-dimensional reflecting layer using the coupled equations of Clemmow and Heading (1954). At the highest electron density considered, 10,000 per cu cm, about 10% of the reflected extraordinary wave amplitude might be due to coupling from the incident ordinary wave. The effect is smaller at lower electron density.
ELECTRICALLY FORCED THICKNESS-SHEAR VIBRATIONS OF QUARTZ PLATE WITH NONLINEAR COUPLING TO EXTENSION
Institute of Scientific and Technical Information of China (English)
Rongxing Wu; Jiashi Yang; Jianke Du; Ji Wang
2008-01-01
We study electrically forced nonlinear thickness-shear vibrations of a quartz plate resonator with relatively large amplitude. It is shown that thickness-shear is nonlinearly coupled to extension due to the well-known Poynting effect in nonlinear elasticity. This coupling is relatively strong when the resonant frequency of the extensional mode is about twice the resonant frequency of the thickness-shear mode. This happens when the plate length/thickness ratio assumes certain values. With this nonlinear coupling, the thickness-shear motion is no longer sinusoidal. Coupling to extension also affects energy trapping which is related to device mounting. When damping is 0.01, nonlinear coupling causes a frequency shift of the order of 10-e which is not insignificant,and an amplitude change of the order of 10-8. The effects are expected to be stronger under real damping of 10-5 or larger. To avoid nonlinear coupling to extension, certain values of the aspect ratio of the plate should be avoided.
Application of partially-coupled hydro-mechanical schemes to multiphase flow problems
Tillner, Elena; Kempka, Thomas
2016-04-01
Utilization of subsurface reservoirs by fluid storage or production generally triggers pore pressure changes and volumetric strains in reservoirs and cap rocks. The assessment of hydro-mechanical effects can be undertaken using different process coupling strategies. The fully-coupled geomechanics and flow simulation, constituting a monolithic system of equations, is rarely applied for simulations involving multiphase fluid flow due to the high computational efforts required. Pseudo-coupled simulations are driven by static tabular data on porosity and permeability changes as function of pore pressure or mean stress, resulting in a rather limited flexibility when encountering complex subsurface utilization schedules and realistic geological settings. Partially-coupled hydro-mechanical simulations can be distinguished into one-way and iterative two-way coupled schemes, whereby the latter one is based on calculations of flow and geomechanics, taking into account the iterative exchange of coupling parameters between the two respective numerical simulators until convergence is achieved. In contrast, the one-way coupling scheme is determined by the provision of pore pressure changes calculated by the flow simulator to the geomechanical simulator neglecting any feedback. In the present study, partially-coupled two-way schemes are discussed in view of fully-coupled single-phase flow and geomechanics, and their applicability to multiphase flow simulations. For that purpose, we introduce a comparison study between the different coupling schemes, using selected benchmarks to identify the main requirements for the partially-coupled approach to converge with the numerical solution of the fully-coupled one.
Jarlebring, Elias; Michiels, Wim
2012-01-01
The partial Schur factorization can be used to represent several eigenpairs of a matrix in a numerically robust way. Different adaptions of the Arnoldi method are often used to compute partial Schur factorizations. We propose here a technique to compute a partial Schur factorization of a nonlinear eigenvalue problem (NEP). The technique is inspired by the algorithm in [8], now called the infinite Arnoldi method. The infinite Arnoldi method is a method designed for NEPs, and can be interpreted as Arnoldi's method applied to a linear infinite-dimensional operator, whose reciprocal eigenvalues are the solutions to the NEP. As a first result we show that the invariant pairs of the operator are equivalent to invariant pairs of the NEP. We characterize the structure of the invariant pairs of the operator and show how one can carry out a modification of the infinite Arnoldi method by respecting the structure. This also allows us to naturally add the feature known as locking. We nest this algorithm with an outer iter...
Controlling of blow-up responses by nonlinear PT -symmetric coupling
Karthiga, S.; Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
2017-03-01
We investigate the dynamics of a coupled waveguide system with competing linear and nonlinear loss-gain profiles which can facilitate power saturation. We show the usefulness of the model in achieving unidirectional beam propagation. In this regard, the considered type of coupled waveguide system has two drawbacks: (i) difficulty in achieving perfect isolation of light in a waveguide and (ii) existence of blow-up-type behavior for certain input power situations. We here show a nonlinear PT -symmetric coupling that helps to overcome these two drawbacks. Such a nonlinear coupling has close connection with the phenomenon of stimulated Raman scattering. In particular, we have elucidated the role of this nonlinear coupling using an integrable PT -symmetric situation. In particular, using the integrals of motion, we have reduced this coupled waveguide problem to the problem of dynamics of a particle in a potential. With the latter picture, we have clearly illustrated the role of the considered nonlinear coupling. The above PT -symmetric case corresponds to a limiting form of a general equation describing the phenomenon of stimulated Raman scattering. We also point out the ability to transport light unidirectionally even in this general case.
Komech, A I; Stuart, D
2008-01-01
The long-time asymptotics is analyzed for finite energy solutions of the 1D Schr\\"odinger equation coupled to a nonlinear oscillator; mathematically the system under study is a nonlinear Schr\\"odinger equation, whose nonlinear term includes a Dirac delta. The coupled system is invariant with respect to the phase rotation group U(1). This article, which extends the results of a previous one, provides a proof of asymptotic stability of solitary wave solutions in the case that the linearization contains a single discrete oscillatory mode satisfying a non-degeneracy assumption of the type known as the Fermi Golden Rule.
Directory of Open Access Journals (Sweden)
Catalina Hurtado Castano
2016-01-01
Full Text Available A detailed procedure is presented to compute analytically the acoustooptic coupling coefficient between copropagating core and lowest-order cladding modes in tapered fiber optics. Based on the effect of the local bending, the linear and nonlinear variations in the refractive index are modeled. A set of equations and parameters are presented in order to calculate the influence of acoustooptic effect in nonlinear pulse propagation. We will show that as the tapered fiber diameter decreases more energy can be transferred to the cladding and the nonlinear phenomena can compensate the coupling coefficients effects.
The nonlinear chemo-mechanic coupled dynamics of the F 1 -ATPase molecular motor.
Xu, Lizhong; Liu, Fang
2012-03-01
The ATP synthase consists of two opposing rotary motors, F0 and F1, coupled to each other. When the F1 motor is not coupled to the F0 motor, it can work in the direction hydrolyzing ATP, as a nanomotor called F1-ATPase. It has been reported that the stiffness of the protein varies nonlinearly with increasing load. The nonlinearity has an important effect on the rotating rate of the F1-ATPase. Here, considering the nonlinearity of the γ shaft stiffness for the F1-ATPase, a nonlinear chemo-mechanical coupled dynamic model of F1 motor is proposed. Nonlinear vibration frequencies of the γ shaft and their changes along with the system parameters are investigated. The nonlinear stochastic response of the elastic γ shaft to thermal excitation is analyzed. The results show that the stiffness nonlinearity of the γ shaft causes an increase of the vibration frequency for the F1 motor, which increases the motor's rotation rate. When the concentration of ATP is relatively high and the load torque is small, the effects of the stiffness nonlinearity on the rotating rates of the F1 motor are obvious and should be considered. These results are useful for improving calculation of the rotating rate for the F1 motor and provide insight about the stochastic wave mechanics of F1-ATPase.
3D early embryogenesis image filtering by nonlinear partial differential equations.
Krivá, Z; Mikula, K; Peyriéras, N; Rizzi, B; Sarti, A; Stasová, O
2010-08-01
We present nonlinear diffusion equations, numerical schemes to solve them and their application for filtering 3D images obtained from laser scanning microscopy (LSM) of living zebrafish embryos, with a goal to identify the optimal filtering method and its parameters. In the large scale applications dealing with analysis of 3D+time embryogenesis images, an important objective is a correct detection of the number and position of cell nuclei yielding the spatio-temporal cell lineage tree of embryogenesis. The filtering is the first and necessary step of the image analysis chain and must lead to correct results, removing the noise, sharpening the nuclei edges and correcting the acquisition errors related to spuriously connected subregions. In this paper we study such properties for the regularized Perona-Malik model and for the generalized mean curvature flow equations in the level-set formulation. A comparison with other nonlinear diffusion filters, like tensor anisotropic diffusion and Beltrami flow, is also included. All numerical schemes are based on the same discretization principles, i.e. finite volume method in space and semi-implicit scheme in time, for solving nonlinear partial differential equations. These numerical schemes are unconditionally stable, fast and naturally parallelizable. The filtering results are evaluated and compared first using the Mean Hausdorff distance between a gold standard and different isosurfaces of original and filtered data. Then, the number of isosurface connected components in a region of interest (ROI) detected in original and after the filtering is compared with the corresponding correct number of nuclei in the gold standard. Such analysis proves the robustness and reliability of the edge preserving nonlinear diffusion filtering for this type of data and lead to finding the optimal filtering parameters for the studied models and numerical schemes. Further comparisons consist in ability of splitting the very close objects which
Directory of Open Access Journals (Sweden)
Jagdev Singh
2014-01-01
Full Text Available The main aim of this work is to present a user friendly numerical algorithm based on homotopy perturbation Sumudu transform method for nonlinear fractional partial differential arising in spatial diffusion of biological populations in animals. The movements are made generally either by mature animals driven out by invaders or by young animals just reaching maturity moving out of their parental territory to establish breeding territory of their own. The homotopy perturbation Sumudu transform method is a combined form of the Sumudu transform method and homotopy perturbation method. The obtained results are compared with Sumudu decomposition method. The numerical solutions obtained by the proposed method indicate that the approach is easy to implement and accurate. These results reveal that the proposed method is computationally very attractive.
Towards Ultrafast Communications: Nonlinear Coupling Dynamics and Light-Semiconductor Interaction
Wang, W.
2007-01-01
This thesis deals with some specific problems concerning the processing of ultrashort optical pulses and their interaction with semiconductors. It includes the investigation of the ultrashort optical pulse propagation and coupling dynamics in the nonlinear coupled waveguide, and the coherent and in
Towards Ultrafast Communications: Nonlinear Coupling Dynamics and Light-Semiconductor Interaction
Wang, W.
2007-01-01
This thesis deals with some specific problems concerning the processing of ultrashort optical pulses and their interaction with semiconductors. It includes the investigation of the ultrashort optical pulse propagation and coupling dynamics in the nonlinear coupled waveguide, and the coherent and
A Solvable Model in Two-Dimensional Gravity Coupled to a Nonlinear Matter Field
Institute of Scientific and Technical Information of China (English)
YAN Jun; WANG Shun-Jin; TAO Bi-You
2001-01-01
The two-dimensional gravity model with a coupling constant k = 4 and a vanishing cosmological constant coupled to a nonlinear matter field is investigated. We found that the classical equations of motion are exactly solvable and the static solutions of the induced metric and scalar curvature can be obtained analytically. These solutions may be used to describe the naked singularity at the origin.``
New Doubly Periodic Solutions for the Coupled Nonlinear Klein-Gordon Equations
Institute of Scientific and Technical Information of China (English)
LIU Chun-Ping
2005-01-01
By using the general solutions of a new coupled Riccati equations, a direct algebraic method is described to construct doubly periodic solutions (Jacobi elliptic function solution) for the coupled nonlinear Klein-Gordon equations.It is shown that more doubly periodic solutions and the corresponding solitary wave solutions and trigonometric function solutions can be obtained in a unified way by this method.
Pinning Synchronization of Delayed Neural Networks with Nonlinear Inner-Coupling
Directory of Open Access Journals (Sweden)
Yangling Wang
2011-01-01
Full Text Available Without assuming the symmetry and irreducibility of the outer-coupling weight configuration matrices, we investigate the pinning synchronization of delayed neural networks with nonlinear inner-coupling. Some delay-dependent controlled stability criteria in terms of linear matrix inequality (LMI are obtained. An example is presented to show the application of the criteria obtained in this paper.
Hayes, E. F.; Kouri, D. J.
1971-01-01
Coupled integral equations are derived for the full scattering amplitudes for both reactive and nonreactive channels. The equations do not involve any partial wave expansion and are obtained using channel operators for reactive and nonreactive collisions. These coupled integral equations are similar in nature to equations derived for purely nonreactive collisions of structureless particles. Using numerical quadrature techniques, these equations may be reduced to simultaneous algebraic equations which may then be solved.
Thermal entanglement in 1D optical lattice chains with nonlinear coupling
Institute of Scientific and Technical Information of China (English)
Zhou Ling; Yi Xue-Xi; Song He-Shan; Guo Yan-Qing
2005-01-01
he thermal entanglement of spin-1 atoms with nonlinear coupling in an optical lattice chain is investigated for two-particle and multi-particle systems. It is found that the relation between linear coupling and nonlinear coupling is the key to determine thermal entanglement, which shows in what kinds of atoms thermal entanglement exists. This result is true both for two-particle and multi-particle systems. For multi-particle systems, the thermal entanglement does not decrease greatly, and the critical temperature decreases only slightly.
UV Nano-Lights - Nonlinear Quantum Dot-Plasmon Coupling
2016-06-20
nanomaterials systems for nonlinear optics. PROJECT TIMELINE The project timeline was segmented into 3 monthly intervals. The PhD students, assisted by...technique to remove the scattering component of light from the fluorescence emission with commonly-used fluorometers [Shortell, Optics Express...nanostructure light interaction and also has helped understand and remove unwanted signal contamination through optical element interference effects as
On the Nonlinear Behavior of the Piezoelectric Coupling on Vibration-Based Energy Harvesters
Directory of Open Access Journals (Sweden)
Luciana L. Silva
2015-01-01
Full Text Available Vibration-based energy harvesting with piezoelectric elements has an increasing importance nowadays being related to numerous potential applications. A wide range of nonlinear effects is observed in energy harvesting devices and the analysis of the power generated suggests that they have considerable influence on the results. Linear constitutive models for piezoelectric materials can provide inconsistencies on the prediction of the power output of the energy harvester, mainly close to resonant conditions. This paper investigates the effect of the nonlinear behavior of the piezoelectric coupling. A one-degree of freedom mechanical system is coupled to an electrical circuit by a piezoelectric element and different coupling models are investigated. Experimental tests available in the literature are employed as a reference establishing the best matches of the models. Subsequently, numerical simulations are carried out showing different responses of the system indicating that nonlinear piezoelectric couplings can strongly modify the system dynamics.
On non-linear dynamics of a coupled electro-mechanical system
DEFF Research Database (Denmark)
Darula, Radoslav; Sorokin, Sergey
2012-01-01
, for mechanical system, is of the second order. The governing equations are coupled via linear and weakly non-linear terms. A classical perturbation method, a method of multiple scales, is used to find a steadystate response of the electro-mechanical system exposed to a harmonic close-resonance mechanical......Electro-mechanical devices are an example of coupled multi-disciplinary weakly non-linear systems. Dynamics of such systems is described in this paper by means of two mutually coupled differential equations. The first one, describing an electrical system, is of the first order and the second one...... excitation. The results are verified using a numerical model created in MATLAB Simulink environment. Effect of non-linear terms on dynamical response of the coupled system is investigated; the backbone and envelope curves are analyzed. The two phenomena, which exist in the electro-mechanical system: (a...
Coupled Nonlinear Schr(o)dinger Equations and the Miura Transformation
Institute of Scientific and Technical Information of China (English)
LOU Yan; ZHU Jun-Yi
2011-01-01
@@ A wide class of coupled nonlinear Schr?dinger(NLS)equations are derived by virtue of the dressing method,and the associated parametric solutions are discussed.As an illustration,the explicit solution of the coupled NLS-type equation associated with σ1 is given.The Miura transformation for a AKNS-type hierarchy is established,from which a modified coupled NLS-type equation is shown to be equivalent to the Heisenberg spin equation.%A wide class of coupled nonlinear Schrodinger (NLS) equations are derived by virtue of the dressing method, and the associated parametric solutions are discussed. As an illustration, the explicit solution of the coupled NLS-type equation associated with O\\ is given. The Miura transformation for a AKNS-type hierarchy is established, from which a modified coupled NLS-type equation is shown to be equivalent to the Heisenberg spin equation.
Garai, S.; Janaki, M. S.; Chakrabarti, N.
2016-09-01
The nonlinear propagation of low frequency waves, in a collisionless, strongly coupled dusty plasma (SCDP) with a density dependent viscosity, has been studied with a proper Galilean invariant generalized hydrodynamic (GH) model. The well known reductive perturbation technique (RPT) has been employed in obtaining the solutions of the longitudinal and transverse perturbations. It has been found that the nonlinear propagation of the acoustic perturbations govern with the modified Korteweg-de Vries (KdV) equation and are decoupled from the sheared fluctuations. In the regions, where transversal gradients of the flow exists, coupling between the longitudinal and transverse perturbations occurs due to convective nonlinearity which is true for the homogeneous case also. The results, obtained here, can have relative significance to astrophysical context as well as in laboratory plasmas.
Nonlinear quantum optics in the (ultra)strong light-matter coupling
Sánchez-Burillo, Eduardo; García-Ripoll, Juan José; Martín-Moreno, Luis; Zueco, David
2014-01-01
The propagation of $N$ photons in one dimensional waveguides coupled to $M$ qubits is discussed, both in the strong and ultrastrong qubit-waveguide coupling. Special emphasis is placed on the characterisation of the nonlinear response and its linear limit for the scattered photons as a function of $N$, $M$, qubit inter distance and light-matter coupling. The quantum evolution is numerically solved via the Matrix Product States technique. Both the time evolution for the field and qubits is com...
Scaling and synchronization in a ring of diffusively coupled nonlinear oscillators
Senthilkumar, D. V.; Muruganandam, P.; Lakshmanan, M.; Kurths, J.
2010-01-01
Chaos synchronization in a ring of diffusively coupled nonlinear oscillators driven by an external identical oscillator is studied. Based on numerical simulations we show that by introducing additional couplings at $(mN_c+1)$-th oscillators in the ring, where $m$ is an integer and $N_c$ is the maximum number of synchronized oscillators in the ring with a single coupling, the maximum number of oscillators that can be synchronized can be increased considerably beyond the limit restricted by siz...
Khan, Zulfiqar Hasan; Gu, Irene Yu-Hua
2013-12-01
This paper proposes a novel Bayesian online learning and tracking scheme for video objects on Grassmann manifolds. Although manifold visual object tracking is promising, large and fast nonplanar (or out-of-plane) pose changes and long-term partial occlusions of deformable objects in video remain a challenge that limits the tracking performance. The proposed method tackles these problems with the main novelties on: 1) online estimation of object appearances on Grassmann manifolds; 2) optimal criterion-based occlusion handling for online updating of object appearances; 3) a nonlinear dynamic model for both the appearance basis matrix and its velocity; and 4) Bayesian formulations, separately for the tracking process and the online learning process, that are realized by employing two particle filters: one is on the manifold for generating appearance particles and another on the linear space for generating affine box particles. Tracking and online updating are performed in an alternating fashion to mitigate the tracking drift. Experiments using the proposed tracker on videos captured by a single dynamic/static camera have shown robust tracking performance, particularly for scenarios when target objects contain significant nonplanar pose changes and long-term partial occlusions. Comparisons with eight existing state-of-the-art/most relevant manifold/nonmanifold trackers with evaluations have provided further support to the proposed scheme.
A Coupled Fixed Point Theorem for Geraghty Contractions in Partially Ordered Metric Spaces
Directory of Open Access Journals (Sweden)
K.P.R. Sastry
2014-07-01
Full Text Available In this paper we establish results on the existence and uniqueness of coupled fixed points of Geraghty contraction on a partially ordered set with a metric, with the continuity of the altering distance function dropped. Our results are improvements over the results of GVR Babu and P.Subhashini [3].
Directory of Open Access Journals (Sweden)
Lucas Jódar
1992-01-01
Full Text Available In this paper coupled implicit initial-boundary value systems of second order partial differential equations are considered. Given a finite domain and an admissible error ϵ an analytic approximate solution whose error is upper bounded by ϵ in the given domain is constructed in terms of the data.
PT-symmetric dimer of coupled nonlinear oscillators
Indian Academy of Sciences (India)
Avinash Khare
2015-11-01
We provide a systematic analysis of a prototypical nonlinear oscillator system respecting PT-symmetry, i.e., one of them has gain and the other an equal and opposite amount of loss. We first discuss various symmetries of the model. We show that both the linear system as well as a special case of the nonlinear system can be derived from a Hamiltonian, whose structure is similar to the Pais–Uhlenbeck Hamiltonian. Exact solutions are obtained in a few special cases. We show that the system is a superintegrable system within the rotating wave approximation (RWA). We also obtain several exact solutions of these RWA equations. Further, we point out a novel superposition in the context of periodic solutions in terms of Jacobi elliptic functions that we obtain in this problem. Finally, we briefly mention numerical results about the stability of some of the solutions.
Directory of Open Access Journals (Sweden)
Brajesh Kumar Singh
2016-01-01
Full Text Available This paper deals with an analytical solution of an initial value system of time dependent linear and nonlinear partial differential equations by implementing reduced differential transform (RDT method. The effectiveness and the convergence of RDT method are tested by means of five test problems, which indicates the validity and great potential of the reduced differential transform method for solving system of partial differential equations.
On a mixed problem for a coupled nonlinear system
Directory of Open Access Journals (Sweden)
Marcondes R. Clark
1997-03-01
Full Text Available In this article we prove the existence and uniqueness of solutions to the mixed problem associated with the nonlinear system $$ u_{tt}-M(int_Omega |abla u|^2dxDelta u+|u|^ ho u+heta =f $$ $$ heta _t -Delta heta +u_{t}=g $$ where $M$ is a positive real function, and $f$ and $g$ are known real functions.
Nonlinear Dynamics of Globally Coupled Sine-Gordon Equations
2011-05-01
studied too, including a triangular configuration of linearly coupled parallel fiber Bragg gratings [15], coupled triplets of Gross-Pitaevskii...B. Dueholm, O. A. Levring, J. Mygind, N. F. Pedersen , O. H. Soerensen, and M. Cirillo, Phys. Rev. Lett. 46, 1299 (1981); E. Joergensen, V. P...Malomed, Phys. Rev. B 37, 9325 (1988); A. V. Ustinov, H. Kohlstedt, M. Cirillo, N. F. Pedersen , G. Hallmanns, and C. Heiden, ibid. B 48, 10614
Finite Element Analysis of Biot’s Consolidation with a Coupled Nonlinear Flow Model
Directory of Open Access Journals (Sweden)
Yue-bao Deng
2016-01-01
Full Text Available A nonlinear flow relationship, which assumes that the fluid flow in the soil skeleton obeys the Hansbo non-Darcian flow and that the coefficient of permeability changes with void ratio, was incorporated into Biot’s general consolidation theory for a consolidation simulation of normally consolidated soft ground with or without vertical drains. The governing equations with the coupled nonlinear flow model were presented first for the force equilibrium condition and then for the continuity condition. Based on the weighted residual method, the finite element (FE formulations were then derived, and an existing FE program was modified accordingly to take the nonlinear flow model into consideration. Comparative analyses using established theoretical solutions and numerical solutions were completed, and the results were satisfactory. On this basis, we investigated the effect of the coupled nonlinear flow on consolidation development.
Institute of Scientific and Technical Information of China (English)
胡业民; 胡希伟
2001-01-01
Numerical analyses for the nonlinear evolutions of stimulated Raman scattering (SRS) and stimulated Brillouin scattering (SBS) processes are given. Various effects of the second- and third-order nonlinear susceptibilities on the SRS and SBS processes are studied. The nonlinear evolutions of SRS and SBS processes are atfected more efficiently than their linear growth rates by the nonlinear susceptibility.
Electrets in soft materials: nonlinearity, size effects, and giant electromechanical coupling.
Deng, Qian; Liu, Liping; Sharma, Pradeep
2014-07-01
Development of soft electromechanical materials is critical for several tantalizing applications such as soft robots and stretchable electronics, among others. Soft nonpiezoelectric materials can be coaxed to behave like piezoelectrics by merely embedding charges and dipoles in their interior and assuring some elastic heterogeneity. Such so-called electret materials have been experimentally shown to exhibit very large electromechanical coupling. In this work, we derive rigorous nonlinear expressions that relate effective electromechanical coupling to the creation of electret materials. In contrast to the existing models, we are able to both qualitatively and quantitatively capture the known experimental results on the nonlinear response of electret materials. Furthermore, we show that the presence of another form of electromechanical coupling, flexoelectricity, leads to size effects that dramatically alter the electromechanical response at submicron feature sizes. One of our key conclusions is that nonlinear deformation (prevalent in soft materials) significantly enhances the flexoelectric response and hence the aforementioned size effects.
Nonlinear regime of the mode-coupling instability in 2D plasma crystals
Röcker, T B; Zhdanov, S K; Nosenko, V; Ivlev, A V; Thomas, H M; Morfill, G E
2014-01-01
The transition between linear and nonlinear regimes of the mode-coupling instability (MCI) operating in a monolayer plasma crystal is studied. The mode coupling is triggered at the centre of the crystal and a melting front is formed, which travels through the crystal. At the nonlinear stage, the mode coupling results in synchronisation of the particle motion and the kinetic temperature of the particles grows exponentially. After melting of the crystalline structure, the mean kinetic energy of the particles continued to grow further, preventing recrystallisation of the melted phase. The effect could not be reproduced in simulations employing a simple point-like wake model. This shows that at the nonlinear stage of the MCI a heating mechanism is working which was not considered so far.
THERMOELASTICALLY COUPLED AXISYMMETRIC NONLINEAR VIBRATION OF SHALLOW SPHERICAL AND CONICAL SHELLS
Institute of Scientific and Technical Information of China (English)
王永岗; 戴诗亮
2004-01-01
The problem of axisymmetric nonlinear vibration for shallow thin spherical and conical shells when temperature and strain fields are coupled is studied. Based on the large deflection theories of von Krmn and the theory of thermoelasticity, the whole governing equations and their simplified type are derived. The time-spatial variables are separated by Galerkin's technique, thus reducing the governing equations to a system of time-dependent nonlinear ordinary differential equation. By means of regular perturbation method and multiple-scales method, the first-order approximate analytical solution for characteristic relation of frequency vs amplitude parameters along with the decay rate of amplitude are obtained, and the effects of different geometric parameters and coupling factors as well as boundary conditions on thermoelastically coupled nonlinear vibration behaviors are discussed.
