Directory of Open Access Journals (Sweden)
Z. Pashazadeh Atabakan
2013-01-01
Full Text Available Spectral homotopy analysis method (SHAM as a modification of homotopy analysis method (HAM is applied to obtain solution of high-order nonlinear Fredholm integro-differential problems. The existence and uniqueness of the solution and convergence of the proposed method are proved. Some examples are given to approve the efficiency and the accuracy of the proposed method. The SHAM results show that the proposed approach is quite reasonable when compared to homotopy analysis method, Lagrange interpolation solutions, and exact solutions.
Directory of Open Access Journals (Sweden)
shadan sadigh behzadi
2012-03-01
Full Text Available In this present paper, we solve a two-dimensional nonlinear Volterra-Fredholm integro-differential equation by using the following powerful, efficient but simple methods: (i Modified Adomian decomposition method (MADM, (ii Variational iteration method (VIM, (iii Homotopy analysis method (HAM and (iv Modified homotopy perturbation method (MHPM. The uniqueness of the solution and the convergence of the proposed methods are proved in detail. Numerical examples are studied to demonstrate the accuracy of the presented methods.
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Ahmad Molabahrami
2013-09-01
Full Text Available In this paper, the integral mean value method is employed to handle the general nonlinear Fredholm integro-differential equations under the mixed conditions. The application of the method is based on the integral mean value theorem for integrals. By using the integral mean value method, an integro-differential equation is transformed to an ordinary differential equation, then by solving it, the obtained solution is transformed to a system of nonlinear algebraic equations to calculate the unknown values. The efficiency of the approach will be shown by applying the procedure on some examples. In this respect, a comparison with series pattern solutions, obtained by some analytic methods, is given. For the approximate solution given by integral mean value method, the bounds of the absolute errors are given. The Mathematica program of the integral mean value method based on the procedure in this paper is designed.
Stability analysis of Runge-Kutta methods for nonlinear neutral delay integro-differential equations
Institute of Scientific and Technical Information of China (English)
2007-01-01
The sufficient conditions for the stability and asymptotic stability of Runge-Kutta methods for nonlinear neutral delay integro-differential equations are derived. A numerical test that confirms the theoretical results is given in the end.
Institute of Scientific and Technical Information of China (English)
Yepeng Xing; Qiong Wang; Valery G. Romanovski
2009-01-01
We prove several new comparison results and develop the monotone iterative tech-nique to show the existence of extremal solutions to a kind of periodic boundary value problem (PBVP) for nonlinear integro-differential equation of mixed type on time scales.
THE NONLINEAR BOUNDARY VALUE PROBLEM FOR A CLASS OF INTEGRO-DIFFERENTIAL SYSTEM
Institute of Scientific and Technical Information of China (English)
Rongrong Tang
2006-01-01
In this paper, using the theory of differential inequalities, we study the nonlinear boundary value problem for a class of integro-differential system. Under appropriate assumptions, the existence of solution is proved and the uniformly valid asymptotic expansions for arbitrary n-th order approximation and the estimation of remainder term are obtained simply and conveniently.
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Berenguer MI
2010-01-01
Full Text Available This paper deals with obtaining a numerical method in order to approximate the solution of the nonlinear Volterra integro-differential equation. We define, following a fixed-point approach, a sequence of functions which approximate the solution of this type of equation, due to some properties of certain biorthogonal systems for the Banach spaces and .
Numerical solution of nonlinear fractional-order Volterra integro-differential equations by SCW
Zhu, Li; Fan, Qibin
2013-05-01
Fractional calculus is an extension of derivatives and integrals to non-integer orders and has been widely used to model scientific and engineering problems. In this paper, we describe the fractional derivative in the Caputo sense and give the second kind Chebyshev wavelet (SCW) operational matrix of fractional integration. Then based on above results we propose the SCW operational matrix method to solve a kind of nonlinear fractional-order Volterra integro-differential equations. The main characteristic of this approach is that it reduces the integro-differential equations into a nonlinear system of algebraic equations. Thus, it can simplify the problem of fractional order equation solving. The obtained numerical results indicate that the proposed method is efficient and accurate for this kind equations.
Institute of Scientific and Technical Information of China (English)
Rui QI; Cheng-jian ZHANG; Yu-jie ZHANG
2012-01-01
This paper is concerned with the numerical dissipativity of multistep Runge-Kutta methods for nonlinear Volterra delay-integro-differential equations. We investigate the dissipativity properties of (k,l)-algebraically stable multistep Runge-Kutta methods with constrained grid and an uniform grid.The finitedimensional and infinite-dimensional dissipativity results of (k,l)-algebraically stable Runge-Kutta methods are obtained.
Nonlinear boundary value problems for first order impulsive integro-differential equations
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Xinzhi Liu
1989-01-01
Full Text Available In this paper, we investigate a class of first order impulsive integro-differential equations subject to certain nonlinear boundary conditions and prove, with the help of upper and lower solutions, that the problem has a solution lying between the upper and lower solutions. We also develop monotone iterative technique and show the existence of multiple solutions of a class of periodic boundary value problems.