Modulational Instability in a Pair of Non-identical Coupled Nonlinear Electrical Transmission Lines
Institute of Scientific and Technical Information of China (English)
Eric Tala-Tebue; Aurelien Kenfack-Jiotsa; Marius Hervé Tatchou-Ntemfack; Timoléon Crépin Kofané
2013-01-01
In this work,we investigate the dynamics of modulated waves non-identical coupled nonlinear transmission lines.Traditional methods for avoiding mode mixing in identical coupled nonlinear electrical lines consist of adding the same number of linear inductors in each branch.Adding linear inductors in a single line leads to asymmetric coupled nonlinear electrical transmission lines which propagate the signal and the mode mixing.On one hand,the difference between the two lines induced the fission for only one mode of propagation.This fission is influenced by the amplitude of the signal and the amount of the input energy as well; it also narrows the width of the input pulse soliton,leading to a possible increasing of the bit rate.On the other hand,the dissymmetry of the two lines converts the network into a good amplifier for the w_ mode which corresponds to the regime admitting low frequencies.
Generalized Two-State Theory for an Atom Laser with Nonlinear Couplings
Institute of Scientific and Technical Information of China (English)
JING Hui; TIAN Li-Jun
2002-01-01
We present a generalized two-state theory to investigate the quantum dynamics and statistics of an atom laser with nonlinear couplings. The rotating wave approximate Hamiltonian of the system is proved to be analytically solvable. The fraction of output atoms is then showed to exhibit an interesting collapse and revival phenomenon with respect to the evolution time, a sign of nonlinear couplings. Several nonclassical effects, such as sub-Poissonian distribution, quadrature squeezing effects, second-order cross-correlation and accompanied violation of Cauchy-Schwartz inequality are also revealed for the output matter wave. The initial global phase of the trapped condensate, in weak nonlinear coupling limits, is found to exert an interesting impact on the quantum statistical properties of the propagating atom laser beam.
Katzav, E; Nechaev, S; Vasilyev, O
2007-06-01
We report some observations concerning the statistics of longest increasing subsequences (LIS). We argue that the expectation of LIS, its variance, and apparently the full distribution function appears in statistical analysis of some simple nonlinear stochastic partial differential equation in the limit of very low noise intensity.
Compressive sensing reconstruction of feed-forward connectivity in pulse-coupled nonlinear networks
Barranca, Victor J.; Zhou, Douglas; Cai, David
2016-06-01
Utilizing the sparsity ubiquitous in real-world network connectivity, we develop a theoretical framework for efficiently reconstructing sparse feed-forward connections in a pulse-coupled nonlinear network through its output activities. Using only a small ensemble of random inputs, we solve this inverse problem through the compressive sensing theory based on a hidden linear structure intrinsic to the nonlinear network dynamics. The accuracy of the reconstruction is further verified by the fact that complex inputs can be well recovered using the reconstructed connectivity. We expect this Rapid Communication provides a new perspective for understanding the structure-function relationship as well as compressive sensing principle in nonlinear network dynamics.
Compressive sensing reconstruction of feed-forward connectivity in pulse-coupled nonlinear networks.
Barranca, Victor J; Zhou, Douglas; Cai, David
2016-06-01
Utilizing the sparsity ubiquitous in real-world network connectivity, we develop a theoretical framework for efficiently reconstructing sparse feed-forward connections in a pulse-coupled nonlinear network through its output activities. Using only a small ensemble of random inputs, we solve this inverse problem through the compressive sensing theory based on a hidden linear structure intrinsic to the nonlinear network dynamics. The accuracy of the reconstruction is further verified by the fact that complex inputs can be well recovered using the reconstructed connectivity. We expect this Rapid Communication provides a new perspective for understanding the structure-function relationship as well as compressive sensing principle in nonlinear network dynamics.
Nonlinear analysis of a cross-coupled quadrature harmonic oscillator
DEFF Research Database (Denmark)
Djurhuus, Torsten; Krozer, Viktor; Vidkjær, Jens;
2005-01-01
The dynamic equations governing the cross-coupled quadrature harmonic oscillator are derived assuming quasi-sinusoidal operation. This allows for an investigation of the previously reported tradeoff between close-to-carrier phase noise and quadrature precision. The results explain how nonlinearit...
Optimizing nonlinear beam coupling in low-symmetry crystals.
Shumelyuk, A; Volkov, A; Odoulov, S; Grabar, A; Stoyka, I; Evans, D R
2014-10-01
The purpose of this paper is to find the polarizations and spatial orientations of the two interacting counterpropagating coherent light waves which ensure the largest beam coupling in monoclinic photorefractive crystal. The results of calculations are presented that are verified experimentally with Sn₂P₂S₆.
General complex envelope solutions of coupled-mode optics with quadratic or cubic nonlinearity
Hesketh, Graham D
2015-01-01
The analytic general solutions for the complex field envelopes are derived using Weierstrass elliptic functions for two and three mode systems of differential equations coupled via quadratic $\\chi_2$ type nonlinearity as well as two mode systems coupled via cubic $\\chi_3$ type nonlinearity. For the first time, a compact form of the solutions is given involving simple ratios of Weierstrass sigma functions (or equivalently Jacobi theta functions). A Fourier series is also given. All possible launch states are considered. The models describe sum and difference frequency generation, polarization dynamics, parity-time dynamics and optical processing applications.
Nonlinear Propagation of Coupling Optical Pulse under Compton Scattering in Laser Medium
Institute of Scientific and Technical Information of China (English)
HAO Dong-shan; ZHANG Xiao-fu
2006-01-01
After considering Kerr nonlinear effect,group velocity dispersion of host and gain distribution of active particle in laser amplifying medium,a basic equation describing propagation of the coupling optical pulse under the multi-photon nonlinear Compton scattering in the laser amplifying medium has been deduced. Besides,the profile and power spectrum of a picosecond-level super-Gaussian coupling pulse in the laser amplifying medium have been discussed when its central frequency coincides with the gain peak frequency of the laser amplifying medium.
EXACT EXPLICIT SOLUTIONS OF THE NONLINEAR SCHR(O)DINGER EQUATION COUPLED TO THE BOUSSINESQ EQUATION
Institute of Scientific and Technical Information of China (English)
姚若侠; 李忠斌
2003-01-01
A system comprised of the nonlinear Schrodinger equation coupled to theBoussinesq equation (S-B equations) which dealing with the stationary propagation of cou-pled non-linear upper-hybrid and magnetosonic waves in magnetized plasma is proposed.To examine its solitary wave solutions, a reduced set of ordinary differential equations areconsidered by a simple traveling wave transformation. It is then shown that several newsolutions (either functional or parametrical) can be obtained systematically, in addition torederiving all known ones by means of our simple and direct algebra method with the helpof the computer algebra system Maple.
Nonlinear ultrasound wave propagation in thermoviscous fluids
DEFF Research Database (Denmark)
Sørensen, Mads Peter
coupled nonlinear partial differential equations, which resembles those of optical chi-2 materials. We think this result makes a remarkable link between nonlinear acoustics and nonlinear optics. Finally our analysis reveal an exact kink solution to the nonlinear acoustic problem. This kink solution...
Coupled Fixed Points for Meir-Keeler Contractions in Ordered Partial Metric Spaces
Directory of Open Access Journals (Sweden)
Thabet Abdeljawad
2012-01-01
Full Text Available In this paper, we prove the existence and uniqueness of a new Meir-Keeler type coupled fixed point theorem for two mappings F:X×X→X and g:X→X on a partially ordered partial metric space. We present an application to illustrate our obtained results. Further, we remark that the metric case of our results proved recently in Gordji et al. (2012 have gaps. Therefore, our results revise and generalize some of those presented in Gordji et al. (2012.
Nonreciprocal wave scattering on nonlinear string-coupled oscillators
Energy Technology Data Exchange (ETDEWEB)
Lepri, Stefano, E-mail: stefano.lepri@isc.cnr.it [Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi, via Madonna del Piano 10, I-50019 Sesto Fiorentino (Italy); Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino (Italy); Pikovsky, Arkady [Department of Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Str 24/25, Potsdam (Germany); Department of Control Theory, Nizhni Novgorod State University, Gagarin Av. 23, 606950, Nizhni Novgorod (Russian Federation)
2014-12-01
We study scattering of a periodic wave in a string on two lumped oscillators attached to it. The equations can be represented as a driven (by the incident wave) dissipative (due to radiation losses) system of delay differential equations of neutral type. Nonlinearity of oscillators makes the scattering non-reciprocal: The same wave is transmitted differently in two directions. Periodic regimes of scattering are analyzed approximately, using amplitude equation approach. We show that this setup can act as a nonreciprocal modulator via Hopf bifurcations of the steady solutions. Numerical simulations of the full system reveal nontrivial regimes of quasiperiodic and chaotic scattering. Moreover, a regime of a “chaotic diode,” where transmission is periodic in one direction and chaotic in the opposite one, is reported.
Energy Technology Data Exchange (ETDEWEB)
Ramos, Daniel, E-mail: daniel.ramos@csic.es; Frank, Ian W.; Deotare, Parag B.; Bulu, Irfan; Lončar, Marko [School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138 (United States)
2014-11-03
We investigate the coupling between mechanical and optical modes supported by coupled, freestanding, photonic crystal nanobeam cavities. We show that localized cavity modes for a given gap between the nanobeams provide weak optomechanical coupling with out-of-plane mechanical modes. However, we show that the coupling can be significantly increased, more than an order of magnitude for the symmetric mechanical mode, due to optical resonances that arise from the interaction of the localized cavity modes with standing waves formed by the reflection from thesubstrate. Finally, amplification of motion for the symmetric mode has been observed and attributed to the strong optomechanical interaction of our hybrid system. The amplitude of these self-sustained oscillations is large enough to put the system into a non-linear oscillation regime where a mixing between the mechanical modes is experimentally observed and theoretically explained.
Existence of solutions for a Schrödinger system with linear and nonlinear couplings
Li, Kui; Zhang, Zhitao
2016-08-01
We study an important system of Schrödinger equations with linear and nonlinear couplings arising from Bose-Einstein condensates. We use the Nehari manifold to prove the existence of a ground state solution; moreover, we give the sign of the solutions depending on linear coupling; by using index theory and Nehari manifold, we prove that there exist infinitely many positive bound state solutions.
Time-varying interaction leads to amplitude death in coupled nonlinear oscillators
Indian Academy of Sciences (India)
Awadhesh Prasad
2013-09-01
A new form of time-varying interaction in coupled oscillators is introduced. In this interaction, each individual oscillator has always time-independent self-feedback while its interaction with other oscillators are modulated with time-varying function. This interaction gives rise to a phenomenon called amplitude death even in diffusively coupled identical oscillators. The nonlinear variation of the locus of bifurcation point is shown. Results are illustrated with Landau–Stuart (LS) and Rössler oscillators.
Solitary waves for a coupled nonlinear Schrodinger system with dispersion management
Directory of Open Access Journals (Sweden)
Panayotis Panayotaros
2010-08-01
Full Text Available We consider a system of coupled nonlinear Schrodinger equations with periodically varying dispersion coefficient that arises in the context of fiber-optics communication. We use Lions's Concentration Compactness principle to show the existence of standing waves with prescribed L^2 norm in an averaged equation that approximates the coupled system. We also use the Mountain Pass Lemma to prove the existence of standing waves with prescribed frequencies.
Institute of Scientific and Technical Information of China (English)
FU Jing-Li; FU Hao
2008-01-01
We deai with the generalization of the field method to weakly non-linear mechanico-electricai coupling systems.The field co-ordinates and field momenta approaches are combined with the method of multiple time scales in order to obtain the amplitudes and phase of oscillations in the frst approximation. An example in mechanico-electrical coupling systems is given to illustrate this method.
Array-induced collective transport in the Brownian motion of coupled nonlinear oscillator systems
Zheng, Zhigang; Hu, Bambi; Hu, Gang
1998-01-01
Brownian motion of an array of harmonically coupled particles subject to a periodic substrate potential and driven by an external bias is investigated. In the linear response limit (small bias), the coupling between particles may enhance the diffusion process, depending on the competition between the harmonic chain and the substrate potential. An analytical formula of the diffusion rate for the single-particle case is also obtained. In the nonlinear response regime, the moving kink may become...
Enhanced continuous-variable entanglement by a pair of nonlinearly coupled waveguides
Institute of Scientific and Technical Information of China (English)
WANG KeQuan; FAN QiuBo
2009-01-01
We seek to analyze a three-level cascade laser with a pair of non,nearly coupled waveguides inside the cavity.Applying the pertinent master equation,we investigate the squeezing and entanglement prop-erties intracavity produced by our system.It is shown that with the help of nonlinearly coupled waveguides highly squeezed as well as macroscopic entangled light with high intensity can be achieved.
[In-situ DRIFTS study of coupling partial oxidation of methane and carbon dioxide reforming].
Ji, Hong-bing; Xu, Jian-hua; Xie, Jun-feng; Chen, Qing-lin
2008-06-01
8%Ru-5%Ce/gamma-Al2O3 catalyst exhibited excellent catalytic performance for low temperature activation of methane. Although the conversion rates of methane were 25.3% for exothermal partial oxidation of methane, and 0.8% for endothermal carbon dioxide reforming, whose activity was rather low, 38.8% of conversion rate of methane could be obtained for the obtained coupling reaction at 500 degrees C owing to the coupling intensification between endothermal carbon dioxide reforming reaction and exothermal partial oxidation of methane. The mechanism of coupling partial oxidation of methane and carbon dioxide reforming on supported Ru catalyst was investigated by in-situ DRIFTS. The adsorption of CO on 8%Ru-5%Ce/gamma-Al2O3 showed that two kinds of doublet peaks which were characteristic adsorption of the gaseous CO at 2167 cm(-1) (2118 cm(-1)) to form Ru(CO)2 at 2031 cm(-1) (2034 cm(-1)) to form Ce(CO)2 were observed. These CO adsorption species wee easy to be desorbed from the surface of the catalyst at high temperature. The results of in-situ DRIFTS showed that carbonate, formal (formate) and carbon monoxide formed on the surface of catalyst, and formal (formate) was intermediate for the methane partial oxidation. This intermediate was formed through the combination of the adsorption species of methane CHx and the lattice oxygen adsorption species on the surface of catalyst, and syngas was produced through the splitting of this intermediate. The DRIFTS researching on carbon dioxide reforming showed that there was no new adsorption species on the surface of the catalyst, which indicated that the mechanism for carbon dioxide reforming was through the dissociation of the adsorbed methane and carbon dioxide. During the reaction of the coupling of carbon dioxide reforming reaction and partial oxidation of methane, there was hydroxyl adsorption species on the surface of catalyst. The mechanism of coupling methane, carbon dioxide and oxygen might be composed of the above
Directory of Open Access Journals (Sweden)
Anatoly V. Klyuchevskii
2013-11-01
Full Text Available The current lithospheric geodynamics and tectonophysics in the Baikal rift are discussed in terms of a nonlinear oscillator with dissipation. The nonlinear oscillator model is applicable to the area because stress change shows up as quasi-periodic inharmonic oscillations at rifting attractor structures (RAS. The model is consistent with the space-time patterns of regional seismicity in which coupled large earthquakes, proximal in time but distant in space, may be a response to bifurcations in nonlinear resonance hysteresis in a system of three oscillators corresponding to the rifting attractors. The space-time distribution of coupled MLH > 5.5 events has been stable for the period of instrumental seismicity, with the largest events occurring in pairs, one shortly after another, on two ends of the rift system and with couples of smaller events in the central part of the rift. The event couples appear as peaks of earthquake ‘migration’ rate with an approximately decadal periodicity. Thus the energy accumulated at RAS is released in coupled large events by the mechanism of nonlinear oscillators with dissipation. The new knowledge, with special focus on space-time rifting attractors and bifurcations in a system of nonlinear resonance hysteresis, may be of theoretical and practical value for earthquake prediction issues. Extrapolation of the results into the nearest future indicates the probability of such a bifurcation in the region, i.e., there is growing risk of a pending M ≈ 7 coupled event to happen within a few years.
Nonlinear to Linear Elastic Code Coupling in 2-D Axisymmetric Media.
Energy Technology Data Exchange (ETDEWEB)
Preston, Leiph [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2017-08-01
Explosions within the earth nonlinearly deform the local media, but at typical seismological observation distances, the seismic waves can be considered linear. Although nonlinear algorithms can simulate explosions in the very near field well, these codes are computationally expensive and inaccurate at propagating these signals to great distances. A linearized wave propagation code, coupled to a nonlinear code, provides an efficient mechanism to both accurately simulate the explosion itself and to propagate these signals to distant receivers. To this end we have coupled Sandia's nonlinear simulation algorithm CTH to a linearized elastic wave propagation code for 2-D axisymmetric media (axiElasti) by passing information from the nonlinear to the linear code via time-varying boundary conditions. In this report, we first develop the 2-D axisymmetric elastic wave equations in cylindrical coordinates. Next we show how we design the time-varying boundary conditions passing information from CTH to axiElasti, and finally we demonstrate the coupling code via a simple study of the elastic radius.
Coupled nonlinear-diffusion color image sharpening based on the chromaticity-brightness model
Saito, Takahiro; Nosaka, Reina; Komatsu, Takashi
2006-01-01
Previously we have presented a selective image sharpening method based on the coupled nonlinear diffusion process composed of a nonlinear diffusion term, a fidelity term and an isotropic peaking term, and it can sharpen only blurred edges without increasing the noise visibility. Our previously presented prototypal color-image sharpening methods based on the coupled nonlinear-diffusion process have been formulated on the linear color models, namely, the channel-bychannel model and the 3D vectorial model. Our prototypal methods can sharpen blurred color step edges, but they do not necessarily enhance contrasts of signal variations in complex texture image regions so well as in simple step-edge regions. To remedy the drawback, this paper extends our coupled nonlinear-diffusion color-image sharpening method to the nonlinear non-flat color model, namely, the chromaticity-brightness model, which is known to be closely relating to human color perception. We modify our time-evolution PDE's for the non-flat space of the chromaticity vector and present its digital implementations. Through experimental simulations, we compare our new color-image sharpening method based on the chromaticity-brightness model with our prototypal color-image sharpening methods based on the linear color models.
Nonlinear Analysis of Ring Oscillator and Cross-Coupled Oscillator Circuits
Ge, Xiaoqing
2010-12-01
Hassan Khalil’s research results and beautifully written textbook on nonlinear systems have influenced generations of researchers, including the authors of this paper. Using nonlinear systems techniques, this paper analyzes ring oscillator and cross-coupled oscillator circuits, which are essential building blocks in digital systems. The paper first investigates local and global stability properties of an n-stage ring oscillator by making use of its cyclic structure. It next studies global stability properties of a class of cross-coupled oscillators which admit the representation of a dynamic system in feedback with a static nonlinearity, and presents su cient conditions for almost global convergence of the solutions to a limit cycle when the feedback gain is in the vicinity of a bifurcation point. The result are also extended to the synchronization of interconnected identical oscillator circuits.
Tang, Ze; Park, Ju H.; Lee, Tae H.
2016-10-01
This paper is devoted to the cluster synchronization issue of nonlinearly coupled Lur'e networks under the distributed adaptive pinning control strategy. The time-varying delayed networks consisted of identical and nonidentical Lur'e systems are discussed respectively by applying the edge-based pinning control scheme. In each cluster, the edges belonging to the spanning tree are pinned. In view of the nonlinearly couplings of the networks, for the first time, an efficient distributed nonlinearly adaptive update law based on the local information of the dynamical behaviors of node is proposed. Sufficient criteria for the achievement of cluster synchronization are derived based on S-procedure, Kronecker product and Lyapunov stability theory. Additionally, some illustrative examples are provided to demonstrate the effectiveness of the theoretical results.
Energy Technology Data Exchange (ETDEWEB)
Wang Dengshan [CEMA and CIAS, Central Univ. of Finance and Economics, BJ (China); BNLCMP, Inst. of Physics, Chinese Academy of Sciences, BJ (China); Liu Yifang [School of Economics, Central Univ. of Finance and Economics, BJ (China)
2010-01-15
In this paper, with the aid of symbolic computation the bright soliton solutions of two variable-coefficient coupled nonlinear Schroedinger equations are obtained by Hirota's method. Some figures are plotted to illustrate the properties of the obtained solutions. The properties are meaningful for the investigation on the stability of soliton propagation in the optical soliton communications. (orig.)
Solitons and periodic solutions to a couple of fractional nonlinear evolution equations
Indian Academy of Sciences (India)
M Mirzazadeh; M Eslami; Anjan Biswas
2014-03-01
This paper studies a couple of fractional nonlinear evolution equations using first integral method. These evolution equations are foam drainage equation and Klein–Gordon equation (KGE), the latter of which is considered in (2 + 1) dimensions. For the fractional evolution, the Jumarie’s modified Riemann–Liouville derivative is considered. Exact solutions to these equations are obtained.
SHARP CRITERIONS OF GLOBAL EXISTENCE AND COLLAPSE FOR COUPLED NONLINEAR SCHR(O)DINGER EQUATIONS
Institute of Scientific and Technical Information of China (English)
Gan Zaihui; Zhang Jian
2004-01-01
In this paper, a series of sharp criterions of global existence and collapse for coupled nonlinear Schrodinger equations are derived out in terms of the characteristics of the ground state and the local theories. And the conclusion that how small the initial data are, the global solutions exist is proved.
Geometry and transport in a model of two coupled quadratic nonlinear waveguides
DEFF Research Database (Denmark)
Stirling, James R.; Bang, Ole; Christiansen, Peter Leth;
2008-01-01
This paper applies geometric methods developed to understand chaos and transport in Hamiltonian systems to the study of power distribution in nonlinear waveguide arrays. The specific case of two linearly coupled X(2) waveguides is modeled and analyzed in terms of transport and geometry in the pha...
On non-linear dynamics of a coupled electro-mechanical system
DEFF Research Database (Denmark)
Darula, Radoslav; Sorokin, Sergey
2012-01-01
excitation. The results are verified using a numerical model created in MATLAB Simulink environment. Effect of non-linear terms on dynamical response of the coupled system is investigated; the backbone and envelope curves are analyzed. The two phenomena, which exist in the electro-mechanical system: (a...
Indian Academy of Sciences (India)
Ranjit Kumar
2012-09-01
Travelling and solitary wave solutions of certain coupled nonlinear diffusion-reaction equations have been constructed using the auxiliary equation method. These equations arise in a variety of contexts not only in biological, chemical and physical sciences but also in ecological and social sciences.
A tightly-coupled domain-decomposition approach for highly nonlinear stochastic multiphysics systems
Taverniers, Søren; Tartakovsky, Daniel M.
2017-02-01
Multiphysics simulations often involve nonlinear components that are driven by internally generated or externally imposed random fluctuations. When used with a domain-decomposition (DD) algorithm, such components have to be coupled in a way that both accurately propagates the noise between the subdomains and lends itself to a stable and cost-effective temporal integration. We develop a conservative DD approach in which tight coupling is obtained by using a Jacobian-free Newton-Krylov (JfNK) method with a generalized minimum residual iterative linear solver. This strategy is tested on a coupled nonlinear diffusion system forced by a truncated Gaussian noise at the boundary. Enforcement of path-wise continuity of the state variable and its flux, as opposed to continuity in the mean, at interfaces between subdomains enables the DD algorithm to correctly propagate boundary fluctuations throughout the computational domain. Reliance on a single Newton iteration (explicit coupling), rather than on the fully converged JfNK (implicit) coupling, may increase the solution error by an order of magnitude. Increase in communication frequency between the DD components reduces the explicit coupling's error, but makes it less efficient than the implicit coupling at comparable error levels for all noise strengths considered. Finally, the DD algorithm with the implicit JfNK coupling resolves temporally-correlated fluctuations of the boundary noise when the correlation time of the latter exceeds some multiple of an appropriately defined characteristic diffusion time.
Synchronization transitions in coupled time-delay electronic circuits with a threshold nonlinearity.
Srinivasan, K; Senthilkumar, D V; Murali, K; Lakshmanan, M; Kurths, J
2011-06-01
Experimental observations of typical kinds of synchronization transitions are reported in unidirectionally coupled time-delay electronic circuits with a threshold nonlinearity and two time delays, namely feedback delay τ(1) and coupling delay τ(2). We have observed transitions from anticipatory to lag via complete synchronization and their inverse counterparts with excitatory and inhibitory couplings, respectively, as a function of the coupling delay τ(2). The anticipating and lag times depend on the difference between the feedback and the coupling delays. A single stability condition for all the different types of synchronization is found to be valid as the stability condition is independent of both the delays. Further, the existence of different kinds of synchronizations observed experimentally is corroborated by numerical simulations and from the changes in the Lyapunov exponents of the coupled time-delay systems.
Non-linear Matter Spectra in Coupled Quintessence
Saracco, F; Tetradis, N; Pettorino, V; Robbers, G
2010-01-01
We consider cosmologies in which a dark-energy scalar field interacts with cold dark matter. The growth of perturbations is followed beyond the linear level by means of the time-renormalization-group method, which is extended to describe a multi-component matter sector. Even in the absence of the extra interaction, a scale-dependent bias is generated as a consequence of the different initial conditions for baryons and dark matter after decoupling. The effect is greatly enhanced by the extra coupling and can be at the percent level in the range of scales of baryonic acoustic oscillations. We compare our results with N-body simulations, finding very good agreement.
Solution of Nonlinear Coupled Heat and Moisture Transport Using Finite Element Method
Directory of Open Access Journals (Sweden)
T. Krejčí
2004-01-01
Full Text Available This paper deals with a numerical solution of coupled of heat and moisture transfer using the finite element method. The mathematical model consists of balance equations of mass, energy and linear momentum and of the appropriate constitutive equations. The chosen macroscopic field variables are temperature, capillary pressures, gas pressure and displacement. In contrast with pure mechanical problems, there are several difficulties which require special attention. Systems of algebraic equations arising from coupled problems are generally nonlinear, and the matrices of such systems are nonsymmetric and indefinite. The first experiences of solving complicated coupled problems are mentioned in this paper.
Fiber-to-fiber nonlinear coupling via a nematic liquid crystal
Nyushkov, B. N.; Trashkeev, S. I.; Ivanenko, A. V.; Kolker, D. B.; Purtov, P. A.
2017-01-01
Nonlinear optical coupling between two single-mode fibers terminated coaxially in a nematic liquid crystal (NLC) was explored for the first time. Light-induced reorientation of nematic molecules can result in the stable self-collimation of light transmitted through the gap between fibers. Thus, high coupling efficiency can be achieved despite large fiber spacing. We demonstrated a coupling efficiency of up to ∼0.7, achieved with spacing equal to four diffraction lengths. This feature opens up possibilities for the development of novel in-line fiber-optic elements based on NLCs. For instance, a polarization controller was proposed and considered.
Almaraz, Pablo; Green, Andy J; Aguilera, Eduardo; Rendón, Miguel A; Bustamante, Javier
2012-09-01
1. Understanding the impact of environmental variability on migrating species requires the estimation of sequential abiotic effects in different geographic areas across the life cycle. For instance, waterfowl (ducks, geese and swans) usually breed widely dispersed throughout their breeding range and gather in large numbers in their wintering headquarters, but there is a lack of knowledge on the effects of the sequential environmental conditions experienced by migrating birds on the long-term community dynamics at their wintering sites. 2. Here, we analyse multidecadal time-series data of 10 waterfowl species wintering in the Guadalquivir Marshes (SW Spain), the single most important wintering site for waterfowl breeding in Europe. We use a multivariate state-space approach to estimate the effects of biotic interactions, local environmental forcing during winter and large-scale climate during breeding and migration on wintering multispecies abundance fluctuations, while accounting for partial observability (observation error and missing data) in both population and environmental data. 3. The joint effect of local weather and large-scale climate explained 31·6% of variance at the community level, while the variability explained by interspecific interactions was negligible (observations through data augmentation increased the estimated magnitude of environmental forcing by an average 30·1% and reduced the impact of stochasticity by 39·3% when accounting for observation error. Interestingly however, the impact of environmental forcing on community dynamics was underestimated by an average 15·3% and environmental stochasticity overestimated by 14·1% when ignoring both observation error and data augmentation. 5. These results provide a salient example of sequential multiscale environmental forcing in a major migratory bird community, which suggests a demographic link between the breeding and wintering grounds operating through nonlinear environmental effects
Vierheilig, Carmen; Grifoni, Milena
2010-01-01
We consider a qubit coupled to a nonlinear quantum oscillator, the latter coupled to an Ohmic bath, and investigate the qubit dynamics. This composed system can be mapped onto that of a qubit coupled to an effective bath. An approximate mapping procedure to determine the spectral density of the effective bath is given. Specifically, within a linear response approximation the effective spectral density is given by the knowledge of the linear susceptibility of the nonlinear quantum oscillator. To determine the actual form of the susceptibility, we consider its periodically driven counterpart, the problem of the quantum Duffing oscillator within linear response theory in the driving amplitude. Knowing the effective spectral density, the qubit dynamics is investigated. In particular, an analytic formula for the qubit's population difference is derived. Within the regime of validity of our theory, a very good agreement is found with predictions obtained from a Bloch-Redfield master equation approach applied to the...
Tackling excess noise from bilinear and nonlinear couplings in gravitational-wave interferometers
Bose, Sukanta; Mazumder, Nairwita; Dhurandhar, Sanjeev; Gupta, Anuradha; Lundgren, Andrew
2016-01-01
We describe a tool we improved to detect excess noise in the gravitational wave (GW) channel arising from its bilinear or nonlinear coupling with fluctuations of various components of a GW interferometer and its environment. We also describe a higher-order statistics tool we developed to characterize these couplings, e.g., by unraveling the frequencies of the fluctuations contributing to such noise, and demonstrate its utility by applying it to understand nonlinear couplings in Advanced LIGO engineering data. Once such noise is detected, it is highly desirable to remove it or correct for it. Such action in the past has been shown to improve the sensitivity of the instrument in searches of astrophysical signals. If this is not possible, then steps must be taken to mitigate its influence, e.g., by characterizing its effect on astrophysical searches. We illustrate this through a study of the effect of transient sine-Gaussian noise artifacts on a compact binary coalescence template bank.
Nonlinear Coupled Analysis of a Single Point Mooring System
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
Coupled effects on a single point mooring (SPM) system subjected to the combined action of wind, waves and current are studied in this paper. Due to the complicatedness of the sea state and the huge size of the vessel, physical experimental study is both time consuming and uneconomical, whereas the numerical study is cost-effective and DNV software provides powerful SESAM software in solving the issues. This paper focuses on the modeling process of the SPM system, catenary equilibrium calculation, static analysis of the vessel in three different scenarios, and dynamic response simulation of the SPM system under environmental excitations. The three scenarios in study are as follows: the SPM is under the combined function of (a) wind, waves and current, (b) wind and waves, (c) current and waves. They are so set that one can compare the contributions of different types of loads in both static and dynamic studies. Numerical study shows that wind and current are the two major factors contributing to the mooring line tension, and surge and sway are the two dominant motions of the moored vessel subjected to environmental excitations.
Indian Academy of Sciences (India)
AYYAZ ALI; MUHAMMAD ASAD IQBAL; SYED TAUSEEF MOHYUD-DIN
2016-11-01
In this article, a variety of solitary wave solutions are found for some nonlinear equations. In mathematical physics, we studied two complex systems, the Maccari system and the coupled Higgs field equation. We construct sufficient exact solutions for nonlinear evolution equations. To study travelling wave solutions, we used a fractional complex transform to convert the particular partial differential equation of fractional order into the corresponding partial differential equation and the rational exp$(−\\psi(\\eta)$)-expansion method is implemented tofind exact solutions of nonlinear equation. We find hyperbolic, trigonometric, rational and exponential function solutions using the above equation. The results of various studies show that the suggested method is very effectiveand can be used as an alternative for finding exact solutions of nonlinear equations in mathematical physics. A comparative study with the other methods gives validity to the technique and shows that the method providesadditional solutions. Graphical representations along with the numerical data reinforce the efficacy of the procedure used. The specified idea is very effective, pragmatic for partial differential equations of fractional order andcould be protracted to other physical phenomena.
Nonlinear local electrovascular coupling. II: From data to neuronal masses.
Riera, J J; Jimenez, J C; Wan, X; Kawashima, R; Ozaki, T
2007-04-01
In the companion article a local electrovascular coupling (LEVC) model was proposed to explain the continuous dynamics of electrical and vascular states within a cortical unit. These states produce certain mesoscopic reflections whose discrete time series can be reconstructed from electroencephalography (EEG) and functional magnetic resonance imaging (fMRI). In this article we develop a recursive optimization algorithm based on the local linearization (LL) filter and an innovation method to make statistical inferences about the LEVC model from both EEG and fMRI data, i.e., to estimate the unobserved states and the unknown parameters of the model. For a better understanding, the LL filter is described from a Bayesian point of view, providing the particulars for the case of hybrid data (e.g., EEG and fMRI), which could be sampled at different rates. The dynamics of the exogenous synaptic inputs going into the cortical unit are also estimated by introducing a set of Gaussian radial basis functions. In order to study the dynamics of the electrical and vascular states in the striate cortex of humans as well as their local interrelationships, we applied this algorithm to EEG and fMRI recordings obtained concurrently from two subjects while passively observing a radial checkerboard with a white/black pattern reversal. The EEG and fMRI data from the first subject was used to estimate the electrical/vascular states and parameters of the LEVC model in V1 for a 4.0 Hz reversion frequency. We used the EEG data from the second subject to investigate the changes in the dynamics of the electrical states when the frequency of reversion is varied from 0.5-4.0 Hz. Then we made use of the estimated electrical states to predict the effects on the vasculature that such variations produce.
Institute of Scientific and Technical Information of China (English)
Ahmed Awad; Wang Haoping
2016-01-01
The acceleration autopilot design for skid-to-turn (STT) missile faces a great challenge owing to coupling effect among planes, variation of missile velocity and its parameters, inexistence of a complete state vector, and nonlinear aerodynamics. Moreover, the autopilot should be designed for the entire flight envelope where fast variations exist. In this paper, a design of inte-grated roll-pitch-yaw autopilot based on global fast terminal sliding mode control (GFTSMC) with a partial state nonlinear observer (PSNLO) for STT nonlinear time-varying missile model, is employed to address these issues. GFTSMC with a novel sliding surface is proposed to nullify the integral error and the singularity problem without application of the sign function. The pro-posed autopilot consisting of two-loop structure, controls STT maneuver and stabilizes the rolling with a PSNLO in order to estimate the immeasurable states as an output while its inputs are missile measurable states and control signals. The missile model considers the velocity variation, gravity effect and parameters’ variation. Furthermore, the environmental conditions’ dynamics are mod-eled. PSNLO stability and the closed loop system stability are studied. Finally, numerical simula-tion is established to evaluate the proposed autopilot performance and to compare it with existing approaches in the literature.
Directory of Open Access Journals (Sweden)
Awad Ahmed
2016-10-01
Full Text Available The acceleration autopilot design for skid-to-turn (STT missile faces a great challenge owing to coupling effect among planes, variation of missile velocity and its parameters, inexistence of a complete state vector, and nonlinear aerodynamics. Moreover, the autopilot should be designed for the entire flight envelope where fast variations exist. In this paper, a design of integrated roll-pitch-yaw autopilot based on global fast terminal sliding mode control (GFTSMC with a partial state nonlinear observer (PSNLO for STT nonlinear time-varying missile model, is employed to address these issues. GFTSMC with a novel sliding surface is proposed to nullify the integral error and the singularity problem without application of the sign function. The proposed autopilot consisting of two-loop structure, controls STT maneuver and stabilizes the rolling with a PSNLO in order to estimate the immeasurable states as an output while its inputs are missile measurable states and control signals. The missile model considers the velocity variation, gravity effect and parameters’ variation. Furthermore, the environmental conditions’ dynamics are modeled. PSNLO stability and the closed loop system stability are studied. Finally, numerical simulation is established to evaluate the proposed autopilot performance and to compare it with existing approaches in the literature.
Micro-/nanoscale multi-field coupling in nonlinear photonic devices
Yang, Qing; Wang, Yubo; Tang, Mingwei; Xu, Pengfei; Xu, Yingke; Liu, Xu
2017-08-01
The coupling of mechanics/electronics/photonics may improve the performance of nanophotonic devices not only in the linear region but also in the nonlinear region. This review letter mainly presents the recent advances on multi-field coupling in nonlinear photonic devices. The nonlinear piezoelectric effect and piezo-phototronic effects in quantum wells and fibers show that large second-order nonlinear susceptibilities can be achieved, and second harmonic generation and electro-optic modulation can be enhanced and modulated. Strain engineering can tune the lattice structures and induce second order susceptibilities in central symmetry semiconductors. By combining the absorption-based photoacoustic effect and intensity-dependent photobleaching effect, subdiffraction imaging can be achieved. This review will also discuss possible future applications of these novel effects and the perspective of their research. The review can help us develop a deeper knowledge of the substance of photon-electron-phonon interaction in a micro-/nano- system. Moreover, it can benefit the design of nonlinear optical sensors and imaging devices with a faster response rate, higher efficiency, more sensitivity and higher spatial resolution which could be applied in environmental detection, bio-sensors, medical imaging and so on.
Energy Technology Data Exchange (ETDEWEB)
Lu, Bin, E-mail: lubinhb@163.com [School of Mathematical Sciences, Anhui University, Hefei 230601 (China)
2012-06-04
In this Letter, the fractional derivatives in the sense of modified Riemann–Liouville derivative and the Bäcklund transformation of fractional Riccati equation are employed for constructing the exact solutions of nonlinear fractional partial differential equations. The power of this manageable method is presented by applying it to several examples. This approach can also be applied to other nonlinear fractional differential equations. -- Highlights: ► Backlund transformation of fractional Riccati equation is presented. ► A new method for solving nonlinear fractional differential equations is proposed. ► Three important fractional differential equations are solved successfully. ► Some new exact solutions of the fractional differential equations are obtained.
Zia, Haider
2017-06-01
This paper describes an updated exponential Fourier based split-step method that can be applied to a greater class of partial differential equations than previous methods would allow. These equations arise in physics and engineering, a notable example being the generalized derivative non-linear Schrödinger equation that arises in non-linear optics with self-steepening terms. These differential equations feature terms that were previously inaccessible to model accurately with low computational resources. The new method maintains a 3rd order error even with these additional terms and models the equation in all three spatial dimensions and time. The class of non-linear differential equations that this method applies to is shown. The method is fully derived and implementation of the method in the split-step architecture is shown. This paper lays the mathematical ground work for an upcoming paper employing this method in white-light generation simulations in bulk material.
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
Kramer, Sean; Bollt, Erik M
2013-09-01
Given multiple images that describe chaotic reaction-diffusion dynamics, parameters of a partial differential equation (PDE) model are estimated using autosynchronization, where parameters are controlled by synchronization of the model to the observed data. A two-component system of predator-prey reaction-diffusion PDEs is used with spatially dependent parameters to benchmark the methods described. Applications to modeling the ecological habitat of marine plankton blooms by nonlinear data assimilation through remote sensing are discussed.
Institute of Scientific and Technical Information of China (English)
LIU Chun-Ping; LING Zhi
2005-01-01
By using the generally projective Riccati equation method, a series of doubly periodic solutions (Jacobi elliptic function solution) for a class of nonlinear partial differential equations are obtained in a unified way. When the module m → 1, these solutions exactly degenerate to the soliton solutions of the equations. Then we reveal the relationship between the soliton-like solutions obtained by other authors and these soliton solutions of the equations.
Directory of Open Access Journals (Sweden)
Hasibun Naher
2012-01-01
Full Text Available We construct new analytical solutions of the (3+1-dimensional modified KdV-Zakharov-Kuznetsev equation by the Exp-function method. Plentiful exact traveling wave solutions with arbitrary parameters are effectively obtained by the method. The obtained results show that the Exp-function method is effective and straightforward mathematical tool for searching analytical solutions with arbitrary parameters of higher-dimensional nonlinear partial differential equation.
Directory of Open Access Journals (Sweden)
Da-Guang Zhang
2015-10-01
Full Text Available For magnetostrictive rods under combined axial pre-stress and magnetic field, a general one-dimension nonlinear magneto-elastic coupled constitutive model was built in this paper. First, the elastic Gibbs free energy was expanded into polynomial, and the relationship between stress and strain and the relationship between magnetization and magnetic field with the polynomial form were obtained with the help of thermodynamic relations. Then according to microscopic magneto-elastic coupling mechanism and some physical facts of magnetostrictive materials, a nonlinear magneto-elastic constitutive with concise form was obtained when the relations of nonlinear strain and magnetization in the polynomial constitutive were instead with transcendental functions. The comparisons between the prediction and the experimental data of different magnetostrictive materials, such as Terfenol-D, Metglas and Ni showed that the predicted magnetostrictive strain and magnetization curves were consistent with experimental results under different pre-stresses whether in the region of low and moderate field or high field. Moreover, the model can fully reflect the nonlinear magneto-mechanical coupling characteristics between magnetic, magnetostriction and elasticity, and it can effectively predict the changes of material parameters with pre-stress and bias field, which is useful in practical applications.
Energy Technology Data Exchange (ETDEWEB)
Zhang, Da-Guang; Li, Meng-Han; Zhou, Hao-Miao, E-mail: zhouhm@cjlu.edu.cn [College of Information Engineering, China Jiliang University, 310018, Hangzhou (China)
2015-10-15
For magnetostrictive rods under combined axial pre-stress and magnetic field, a general one-dimension nonlinear magneto-elastic coupled constitutive model was built in this paper. First, the elastic Gibbs free energy was expanded into polynomial, and the relationship between stress and strain and the relationship between magnetization and magnetic field with the polynomial form were obtained with the help of thermodynamic relations. Then according to microscopic magneto-elastic coupling mechanism and some physical facts of magnetostrictive materials, a nonlinear magneto-elastic constitutive with concise form was obtained when the relations of nonlinear strain and magnetization in the polynomial constitutive were instead with transcendental functions. The comparisons between the prediction and the experimental data of different magnetostrictive materials, such as Terfenol-D, Metglas and Ni showed that the predicted magnetostrictive strain and magnetization curves were consistent with experimental results under different pre-stresses whether in the region of low and moderate field or high field. Moreover, the model can fully reflect the nonlinear magneto-mechanical coupling characteristics between magnetic, magnetostriction and elasticity, and it can effectively predict the changes of material parameters with pre-stress and bias field, which is useful in practical applications.
Directory of Open Access Journals (Sweden)
Liang Hu
2016-10-01
Full Text Available A nonlinear coupled dynamic model of a rod fastening rotor under rub-impact and initial permanent deflection was developed in this paper. The governing motion equation was derived by the D’Alembert principle considering the contact characteristic between disks, nonlinear oil-film force, rub-impact force, unbalance mass, etc. The contact effects between disks was modeled as a flexural spring with cubical nonlinear stiffness. The coupled nonlinear dynamic phenomena of the rub-impact rod fastening rotor bearing system with initial permanent deflection were investigated by the fourth-order Runge-Kutta method. Bifurcation diagram, vibration waveform, frequency spectrum, shaft orbit and Poincaré map are used to illustrate the rich diversity of the system response with complicated dynamics. The studies indicate that the coupled dynamic responses of the rod fastening rotor bearing system under rub-impact and initial permanent deflection exhibit a rich nonlinear dynamic diversity, synchronous periodic-1 motion, multiple periodic motion, quasi-periodic motion and chaotic motion can be observed under certain conditions. Larger radial stiffness of the stator will simplify the system motion and make the oil whirl weaker or even disappear at a certain rotating speed. With the increase of initial permanent deflection length, the instability speed of the system gradually rises, and the chaotic motion region gets smaller and smaller. The corresponding results can provide guidance for the fault diagnosis of a rub-impact rod fastening rotor with initial permanent deflection and contribute to the further understanding of the nonlinear dynamic characteristics of the rod fastening rotor bearing system.
Baldi, Marco
2010-01-01
We present a complete numerical study of cosmological models with a time dependent coupling between the dark energy component driving the present accelerated expansion of the Universe and the Cold Dark Matter (CDM) fluid. Depending on the functional form of the coupling strength, these models show a range of possible intermediate behaviors between the standard LCDM background evolution and the widely studied case of interacting dark energy models with a constant coupling. These different background evolutions play a crucial role in the growth of cosmic structures, and determine strikingly different effects of the coupling on the internal dynamics of nonlinear objects. By means of a suitable modification of the cosmological N-body code GADGET-2 we have performed a series of high-resolution N-body simulations of structure formation in the context of interacting dark energy models with variable couplings. Depending on the type of background evolution, the halo density profiles are found to be either less or more...
Chouhan, Romita; Baraskar, Priyanka; Agrawal, Arpana; Gupta, Mukul; Sen, Pranay K.; Sen, Pratima
2017-07-01
We report annealing induced sign reversal of dispersive optical nonlinearity in ion beam sputtered NiO thin films deposited at 30% and 70% oxygen partial pressures. In the Ultraviolet-visible spectra of the samples, the transmission peak corresponding to d-d transitions is observed near 2 eV. A shift in this peak towards higher energy was observed when the same films were annealed at 523 K. The near resonant photoinduced transitions produced giant nonlinear optical susceptibilities of both third- and fifth- orders when the annealed film was irradiated by a continuous wave 632.8 nm He-Ne laser. The role of the thermo-optic effect has been examined critically. Experimental studies further reveal that the oxygen partial pressure influences the growth direction of the grains in the thin films. The well known Z-scan experimental procedure has been followed for measurements of optical nonlinearities in all the NiO films. The nonlinear refractive indices of both the as-deposited and annealed NiO thin films are defined in terms of the thermo-optic coefficients (d/nd T ) T =T0 and (d/2nd T2 ) T =T0 .
1:2 INTERNAL RESONANCE OF COUPLED DYNAMIC SYSTEM WITH QUADRATIC AND CUBIC NONLINEARITIES
Institute of Scientific and Technical Information of China (English)
陈予恕; 杨彩霞; 吴志强; 陈芳启
2001-01-01
The 1:2 internal resonance of coupled dynamic system with quadratic and cubic nonlinearities is studied. The normal forms of this system in 1: 2 internal resonance were derived by using the direct method of normal form. In the normal forms, quadratic and cubic nonlinearities were remained. Based on a new convenient transformation technique, the 4-dimension bifurcation equations were reduced to 3-dimension. A bifurcation equation with one-dimension was obtained. Then the bifurcation behaviors of a universal unfolding were studied by using the singularity theory. The method of this paper can be applied to analyze the bifurcation behavior in strong internal resonance on 4-dimension center manifolds.
Zhu, Chengjie; Huang, Guoxiang
2011-11-07
We study linear and nonlinear propagations of probe and signal pulses in a multiple quantum-well structure with a four-level, double Λ-type configuration. We show that slow, mutually matched group velocities and giant Kerr nonlinearity of the probe and the signal pulses may be achieved with nearly vanishing optical absorption. Based on these properties we demonstrate that two-qubit quantum polarization phase gates can be constructed and highly entangled photon pairs may be produced. In addition, we show that coupled slow-light soliton pairs with very low generation power can be realized in the system.
Linear and nonlinear optical susceptibilities in a laterally coupled quantum-dot–quantum-ring system
Energy Technology Data Exchange (ETDEWEB)
Zeng, Zaiping; Garoufalis, Christos S.; Baskoutas, Sotirios, E-mail: bask@upatras.gr
2014-07-18
Linear and nonlinear optical susceptibilities in a laterally coupled quantum-dot–quantum-ring system have been theoretically studied. In general, we find that the structure parameters of the coupled system significantly affect the optical susceptibilities. The enhancement of the coupling effects between the dot and ring is found to increase considerably the optical susceptibilities and redshift drastically the transition energies. Comparing to the linear susceptibility, the nonlinear optical susceptibility is found to be more sensitive to the variation of the structure parameters. A comprehensive analysis of the electron probability density movement with respect to the modification of the structure parameters is provided, which offers a unique perspective of the ground-state localization. - Highlights: • Optical susceptibilities in a quantum-dot–quantum-ring system are studied. • The structure parameters significantly affect the optical susceptibilities. • The enhancement of the coupling effects increases the optical susceptibilities. • The nonlinear susceptibility is more sensitive to the change in structure parameters. • A comprehensive analysis of the electron probability density movement is provided.
A three-dimensional coupled numerical model of nonlinear waves in a harbor
Institute of Scientific and Technical Information of China (English)
L.G.THAM
2008-01-01
A 3-D time-domain numerical coupled model for nonlinear waves acting on a ship in a harbor has been developed in the present study.The whole domain is divided into the inner domain and the outer domain.The inner domain is the area around the ship,where the flow is expressed by the Laplace equation and numerically solved by the finite element method.The other area is the outer domain,where the flow is described by the higher-order Boussinesq equations and numerically solved by the finite difference method.The matching conditions on the interfaces between the inner domain and the outer domain,the procedure of coupled solution,the length of common domain and the mesh generation in the inner domain are discussed in detail.The other coupled model with the flow in the inner domain governed by the simplified linear Euler equations and relevant physical experiment are adopted to validate the present coupled model,and it is shown that the numerical results of the present model agree with the experimental data,so the present model can be used for the study on the effect of nonlinear waves acting on a fixed ship in a large area and provide a reference for the time-domain simulation of nonlinear wave forces on an arbitrary object in a large harbor and the 3-D district computation in the future.
Nguyen, Howard; Willacy, Karen; Allen, Mark
2012-01-01
KINETICS is a coupled dynamics and chemistry atmosphere model that is data intensive and computationally demanding. The potential performance gain from using a supercomputer motivates the adaptation from a serial version to a parallelized one. Although the initial parallelization had been done, bottlenecks caused by an abundance of communication calls between processors led to an unfavorable drop in performance. Before starting on the parallel optimization process, a partial overhaul was required because a large emphasis was placed on streamlining the code for user convenience and revising the program to accommodate the new supercomputers at Caltech and JPL. After the first round of optimizations, the partial runtime was reduced by a factor of 23; however, performance gains are dependent on the size of the data, the number of processors requested, and the computer used.
Fu, Yinan; Wand, A Joshua
2013-08-01
High-pressure NMR spectroscopy has emerged as a complementary approach for investigating various structural and thermodynamic properties of macromolecules. Noticeably absent from the array of experimental restraints that have been employed to characterize protein structures at high hydrostatic pressure is the residual dipolar coupling, which requires the partial alignment of the macromolecule of interest. Here we examine five alignment media that are commonly used at ambient pressure for this purpose. We find that the spontaneous alignment of Pf1 phage, d(GpG) and a C12E5/n-hexnanol mixture in a magnetic field is preserved under high hydrostatic pressure. However, DMPC/DHPC bicelles and collagen gel are found to be unsuitable. Evidence is presented to demonstrate that pressure-induced structural changes can be identified using the residual dipolar coupling.
Energy Technology Data Exchange (ETDEWEB)
Fu, Yinan; Wand, A. Joshua, E-mail: wand@mail.med.upenn.edu [University of Pennsylvania, Department of Biochemistry and Biophysics, Johnson Research Foundation (United States)
2013-08-15
High-pressure NMR spectroscopy has emerged as a complementary approach for investigating various structural and thermodynamic properties of macromolecules. Noticeably absent from the array of experimental restraints that have been employed to characterize protein structures at high hydrostatic pressure is the residual dipolar coupling, which requires the partial alignment of the macromolecule of interest. Here we examine five alignment media that are commonly used at ambient pressure for this purpose. We find that the spontaneous alignment of Pf1 phage, d(GpG) and a C12E5/n-hexnanol mixture in a magnetic field is preserved under high hydrostatic pressure. However, DMPC/DHPC bicelles and collagen gel are found to be unsuitable. Evidence is presented to demonstrate that pressure-induced structural changes can be identified using the residual dipolar coupling.
Directory of Open Access Journals (Sweden)
Jose Ernie C. Lope
2013-12-01
Full Text Available In their 2012 work, Lope, Roque, and Tahara considered singular nonlinear partial differential equations of the form tut = F(t; x; u; ux, where the function F is assumed to be continuous in t and holomorphic in the other variables. They have shown that under some growth conditions on the coefficients of the partial Taylor expansion of F as t 0, the equation has a unique solution u(t; x with the same growth order as that of F(t; x; 0; 0. Koike considered systems of partial differential equations using the Banach fixed point theorem and the iterative method of Nishida and Nirenberg. In this paper, we prove the result obtained by Lope and others using the method of Koike, thereby avoiding the repetitive step of differentiating a recursive equation with respect to x as was done by the aforementioned authors.
Nonlinear electromagnetic fields in 0.5 MHz inductively coupled plasmas
DEFF Research Database (Denmark)
Ostrikov, K.N.; Tsakadze, E.L.; Xu, S.
2003-01-01
Radial profiles of magnetic fields in the electrostatic (E) and electromagnetic (H) modes of low-frequency (similar to500 kHz) inductively coupled plasmas have been measured using miniature magnetic probes. In the low-power (similar to170 W) E-mode, the magnetic field pattern is purely linear......, with the fundamental frequency harmonics only. After transition to higher-power (similar to1130 W) H-mode, the second-harmonic nonlinear azimuthal magnetic field B-phi(2omega) that is in 4-6 times larger than the fundamental frequency component B-phi(omega), has been observed. A simplified plasma fluid model...... explaining the generation of the second harmonics of the azimuthal magnetic field in the plasma source is proposed. The nonlinear second harmonic poloidal (r-z) rf current generating the azimuthal magnetic field B-phi(2omega) is attributed to nonlinear interactions between the fundamental frequency radial...
Cotta, R. M.; Naveira-Cotta, C. P.; Knupp, D. C.; Zotin, J. L. Z.; Pontes, P. C.
2016-09-01
This lecture offers an updated review on the Generalized Integral Transform Technique (GITT), with focus on handling complex geometries, coupled problems, and nonlinear convection-diffusion, so as to illustrate some new application paradigms. Special emphasis is given to demonstrating novel developments, such as a single domain reformulation strategy that simplifies the treatment of complex geometries, an integral balance scheme in handling multiscale problems, the adoption of convective eigenvalue problems in dealing with strongly convective formulations, and the direct integral transformation of nonlinear convection-diffusion problems based on nonlinear eigenvalue problems. Representative application examples are then provided that employ recent extensions on the Generalized Integral Transform Technique (GITT), and a few numerical results are reported to illustrate the convergence characteristics of the proposed eigenfunction expansions.
Weakly coupled heat bath models for Gibbs-like invariant states in nonlinear wave equations
J. Bajars (Janis); J.E. Frank (Jason); B.J. Leimkuhler (Ben)
2013-01-01
textabstractThermal bath coupling mechanisms as utilized in molecular dynamics are applied to partial differential equation models. Working from a semi-discrete (Fourier mode) formulation for the Burgers–Hopf or Korteweg–de Vries equation, we introduce auxiliary variables and stochastic
Numerical Study of Frequency-dependent Seismoelectric Coupling in Partially-saturated Porous Media
Directory of Open Access Journals (Sweden)
Djuraev Ulugbek
2017-01-01
Full Text Available The seismoelectric phenomenon associated with propagation of seismic waves in fluid-saturated porous media has been studied for many decades. The method has a great potential to monitor subsurface fluid saturation changes associated with production of hydrocarbons. Frequency of the seismic source has a significant impact on measurement of the seismoelectric effects. In this paper, the effects of seismic wave frequency and water saturation on the seismoelectric response of a partially-saturated porous media is studied numerically. The conversion of seismic wave to electromagnetic wave was modelled by extending the theoretically developed seismoelectric coupling coefficient equation. We assumed constant values of pore radius and zeta-potential of 80 micrometers and 48 microvolts, respectively. Our calculations of the coupling coefficient were conducted at various water saturation values in the frequency range of 10 kHz to 150 kHz. The results show that the seismoelectric coupling is frequency-dependent and decreases exponentially when frequency increases. Similar trend is seen when water saturation is varied at different frequencies. However, when water saturation is less than about 0.6, the effect of frequency is significant. On the other hand, when the water saturation is greater than 0.6, the coupling coefficient shows monotonous trend when water saturation is increased at constant frequency.
Institute of Scientific and Technical Information of China (English)
R.Mokhtari; A.Samadi Toodar; N.G.Chegini
2011-01-01
@@ We the extend application of the generalized differential quadrature method (GDQM) to solve some coupled nonlinear Schr(o)dinger equations.The cosine-based GDQM is employed and the obtained system of ordinary differential equations is solved via the fourth order Runge-Kutta method.The numerical solutions coincide with the exact solutions in desired machine precision and invariant quantities are conserved sensibly.Some comparisons with the methods applied in the literature are carried out.%We the extend application of the generalized differential quadrature method (GDQM) to solve some coupled nonlinear Schrodinger equations. The cosine-based GDQM is employed and the obtained system of ordinary differential equations is solved via the fourth order Runge-Kutta method. The numerical solutions coincide with the exact solutions in desired machine precision and invariant quantities are conserved sensibly. Some comparisons with the methods applied in the literature are carried out.
Breathers and rogue waves: Demonstration with coupled nonlinear Schrödinger family of equations
Indian Academy of Sciences (India)
N Vishnu Priya; M Senthilvelan; M Lakshmanan
2015-03-01
Different types of breathers and rogue waves (RWs) are some of the important coherent structures which have been recently realized in several physical phenomena in hydrodynamics, nonlinear optics, Bose–Einstein condensates, etc. Mathematically, they have been deduced in non-linear Schrödinger (NLS) equations. Here we show the existence of general breathers, Akhmediev breathers, Ma soliton and rogue wave solutions in coupled Manakov-type NLS equations and coupled generalized NLS equations representing four-wave mixing. We deduce their explicit forms using Hirota bilinearization procedure and bring out their exact structures and important properties. We also show the method to deduce the various breather solutions from rogue wave solutions using factorization form and the so-called imbricate series.
Directory of Open Access Journals (Sweden)
Ahmad Bashir
2010-01-01
Full Text Available We study an initial value problem for a coupled Caputo type nonlinear fractional differential system of higher order. As a first problem, the nonhomogeneous terms in the coupled fractional differential system depend on the fractional derivatives of lower orders only. Then the nonhomogeneous terms in the fractional differential system are allowed to depend on the unknown functions together with the fractional derivative of lower orders. Our method of analysis is based on the reduction of the given system to an equivalent system of integral equations. Applying the nonlinear alternative of Leray-Schauder, we prove the existence of solutions of the fractional differential system. The uniqueness of solutions of the fractional differential system is established by using the Banach contraction principle. An illustrative example is also presented.
Stochastic Analysis of Nonlinear Coupled Heave-Pitch Motion for the Truss Spar Platform
Institute of Scientific and Technical Information of China (English)
Wenjun Shen; Yougang Tang
2011-01-01
Considering the static stability and the change of the displacement volume,including the influences of higher order nonlinear terms and the instantaneous wave surface,the nonlinear coupled heave-pitch motion was established in stochastic waves.The responses of heave-pitch coupling motion for the Truss Spar platform were investigated.It was found that,when the characteristic frequency of a stochastic wave is close to the natural heave frequency,the large amplitude pitch motion is induced under the parametric-forced excitation,which is called the Mathieu instability.It was observed that the heave mode energy is transferred to pitch mode when the heave motion amplitude exceeds a certain extent.In addition,the probability of internal resonant heave-pitch motion is greatly reduced while the characteristic wave frequency is away from the natural heave frequency.
Nonlinear analysis on the coupling process of electromagnetic vibrator and earth
Institute of Scientific and Technical Information of China (English)
CHEN; Zubin; TENG; Jiwen; LIN; Jun; ZHANG; Linhang; JIANG
2005-01-01
The linear model based on the hydraulic pressure vibrator has been no longer adaptable to the electromagnetic vibrator. In order to realize the effective transmission of the limited energy from the vibrator to the ground, it is important to study the coupling model of the electromagnetic vibrator and the earth. In this paper, a nonlinear restore term was introduced to the coupling model because of the existence of a large amount of harmonics in the vibrator baseplate. The nonlinear vibration analysis was applied to the model by the multiscale method. In the course of energy transmission from the vibrator to the ground, ultraharmonic resonance was used to explain the generation of harmonics. An improved scheme was advanced to select the cross correlation reference signal in the vibrator seismic exploration. Good application results were obtained in field experiments.
A conservative Fourier pseudospectral algorithm for a coupled nonlinear Schr(o)dinger system
Institute of Scientific and Technical Information of China (English)
Cai Jia-Xiang; Wang Yu-Shun
2013-01-01
We derive a new method for a coupled nonlinear Schr(o)dinger system by using the square of first-order Fourier spectral differentiation matrix D1 instead of traditional second-order Fourier spectral differentiation matrix D2 to approximate the second derivative.We prove the proposed method preserves the charge and energy conservation laws exactly.In numerical tests,we display the accuracy of numerical solution and the role of the nonlinear coupling parameter in cases of soliton collisions.Numerical experiments also exhibit the excellent performance of the method in preserving the charge and energy conservation laws.These numerical results verify that the proposed method is both a charge-preserving and an energy-preserving algorithm.
Spurious cross-frequency amplitude-amplitude coupling in nonstationary, nonlinear signals
Yeh, Chien-Hung; Lo, Men-Tzung; Hu, Kun
2016-07-01
Recent studies of brain activities show that cross-frequency coupling (CFC) plays an important role in memory and learning. Many measures have been proposed to investigate the CFC phenomenon, including the correlation between the amplitude envelopes of two brain waves at different frequencies - cross-frequency amplitude-amplitude coupling (AAC). In this short communication, we describe how nonstationary, nonlinear oscillatory signals may produce spurious cross-frequency AAC. Utilizing the empirical mode decomposition, we also propose a new method for assessment of AAC that can potentially reduce the effects of nonlinearity and nonstationarity and, thus, help to avoid the detection of artificial AACs. We compare the performances of this new method and the traditional Fourier-based AAC method. We also discuss the strategies to identify potential spurious AACs.
Chaotic behaviour of nonlinear coupled reaction–diffusion system in four-dimensional space
Indian Academy of Sciences (India)
Li Zhang; Shutang Liu; Chenglong Yu
2014-06-01
In recent years, nonlinear coupled reaction–diffusion (CRD) system has been widely investigated by coupled map lattice method. Previously, nonlinear behaviour was observed dynamically when one or two of the three variables in the discrete system change. In this paper, we consider the chaotic behaviour when three variables change, which is called as four-dimensional chaos. When two parameters in the discrete system are unknown, we first give the existing condition of the chaos in four-dimensional space by the generalized definitions of spatial periodic orbits and spatial chaos. In addition, the chaotic behaviour will vary with the parameters. Then we propose a generalized Lyapunov exponent in four-dimensional space to characterize the different effects of parameters on the chaotic behaviour, which has not been studied in detail. In order to verify the chaotic behaviour of the system and the different effects clearly, we simulate the dynamical behaviour in two- and three-dimensional spaces.
Directory of Open Access Journals (Sweden)
Shaheed N. Huseen
2013-01-01
Full Text Available A modified q-homotopy analysis method (mq-HAM was proposed for solving nth-order nonlinear differential equations. This method improves the convergence of the series solution in the nHAM which was proposed in (see Hassan and El-Tawil 2011, 2012. The proposed method provides an approximate solution by rewriting the nth-order nonlinear differential equation in the form of n first-order differential equations. The solution of these n differential equations is obtained as a power series solution. This scheme is tested on two nonlinear exactly solvable differential equations. The results demonstrate the reliability and efficiency of the algorithm developed.
Photon antibunching and nonlinear effects for a quantum dot coupled to a semiconductor cavity
Bello, F.; Whittaker, D. M.
2010-09-01
The models presented simulate pumping techniques that can be used on modern semiconductor devices which are capable of coupling a quantum dot and cavity mode in order to determine a more efficient method of producing a single-photon emitter while taking into consideration typical parameters which are achievable given today’s standards of coupling strength. Cavity quantum electrodynamics are incorporated in the calculations as we compare various pumping schemes for the system that either use on-resonant laser excitation or nonresonant excitation due to a wetting layer. In particular, we look to study how antibunching effects change for each method as the cavity finesse is increased toward the strong coupling regime. Experimentally these studies are equivalent to nonlinear pump-probe measurements, where a strong pump, either resonant or nonresonant, is used to excite the coupled system, and the resulting state is characterized using a weak, resonant probe beam.
Optical transistor action by nonlinear coupling of stimulated emission and coherent scattering
Andrews, David L.; Bradshaw, David S.
2010-08-01
In the pursuit of improved platforms for computing, communications and internet connectivity, all-optical systems offer excellent prospects for a speed and fidelity of data transmission that will greatly surpass conventional electronics, alongside the anticipated benefits of reduced energy loss. With a diverse range of sources and fiber optical connections already in production, much current effort is being devoted towards forging optical components for signal switching, such as an all-optical transistor. Achievement of the desired characteristics for any practicable device can be expected to depend crucially on the engagement of a strongly nonlinear optical response. The innovative scheme proposed in the present work is based upon a third-order nonlinearity - its effect enhanced by stimulated emission - operating within a system designed to exploit the highly nonlinear response observed at the threshold for laser emission. Here, stimulated emission is strongly driven by coupling to the coherent scattering of a signal input beam whose optical frequency is purposely off-set from resonance. An electrodynamical analysis of the all-optical coupling process shows that the signal beam can significantly modify the kinetics of emission, and so lead to a dramatically enhanced output of resonant radiation. The underlying nonlinear optical mechanism is analyzed, model calculations are performed for realizable three-level laser systems, and the results exhibited graphically. The advantages of implementing this all-optical transistor scheme, compared to several previously envisaged proposals, are then outlined.
Nonlinear mode coupling and internal resonances in MoS2 nanoelectromechanical system
Samanta, C.; Yasasvi Gangavarapu, P. R.; Naik, A. K.
2015-10-01
Atomically thin two dimensional (2D) layered materials have emerged as a new class of material for nanoelectromechanical systems (NEMS) due to their extraordinary mechanical properties and ultralow mass density. Among them, graphene has been the material of choice for nanomechanical resonator. However, recent interest in 2D chalcogenide compounds has also spurred research in using materials such as MoS2 for the NEMS applications. As the dimensions of devices fabricated using these materials shrink down to atomically thin membrane, strain and nonlinear effects have become important. A clear understanding of the nonlinear effects and the ability to manipulate them is essential for next generation sensors. Here, we report on all electrical actuation and detection of few-layer MoS2 resonator. The ability to electrically detect multiple modes and actuate the modes deep into the nonlinear regime enables us to probe the nonlinear coupling between various vibrational modes. The modal coupling in our device is strong enough to detect three distinct internal resonances.
Smith, David D.
2002-01-01
This talk will review the linear and nonlinear optical properties of metal nanoparticles and dielectric microparticles, with an emphasis on local field effects, and whispering gallery modes (WGMs), as well as the conjunction of these two effects for enhanced Raman. In particular, enhanced optical properties that result from electromagnetic coupling effects will be discussed in the context of Mie scattering from concentric spheres and bispheres. Predictions of mode splitting and photonic bandgaps in micro-spheres will be presented and will be shown to be analogous to effects that occur in coupled resonator optical waveguides (CROW). Slow and fast light in SCISSOR / CROW configurations will also be discussed.
Asymptotic Spreading Fastened by Inter-Specific Coupled Nonlinearities: a Cooperative System
Lin, Guo
2010-01-01
This paper is concerned with the asymptotic spreading of a Lotka-Volterra cooperative system. Utilizing the theory developed by Berestycki et al. [Asymptotic spreading in heterogeneous diffusive excitable media, J. Funct. Anal. \\textbf{255} (2008), 2146-2189] for nonautonomous scalar equations, the lower bounds of spreading speeds of unknown functions formulated by a coupled system are estimated. Our results imply that the asymptotic spreading of one species can be significantly fastened by introducing a mutual species, which indicates the role of cooperation described by the coupled nonlinearities.
Numerical Solutions of a New Type of Fractional Coupled Nonlinear Equations
Institute of Scientific and Technical Information of China (English)
WANG Ling; CHEN Yong; DONG Zhong-Zhou; AN Hong-Li
2008-01-01
In this paper, we investigate a new type of fractional coupled nonlinear equations. By introducing the frac-tional derivative that satisfies the Caputo's definition, we directly extend the applications of the Adomian decomposition method to the new system. As a result, with the aid of Maple, the realistic and convergent rapidly series solutions are obtained with easily computable components. Two famous fractional coupled examples: KdV and mKdV equations, are used to illustrate the efficiency and accuracy of the proposed method.
BIFURCATIONS OF TRAVELLING WAVE SOLUTIONS TO A COUPLED NONLINEAR WAVE SYSTEM
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
Employ theory of bifurcations of dynamical systems to a system of coupled nonlin-ear equations, the existence of solitary wave solutions, kink wave solutions, anti-kink wave solutions and periodic wave solutions is obtained. Under different parametric conditions, various suffcient conditions to guarantee the existence of the above so-lutions are given. Some exact explicit parametric representations of travelling wave solutions are derived.
Uniqueness of ground states of some coupled nonlinear Schrodinger systems and their application
MA,LI; Lin ZHAO
2007-01-01
We establish the uniqueness of ground states of some coupled nonlinear Schrodinger systems in the whole space. We firstly use Schwartz symmetrization to obtain the existence of ground states for a more general case. To prove the uniqueness of ground states, we use the radial symmetry of the ground states to transform the systems into an ordinary differential system, and then we use the integral forms of the system. More interestingly, as an application of our uniqueness results, we derive a s...
ORBITAL INSTABILITY OF STANDING WAVES FOR THE COUPLED NONLINEAR KLEIN-GORDON EQUATIONS
Institute of Scientific and Technical Information of China (English)
Gan Zaihui; Guo Boling; Zhang Jian
2008-01-01
This paper deals with a type of standing waves for the coupled nonlin-ear Klein-Gordon equations in three space dimensions. First we construct a suitable constrained variational problem and obtain the existence of the standing waves with ground state by using variational argument. Then we prove the orbital instability of the standing waves by defining invariant sets and applying some priori estimates.
Periodic wavetrains for systems of coupled nonlinear Schrödinger equations
Indian Academy of Sciences (India)
Kwok W Chow; Derek W C Lal
2001-11-01
Exact, periodic wavetrains for systems of coupled nonlinear Schrödinger equations are obtained by the Hirota bilinear method and theta functions identities. Both the bright and dark soliton regimes are treated, and the solutions involve products of elliptic functions. The validity of these solutions is veriﬁed independently by a computer algebra software. The long wave limit is studied. Physical implications will be assessed.
Singular solitons and other solutions to a couple of nonlinear wave equations
Institute of Scientific and Technical Information of China (English)
Mustafa Inc; Esma Uluta(s); Anjan Biswas
2013-01-01
This paper addresses the extended (G′/G)-expansion method and applies it to a couple of nonlinear wave equations.These equations are modified the Benjamin-Bona-Mahoney equation and the Boussinesq equation.This extended method reveals several solutions to these equations.Additionally,the singular soliton solutions are revealed,for these two equations,with the aid of the ansatz method.
Darboux Transformation for Coupled Non-Linear Schrödinger Equation and Its Breather Solutions
Feng, Lili; Yu, Fajun; Li, Li
2017-01-01
Starting from a 3×3 spectral problem, a Darboux transformation (DT) method for coupled Schrödinger (CNLS) equation is constructed, which is more complex than 2×2 spectral problems. A scheme of soliton solutions of an integrable CNLS system is realised by using DT. Then, we obtain the breather solutions for the integrable CNLS system. The method is also appropriate for more non-linear soliton equations in physics and mathematics.
Lattice solitons in nonlinear Schrödinger equation with coupling-to-a-mean-term
Bağcı, Mahmut; Bakırtaş, İlkay; Antar, Nalan
2017-01-01
Wave collapse is arrested in the self-focusing nonlinear Schrödinger equation with coupling to a mean term (NLSM) by adding an external potential (lattice) to the governing equation. It is numerically demonstrated that collapse will eventually occur in a lattice-free system and it can be suppressed by adding an external periodic lattice to the governing system. It is numerically shown that lattice depth provides great controllability on soliton stability and more robust solitons can be obtained.
Classical FEM-BEM coupling methods: nonlinearities, well-posedness, and adaptivity
Aurada, Markus; Feischl, Michael; Führer, Thomas; Karkulik, Michael; Melenk, Jens Markus; Praetorius, Dirk
2013-04-01
We consider a (possibly) nonlinear interface problem in 2D and 3D, which is solved by use of various adaptive FEM-BEM coupling strategies, namely the Johnson-Nédélec coupling, the Bielak-MacCamy coupling, and Costabel's symmetric coupling. We provide a framework to prove that the continuous as well as the discrete Galerkin solutions of these coupling methods additionally solve an appropriate operator equation with a Lipschitz continuous and strongly monotone operator. Therefore, the original coupling formulations are well-defined, and the Galerkin solutions are quasi-optimal in the sense of a Céa-type lemma. For the respective Galerkin discretizations with lowest-order polynomials, we provide reliable residual-based error estimators. Together with an estimator reduction property, we prove convergence of the adaptive FEM-BEM coupling methods. A key point for the proof of the estimator reduction are novel inverse-type estimates for the involved boundary integral operators which are advertized. Numerical experiments conclude the work and compare performance and effectivity of the three adaptive coupling procedures in the presence of generic singularities.
Experimental characterization and modeling of non-linear coupling of the LHCD power on Tore Supra
Preynas, M.; Goniche, M.; Hillairet, J.; Litaudon, X.; Ekedahl, A.
2014-02-01
To achieve steady state operation on future tokamaks, in particular on ITER, the unique capability of a LHCD system to efficiently drive off-axis non-inductive current is needed. In this context, it is of prime importance to study and master the coupling of LH wave to the core plasma at high power density (tens of MW/m2). In some specific conditions, deleterious effects on the LHCD coupling are sometimes observed on Tore Supra. At high power the waves may modify the edge parameters that change the wave coupling properties in a non-linear manner. In this way, dedicated LHCD experiments have been performed using the LHCD system of Tore Supra, composed of two different conceptual designs of launcher: the Fully Active Multijunction (FAM) and the new Passive Active Multijunction (PAM) antennas. A nonlinear interaction between the electron density and the electric field has been characterized in a thin plasma layer in front of the two LHCD antennas. The resulting dependence of the power reflection coefficient with the LHCD power, leading occasionally to trips in the output power, is not predicted by the standard linear theory of the LH wave coupling. Therefore, it is important to investigate and understand the possible origin of such non-linear effects in order to avoid their possible deleterious consequences. The PICCOLO-2D code, which self-consistently treats the wave propagation in the antenna vicinity and its interaction with the local edge plasma density, is used to simulate Tore Supra discharges. The simulation reproduces very well the occurrence of a non-linear behavior in the coupling observed in the LHCD experiments. The important differences and trends between the FAM and the PAM antennas, especially a larger increase in RC for the FAM, are also reproduced by the PICCOLO-2D simulation. The working hypothesis of the contribution of the ponderomotive effect in the non-linear observations of LHCD coupling is therefore validated through this comprehensive modeling
Transport of quantum excitations coupled to spatially extended nonlinear many-body systems
Iubini, Stefano; Boada, Octavi; Omar, Yasser; Piazza, Francesco
2015-11-01
The role of noise in the transport properties of quantum excitations is a topic of great importance in many fields, from organic semiconductors for technological applications to light-harvesting complexes in photosynthesis. In this paper we study a semi-classical model where a tight-binding Hamiltonian is fully coupled to an underlying spatially extended nonlinear chain of atoms. We show that the transport properties of a quantum excitation are subtly modulated by (i) the specific type (local versus non-local) of exciton-phonon coupling and by (ii) nonlinear effects of the underlying lattice. We report a non-monotonic dependence of the exciton diffusion coefficient on temperature, in agreement with earlier predictions, as a direct consequence of the lattice-induced fluctuations in the hopping rates due to long-wavelength vibrational modes. A standard measure of transport efficiency confirms that both nonlinearity in the underlying lattice and off-diagonal exciton-phonon coupling promote transport efficiency at high temperatures, preventing the Zeno-like quench observed in other models lacking an explicit noise-providing dynamical system.
Nitzan, Sarah H; Zega, Valentina; Li, Mo; Ahn, Chae H; Corigliano, Alberto; Kenny, Thomas W; Horsley, David A
2015-01-01
Parametric amplification, resulting from intentionally varying a parameter in a resonator at twice its resonant frequency, has been successfully employed to increase the sensitivity of many micro- and nano-scale sensors. Here, we introduce the concept of self-induced parametric amplification, which arises naturally from nonlinear elastic coupling between the degenerate vibration modes in a micromechanical disk-resonator, and is not externally applied. The device functions as a gyroscope wherein angular rotation is detected from Coriolis coupling of elastic vibration energy from a driven vibration mode into a second degenerate sensing mode. While nonlinear elasticity in silicon resonators is extremely weak, in this high quality-factor device, ppm-level nonlinear elastic effects result in an order-of-magnitude increase in the observed sensitivity to Coriolis force relative to linear theory. Perfect degeneracy of the primary and secondary vibration modes is achieved through electrostatic frequency tuning, which also enables the phase and frequency of the parametric coupling to be varied, and we show that the resulting phase and frequency dependence of the amplification follow the theory of parametric resonance. We expect that this phenomenon will be useful for both fundamental studies of dynamic systems with low dissipation and for increasing signal-to-noise ratio in practical applications such as gyroscopes.
Variational principles for some nonlinear partial differential equations with variable coefficients
Energy Technology Data Exchange (ETDEWEB)
He Jihuan E-mail: jhhe@dhu.edu.cn
2004-03-01
Variational principles for generalized Korteweg-de Vries equation and nonlinear Schroedinger's equation are obtained by the semi-inverse method. The most interesting features of the proposed method are its extreme simplicity and concise forms of variational functionals for a wide range of nonlinear problems. Comparison with the results obtained by the Noether's theorem is made, revealing the present theorem is a straightforward and attracting mathematical tool.
Directory of Open Access Journals (Sweden)
T. D. Frank
2016-12-01
Full Text Available In physics, several attempts have been made to apply the concepts and tools of physics to the life sciences. In this context, a thermostatistic framework for active Nambu systems is proposed. The so-called free energy Fokker–Planck equation approach is used to describe stochastic aspects of active Nambu systems. Different thermostatistic settings are considered that are characterized by appropriately-defined entropy measures, such as the Boltzmann–Gibbs–Shannon entropy and the Tsallis entropy. In general, the free energy Fokker–Planck equations associated with these generalized entropy measures correspond to nonlinear partial differential equations. Irrespective of the entropy-related nonlinearities occurring in these nonlinear partial differential equations, it is shown that semi-analytical solutions for the stationary probability densities of the active Nambu systems can be obtained provided that the pumping mechanisms of the active systems assume the so-called canonical-dissipative form and depend explicitly only on Nambu invariants. Applications are presented both for purely-dissipative and for active systems illustrating that the proposed framework includes as a special case stochastic equilibrium systems.
Alpha/sub 1/ receptor coupling events initiated by methoxy-substituted tolazoline partial agonists
Energy Technology Data Exchange (ETDEWEB)
Wick, P.; Keung, A.; Deth, R.
1986-03-01
A series of mono- and dimethyoxy substituted tolazoline derivatives, known to be partial agonists at the alpha/sub 1/ receptor, were compared with the ..cap alpha../sub 1/ selective full agonist phenylephrine (PE) on isolated strips of rabbit aorta Agonist activity was evaluated in contraction, /sup 45/Ca influx, /sup 45/Ca efflux, and /sup 32/P-Phospholipid labelling studies. Maximum contractile responses for the 2-, 3-, and 3, 5- methoxy substituted tolazoline derivatives (10/sup -5/M) were 53.8, 67.6 and 99.7% of the PE (10/sup -5/M) response respectively. These same partial agonists caused a stimulation of /sup 45/Ca influx to the extent of 64, 86, and 95% of the PE response respectively. In /sup 45/Ca efflux studies, (a measure of the intracellular Ca/sup +2/ release) the tolazolines caused: 30%, 63%, and 78% of the PE stimulated level. /sup 32/P-Phosphatidic acid (PA) labelling was measured as an index of PI turnover after ..cap alpha../sub 1/ receptor stimulation. Compared to PE, the 2-, 3-, and 3,5- methoxy substituted tolazoline derivatives caused 22, 46, and 72% PA labelling. The above values are all in reasonable accord with the rank order or agonist activity shown in maximum contractile responses. The results of this investigation suggest that partial agonists stimulate ..cap alpha.. receptor coupling events at a level which is quantitatively comparable to their potencies in causing contraction of arterial smooth muscle.
Directory of Open Access Journals (Sweden)
Hui Cao
2014-01-01
Full Text Available Quantitative analysis for the flue gas of natural gas-fired generator is significant for energy conservation and emission reduction. The traditional partial least squares method may not deal with the nonlinear problems effectively. In the paper, a nonlinear partial least squares method with extended input based on radial basis function neural network (RBFNN is used for components prediction of flue gas. For the proposed method, the original independent input matrix is the input of RBFNN and the outputs of hidden layer nodes of RBFNN are the extension term of the original independent input matrix. Then, the partial least squares regression is performed on the extended input matrix and the output matrix to establish the components prediction model of flue gas. A near-infrared spectral dataset of flue gas of natural gas combustion is used for estimating the effectiveness of the proposed method compared with PLS. The experiments results show that the root-mean-square errors of prediction values of the proposed method for methane, carbon monoxide, and carbon dioxide are, respectively, reduced by 4.74%, 21.76%, and 5.32% compared to those of PLS. Hence, the proposed method has higher predictive capabilities and better robustness.
Cao, Hui; Yan, Xingyu; Li, Yaojiang; Wang, Yanxia; Zhou, Yan; Yang, Sanchun
2014-01-01
Quantitative analysis for the flue gas of natural gas-fired generator is significant for energy conservation and emission reduction. The traditional partial least squares method may not deal with the nonlinear problems effectively. In the paper, a nonlinear partial least squares method with extended input based on radial basis function neural network (RBFNN) is used for components prediction of flue gas. For the proposed method, the original independent input matrix is the input of RBFNN and the outputs of hidden layer nodes of RBFNN are the extension term of the original independent input matrix. Then, the partial least squares regression is performed on the extended input matrix and the output matrix to establish the components prediction model of flue gas. A near-infrared spectral dataset of flue gas of natural gas combustion is used for estimating the effectiveness of the proposed method compared with PLS. The experiments results show that the root-mean-square errors of prediction values of the proposed method for methane, carbon monoxide, and carbon dioxide are, respectively, reduced by 4.74%, 21.76%, and 5.32% compared to those of PLS. Hence, the proposed method has higher predictive capabilities and better robustness.
A hybrid algorithm for coupling partial differential equation and compartment-based dynamics.
Harrison, Jonathan U; Yates, Christian A
2016-09-01
Stochastic simulation methods can be applied successfully to model exact spatio-temporally resolved reaction-diffusion systems. However, in many cases, these methods can quickly become extremely computationally intensive with increasing particle numbers. An alternative description of many of these systems can be derived in the diffusive limit as a deterministic, continuum system of partial differential equations (PDEs). Although the numerical solution of such PDEs is, in general, much more efficient than the full stochastic simulation, the deterministic continuum description is generally not valid when copy numbers are low and stochastic effects dominate. Therefore, to take advantage of the benefits of both of these types of models, each of which may be appropriate in different parts of a spatial domain, we have developed an algorithm that can be used to couple these two types of model together. This hybrid coupling algorithm uses an overlap region between the two modelling regimes. By coupling fluxes at one end of the interface and using a concentration-matching condition at the other end, we ensure that mass is appropriately transferred between PDE- and compartment-based regimes. Our methodology gives notable reductions in simulation time in comparison with using a fully stochastic model, while maintaining the important stochastic features of the system and providing detail in appropriate areas of the domain. We test our hybrid methodology robustly by applying it to several biologically motivated problems including diffusion and morphogen gradient formation. Our analysis shows that the resulting error is small, unbiased and does not grow over time.
Anatomy of flavour-changing Z couplings in models with partial compositeness
Straub, David M
2013-01-01
In models with partially composite quarks, the couplings of quarks to the Z boson generically receive non-universal corrections that are not only constrained by electroweak precision tests but also lead to flavour-changing neutral currents at tree level. The impact of these flavour-changing couplings on rare K and B decays is studied in two-site models for three scenarios: an anarchic strong sector with two different choices of fermion representations both leading to a custodial protection of the Z->bb coupling, and for a strong sector invariant under a U(2)^3 flavour symmetry. In the complete numerical analysis, all relevant constraints from Delta(F)=2 processes are taken into account. In all scenarios, visible effects in rare K and B decays like K->pi nu anti-nu, B(s)->mu+mu- and B->K*mu+mu- are possible that can be scrutinized experimentally in the near future. Characteristic correlations between observables allow to distinguish the different cases. To sample the large parameter space of the anarchic model...
Energy Technology Data Exchange (ETDEWEB)
Wang Qi [Department of Applied Mathematics, Dalian University of Technology, Dalian 116024 (China) and Key Laboratory of Mathematics Mechanization, Chinese Academy of Sciences, Beijing 100080 (China)]. E-mail: wangqi_dlut@yahoo.com.cn; Chen Yong [Nonlinear Science Center, Department of Mathematics, Ningbo University, Ningbo 315211 (China)
2007-01-15
With the aid of symbolic computation, some algorithms are presented for the rational expansion methods, which lead to closed-form solutions of nonlinear partial differential equations (PDEs). The new algorithms are given to find exact rational formal polynomial solutions of PDEs in terms of Jacobi elliptic functions, solutions of the Riccati equation and solutions of the generalized Riccati equation. They can be implemented in symbolic computation system Maple. As applications of the methods, we choose some nonlinear PDEs to illustrate the methods. As a result, we not only can successfully obtain the solutions found by most existing Jacobi elliptic function methods and Tanh-methods, but also find other new and more general solutions at the same time.
Zaheer, Muhammad Hamad; Rehan, Muhammad; Mustafa, Ghulam; Ashraf, Muhammad
2014-11-01
This paper proposes a novel state feedback delay-range-dependent control approach for chaos synchronization in coupled nonlinear time-delay systems. The coupling between two systems is esteemed to be nonlinear subject to time-lags. Time-varying nature of both the intrinsic and the coupling delays is incorporated to broad scope of the present study for a better-quality synchronization controller synthesis. Lyapunov-Krasovskii (LK) functional is employed to derive delay-range-dependent conditions that can be solved by means of the conventional linear matrix inequality (LMI)-tools. The resultant control approach for chaos synchronization of the master-slave time-delay systems considers non-zero lower bound of the intrinsic as well as the coupling time-delays. Further, the delay-dependent synchronization condition has been established as a special case of the proposed LK functional treatment. Furthermore, a delay-range-dependent condition, independent of the delay-rate, has been provided to address the situation when upper bound of the delay-derivative is unknown. A robust state feedback control methodology is formulated for synchronization of the time-delay chaotic networks against the L2 norm bounded perturbations by minimizing the L2 gain from the disturbance to the synchronization error. Numerical simulation results are provided for the time-delay chaotic networks to show effectiveness of the proposed delay-range-dependent chaos synchronization methodologies. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.
Directory of Open Access Journals (Sweden)
Gui Mu
2013-01-01
Full Text Available The existence of the exponential attractors for coupled Ginzburg-Landau equations describing Bose-Einstein condensates and nonlinear optical waveguides and cavities with periodic initial boundary is obtained by showing Lipschitz continuity and the squeezing property.
Directory of Open Access Journals (Sweden)
Taha Aziz
2012-01-01
Full Text Available The unsteady unidirectional flow of an incompressible fourth grade fluid bounded by a suddenly moved rigid plate is studied. The governing nonlinear higher order partial differential equation for this flow in a semiinfinite domain is modelled. Translational symmetries in variables and are employed to construct two different classes of closed-form travelling wave solutions of the model equation. A conditional symmetry solution of the model equation is also obtained. The physical behavior and the properties of various interesting flow parameters on the structure of the velocity are presented and discussed. In particular, the significance of the rheological effects are mentioned.
A Non-Hermitian Approach to Non-Linear Switching Dynamics in Coupled Cavity-Waveguide Systems
DEFF Research Database (Denmark)
Heuck, Mikkel; Kristensen, Philip Trøst; Mørk, Jesper
2012-01-01
We present a non-Hermitian perturbation theory employing quasi-normal modes to investigate non-linear all-optical switching dynamics in a photonic crystal coupled cavity-waveguide system and compare with finite-difference-time-domain simulations.......We present a non-Hermitian perturbation theory employing quasi-normal modes to investigate non-linear all-optical switching dynamics in a photonic crystal coupled cavity-waveguide system and compare with finite-difference-time-domain simulations....
Fiber-coupled nanophotonic devices for nonlinear optics and cavity QED
Barclay, Paul Edward
2007-10-01
The sub-wavelength optical confinement and low optical loss of nanophotonic devices dramatically enhances the interaction between light and matter within these structures. When nanophotonic devices are combined with an efficient optical coupling channel, nonlinear optical behavior can be observed at low power levels in weakly-nonlinear materials. In a similar vein, when resonant atomic systems interact with nanophotonic devices, atom-photon coupling effects can be observed at a single quanta level. Crucially, the chip based nature of nanophotonics provides a scalable platform from which to study these effects. This thesis addresses the use of nanophotonic devices in nonlinear and quantum optics, including device design, optical coupling, fabrication and testing, modeling, and integration with more complex systems. We present a fiber taper coupling technique that allows efficient power transfer from an optical fiber into a photonic crystal waveguide. Greater than 97% power transfer into a silicon photonic crystal waveguide is demonstrated. This optical channel is then connected to a high-Q (> 40,000), ultra-small mode volume (V 44% of the photons input to a fiber. This permits the observation of optical bistability in silicon for sub-mW input powers at telecommunication wavelengths. To port this technology to cavity QED experiments at near-visible wavelengths, we also study silicon nitride microdisk cavities at wavelengths near 852 nm, and observe resonances with Q > 3 million and V device with an atom chip, creating an "atom-cavity chip" which can magnetically trap laser cooled atoms above the microcavity. Calculations of the microcavity single atom sensitivity as a function of Q/V are presented and compared with numerical simulations. Taking into account non-idealities, these cavities should allow detection of single laser cooled cesium atoms.
Linear and nonlinear heavy ion-acoustic waves in a strongly coupled plasma
Energy Technology Data Exchange (ETDEWEB)
Ema, S. A., E-mail: ema.plasma@gmail.com; Mamun, A. A. [Department of Physics, Jahangirnagar University, Savar, Dhaka-1342 (Bangladesh); Hossen, M. R. [Deparment of Natural Sciences, Daffodil International University, Sukrabad, Dhaka-1207 (Bangladesh)
2015-09-15
A theoretical study on the propagation of linear and nonlinear heavy ion-acoustic (HIA) waves in an unmagnetized, collisionless, strongly coupled plasma system has been carried out. The plasma system is assumed to contain adiabatic positively charged inertial heavy ion fluids, nonextensive distributed electrons, and Maxwellian light ions. The normal mode analysis is used to study the linear behaviour. On the other hand, the well-known reductive perturbation technique is used to derive the nonlinear dynamical equations, namely, Burgers equation and Korteweg-de Vries (K-dV) equation. They are also numerically analyzed in order to investigate the basic features of shock and solitary waves. The adiabatic effects on the HIA shock and solitary waves propagating in such a strongly coupled plasma are taken into account. It has been observed that the roles of the adiabatic positively charged heavy ions, nonextensivity of electrons, and other plasma parameters arised in this investigation have significantly modified the basic features (viz., polarity, amplitude, width, etc.) of the HIA solitary/shock waves. The findings of our results obtained from this theoretical investigation may be useful in understanding the linear as well as nonlinear phenomena associated with the HIA waves both in space and laboratory plasmas.
Viscosity solutions of fully nonlinear second-order elliptic partial differential equations
Ishii, H.; Lions, P. L.
We investigate comparison and existence results for viscosity solutions of fully nonlinear, second-order, elliptic, possibly degenerate equations. These results complement those recently obtained by R. Jensen and H. Ishii. We consider various boundary conditions like for instance Dirichlet and Neumann conditions. We also apply these methods and results to quasilinear Monge-Ampère equations. Finally, we also address regularity questions.
Stabilization of Networked Distributed Systems with Partial and Event-Based Couplings
Directory of Open Access Journals (Sweden)
Sufang Zhang
2015-01-01
Full Text Available The stabilization problem of networked distributed systems with partial and event-based couplings is investigated. The channels, which are used to transmit different levels of information of agents, are considered. The channel matrix is introduced to indicate the work state of the channels. An event condition is designed for each channel to govern the sampling instants of the channel. Since the event conditions are separately given for different channels, the sampling instants of channels are mutually independent. To stabilize the system, the state feedback controllers are implemented in the system. The control signals also suffer from the two communication constraints. The sufficient conditions in terms of linear matrix equalities are proposed to ensure the stabilization of the controlled system. Finally, a numerical example is given to demonstrate the advantage of our results.
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. ...
Iaquaniello, G; Salladini, A; Palo, E; Centi, G
2015-02-01
Catalytic partial oxidation coupled with membrane purification is a new process scheme to improve resource and energy efficiency in a well-established and large scale-process like syngas production. Experimentation in a semi industrial-scale unit (20 Nm(3) h(-1) production) shows that a novel syngas production scheme based on a pre-reforming stage followed by a membrane for hydrogen separation, a catalytic partial oxidation step, and a further step of syngas purification by membrane allows the oxygen-to-carbon ratio to be decreased while maintaining levels of feed conversion. For a total feed conversion of 40 %, for example, the integrated novel architecture reduces oxygen consumption by over 50 %, with thus a corresponding improvement in resource efficiency and an improved energy efficiency and economics, these factors largely depending on the air separation stage used to produce pure oxygen. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Murrell, J K J
2001-01-01
previously unexplored regions of parameter space. We show that these calculations predict a range of previously unreported dynamical I-V characterises for SQUID rings in the strongly hysteretic regime. Finally, we present the successful realisation of a novel experimental technique that permits the weak link of a SQUID to be probed independently of the associated ring structure by mechanically opening and closing the ring. We demonstrate that this process can be completed during the same experimental run without the need for warming and re-cooling of the sample. This thesis is concerned with the investigation of the non-linear behaviour of a Superconducting Quantum Interference Device (SQUID) coupled to a RF tank circuit. We consider two regimes, one where the underlying SQUID behaviour is non-hysteretic with respect to an externally applied magnetic flux, and the other where hysteretic (dissipative) behaviour is observed. We show that, by following non-linearities induced in the tank circuit response, the un...
Mukamel, Shaul
2003-08-01
Computing response functions by following the time evolution of superoperators in Liouville space (whose vectors are ordinary Hilbert space operators) offers an attractive alternative to the diagrammatic perturbative expansion of many-body equilibrium and nonequilibrium Green's functions. The bookkeeping of time ordering is naturally maintained in real (physical) time, allowing the formulation of Wick's theorem for superoperators, giving a factorization of higher order response functions in terms of two fundamental Green's functions. Backward propagations and analytic continuations using artificial times (Keldysh loops and Matsubara contours) are avoided. A generating functional for nonlinear response functions unifies quantum field theory and the classical mode coupling formalism of nonlinear hydrodynamics and may be used for semiclassical expansions. Classical response functions are obtained without the explicit computation of stability matrices.
Nonlinear localized flat-band modes with spin-orbit coupling
Gligorić, G.; Maluckov, A.; Hadžievski, Lj.; Flach, Sergej; Malomed, Boris A.
2016-10-01
We report the coexistence and properties of stable compact localized states (CLSs) and discrete solitons (DSs) for nonlinear spinor waves on a flat-band network with spin-orbit coupling (SOC). The system can be implemented by means of a binary Bose-Einstein condensate loaded in the corresponding optical lattice. In the linear limit, the SOC opens a minigap between flat and dispersive bands in the system's band-gap structure, and preserves the existence of CLSs at the flat-band frequency, simultaneously lowering their symmetry. Adding on-site cubic nonlinearity, the CLSs persist and remain available in an exact analytical form, with frequencies that are smoothly tuned into the minigap. Inside of the minigap, the CLS and DS families are stable in narrow areas adjacent to the FB. Deep inside the semi-infinite gap, both the CLSs and DSs are stable too.
Scalar-tensor black holes coupled to Born-Infeld nonlinear electrodynamics
Stefanov, Ivan Zh; Todorov, Michail D
2007-01-01
The non-existence of asymptotically flat, neutral black holes and asymptotically flat, charged black holes in the Maxwell electrodynamics, with non-trivial scalar field has been proved for a large class of scalar-tensor theories. The no-scalar-hair theorems, however, do not apply in the case of non-linear electrodynamics. In the present work numerical solutions describing charged black holes coupled to Born-Infeld type non-linear electrodynamics in scalar-tensor theories of gravity with massless scalar field are found. The causal structure and properties of the solutions are studied, and a comparison between these solutions and the corresponding solutions in the General Relativity is made. The presence of the scalar field leads to a much more simple causal structure. The present class of black holes has a single, non-degenerate horizon, i.e., its causal structure resembles that of the Schwarzschild black hole.
Scalar-tensor black holes coupled to Euler-Heisenberg nonlinear electrodynamics
Stefanov, Ivan Zh; Todorov, Michail D
2007-01-01
The no-scalar-hair conjecture rules out the existence of asymptotically flat black holes with a scalar dressing for a large class of theories. No-scalar-hair theorems have been proved for the cases of neutral black holes and for charged black holes in the Maxwell electrodynamics. These theorems, however, do not apply in the case of non-linear electrodynamics. In the present work numerical solutions describing charged black holes coupled to Euler-Heisenberg type non-linear electrodynamics in scalar-tensor theories of gravity with massless scalar field are found. In comparison to the corresponding solution in General Relativity the presented solution has a simpler causal structure the reason for which is the presence of the scalar field. The present class of black holes has a single, non-degenerate horizon, i.e., its causal structure resembles that of the Schwarzschild black hole.
Directory of Open Access Journals (Sweden)
El Aroudi A.
2014-01-01
Full Text Available Nonlinearities have been shown to play an important role in increasing the extracted energy of energy harvesting devices at the macro and micro scales. Vibration-based energy harvesting on the nano scale has also received attention. In this paper, we characterize the nonlinear dynamical behavior of an array of three coupled strained nanostructured graphene for its potential use in energy harvesting applications. The array is formed by three compressed vibrating membrane graphene sheet subject to external vibrational noise excitation. We present the continuous time dynamical model of the system in the form of a double-well three degree of freedom system. Random vibrations are considered as the main ambient energy source for the system and its performances in terms of the probability density function, RMS or amplitude value of the position, FFT spectra and state plane trajectories are presented in the steady state non-equilibrium regime when the noise level is considered as a control parameter.
Geometry effect on energy transfer rate in a coupled-quantum-well structure: nonlinear regime
Salavati-fard, T.; Vazifehshenas, T.
2014-12-01
We study theoretically the effect of geometry on the energy transfer rate at nonlinear regime in a coupled-quantum-well system using the balance equation approach. To investigate comparatively the effect of both symmetric and asymmetric geometry, different structures are considered. The random phase approximation dynamic dielectric function is employed to include the contributions from both quasiparticle and plasmon excitations. Also, the short-range exchange interaction is taken into account through the Hubbard approximation. Our numerical results show that the energy transfer rate increases by increasing the well thicknesses in symmetric structures. Furthermore, by increasing spatial asymmetry, the energy transfer rate decreases for the electron temperature range of interest. From numerical calculations, it is obtained that the nonlinear energy transfer rate is proportional to the square of electron drift velocity in all structures and also, found that the influence of Hubbard local field correction on the energy transfer rate gets weaker by increasing the strength of applied electric field.
A Haar wavelet collocation method for coupled nonlinear Schrödinger-KdV equations
Oruç, Ömer; Esen, Alaattin; Bulut, Fatih
2016-04-01
In this paper, to obtain accurate numerical solutions of coupled nonlinear Schrödinger-Korteweg-de Vries (KdV) equations a Haar wavelet collocation method is proposed. An explicit time stepping scheme is used for discretization of time derivatives and nonlinear terms that appeared in the equations are linearized by a linearization technique and space derivatives are discretized by Haar wavelets. In order to test the accuracy and reliability of the proposed method L2, L∞ error norms and conserved quantities are used. Also obtained results are compared with previous ones obtained by finite element method, Crank-Nicolson method and radial basis function meshless methods. Error analysis of Haar wavelets is also given.
Flow-induced vibrations of long circular cylinders modeled by coupled nonlinear oscillators
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
The dynamics of long slender cylinders undergoing vortex-induced vibrations (VIV) is studied in this work. Long slender cylinders such as risers or tension legs are widely used in the field of ocean engineering. When the sea current flows past a cylinder, it will be excited due to vortex shedding. A three-dimensional time domain model is formulated to describe the response of the cylinder, in which the in-line (IL) and cross-flow (CF) deflections are coupled. The wake dynamics, including in-line and cross-flow vibrations, is represented using a pair of non-linear oscillators distributed along the cylinder. The wake oscillators are coupled to the dynamics of the long cylinder with the acceleration coupling term. A non-linear fluid force model is accounted for to reflect the relative motion of cylinder to current. The model is validated against the published data from a tank experiment with the free span riser. The comparisons show that some aspects due to VIV of long flexible cylinders can be reproduced by the proposed model, such as vibrating frequency, dominant mode number, occurrence and transition of the standing or traveling waves. In the case study, the simulations show that the IL curvature is not smaller than CF curvature, which indicates that both IL and CF vibrations are important for the structural fatigue damage.
Jiang, Zhongzheng; Zhao, Wenwen
2016-01-01
Non-equilibrium effects play a vital role in high-speed and rarefied gas flows and the accurate simulation of these flow regimes are far beyond the capability of near-local-equilibrium Navier-Stokes-Fourier equations. Eu proposed generalized hydrodynamic equations which are consistent with the laws of irreversible thermodynamics to solve this problem. Based on Eu's generalized hydrodynamics equations, a computational model, namely the nonlinear coupled constitutive relations(NCCR),was developed by R.S.Myong and applied successfully to one-dimensional shock wave structure and two-dimensional rarefied flows. In this paper, finite volume schemes, including LU-SGS time advance scheme, MUSCL interpolation and AUSMPW+ scheme, are fistly adopted to investigate NCCR model's validity and potential in three-dimensional complex hypersonic rarefied gas flows. Moreover, in order to solve the computational stability problems in 3D complex flows,a modified solution is developed for the NCCR model. Finally, the modified solu...
A partially open porous media flow with chaotic advection: towards a model of coupled fields.
Metcalfe, Guy; Lester, Daniel; Ord, Alison; Kulkarni, Pandurang; Trefry, Mike; Hobbs, Bruce E; Regenaur-Lieb, Klaus; Morris, Jeffery
2010-01-13
In nature, dissipative fluxes of fluid, heat and/or reacting species couple to each other and may also couple to deformation of a surrounding porous matrix. We use the well-known analogy of Hele-Shaw flow to Darcy flow to make a model porous medium with porosity proportional to local cell height. Time- and space-varying fluid injection from multiple source/sink wells lets us create many different kinds of chaotic flows and chemical concentration patterns. Results of an initial time-dependent potential flow model illustrate that this is a partially open flow, in which parts of the material transported by the flow remain in the cell forever and parts pass through with residence time and exit time distributions that have self-similar features in the control parameter space of the stirring. We derive analytically the existence boundary in stirring control parameter space between where isolated fluid regions can and cannot remain forever in the open flow. Experiments confirm the predictions.
Mittal, R. C.; Jain, R. K.
2012-12-01
In this paper, a numerical method is proposed to approximate the solution of the nonlinear parabolic partial differential equation with Neumann's boundary conditions. The method is based on collocation of cubic B-splines over finite elements so that we have continuity of the dependent variable and its first two derivatives throughout the solution range. We apply cubic B-splines for spatial variable and its derivatives, which produce a system of first order ordinary differential equations. We solve this system by using SSP-RK3 scheme. The numerical approximate solutions to the nonlinear parabolic partial differential equations have been computed without transforming the equation and without using the linearization. Four illustrative examples are included to demonstrate the validity and applicability of the technique. In numerical test problems, the performance of this method is shown by computing L∞andL2error norms for different time levels. Results shown by this method are found to be in good agreement with the known exact solutions.
Cortes, Adriano Mauricio
2014-01-01
In this paper we present PetIGA, a high-performance implementation of Isogeometric Analysis built on top of PETSc. We show its use in solving nonlinear and time-dependent problems, such as phase-field models, by taking advantage of the high-continuity of the basis functions granted by the isogeometric framework. In this work, we focus on the Cahn-Hilliard equation and the phase-field crystal equation.
3-D zebrafish embryo image filtering by nonlinear partial differential equations.
Rizzi, Barbara; Campana, Matteo; Zanella, Cecilia; Melani, Camilo; Cunderlik, Robert; Krivá, Zuzana; Bourgine, Paul; Mikula, Karol; Peyriéras, Nadine; Sarti, Alessandro
2007-01-01
We discuss application of nonlinear PDE based methods to filtering of 3-D confocal images of embryogenesis. We focus on the mean curvature driven and the regularized Perona-Malik equations, where standard as well as newly suggested edge detectors are used. After presenting the related mathematical models, the practical results are given and discussed by visual inspection and quantitatively using the mean Hausdorff distance.
Superdiffusions and positive solutions of non-linear partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Dynkin, E B [Cornell University, New York (United States)
2004-02-28
By using super-Brownian motion, all positive solutions of the non-linear differential equation {delta}u=u{sup {alpha}} with 1<{alpha}{<=}2 in a bounded smooth domain E are characterized by their (fine) traces on the boundary. This solves a problem posed by the author a few years ago. The special case {alpha}=2 was treated by B. Mselati in 2002.
An Efficient Implementation of Partial Condensing for Nonlinear Model Predictive Control
DEFF Research Database (Denmark)
Frison, Gianluca; Kouzoupis, Dimitris; Jørgensen, John Bagterp
2016-01-01
Partial (or block) condensing is a recently proposed technique to reformulate a Model Predictive Control (MPC) problem into a form more suitable for structure-exploiting Quadratic Programming (QP) solvers. It trades off horizon length for input vector size, and this degree of freedom can be emplo......Partial (or block) condensing is a recently proposed technique to reformulate a Model Predictive Control (MPC) problem into a form more suitable for structure-exploiting Quadratic Programming (QP) solvers. It trades off horizon length for input vector size, and this degree of freedom can...
Energy Technology Data Exchange (ETDEWEB)
Schüler, D.; Alonso, S.; Bär, M. [Physikalisch-Technische Bundesanstalt, Abbestrasse 2-12, 10587 Berlin (Germany); Torcini, A. [CNR-Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi - Via Madonna del Piano 10, I-50019 Sesto Fiorentino (Italy); INFN Sez. Firenze, via Sansone 1, I-50019 Sesto Fiorentino (Italy)
2014-12-15
Pattern formation often occurs in spatially extended physical, biological, and chemical systems due to an instability of the homogeneous steady state. The type of the instability usually prescribes the resulting spatio-temporal patterns and their characteristic length scales. However, patterns resulting from the simultaneous occurrence of instabilities cannot be expected to be simple superposition of the patterns associated with the considered instabilities. To address this issue, we design two simple models composed by two asymmetrically coupled equations of non-conserved (Swift-Hohenberg equations) or conserved (Cahn-Hilliard equations) order parameters with different characteristic wave lengths. The patterns arising in these systems range from coexisting static patterns of different wavelengths to traveling waves. A linear stability analysis allows to derive a two parameter phase diagram for the studied models, in particular, revealing for the Swift-Hohenberg equations, a co-dimension two bifurcation point of Turing and wave instability and a region of coexistence of stationary and traveling patterns. The nonlinear dynamics of the coupled evolution equations is investigated by performing accurate numerical simulations. These reveal more complex patterns, ranging from traveling waves with embedded Turing patterns domains to spatio-temporal chaos, and a wide hysteretic region, where waves or Turing patterns coexist. For the coupled Cahn-Hilliard equations the presence of a weak coupling is sufficient to arrest the coarsening process and to lead to the emergence of purely periodic patterns. The final states are characterized by domains with a characteristic length, which diverges logarithmically with the coupling amplitude.
Non-linear curvature perturbation in multi-field inflation models with non-minimal coupling
Energy Technology Data Exchange (ETDEWEB)
White, Jonathan; Minamitsuji, Masato; Sasaki, Misao, E-mail: jwhite@yukawa.kyoto-u.ac.jp, E-mail: masato.minamitsuji@ist.utl.pt, E-mail: misao@yukawa.kyoto-u.ac.jp [Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502 (Japan)
2013-09-01
Using the δN formalism we consider the non-linear curvature perturbation in multi-field models of inflation with non-minimal coupling. In particular, we focus on the relation between the δN formalism as applied in the conformally related Jordan and Einstein frames. Exploiting results already known in the Einstein frame, we give expressions for the power spectrum, spectral tilt and non-gaussianity associated with the Jordan frame curvature perturbation. In the case that an adiabatic limit has not been reached, we find that in general these quantities differ from those associated with the Einstein frame curvature perturbation, and also confirm their equivalence in the absence of isocurvature modes. We then proceed to consider two analytically soluble examples, the first involving a non-minimally coupled 'spectator' field and the second being a non-minimally coupled extension of the multi-brid inflation model. In the first model we find that predictions can easily be brought into agreement with the recent Planck results, as the tensor-to-scalar ratio is generally small, the spectral tilt tuneable and the non-gaussianity suppressed. In the second model we find that predictions for all three parameters can differ substantially from those predicted in the minimally coupled case, and that the recent Planck results for the spectral tilt can be used to constrain the non-minimal coupling parameters.
Coupled Nonlinear Schr(o)dinger Equation: Symmetries and Exact Solutions
Institute of Scientific and Technical Information of China (English)
LIU Ping; LOU Sen-Yue
2009-01-01
The symmetries, symmetry reductions, and exact solutions of a coupled nonlinear Schr(o)dinger (CNLS) equation derived from the governing system for atmospheric gravity waves are researched by means of classical Lie group approach in this paper. Calculation shows the CNLS equation is invariant under some Galilean transformations, scaling transformations, phase shifts, and space-time translations. Some ordinary differential equations are derived from the CNLS equation. Several exact solutions including envelope cnoidal waves, solitary waves and trigonometric function solutions for the CNLS equation are also obtained by making use of symmetries.
Coexistence of synchrony and incoherence in oscillatory media under nonlinear global coupling
Energy Technology Data Exchange (ETDEWEB)
Schmidt, Lennart; García-Morales, Vladimir [Physik-Department, Nonequilibrium Chemical Physics, Technische Universität München, James-Franck-Str. 1, D-85748 Garching (Germany); Institute for Advanced Study, Technische Universität München, Lichtenbergstr. 2a, D-85748 Garching (Germany); Schönleber, Konrad; Krischer, Katharina, E-mail: krischer@tum.de [Physik-Department, Nonequilibrium Chemical Physics, Technische Universität München, James-Franck-Str. 1, D-85748 Garching (Germany)
2014-03-15
We report a novel mechanism for the formation of chimera states, a peculiar spatiotemporal pattern with coexisting synchronized and incoherent domains found in ensembles of identical oscillators. Considering Stuart-Landau oscillators, we demonstrate that a nonlinear global coupling can induce this symmetry breaking. We find chimera states also in a spatially extended system, a modified complex Ginzburg-Landau equation. This theoretical prediction is validated with an oscillatory electrochemical system, the electro-oxidation of silicon, where the spontaneous formation of chimeras is observed without any external feedback control.
Directory of Open Access Journals (Sweden)
Helge Holden
2003-04-01
Full Text Available We prove existence and uniqueness of entropy solutions for the Cauchy problem of weakly coupled systems of nonlinear degenerate parabolic equations. We prove existence of an entropy solution by demonstrating that the Engquist-Osher finite difference scheme is convergent and that any limit function satisfies the entropy condition. The convergence proof is based on deriving a series of a priori estimates and using a general $L^p$ compactness criterion. The uniqueness proof is an adaption of Kruzkov's ``doubling of variables'' proof. We also present a numerical example motivated by biodegradation in porous media.
Nonlinear Parasitic Capacitance Modelling of High Voltage Power MOSFETs in Partial SOI Process
DEFF Research Database (Denmark)
Fan, Lin; Knott, Arnold; Jørgensen, Ivan Harald Holger
2016-01-01
: off-state, sub-threshold region, and on-state in the linear region. A high voltage power MOSFET is designed in a partial Silicon on Insulator (SOI) process, with the bulk as a separate terminal. 3D plots and contour plots of the capacitances versus bias voltages for the transistor summarize...
Optimization of Nonlinear Figure-of-Merits of Integrated Power MOSFETs in Partial SOI Process
DEFF Research Database (Denmark)
Fan, Lin; Jørgensen, Ivan Harald Holger; Knott, Arnold
2016-01-01
different operating conditions. A systematic analysis of the optimization of these FOMs has not been previously established. The optimization methods are verified on a 100 V power MOSFET implemented in a 0.18 µm partial SOI process. Its FOMs are lowered by 1.3-18.3 times and improved by 22...
Oscillations of the Solutions of Nonlinear Delay Hyperbolic Partial Differential Equations
Institute of Scientific and Technical Information of China (English)
LIU An-ping; GUO Yan-feng; YANG Xiang-hui
2004-01-01
In this paper, oscillatory properties of solutions of certain hyperbolic partial differential equations with multi-delays are investigated and a series of sufficient conditions for oscillations of the equations are established. Theresults fully indicate that the oscillations are caused by delays.
Institute of Scientific and Technical Information of China (English)
CHEN Nan-xiang; CAO Lian-hai; HUANG Qiang
2005-01-01
Scientific forecasting water yield of mine is of great significance to the safety production of mine and the colligated using of water resources. The paper established the forecasting model for water yield of mine, combining neural network with the partial least square method. Dealt with independent variables by the partial least square method, it can not only solve the relationship between independent variables but also reduce the input dimensions in neural network model, and then use the neural network which can solve the non-linear problem better. The result of an example shows that the prediction has higher precision in forecasting and fitting.
Nonlinear coupling analysis of coal seam floor during mining based on FLAC3D
Institute of Scientific and Technical Information of China (English)
YAO Duo-xi; XU Ji-ying; LU Hai-feng
2011-01-01
Based on the hydro-geological conditions of 1028 mining face in Suntuan Coal Mine, mining seepage strain mechanism of seam floor was simulated by a nonlinear coupling method, which applied fluid-solid coupling analysis module of FLAC3D. The results indicate that the permeability coefficient of adjoining rock changes a lot due to mining. The maximum value reaches 1 379.9 times to the original value, where it is at immediate roof of the mined-out area. According to the analysis on the seepage field, mining does not destroy water resistance of the floor aquiclude. The mining fissure does not conduct lime-stone aquifer, and it is less likely to form damage. The plastic zone does not exactly correspond to the seepage area, and the scope of the altered seepage area is much larger than the plastic zone.
Subharmonic phase clusters in the complex Ginzburg-Landau equation with nonlinear global coupling.
García-Morales, Vladimir; Orlov, Alexander; Krischer, Katharina
2010-12-01
A wide variety of subharmonic n -phase cluster patterns was observed in experiments with spatially extended chemical and electrochemical oscillators. These patterns cannot be captured with a phase model. We demonstrate that the introduction of a nonlinear global coupling (NGC) in the complex Ginzburg-Landau equation has subharmonic cluster pattern solutions in wide parameter ranges. The NGC introduces a conservation law for the oscillatory state of the homogeneous mode, which describes the strong oscillations of the mean field in the experiments. We show that the NGC causes a pronounced 2:1 self-resonance on any spatial inhomogeneity, leading to two-phase subharmonic clustering, as well as additional higher resonances. Nonequilibrium Ising-Bloch transitions occur as the coupling strength is varied.
Institute of Scientific and Technical Information of China (English)
Cai-Wan Chang-Jian; Her-Terng Yau
2007-01-01
This study performs a dynamic analysis of a rotor supported by two squeeze couple stress fluid film journal bearings with nonlinear suspension. The numerical results show that the stability of the system varies with the non-dimensional speed ratios and the dimensionless parameter l*. It is found that the system is more stable with higher dimensionless parameter l*.Thus it can conclude that the rotor-bearing system lubricated with the couple stress fluid is more stable than that with the conventional Newtonian fluid. The modeling results thus obtained by using the method proposed in this paper can be used to predict the stability of the rotor-bearing system and the undesirable behavior of the rotor and bearing center can be avoided.
Nonlinear coupled dynamics of liquid-filled spherical container in microgravity
Institute of Scientific and Technical Information of China (English)
YUE Bao-zeng
2008-01-01
Nonlinear coupled dynamics of a liquid-filled spherical container in micro- gravity are investigated. The governing equations of the low-gravity liquid sloshing in a convex axisymmetrical container subjected to lateral excitation is obtained by the vari- ational principle and solved with a modal analysis method. The variational formulas are transformed into a frequency equation in the form of a standard eigenvalue problem by the Galerkin method, in which admissible functions for the velocity potential and the liquid free surface displacement are determined analytically in terms of the Gaussian hypergeometric series. The coupled dynamic equations of the liquid-filed container are derived using the Lagrange's method and are numerically solved. The time histories of the modal solutions are obtained in numerical simulations.
Jameson, A.
1976-01-01
A review is presented of some recently developed numerical methods for the solution of nonlinear equations of mixed type. The methods considered use finite difference approximations to the differential equation. Central difference formulas are employed in the subsonic zone and upwind difference formulas are used in the supersonic zone. The relaxation method for the small disturbance equation is discussed and a description is given of difference schemes for the potential flow equation in quasi-linear form. Attention is also given to difference schemes for the potential flow equation in conservation form, the analysis of relaxation schemes by the time dependent analogy, the accelerated iterative method, and three-dimensional calculations.
Nonlinear Second-Order Partial Differential Equation-Based Image Smoothing Technique
Directory of Open Access Journals (Sweden)
Tudor Barbu
2016-09-01
Full Text Available A second-order nonlinear parabolic PDE-based restoration model is provided in this article. The proposed anisotropic diffusion-based denoising approach is based on some robust versions of the edge-stopping function and of the conductance parameter. Two stable and consistent approximation schemes are then developed for this differential model. Our PDE-based filtering technique achieves an efficient noise removal while preserving the edges and other image features. It outperforms both the conventional filters and also many PDE-based denoising approaches, as it results from the successful experiments and method comparison applied.
The non-linear coupled spin 2-spin 3 Cotton equation in three dimensions
Linander, Hampus; Nilsson, Bengt E. W.
2016-07-01
In the context of three-dimensional conformal higher spin theory we derive, in the frame field formulation, the full non-linear spin 3 Cotton equation coupled to spin 2. This is done by solving the corresponding Chern-Simons gauge theory system of equations, that is, using F = 0 to eliminate all auxiliary fields and thus expressing the Cotton equation in terms of just the spin 3 frame field and spin 2 covariant derivatives and tensors (Schouten). In this derivation we neglect the spin 4 and higher spin sectors and approximate the star product commutator by a Poisson bracket. The resulting spin 3 Cotton equation is complicated but can be related to linearized versions in the metric formulation obtained previously by other authors. The expected symmetry (spin 3 "translation", "Lorentz" and "dilatation") properties are verified for Cotton and other relevant tensors but some perhaps unexpected features emerge in the process, in particular in relation to the non-linear equations. We discuss the structure of this non-linear spin 3 Cotton equation but its explicit form is only presented here, in an exact but not completely refined version, in appended files obtained by computer algebra methods. Both the frame field and metric formulations are provided.
Arqub, Omar Abu; El-Ajou, Ahmad; Momani, Shaher
2015-07-01
Building fractional mathematical models for specific phenomena and developing numerical or analytical solutions for these fractional mathematical models are crucial issues in mathematics, physics, and engineering. In this work, a new analytical technique for constructing and predicting solitary pattern solutions of time-fractional dispersive partial differential equations is proposed based on the generalized Taylor series formula and residual error function. The new approach provides solutions in the form of a rapidly convergent series with easily computable components using symbolic computation software. For method evaluation and validation, the proposed technique was applied to three different models and compared with some of the well-known methods. The resultant simulations clearly demonstrate the superiority and potentiality of the proposed technique in terms of the quality performance and accuracy of substructure preservation in the construct, as well as the prediction of solitary pattern solutions for time-fractional dispersive partial differential equations.
Energy Technology Data Exchange (ETDEWEB)
Zenchuk, A I, E-mail: zenchuk@itp.ac.r [Institute of Problems of Chemical Physics, RAS Acad. Semenov av., 1 Chernogolovka, Moscow region 142432 (Russian Federation)
2010-06-18
We develop a new integration technique allowing one to construct a rich manifold of particular solutions to multidimensional generalizations of classical C- and S-integrable partial differential equations (PDEs). Generalizations of (1+1)-dimensional C-integrable and (2+1)-dimensional S-integrable N-wave equations are derived among examples. Examples of multidimensional second-order PDEs are represented as well.
XMDS2: Fast, scalable simulation of coupled stochastic partial differential equations
Dennis, Graham R.; Hope, Joseph J.; Johnsson, Mattias T.
2013-01-01
XMDS2 is a cross-platform, GPL-licensed, open source package for numerically integrating initial value problems that range from a single ordinary differential equation up to systems of coupled stochastic partial differential equations. The equations are described in a high-level XML-based script, and the package generates low-level optionally parallelised C++ code for the efficient solution of those equations. It combines the advantages of high-level simulations, namely fast and low-error development, with the speed, portability and scalability of hand-written code. XMDS2 is a complete redesign of the XMDS package, and features support for a much wider problem space while also producing faster code. Program summaryProgram title: XMDS2 Catalogue identifier: AENK_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENK_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License, version 2 No. of lines in distributed program, including test data, etc.: 872490 No. of bytes in distributed program, including test data, etc.: 45522370 Distribution format: tar.gz Programming language: Python and C++. Computer: Any computer with a Unix-like system, a C++ compiler and Python. Operating system: Any Unix-like system; developed under Mac OS X and GNU/Linux. RAM: Problem dependent (roughly 50 bytes per grid point) Classification: 4.3, 6.5. External routines: The external libraries required are problem-dependent. Uses FFTW3 Fourier transforms (used only for FFT-based spectral methods), dSFMT random number generation (used only for stochastic problems), MPI message-passing interface (used only for distributed problems), HDF5, GNU Scientific Library (used only for Bessel-based spectral methods) and a BLAS implementation (used only for non-FFT-based spectral methods). Nature of problem: General coupled initial-value stochastic partial differential equations. Solution method: Spectral method
Model of nonlinear coupled thermo-hydro-elastodyanamics response for a saturated poroelastic medium
Institute of Scientific and Technical Information of China (English)
LIU GanBin; XIE KangHe; ZHENG RongYue
2009-01-01
Based on the Blot's wave equation and theory of thermodynamic,Darcy law of fluid and the modified Fourier law of heat conduction,a nonlinear fully coupled thermo-hydro-elastodynamic response model(THMD)for saturated porous medium is derived.The compressibility of the medium,the influence of fluid flux on the heat flux,and the influence of change of temperature on the fluid flux are considered in this model.With some simplification,the coupled nonlinear thermo-hydro-elastodynamic response model can be reduced to the thermo-elastodynamic(TMD)model based on the traditional Fourier law and,further more,to the Blot's wave equation without considering the heat phase.At last,the problem of one dimensional cylindrical cavity subjected to a time-dependent thermal/mechanical shock is analyzed by using the Laplace technique,the numerical results are used to discuss the influence of Blot's modulus M and coefficient of thermo-osmosis on displacement and to compare with the results of thermo-elastodynamic response to ascertain the validity of this model.
Model of nonlinear coupled thermo-hydro-elastodynamics response for a saturated poroelastic medium
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
Based on the Biot’s wave equation and theory of thermodynamic, Darcy law of fluid and the modified Fourier law of heat conduction, a nonlinear fully coupled thermo-hydro-elastodynamic response model (THMD) for saturated porous medium is derived. The compressibility of the medium, the influence of fluid flux on the heat flux, and the influence of change of temperature on the fluid flux are considered in this model. With some simplification, the coupled nonlinear thermo-hydro-elastodynamic response model can be reduced to the thermo-elastodynamic (TMD) model based on the traditional Fourier law and, further more, to the Biot’s wave equation without considering the heat phase. At last, the problem of one dimensional cylindrical cavity subjected to a time-dependent thermal/mechanical shock is analyzed by using the Laplace technique, the numerical results are used to discuss the influence of Biot’s modulus M and coefficient of thermoos-mosis on displacement and to compare with the results of thermo-elastodynamic response to ascertain the validity of this model.
Localized waves in three-component coupled nonlinear Schrödinger equation
Xu, Tao; Chen, Yong
2016-09-01
We study the generalized Darboux transformation to the three-component coupled nonlinear Schrödinger equation. First- and second-order localized waves are obtained by this technique. In first-order localized wave, we get the interactional solutions between first-order rogue wave and one-dark, one-bright soliton respectively. Meanwhile, the interactional solutions between one-breather and first-order rogue wave are also given. In second-order localized wave, one-dark-one-bright soliton together with second-order rogue wave is presented in the first component, and two-bright soliton together with second-order rogue wave are gained respectively in the other two components. Besides, we observe second-order rogue wave together with one-breather in three components. Moreover, by increasing the absolute values of two free parameters, the nonlinear waves merge with each other distinctly. These results further reveal the interesting dynamic structures of localized waves in the three-component coupled system. Project supported by the Global Change Research Program of China (Grant No. 2015CB953904), the National Natural Science Foundation of China (Grant Nos. 11275072 and 11435005), the Doctoral Program of Higher Education of China (Grant No. 20120076110024), the Network Information Physics Calculation of Basic Research Innovation Research Group of China (Grant No. 61321064), and Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things, China (Grant No. ZF1213).
The Relationship between Tsallis Statistics, the Fourier Transform, and Nonlinear Coupling
Nelson, Kenric P
2008-01-01
Tsallis statistics (or q-statistics) in nonextensive statistical mechanics is a one-parameter description of correlated states. In this paper we use a translated entropic index: $1 - q \\to q$ . The essence of this translation is to improve the mathematical symmetry of the q-algebra and make q directly proportional to the nonlinear coupling. A conjugate transformation is defined $\\hat q \\equiv \\frac{{- 2q}}{{2 + q}}$ which provides a dual mapping between the heavy-tail q-Gaussian distributions, whose translated q parameter is between $ - 2 < q < 0$, and the compact-support q-Gaussians, between $0 < q < \\infty $ . This conjugate transformation is used to extend the definition of the q-Fourier transform to the domain of compact support. A conjugate q-Fourier transform is proposed which transforms a q-Gaussian into a conjugate $\\hat q$ -Gaussian, which has the same exponential decay as the Fourier transform of a power-law function. The nonlinear statistical coupling is defined such that the conjugate ...
Nonlinear optical rectification in laterally-coupled quantum well wires with applied electric field
Liu, Guanghui; Guo, Kangxian; Zhang, Zhongmin; Hassanbadi, Hassan; Lu, Liangliang
2017-03-01
Nonlinear optical rectification coefficient χ0(2) in laterally-coupled AlxGa1-xAs/GaAs quantum well wires with an applied electric field is theoretically investigated using the effective mass approximation as well as the numerical energy levels and wavefunctions of electrons. We find that χ0(2) is greatly influenced by the electric field as well as both the distance and the radius of the coupled system. A blue shift of χ0(2) with increasing electric field is exhibited while a red shift followed by a blue shift with increasing distance or radius is exhibited. A nonmonotonic behavior can be found in the resonant peak values of χ0(2) along with the increase of the electric field, the distance or the radius. One or two of the following physical mechanisms: the increased localization of the ground and first-excited states, the reduced coupling and the reduced quantum confinement effect are applied to elucidate the results above. Our results play a potential role in infrared photodetectors based on the coupled system.
Institute of Scientific and Technical Information of China (English)
GU Ji-jun; AN Chen; LEVI Carlos; SU Jian
2012-01-01
The Generalized Integral Transform Technique (GITT) was applied to predict dynamic response of Vortex-Induced Vibration (VIV) of a long flexible cylinder.A nonlinear wake oscillator model was used to represent the cross-flow force acting on the cylinder,leading to a coupled system of second-order Partial Differential Equations (PDEs) in temporal variable.The GITT approach was used to transform the system of PDEs to a system of Ordinary Differential Equations (ODEs),which was numerically solved by using the Adams-Moulton and Gear method (DIVPAG) developed by the International Mathematics and Statistics Library (IMSL).Numerical results were presented for comparison to those given by the finite difference method and experimental results,allowing a critical evaluation of the technique performance.The influence of variation of mean axial tension induced by elongation of flexible cylinder was evaluated,which was shown to be not negligible in numerical simulation of VIV of a long flexible cylinder.
The oriented-couple partial differential equations for filtering in wrapped phase patterns.
Tang, Chen; Han, Lin; Ren, Hongwei; Gao, Tao; Wang, Zhifang; Tang, Ke
2009-03-30
We derive the new oriented-couple partial differential equation (PDE) models based on the variational methods for filtering in electronic speckle pattern interferometry phase fringe patterns. In the filtering methods based on the oriented PDE models, filtering along fringe orientation for the entire image is simply realized through solving the PDEs numerically, without having to laboriously establish the small filtering window along the fringe orientation and move this filtering window over each pixel in an image. We test the proposed models on two computer-simulated speckle phase fringe patterns and an experimentally obtained phase fringe pattern, respectively, in which the fringe density is variable, and compare our models with related PDE models. Further, we quantitatively evaluate the performance of these PDE models with a comparative parameter, named the image fidelity. We also compare the computational time of our method with that of a traditional filtering method along the fringe orientation. The experimental results demonstrate the performance of our new oriented PDE models.
Directory of Open Access Journals (Sweden)
Jacqueline Fleckinger
2001-12-01
Full Text Available We study the asymptotic behavior of positive solutions $u$ of $$ -Delta_p u(x = V(x u(x^{p-1}, quad p>1; x in Omega,$$ and related partial differential inequalities, as well as conditions for existence of such solutions. Here, $Omega$ contains the exterior of a ball in $mathbb{R}^N$ $1
Determination of the chiral coupling constants c(3) and c(4) in new pp and np partial-wave analyses
Rentmeester, MCM; Timmermans, RGE; de Swart, JJ
2003-01-01
As a first result of two new partial-wave analyses, one of the pp and another one of the np scattering data below 500 MeV, we report a study of the long-range chiral two-pion exchange interaction which contains the chiral coupling constants c(1), c(3), and c(4). By using as input a theoretical value
Beck, Christian; E, Weinan; Jentzen, Arnulf
2017-01-01
High-dimensional partial differential equations (PDE) appear in a number of models from the financial industry, such as in derivative pricing models, credit valuation adjustment (CVA) models, or portfolio optimization models. The PDEs in such applications are high-dimensional as the dimension corresponds to the number of financial assets in a portfolio. Moreover, such PDEs are often fully nonlinear due to the need to incorporate certain nonlinear phenomena in the model such as default risks, ...
Energy Technology Data Exchange (ETDEWEB)
Lin, Jaw-Ren; Hung, Chi-Ren; Lu, Rong-Fang [Nanya Institute of Technology, Jhongli, Taiwan (China). Dept. of Mechanical Engineering; Chu, Li-Ming [I-Shou Univ., Kaohsiung, Taiwan (China). Dept. of Mechanical and Automation Engineering
2011-08-15
According to the experimental work of C. Barus in Am. J. Sci. 45, 87 (1893), the dependency of liquid viscosity on pressure is exponential. Therefore, we extend the study of squeeze film problems of long partial journal bearings for Stokes non-Newtonian couple stress fluids by considering the pressure-dependent viscosity in the present paper. Through a small perturbation technique, we derive a first-order closed-form solution for the film pressure, the load capacity, and the response time of partial-bearing squeeze films. It is also found that the non-Newtonian couple-stress partial bearings with pressure-dependent viscosity provide better squeeze-film characteristics than those of the bearing with constant-viscosity situation. (orig.)
Lin, Jaw-Ren; Chu, Li-Ming; Hung, Chi-Ren; Lu, Rong-Fang
2011-09-01
According to the experimental work of C. Barus in Am. J. Sci. 45, 87 (1893) [1], the dependency of liquid viscosity on pressure is exponential. Therefore, we extend the study of squeeze film problems of long partial journal bearings for Stokes non-Newtonian couple stress fluids by considering the pressure-dependent viscosity in the present paper. Through a small perturbation technique, we derive a first-order closed-form solution for the film pressure, the load capacity, and the response time of partial-bearing squeeze films. It is also found that the non-Newtonian couple-stress partial bearings with pressure-dependent viscosity provide better squeeze-film characteristics than those of the bearing with constant-viscosity situation.
Owolabi, Kolade M.
2017-03-01
In this paper, some nonlinear space-fractional order reaction-diffusion equations (SFORDE) on a finite but large spatial domain x ∈ [0, L], x = x(x , y , z) and t ∈ [0, T] are considered. Also in this work, the standard reaction-diffusion system with boundary conditions is generalized by replacing the second-order spatial derivatives with Riemann-Liouville space-fractional derivatives of order α, for 0 < α < 2. Fourier spectral method is introduced as a better alternative to existing low order schemes for the integration of fractional in space reaction-diffusion problems in conjunction with an adaptive exponential time differencing method, and solve a range of one-, two- and three-components SFORDE numerically to obtain patterns in one- and two-dimensions with a straight forward extension to three spatial dimensions in a sub-diffusive (0 < α < 1) and super-diffusive (1 < α < 2) scenarios. It is observed that computer simulations of SFORDE give enough evidence that pattern formation in fractional medium at certain parameter value is practically the same as in the standard reaction-diffusion case. With application to models in biology and physics, different spatiotemporal dynamics are observed and displayed.
Directory of Open Access Journals (Sweden)
Xiaoyan Lei
2016-01-01
Full Text Available A model for dynamic analysis of the vehicle-track nonlinear coupling system is established by the finite element method. The whole system is divided into two subsystems: the vehicle subsystem and the track subsystem. Coupling of the two subsystems is achieved by equilibrium conditions for wheel-to-rail nonlinear contact forces and geometrical compatibility conditions. To solve the nonlinear dynamics equations for the vehicle-track coupling system, a cross iteration algorithm and a relaxation technique are presented. Examples of vibration analysis of the vehicle and slab track coupling system induced by China’s high speed train CRH3 are given. In the computation, the influences of linear and nonlinear wheel-to-rail contact models and different train speeds are considered. It is found that the cross iteration algorithm and the relaxation technique have the following advantages: simple programming; fast convergence; shorter computation time; and greater accuracy. The analyzed dynamic responses for the vehicle and the track with the wheel-to-rail linear contact model are greater than those with the wheel-to-rail nonlinear contact model, where the increasing range of the displacement and the acceleration is about 10%, and the increasing range of the wheel-to-rail contact force is less than 5%.
Discrete and continuum links to a nonlinear coupled transport problem of interacting populations
Duong, M. H.; Muntean, A.; Richardson, O. M.
2017-02-01
We are interested in exploring interacting particle systems that can be seen as microscopic models for a particular structure of coupled transport flux arising when different populations are jointly evolving. The scenarios we have in mind are inspired by the dynamics of pedestrian flows in open spaces and are intimately connected to cross-diffusion and thermo-diffusion problems holding a variational structure. The tools we use include a suitable structure of the relative entropy controlling TV-norms, the construction of Lyapunov functionals and particular closed-form solutions to nonlinear transport equations, a hydrodynamics limiting procedure due to Philipowski, as well as the construction of numerical approximates to both the continuum limit problem in 2D and to the original interacting particle systems.
Dymnikova, Irina
2015-01-01
In nonlinear electrodynamics coupled to gravity, regular spherically symmetric electrically charged solutions satisfy the weak energy condition and have obligatory de Sitter centre. By the G\\"urses-G\\"ursey algorithm they are transformed to spinning electrically charged solutions asymptotically Kerr-Newman for a distant observer. Rotation transforms de Sitter center into de Sitter vacuum surface which contains equatorial disk $r=0$ as a bridge. We present general analysis of the horizons, ergoregions and de Sitter surfaces, as well as the conditions of the existence of regular solutions to the field equations. We find asymptotic solutions and show that de Sitter vacuum surfaces have properties of a perfect conductor and ideal diamagnetic, violation of the weak energy condition is prevented by the basic requirement of electrodynamics of continued media, and the Kerr ring singularity is replaced with the superconducting current.
Low-Dimensional Models for Physiological Systems: Nonlinear Coupling of Gas and Liquid Flows
Staples, A. E.; Oran, E. S.; Boris, J. P.; Kailasanath, K.
2006-11-01
Current computational models of biological organisms focus on the details of a specific component of the organism. For example, very detailed models of the human heart, an aorta, a vein, or part of the respiratory or digestive system, are considered either independently from the rest of the body, or as interacting simply with other systems and components in the body. In actual biological organisms, these components and systems are strongly coupled and interact in complex, nonlinear ways leading to complicated global behavior. Here we describe a low-order computational model of two physiological systems, based loosely on a circulatory and respiratory system. Each system is represented as a one-dimensional fluid system with an interconnected series of mass sources, pumps, valves, and other network components, as appropriate, representing different physical organs and system components. Preliminary results from a first version of this model system are presented.
The non-linear coupled spin 2 - spin 3 Cotton equation in three dimensions
Linander, Hampus
2016-01-01
In the context of three-dimensional conformal higher spin theory we derive, in the frame field formulation, the full non-linear spin 3 Cotton equation coupled to spin 2. This is done by solving the corresponding Chern-Simons gauge theory system of equations, that is, using $F=0$ to eliminate all auxiliary fields and thus expressing the Cotton equation in terms of just the spin 3 frame field and spin 2 covariant derivatives and tensors (Schouten). In this derivation we neglect the spin 4 and higher spin sectors and approximate the star product commutator by a Poisson bracket. The resulting spin 3 Cotton equation is complicated but can be related to linearized versions in the metric formulation obtained previously by other authors. The expected symmetry (spin 3 "translation", "Lorentz" and "dilatation") properties are verified for Cotton and other relevant tensors but some perhaps unexpected features emerge in the process, in particular in relation to the non-linear equations. We discuss the structure of this n...
Phases of 4D Scalar-tensor black holes coupled to Born-Infeld nonlinear electrodynamics
Stefanov, Ivan Zh; Todorov, Michail D
2007-01-01
Recent results show that when non-linear electrodynamics is considered the no-scalar-hair theorems in the scalar-tensor theories (STT) of gravity, which are valid for the cases of neutral black holes and charged black holes in the Maxwell electrodynamics, can be circumvented. What is even more, in the present work, we find new non-unique, numerical solutions describing charged black holes coupled to non-linear electrodynamics in a special class of scalar-tensor theories. One of the phases has a trivial scalar field and coincides with the corresponding solution in General Relativity. The other four phases that we find are characterized by the value of the scalar field charge. The causal structure and some aspects of the stability of the solutions have also been studied. For the scalar-tensor theories considered, the black holes have a single, non-degenerate horizon, i.e., their causal structure resembles that of the Schwarzschild black hole. The thermodynamic analysis of the stability of the solutions indicate...
A Nonlinear Coupled-Mode System for Water Waves over a General Bathymetry
Athanassoulis, G. A.; Belibassakis, K. A.
2003-04-01
Athanassoulis 2002) problems, over variable bathymetry regions. Using the local-mode expansion in conjunction with the variational principle the original problem is reformulated as an infinite, coupled-mode system of second-order differential equations in the propagation (horizontal) space, fully accounting for the effects of non-linearity and dispersion. Various simplified equations, like Boussinesq-type models, in shallow water depth, and non-linear mild-slope models, in intermediate depth, can be obtained as limiting forms. As a first step towards the solution of fully nonlinear coupled-mode system, the system is simplified keeping only up to second-order terms in the system coefficients, and the derived weakly non-linear model has been applied to water waves propagating over a flat bottom and over an arbitrary bathymetry. This model is solved numerically in the frequency and in the time domain, providing very good results in a wide range of water depths. In the case of monochromatic waves propagating over a flat bottom, it is shown that the present model correctly treats the dispersion effects in the whole range of relative water depths from practically deep to shallow water. In the same case, it is also shown that the present model reproduces correctly the second-order Stokes solutions. In the general case, the solution of the coupled-mode system is obtained numerically by truncating the local-mode series into a finite number of terms, and using finite differences for approximating the derivatives on the horizontal plane. Numerical results presented for a smooth underwater shoaling with a steep bottom slope, demonstrate that the rate of decay of the modal-amplitude functions is very fast, in conformity with similar behaviour in the linear case (Athanassoulis and Belibassakis 1999). This means that a small number of modes (up to 5 or 7) are sufficient for precise numerical solution, provided that the two new modes (the free-surface and the sloping-bottom ones) are included
Mode Coupling and Nonlinear Resonances of MEMS Arch Resonators for Bandpass Filters
Hajjaj, Amal Z.
2017-01-30
We experimentally demonstrate an exploitation of the nonlinear softening, hardening, and veering phenomena (near crossing), where the frequencies of two vibration modes get close to each other, to realize a bandpass filter of sharp roll off from the passband to the stopband. The concept is demonstrated based on an electrothermally tuned and electrostatically driven MEMS arch resonator operated in air. The in-plane resonator is fabricated from a silicon-on-insulator wafer with a deliberate curvature to form an arch shape. A DC current is applied through the resonator to induce heat and modulate its stiffness, and hence its resonance frequencies. We show that the first resonance frequency increases up to twice of the initial value while the third resonance frequency decreases until getting very close to the first resonance frequency. This leads to the phenomenon of veering, where both modes get coupled and exchange energy. We demonstrate that by driving both modes nonlinearly and electrostatically near the veering regime, such that the first and third modes exhibit softening and hardening behavior, respectively, sharp roll off from the passband to the stopband is achievable. We show a flat, wide, and tunable bandwidth and center frequency by controlling the electrothermal actuation voltage.
Directory of Open Access Journals (Sweden)
A. Sheykhi
2016-01-01
Full Text Available We construct a new class of charged rotating black brane solutions in the presence of logarithmic nonlinear electrodynamics with complete set of the rotation parameters in arbitrary dimensions. The topology of the horizon of these rotating black branes is flat, while due to the presence of the dilaton field the asymptotic behavior of them is neither flat nor (anti-de Sitter [(AdS]. We investigate the physical properties of the solutions. The mass and angular momentum of the spacetime are obtained by using the counterterm method inspired by AdS/CFT correspondence. We derive temperature, electric potential, and entropy associated with the horizon and check the validity of the first law of thermodynamics on the black brane horizon. We study thermal stability of the solutions in both canonical and grand-canonical ensemble and disclose the effects of the rotation parameter, nonlinearity of electrodynamics, and dilaton field on the thermal stability conditions. We find the solutions are thermally stable for α1 the solutions may encounter an unstable phase, where α is dilaton-electromagnetic coupling constant.
All-electrical nonlinear fano resonance in coupled quantum point contacts
Xiao, Shiran
This thesis is motivated by recent interest in the Fano resonance (FR). As a wave-interference phenomenon, this resonance is of increasing importance in optics, plasmon-ics, and metamaterials, where its ability to cause rapid signal modulations under variation of some suitable parameter makes it desirable for a variety of applications. In this thesis, I focus on a novel manifestation of this resonance in systems of coupled quantum point contacts (QPCs). The major finding of this work is that the FR in this system may be ma-nipulated by applying a nonlinear DC bias to the system. Under such conditions, we are able to induce significant distortions of resonance lineshape, providing a pathway to all-electrical manipulation of the FR. To interpret this behavior we apply a recently-developed model for a three-path FR, involving an additional "intruder" continuum. We have previously used this model to account for the magnetic-field induced distortions of the FR observed in coupled QPCs, and show here that this model also provides a frame-work for understanding the observed nonlinear behavior. Our work therefore reveals a new manifestation of the FR that can be sensitively tailored by external control, a finding that may eventually allow the application of this feature to nanoelectronics. Since the in-terference scheme involves in this thesis is a completely general one, it should be broadly applicable across a variety of different wave-based systems, including those in both pho-tonics and electronics and opening up the possibility of new applications in areas such as chemical and biological sensing and secure communications.
You, Bin Di; Wen, Jian Min; Zhao, Yang
2014-03-01
In this paper, a nonlinear dynamic modeling method for a rigid-flexible coupling satellite antenna system composed of laminated shell reflector is proposed undergoing a large overall motion. For the study of the characteristics of the reflector using laminated shell structure, the displacement field description of a point in a 3-noded shell element is acquired in conjunction with the length stretch, lateral bending and torsional deformation. Hence, a nonlinear dynamic model of the satellite antenna system is deduced based on Lagrange's equations. The complete expressions of nonlinear terms of elastic deformation and coupling terms between rigid motion and large deflection are considered in the dynamic equations, and the dynamic behavior of the rigid-flexible coupling system is analyzed using linear model and nonlinear model, respectively. In order to eliminate the system vibration, the PD with vibration force feedback control strategy is used to achieve its desired angles and velocity in a much shorter duration, and can further accomplish reduction of residual vibration. Then, the asymptotic stability of the system is proved based on the Lyapunov method. Through numerical computation, the results show that the linear model cannot capture the motion-induced coupling terms and geometric nonlinearity variations. However, the nonlinear model is suitable for dealing with large deformation rigid-flexible problem undergoing large overall motions. Hence, the satellite antenna pointing accuracy would be predicted based on the nonlinear model. Furthermore, the results also show that the proposed control strategy can suppress system vibration quickly. The above conclusions would have important academic significance and engineering value.
Pakhomov, A V; Babushkin, I V; Arkhipov, M V; Tolmachev, Yu A; Rosanov, N N
2016-01-01
We study the optical response of a resonant medium possessing the nonlinear coupling to external field under excitation by few-cycle pump pulses. A theoretical approach is developed, allowing to analyze unipolar half-cycle pulse generation in such a geometry. Our approach is applicable for the arbitrary coupling functions as well as arbitrarily curved pump pulse wavefronts and defines a general framework to produce unipolar pulses of desired form.
Müstecaplıoğlu, Özgür; Hardal, Ali Ümit
2014-01-01
We investigate spin squeezing, quantum entanglement, and second-order coherence in two coupled, driven, dissipative, nonlinear cavities. We compare these quantum statistical properties for the cavities coupled with either single- or two-photon exchange. Solving the quantum optical master equation of the system numerically in the steady state, we calculate the zero-time delay second-order correlation function for the coherent, genuine two-mode entanglement parameters, an optimal spin squeezing...
非线性偏微分方程的约化和精确解%REDUCTION OF NONLINEAR PARTIAL DIFFERENTIAL EQUATION AND EXACT SOLUTIONS
Institute of Scientific and Technical Information of China (English)
叶彩儿; 潘祖梁
2003-01-01
Nonlinear partial differetial equation(NLPDE) is converted into ordinary differentialequation (ODE) via a new ansatzUsing undetermined function method ,the ODE obtained aboveis replaced by a set of algebraic equations which are solved out with the aid of MathematicaTheexact solutions and solitary solutions of NLPDE are obtained.
Fully coupled heat conduction and deformation analyses of nonlinear viscoelastic composites
Khan, Kamran
2012-05-01
This study presents an integrated micromechanical model-finite element framework for analyzing coupled heat conduction and deformations of particle-reinforced composite structures. A simplified micromechanical model consisting of four sub-cells, i.e., one particle and three matrix sub-cells is formulated to obtain the effective thermomechanical properties and micro-macro field variables due to coupled heat conduction and nonlinear thermoviscoelastic deformation of a particulate composite that takes into account the dissipation of energy from the viscoelastic constituents. A time integration algorithm for simultaneously solving the equations that govern heat conduction and thermoviscoelastic deformations of isotropic homogeneous materials is developed. The algorithm is then integrated to the proposed micromechanical model. A significant temperature generation due to the dissipation effect in the viscoelastic matrix was observed when the composite body is subjected to cyclic mechanical loadings. Heat conduction due to the dissipation of the energy cannot be ignored in predicting the factual temperature and deformation fields within the composite structure, subjected to cyclic loading for a long period. A higher creep resistant matrix material or adding elastic particles can lower the temperature generation. Our analyses suggest that using particulate composites and functionally graded materials can reduce the heat generation due to energy dissipation. © 2012 Elsevier Ltd.
Study on electromechanical coupling nonlinear vibration of flywheel energy storage system
Institute of Scientific and Technical Information of China (English)
JIANG; Shuyun
2006-01-01
The electromechanical coupling dynamics of the flywheel energy storage system (FESS) with a hybrid permanent magnetic-dynamic spiral groove bearing has been studied. The functions of the kinetic energy, the potential energys, the magnetic field energy in air gap of the flywheel motor and the energy dissipation of the whole system were obtained, and the differential equations set with electromagnetic parameters of FESS was established by applying the extended Lagrange-Maxwell equation. The four-order implicit Runge-Kutta formula to the equations was derived, and the nonlinear algebraic equations were solved by using the Gauss-Newton method. The analytical solution of an example shows that the upper damping coefficient, the lower damping coefficient and the residual magnetic induction of the rare earth permanent magnet play an important role in electromechanical resonance of the flywheel rotor system. There is a small change for the electromechanical coupling resonance frequency with the upper damping coefficient increasing, but the resonance amplitude decreases with the upper damping coefficient increasing. With the lower damping coefficient increasing, the resonance frequency increases, and the resonance amplitude decreases. With the residual magnetic induction of the permanent magnet increasing, the resonance frequency decreases, and the resonance amplitude increases.
Standing waves for coupled nonlinear Schrödinger equations with decaying potentials
Energy Technology Data Exchange (ETDEWEB)
Chen, Zhijie, E-mail: chenzhijie1987@sina.com; Zou, Wenming, E-mail: wzou@math.tsinghua.edu.cn [Department of Mathematical Sciences, Tsinghua University, Beijing 100084 (China)
2013-11-15
We study the following singularly perturbed problem for a coupled nonlinear Schrödinger system which arises in Bose-Einstein condensate: −ε{sup 2}Δu + a(x)u = μ{sub 1}u{sup 3} + βuv{sup 2} and −ε{sup 2}Δv + b(x)v = μ{sub 2}v{sup 3} + βu{sup 2}v in R{sup 3} with u, v > 0 and u(x), v(x) → 0 as |x| → ∞. Here, a, b are non-negative continuous potentials, and μ{sub 1}, μ{sub 2} > 0. We consider the case where the coupling constant β > 0 is relatively large. Then for sufficiently small ε > 0, we obtain positive solutions of this system which concentrate around local minima of the potentials as ε → 0. The novelty is that the potentials a and b may vanish at someplace and decay to 0 at infinity.
Nonlinear Brillouin amplification of finite-duration seeds in the strong coupling regime
Lehmann, G.; Spatschek, K. H.
2013-07-01
Parametric plasma processes received renewed interest in the context of generating ultra-intense and ultra-short laser pulses up to the exawatt-zetawatt regime. Both Raman as well as Brillouin amplifications of seed pulses were proposed. Here, we investigate Brillouin processes in the one-dimensional (1D) backscattering geometry with the help of numerical simulations. For optimal seed amplification, Brillouin scattering is considered in the so called strong coupling (sc) regime. Special emphasis lies on the dependence of the amplification process on the finite duration of the initial seed pulses. First, the standard plane-wave instability predictions are generalized to pulse models, and the changes of initial seed pulse forms due to parametric instabilities are investigated. Three-wave-interaction results are compared to predictions by a new (kinetic) Vlasov code. The calculations are then extended to the nonlinear region with pump depletion. Generation of different seed layers is interpreted by self-similar solutions of the three-wave interaction model. Similar to Raman amplification, shadowing of the rear layers by the leading layers of the seed occurs. The shadowing is more pronounced for initially broad seed pulses. The effect is quantified for Brillouin amplification. Kinetic Vlasov simulations agree with the three-wave interaction predictions and thereby affirm the universal validity of self-similar layer formation during Brillouin seed amplification in the strong coupling regime.
Rury, Aaron S.
2016-06-01
This study reports experimental, computational, and theoretical evidence for a previously unobserved coherent phonon-phonon interaction in an organic solid that can be described by the application of Fano's analysis to a case without the presence of a continuum. Using Raman spectroscopy of the hydrogen-bonded charge-transfer material quinhydrone, two peaks appear near 700 cm-1 we assign as phonons whose position and line-shape asymmetry depend on the sample temperature and light scattering excitation energy. Density functional theory calculations find two nearly degenerate phonons possessing frequencies near the values found in experiment that share similar atomic motion out of the aromatic plane of electron donor and acceptor molecules of quinhydrone. Further analytical modeling of the steady-state light scattering process using the Peierls-Hubbard Hamiltonian and time-dependent perturbation theory motivates assignment of the physical origin of the asymmetric features of each peak's line shape to an interaction between two discrete phonons via nonlinear electron-phonon coupling. In the context of analytical model results, characteristics of the experimental spectra upon 2.33 eV excitation of the Raman scattering process are used to qualify the temperature dependence of the magnitude of this coupling in the valence band of quinhydrone. These results broaden the range of phonon-phonon interactions in materials in general while also highlighting the rich physics and fundamental attributes specific to organic solids that may determine their applicability in next generation electronics and photonics technologies.
Beninato, A.; Emery, T.; Baglio, S.; Andò, B.; Bulsara, A. R.; Jenkins, C.; Palkar, V.
2013-12-01
Multiferroic (MF) composites, in which magnetic and ferroelectric orders coexist, represent a very attractive class of materials with promising applications in areas, such as spintronics, memories, and sensors. One of the most important multiferroics is the perovskite phase of bismuth ferrite, which exhibits weak magnetoelectric properties at room temperature; its properties can be enhanced by doping with other elements such as dysprosium. A recent paper has demonstrated that a thin film of Bi0.7Dy0.3FeO3 shows good magnetoelectric coupling. In separate work it has been shown that a carefully crafted ring connection of N (N odd and N ≥ 3) ferroelectric capacitors yields, past a critical point, nonlinear oscillations that can be exploited for electric (E) field sensing. These two results represent the starting point of our work. In this paper the (electrical) hysteresis, experimentally measured in the MF material Bi0.7Dy0.3FeO3, is characterized with the applied magnetic field (B) taken as a control parameter. This yields a "blueprint" for a magnetic (B) field sensor: a ring-oscillator coupling of N = 3 Sawyer-Tower circuits each underpinned by a mutliferroic element. In this configuration, the changes induced in the ferroelectric behavior by the external or "target" B-field are quantified, thus providing a pathway for very low power and high sensitivity B-field sensing.
Liu, Shuang; Zhao, Shuang-Shuang; Wang, Zhao-Long; Li, Hai-Bin
2015-01-01
The stability and the Hopf bifurcation of a nonlinear electromechanical coupling system with time delay feedback are studied. By considering the energy in the air-gap field of the AC motor, the dynamical equation of the electromechanical coupling transmission system is deduced and a time delay feedback is introduced to control the dynamic behaviors of the system. The characteristic roots and the stable regions of time delay are determined by the direct method, and the relationship between the feedback gain and the length summation of stable regions is analyzed. Choosing the time delay as a bifurcation parameter, we find that the Hopf bifurcation occurs when the time delay passes through a critical value. A formula for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions is given by using the normal form method and the center manifold theorem. Numerical simulations are also performed, which confirm the analytical results. Project supported by the National Natural Science Foundation of China (Grant No. 61104040), the Natural Science Foundation of Hebei Province, China (Grant No. E2012203090), and the University Innovation Team of Hebei Province Leading Talent Cultivation Project, China (Grant No. LJRC013).
Zhang, Guoqiang; Yan, Zhenya; Wen, Xiao-Yong; Chen, Yong
2017-04-01
We investigate the defocusing coupled nonlinear Schrödinger equations from a 3 ×3 Lax pair. The Darboux transformations with the nonzero plane-wave solutions are presented to derive the newly localized wave solutions including dark-dark and bright-dark solitons, breather-breather solutions, and different types of new vector rogue wave solutions, as well as interactions between distinct types of localized wave solutions. Moreover, we analyze these solutions by means of parameters modulation. Finally, the perturbed wave propagations of some obtained solutions are explored by means of systematic simulations, which demonstrates that nearly stable and strongly unstable solutions. Our research results could constitute a significant contribution to explore the distinct nonlinear waves (e.g., dark solitons, breather solutions, and rogue wave solutions) dynamics of the coupled system in related fields such as nonlinear optics, plasma physics, oceanography, and Bose-Einstein condensates.
Offrein, B.J.; Offrein, B.J.; van Schoot, J.B.P.; van Schoot, J.B.P.; Driessen, A.; Hoekstra, Hugo; Popma, T.J.A.
1993-01-01
Materials with an intensity dependent index of refraction and absorption coefficient¿third-order optical non-linear (ONL) effects¿offer the possibility of all-optical signal processing. Prism coupling is a well-known tool to investigate the intensity dependent refractive index, however, such experim
Energy Technology Data Exchange (ETDEWEB)
Macias-Diaz, J.E. [Departamento de Matematicas y Fisica, Universidad Autonoma de Aguascalientes, Aguascalientes, Ags. 20100 (Mexico) and Department of Physics, University of New Orleans, New Orleans, LA 70148 (United States)]. E-mail: jemacias@correo.uaa.mx; Puri, A. [Department of Physics, University of New Orleans, New Orleans, LA 70148 (United States)]. E-mail: apuri@uno.edu
2007-07-02
In the present Letter, we simulate the propagation of binary signals in semi-infinite, mechanical chains of coupled oscillators harmonically driven at the end, by making use of the recently discovered process of nonlinear supratransmission. Our numerical results-which are based on a brand-new computational technique with energy-invariant properties-show an efficient and reliable transmission of information.
Institute of Scientific and Technical Information of China (English)
Song Wei
2009-01-01
We have investigated the intrinsic decoherence on the entanglement of a two-qutrit one-dimensional (1D) optical lattice chain with nonlinear coupling.As a measure of the entanglement,the negativity of the system is calculated.It is shown that the influence of intrinsic decoherence on the entanglement varies in different initial systems.
Nonlinear effects caused by coupling misalignment in rotors equipped with journal bearings
Pennacchi, Paolo; Vania, Andrea; Chatterton, Steven
2012-07-01
Misalignment is one of the most common sources of trouble of rotating machinery when rigid couplings connect the shafts. Ideal alignment of the shafts is difficult to be obtained and rotors may present angular and/or parallel misalignment (defined also as radial misalignment or offset). During a complete shaft revolution, a periodical change of the bearings load occurs in hyperstatic shaft-lines, if coupling misalignment between the shafts is excessive. If the rotating machine is equipped with fluid-film journal bearings, the change of the loads on the bearing causes also the variation of their instantaneous dynamic characteristics, i.e. damping and stiffness, and the complete system cannot be considered any longer as linear. Despite misalignment is often observed in the practice, there are relatively few studies about this phenomenon in literature and their results are sometimes conflicting. The authors aim at modeling accurately this phenomenon, for the first time in this paper, and giving pertinent diagnostic information. The proposed method is suitable for every type of shaft-line supported by journal bearings. A finite element model is used for the hyperstatic shaft-line, while bearing characteristics are calculated by integrating Reynolds equation as a function of the instantaneous load acting on the bearings, caused also by the coupling misalignment. The results obtained by applying the proposed method are shown by means of the simulation, in the time domain, of the dynamical response of a hyperstatic shaft-line. Nonlinear effects are highlighted and the spectral components of the system response are analyzed, in order to give diagnostic information about the signature of this type of fault.
Unlocking the full potential of wave-matter nonlinear coupling in the epsilon-near-zero regime
Ciattoni, Alessandro; Marini, Andrea; Di Falco, Andrea; Faccio, Daniele; Scalora, Michael
2015-01-01
In recent years, unconventional metamaterial properties have triggered a revolution of electromagnetic research which has unveiled novel scenarios of wave-matter interaction. A very small dielectric permittivity is a leading example of such unusual features, since it produces an exotic static-like regime where the electromagnetic field is spatially slowly-varying over a physically large region. The so-called epsilon-near-zero metamaterials thus offer an ideal platform where to manipulate the inner details of the "stretched" field. Here we theoretically prove that a standard nonlinearity is able to operate such a manipulation to the point that even a thin slab produces a dramatic nonlinear pulse transformation, if the dielectric permittivity is very small within the field bandwidth. The predicted non-resonant releasing of full nonlinear coupling produced by the epsilon-near-zero condition does not resort to any field enhancement mechanisms and opens novel routes to exploiting matter nonlinearity for steering t...
Energy Technology Data Exchange (ETDEWEB)
Vakhnenko, Oleksiy O., E-mail: vakhnenko@bitp.kiev.ua
2016-05-27
Highlights: • The integrable nonlinear Schrödinger system on a triangular-lattice ribbon is inclined to metamorphoses. • The system under study is capable to incorporate the effect of external linear potential. • The system criticality against the background parameter reduces the number of independent field variables. • At critical point the system Poisson structure becomes degenerate. • The effect of criticality is elucidated by the system one-soliton solution. - Abstract: The variativity of governing coupling parameters in the integrable nonlinear Schrödinger system on a triangular-lattice ribbon is shown to ensure the important qualitative rearrangements in the system dynamics. There are at least the two types of system crucial modifications stipulated by the two types of governing parameters. Thus the longitudinal coupling parameters regulated mainly by the background values of concomitant field variables are responsible for the bifurcation of primary integrable nonlinear system into the integrable nonlinear system of Ablowitz–Ladik type. As a consequence in a critical point the number of independent field variables is reduced by a half and the system Poisson structure turns out to be degenerate. On the other hand the transverse coupling parameters regulated basically by the choice of their a priori arbitrary dependencies on time are capable to incorporate the effect of external linear potential. As a consequence the primary integrable nonlinear system with appropriately adjusted parametrical driving becomes isomorphic to the system modeling the Bloch oscillations of charged nonlinear carriers in an electrically biased ribbon of triangular lattice. The multi-component structure of basic integrable system alongside with the attractive character of system nonlinearities has predetermined the logic of whole consideration.
Sabeen, A.; Masood, W.; Qureshi, M. N. S.; Shah, H. A.
2017-07-01
In this paper, linear and nonlinear coupling of kinetic Alfven and acoustic waves has been studied in a dusty plasma in the presence of trapping and self-gravitation effects. In this regard, we have derived the linear dispersion relations for positively and negatively coupled dust kinetic Alfven-acoustic waves. Stability analysis of the coupled dust kinetic Alfven-acoustic wave has also been presented. The formation of solitary structures has been investigated following the Sagdeev potential approach by using the two-potential theory. Numerical results show that the solitary structures can be obtained only for sub-Alfvenic regimes in the scenario of space plasmas.
Interpreting the nonlinear dielectric response of glass-formers in terms of the coupling model
Energy Technology Data Exchange (ETDEWEB)
Ngai, K. L. [CNR-IPCF, Largo Bruno Pontecorvo 3, I-56127 Pisa, Italy and Dipartimento di Fisica, Università di Pisa, Largo B. Pontecorvo 3, I-56127 Pisa (Italy)
2015-03-21
Nonlinear dielectric measurements at high electric fields of glass-forming glycerol and propylene carbonate initially were carried out to elucidate the dynamic heterogeneous nature of the structural α-relaxation. Recently, the measurements were extended to sufficiently high frequencies to investigate the nonlinear dielectric response of faster processes including the so-called excess wing (EW), appearing as a second power law at high frequencies in the loss spectra of many glass formers without a resolved secondary relaxation. While a strong increase of dielectric constant and loss is found in the nonlinear dielectric response of the α-relaxation, there is a lack of significant change in the EW. A surprise to the experimentalists finding it, this difference in the nonlinear dielectric properties between the EW and the α-relaxation is explained in the framework of the coupling model by identifying the EW investigated with the nearly constant loss (NCL) of caged molecules, originating from the anharmonicity of the intermolecular potential. The NCL is terminated at longer times (lower frequencies) by the onset of the primitive relaxation, which is followed sequentially by relaxation processes involving increasing number of molecules until the terminal Kohlrausch α-relaxation is reached. These intermediate faster relaxations, combined to form the so-called Johari-Goldstein (JG) β-relaxation, are spatially and dynamically heterogeneous, and hence exhibit nonlinear dielectric effects, as found in glycerol and propylene carbonate, where the JG β-relaxation is not resolved and in D-sorbitol where it is resolved. Like the linear susceptibility, χ{sub 1}(f), the frequency dispersion of the third-order dielectric susceptibility, χ{sub 3}(f), was found to depend primarily on the α-relaxation time, and independent of temperature T and pressure P. I show this property of the frequency dispersions of χ{sub 1}(f) and χ{sub 3}(f) is the characteristic of the many
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.
Institute of Scientific and Technical Information of China (English)
Xingzhe Wang; Xiaojing Zheng
2009-01-01
Based on the generalized variational principle of magneto-thermo-elasticity of a ferromagnetic thin shell established (see, Analyses on nonlinear coupling of magneto-thermo-elasticity of ferromagnetic thin shell-Ⅰ), the present paper developed a finite element modeling for the mechanical-magneto-thermal multi-field coupling of a ferromagnetic thin shell. The numerical modeling composes of finite element equations for three sub-systems of magnetic, thermal and deformation fields, as well as iterative methods for nonlinearities of the geometrical large-deflection and the multi-field coupling of the ferromagnetic shell. As examples, the numerical simulations on magneto-elastic behaviors of a ferromagnetic cylindrical shell in an applied magnetic field, and magneto-thermo-elastic behaviors of the shell in applied magnetic and thermal fields are carried out. The results are in good agreement with the experimental ones.
Cao, Hui; Li, Yao-Jiang; Zhou, Yan; Wang, Yan-Xia
2014-11-01
To deal with nonlinear characteristics of spectra data for the thermal power plant flue, a nonlinear partial least square (PLS) analysis method with internal model based on neural network is adopted in the paper. The latent variables of the independent variables and the dependent variables are extracted by PLS regression firstly, and then they are used as the inputs and outputs of neural network respectively to build the nonlinear internal model by train process. For spectra data of flue gases of the thermal power plant, PLS, the nonlinear PLS with the internal model of back propagation neural network (BP-NPLS), the non-linear PLS with the internal model of radial basis function neural network (RBF-NPLS) and the nonlinear PLS with the internal model of adaptive fuzzy inference system (ANFIS-NPLS) are compared. The root mean square error of prediction (RMSEP) of sulfur dioxide of BP-NPLS, RBF-NPLS and ANFIS-NPLS are reduced by 16.96%, 16.60% and 19.55% than that of PLS, respectively. The RMSEP of nitric oxide of BP-NPLS, RBF-NPLS and ANFIS-NPLS are reduced by 8.60%, 8.47% and 10.09% than that of PLS, respectively. The RMSEP of nitrogen dioxide of BP-NPLS, RBF-NPLS and ANFIS-NPLS are reduced by 2.11%, 3.91% and 3.97% than that of PLS, respectively. Experimental results show that the nonlinear PLS is more suitable for the quantitative analysis of glue gas than PLS. Moreover, by using neural network function which can realize high approximation of nonlinear characteristics, the nonlinear partial least squares method with internal model mentioned in this paper have well predictive capabilities and robustness, and could deal with the limitations of nonlinear partial least squares method with other internal model such as polynomial and spline functions themselves under a certain extent. ANFIS-NPLS has the best performance with the internal model of adaptive fuzzy inference system having ability to learn more and reduce the residuals effectively. Hence, ANFIS-NPLS is an
Ding, Hui; Greatbatch, Richard J.; Latif, Mojib; Park, Wonsun
2015-07-01
We examine the impact of sea surface temperature (SST) bias on interannual variability during boreal summer over the equatorial Atlantic using two suites of partially coupled model (PCM) experiments with and without surface heat flux correction. In the experiments, surface wind stress anomalies are specified from observations while the thermodynamic coupling between the atmospheric and oceanic components is still active as in the fully coupled model. The results show that the PCM can capture around 50% of the observed variability associated with the Atlantic Niño from 1958 to 2013, but only when the bias is substantially reduced using heat flux correction, with no skill otherwise. We further show that ocean dynamics explain a large part of the SST variability in the eastern equatorial Atlantic in both observations (50-60%) and the PCM experiments (50-70%) with heat flux correction, implying that the seasonal predictability potential may be higher than currently thought.
Sigalov, G; Gendelman, O V; AL-Shudeifat, M A; Manevitch, L I; Vakakis, A F; Bergman, L A
2012-03-01
We show that nonlinear inertial coupling between a linear oscillator and an eccentric rotator can lead to very interesting interchanges between regular and chaotic dynamical behavior. Indeed, we show that this model demonstrates rather unusual behavior from the viewpoint of nonlinear dynamics. Specifically, at a discrete set of values of the total energy, the Hamiltonian system exhibits non-conventional nonlinear normal modes, whose shape is determined by phase locking of rotatory and oscillatory motions of the rotator at integer ratios of characteristic frequencies. Considering the weakly damped system, resonance capture of the dynamics into the vicinity of these modes brings about regular motion of the system. For energy levels far from these discrete values, the motion of the system is chaotic. Thus, the succession of resonance captures and escapes by a discrete set of the normal modes causes a sequence of transitions between regular and chaotic behavior, provided that the damping is sufficiently small. We begin from the Hamiltonian system and present a series of Poincaré sections manifesting the complex structure of the phase space of the considered system with inertial nonlinear coupling. Then an approximate analytical description is presented for the non-conventional nonlinear normal modes. We confirm the analytical results by numerical simulation and demonstrate the alternate transitions between regular and chaotic dynamics mentioned above. The origin of the chaotic behavior is also discussed.
Directory of Open Access Journals (Sweden)
Hideki Gotoh
2014-10-01
Full Text Available Optical nonlinear effects are examined using a two-color micro-photoluminescence (micro-PL method in a coherently coupled exciton-biexciton system in a single quantum dot (QD. PL and photoluminescence excitation spectroscopy (PLE are employed to measure the absorption spectra of the exciton and biexciton states. PLE for Stokes and anti-Stokes PL enables us to clarify the nonlinear optical absorption properties in the lowest exciton and biexciton states. The nonlinear absorption spectra for excitons exhibit asymmetric shapes with peak and dip structures, and provide a distinct contrast to the symmetric dip structures of conventional nonlinear spectra. Theoretical analyses with a density matrix method indicate that the nonlinear spectra are caused not by a simple coherent interaction between the exciton and biexciton states but by coupling effects among exciton, biexciton and continuum states. These results indicate that Fano quantum interference effects appear in exciton-biexciton systems at QDs and offer important insights into their physics.
Institute of Scientific and Technical Information of China (English)
ZHOU Shihua; SONG Guiqiu; REN Zhaohui; WEN Bangchun
2016-01-01
Extensive studies on nonlinear dynamics of gear systems with internal excitation or external excitation respectively have been carried out. However, the nonlinear characteristics of gear systems under combined internal and external excitations are scarcely investigated. An eight-degree-of-freedom(8-DOF) nonlinear spur gear-rotor-bearing model, which contains backlash, transmission error, eccentricity, gravity and input/output torque, is established, and the coupled lateral-torsional vibration characteristics are studied. Based on the equations of motion, the coupled spur gear-rotor-bearing system(SGRBS) is investigated using the Runge-Kutta numerical method, and the effects of rotational speed, error fluctuation and load fluctuation on the dynamic responses are explored. The results show that a diverse range of nonlinear dynamic characteristics such as periodic motion, quasi-periodic motion, chaotic behaviors and impacts exhibited in the system are strongly attributed to the interaction between internal and external excitations. Significantly, the changing rotational speed could effectively control the vibration of the system. Vibration level increases with the increasing error fluctuation. Whereas the load fluctuation has an influence on the nonlinear dynamic characteristics and the increasing excitation force amplitude makes the vibration amplitude increase, the chaotic motion may be restricted. The proposed model and numerical results can be used for diagnosis of faults and vibration control of practical SGRBS.
Zhou, Shihua; Song, Guiqiu; Ren, Zhaohui; Wen, Bangchun
2016-03-01
Extensive studies on nonlinear dynamics of gear systems with internal excitation or external excitation respectively have been carried out. However, the nonlinear characteristics of gear systems under combined internal and external excitations are scarcely investigated. An eight-degree-of-freedom(8-DOF) nonlinear spur gear-rotor-bearing model, which contains backlash, transmission error, eccentricity, gravity and input/output torque, is established, and the coupled lateral-torsional vibration characteristics are studied. Based on the equations of motion, the coupled spur gear-rotor-bearing system(SGRBS) is investigated using the Runge-Kutta numerical method, and the effects of rotational speed, error fluctuation and load fluctuation on the dynamic responses are explored. The results show that a diverse range of nonlinear dynamic characteristics such as periodic motion, quasi-periodic motion, chaotic behaviors and impacts exhibited in the system are strongly attributed to the interaction between internal and external excitations. Significantly, the changing rotational speed could effectively control the vibration of the system. Vibration level increases with the increasing error fluctuation. Whereas the load fluctuation has an influence on the nonlinear dynamic characteristics and the increasing excitation force amplitude makes the vibration amplitude increase, the chaotic motion may be restricted. The proposed model and numerical results can be used for diagnosis of faults and vibration control of practical SGRBS.
Directory of Open Access Journals (Sweden)
Yong Zhao
1997-01-01
Full Text Available A nonlinear three dimensional (3D single rack model and a nonlinear 3D whole pool multi-rack model are developed for the spent fuel storage racks of a nuclear power plant (NPP to determine impacts and frictional motion responses when subjected to 3D excitations from the supporting building floor. The submerged free standing rack system and surrounding water are coupled due to hydrodynamic fluid-structure interaction (FSI using potential theory. The models developed have features that allow consideration of geometric and material nonlinearities including (1 the impacts of fuel assemblies to rack cells, a rack to adjacent racks or pool walls, and rack support legs to the pool floor; (2 the hydrodynamic coupling of fuel assemblies with their storing racks, and of a rack with adjacent racks, pool walls, and the pool floor; and (3 the dynamic motion behavior of rocking, twisting, and frictional sliding of rack modules. Using these models 3D nonlinear time history dynamic analyses are performed per the U.S. Nuclear Regulatory Commission (USNRC criteria. Since few such modeling, analyses, and results using both the 3D single and whole pool multiple rack models are available in the literature, this paper emphasizes description of modeling and analysis techniques using the SOLVIA general purpose nonlinear finite element code. Typical response results with different Coulomb friction coefficients are presented and discussed.
Hamedi, H. R.; Ruseckas, J.; Juzeliūnas, G.
2017-09-01
We consider propagation of a probe pulse in an atomic medium characterized by a combined tripod and Lambda (Λ) atom-light coupling scheme. The scheme involves three atomic ground states coupled to two excited states by five light fields. It is demonstrated that dark states can be formed for such an atom-light coupling. This is essential for formation of the electromagnetically induced transparency (EIT) and slow light. In the limiting cases the scheme reduces to conventional Λ- or N-type atom-light couplings providing the EIT or absorption, respectively. Thus, the atomic system can experience a transition from the EIT to the absorption by changing the amplitudes or phases of control lasers. Subsequently the scheme is employed to analyze the nonlinear pulse propagation using the coupled Maxwell-Bloch equations. It is shown that a generation of stable slow light optical solitons is possible in such a five-level combined tripod and Λ atomic system.
Energy Technology Data Exchange (ETDEWEB)
Martínez-Orozco, J.C. [Unidad Académica de Física. Universidad Autónoma de Zacatecas, Calzada Solidaridad esquina con Paseo la Bufa S/N, C.P. 98060. Zacatecas, Zac. (Mexico); Grupo de Materia Condensada-UdeA, Instituto de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Antioquia UdeA, Calle 70 No. 52-21, Medellín (Colombia); Mora-Ramos, M.E. [Facultad de Ciencias, Universidad Autónoma del Estado de Morelos, Ave. Universidad 1001, CP 62209, Cuernavaca, Morelos (Mexico); Duque, C.A., E-mail: cduque@fisica.udea.edu.co [Grupo de Materia Condensada-UdeA, Instituto de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Antioquia UdeA, Calle 70 No. 52-21, Medellín (Colombia)
2014-11-01
The conduction band states of GaAs-based vertically coupled double triangular quantum dots in two dimensions are investigated within the effective mass and parabolic approximation, using a diagonalization procedure to solve the corresponding Schrödinger-like equation. The effect of an externally applied static electric field is included in the calculation, and the variation of the lowest confined energy levels as a result of the change of the field strength is reported for different geometrical setups. The linear and nonlinear optical absorptions and the relative change of the refractive index, associated with the energy transition between the ground and the first excited state in the system, are studied as a function of the incident light frequency for distinct configurations of inter-dot distance and electric field intensities. The blueshift of the resonant absorption peaks is detected as a consequence of the increment in the field intensity, whereas the opposite effect is obtained from the increase of inter-dot vertical distance. It is also shown that for large enough values of the electric field there is a quenching of the optical absorption due to field-induced change of symmetry of the first excited state wavefunction, in the case of triangular dots of equal shape and size.
Coupled force-balance and scattering equations for nonlinear transport in quantum wires
Huang, Danhong; Gumbs, Godfrey
2009-07-01
The coupled force-balance and scattering equations have been derived and applied to study nonlinear transport of electrons subjected to a strong dc electric field in an elastic-scattering-limited quantum wire. Numerical results have demonstrated both field-induced heating-up and cooling-down behaviors in the nonequilibrium part of the total electron-distribution function by varying the impurity density or the width of the quantum wire. The obtained asymmetric distribution function in momentum space invalidates the application of the energy-balance equation to our quantum-wire system in the center-of-mass frame. The experimentally observed suppression of mobility by a driving field for the center-of-mass motion in the quantum-wire system has been reproduced [see K. Tsubaki , Electr. Lett. 24, 1267 (1988); M. Hauser , Sci. Technol. 9, 951 (1994)]. In addition, the thermal enhancement of mobility in the elastic-scattering-limited system has been demonstrated, in accordance with a similar prediction made for graphene nanoribbons [see T. Fang , Phys. Rev. B 78, 205403 (2008)]. This thermal enhancement has been found to play a more and more significant role with higher lattice temperature and becomes stronger for a low-driving field.
Takatsuka, Kazuo
Nonlinear dynamics and chaos are studied in a system for which a complete set of equations of motion such as equations of Newton, Navier-Stokes and Van der Pol, is not available. As a very general system as such, we consider coupled classical spins (pendulums), each of which is under control by a fuzzy system that is designed to align the spin to an unstable fixed point. The fuzzy system provides a deterministic procedure to control an object without use of a differential equation. The positions and velocities of the spins are monitored periodically and each fuzzy control gives a momentum to its associated spin in the reverse directions. If the monitoring is made with an interval short enough, the spin-spin interactions are overwhelmed by the fuzzy control and the system converges to a state as designed. However, a long-interval monitoring induces dynamics of “too-late response”, and thereby results in chaos. A great variety of dynamics are generated under very delicate balance between the fuzzy control and the spin-spin interaction, in which two independent mechanisms of creating negative and positive “Liapunov exponents” interact with each other.
Nonlinear coupled rotor-fuselage helicopter vibration studies with higher harmonic control
Friedmann, P. P.; Venkatesan, C.; Papavassiliou, I.
1990-01-01
This paper addresses the problem of vibration prediction and vibration reduction in helicopters by means of active control methodologies. The nonlinear equations of a coupled rotor/flexible-fuselage system have been derived using computer algebra, thus relegating this tedious task to the computer. In the solution procedure the trim state and vibratory response of the helicopter are obtained in a single pass by using a harmonic balance technique and simultaneously satisfying the trim and the vibratory response of the helicopter in all the rotor and fuselage degrees of freedom. Using this solution procedure, the influence of the fuselage flexibility on the vibratory response is studied. In addition, it is shown that the conventional single frequency HHC is capable of reducing either the hub loads or only the fuselage vibrations but not both simultaneously. A new scheme called MHHC, having multiple higher harmonic pitch inputs, was used to accomplish this task of simultaneously reducing both the vibratory hub loads and fuselage vibratory response. In addition, the uniqueness of this MHHC scheme is explained in detail.
A nonlinear electromechanical coupling model for electropore expansion in cell electroporation
Deng, Peigang; Lee, Yi-Kuen; Zhang, Tong-Yi
2014-11-01
Under an electric field, the electric tractions acting on a cell membrane containing a pore-nucleus are investigated by using a nonlinear electromechanical coupling model, in which the cell membrane is treated as a hyperelastic material. Iterations between the electric field and the structure field are performed to reveal the electrical forces exerting on the pore region and the subsequent pore expansion process. An explicit exponential decay of the membrane’s edge energy as a function of pore radius is defined for a hydrophilic pore and the transition energy as a hydrophobic pore converts to a hydrophilic pore during the initial stage of pore formation is investigated. It is found that the edge energy for the creation of an electropore edge plays an important role at the atomistic scale and it determines the hydrophobic-hydrophilic transition energy barrier. Various free energy evolution paths are exhibited, depending on the applied electric field, which provides further insight towards the electroporation (EP) phenomenon. In comparison with previous EP models, the proposed model has the ability to predict the metastable point on the free energy curve that is relevant to the lipid ion channel. In addition, the proposed model can also predict the critical transmembrane potential for the activation of an effective electroporation that is in a good agreement with previously published experimental data.
Simulating the Effect of Non-Linear Mode-Coupling in Cosmological Parameter Estimation
Kiessling, A; Heavens, A F
2011-01-01
Fisher Information Matrix methods are commonly used in cosmology to estimate the accuracy that cosmological parameters can be measured with a given experiment, and to optimise the design of experiments. However, the standard approach usually assumes both data and parameter estimates are Gaussian-distributed. Further, for survey forecasts and optimisation it is usually assumed the power-spectra covariance matrix is diagonal in Fourier-space. But in the low-redshift Universe, non-linear mode-coupling will tend to correlate small-scale power, moving information from lower to higher-order moments of the field. This movement of information will change the predictions of cosmological parameter accuracy. In this paper we quantify this loss of information by comparing naive Gaussian Fisher matrix forecasts with a Maximum Likelihood parameter estimation analysis of a suite of mock weak lensing catalogues derived from N-body simulations, based on the SUNGLASS pipeline, for a 2-D and tomographic shear analysis of a Eucl...