Systems of nonlinear Volterra integro-differential equations of arbitrary order
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Kourosh Parand
2018-10-01
Full Text Available In this paper, a new approximate method for solving of systems of nonlinear Volterra integro-differential equations of arbitrary (integer and fractional order is introduced. For this purpose, the generalized fractional order of the Chebyshev orthogonal functions (GFCFs based on the classical Chebyshev polynomials of the first kind has been introduced that can be used to obtain the solution of the integro-differential equations (IDEs. Also, we construct the fractional derivative operational matrix of order $\\alpha$ in the Caputo's definition for GFCFs. This method reduced a system of IDEs by collocation method into a system of algebraic equations. Some examples to illustrate the simplicity and the effectiveness of the propose method have been presented.
Energy Technology Data Exchange (ETDEWEB)
Ibragimov, Nail H [Department of Mathematics and Science, Blekinge Institute of Technology, SE-371 79 Karlskrona (Sweden); Meleshko, Sergey V [School of Mathematics, Institute of Science, Suranaree University of Technology, Nakhon Ratchasima 30000 (Thailand); Rudenko, Oleg V, E-mail: nib@bth.se, E-mail: sergey@math.sut.ac.th, E-mail: rudenko@acs366.phys.msu.ru [Department of Physics, Moscow State University, 119991 Moscow (Russian Federation)
2011-08-05
The paper deals with an evolutionary integro-differential equation describing nonlinear waves. A particular choice of the kernel in the integral leads to well-known equations such as the Khokhlov-Zabolotskaya equation, the Kadomtsev-Petviashvili equation and others. Since the solutions of these equations describe many physical phenomena, the analysis of the general model studied in this paper is important. One of the methods for obtaining solutions of differential equations is provided by the Lie group analysis. However, this method is not applicable to integro-differential equations. Therefore, we discuss new approaches developed in modern group analysis and apply them to the general model considered in this paper. Reduced equations and exact solutions are also presented.
Institute of Scientific and Technical Information of China (English)
崔霞
2002-01-01
Alternating direction finite element (ADFE) scheme for d-dimensional nonlinear system of parabolic integro-differential equations is studied. By using a local approximation based on patches of finite elements to treat the capacity term qi(u), decomposition of the coefficient matrix is realized; by using alternating direction, the multi-dimensional problem is reduced to a family of single space variable problems, calculation work is simplified; by using finite element method, high accuracy for space variant is kept; by using inductive hypothesis reasoning, the difficulty coming from the nonlinearity of the coefficients and boundary conditions is treated; by introducing Ritz-Volterra projection, the difficulty coming from the memory term is solved. Finally, by using various techniques for priori estimate for differential equations, the unique resolvability and convergence properties for both FE and ADFE schemes are rigorously demonstrated, and optimal H1 and L2norm space estimates and O((△t)2) estimate for time variant are obtained.
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.
Institute of Scientific and Technical Information of China (English)
SHI Dong-yang; WANG Hui-min; LI Zhi-yan
2009-01-01
A lumped mass approximation scheme of a low order Crouzeix-Raviart type nonconforming triangular finite element is proposed to a kind of nonlinear parabolic integro-differential equations. The L2 error estimate is derived on anisotropic meshes without referring to the traditional nonclassical elliptic projection.
Liang Yue; Yang He
2011-01-01
Abstract The paper deals with the existence of positive solutions for Neumann boundary value problems of nonlinear second-order integro-differential equations - u ″ ( t ) + M u ( t ) = f ( t , u ( t ) , ( S u ) ( t ) ) , 0 < t < 1 , u ′ ( 0 ) = u ′ ( 1 ) = θ and u ″ ( t ) + M u ( t ) = f ( t , u ( t ) , ( S u ) ( t ) ) , 0 < t < 1 , u ′ ( 0 ) ...
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Alsaedi Ahmed
2009-01-01
Full Text Available A generalized quasilinearization technique is developed to obtain a sequence of approximate solutions converging monotonically and quadratically to a unique solution of a boundary value problem involving Duffing type nonlinear integro-differential equation with integral boundary conditions. The convergence of order for the sequence of iterates is also established. It is found that the work presented in this paper not only produces new results but also yields several old results in certain limits.
Zhidkov, E P
2000-01-01
We consider a nonlinear integro-differential equation on a segment with zero Dirichlet boundary conditions and a normalization condition, containing a spectral parameter, which can arise in the mean field approximation for a quantum-mechanical description of a solid. We prove the existence of a countable set of solutions and investigate properties of these solutions. The main result consists in proving the property of being a Bary basis for a sequence of solutions of the problem, possessing a given behavior, the existence of which is proved.
Imbert, Cyril
2009-01-01
The main purpose of this paper is to approximate several non-local evolution equations by zero-sum repeated games in the spirit of the previous works of Kohn and the second author (2006 and 2009): general fully non-linear parabolic integro-differential equations on the one hand, and the integral curvature flow of an interface (Imbert, 2008) on the other hand. In order to do so, we start by constructing such a game for eikonal equations whose speed has a non-constant sign. This provides a (discrete) deterministic control interpretation of these evolution equations. In all our games, two players choose positions successively, and their final payoff is determined by their positions and additional parameters of choice. Because of the non-locality of the problems approximated, by contrast with local problems, their choices have to "collect" information far from their current position. For integral curvature flows, players choose hypersurfaces in the whole space and positions on these hypersurfaces. For parabolic i...
Institute of Scientific and Technical Information of China (English)
Shu-hua Zhang; Tao Lin; Yan-ping Lin; Ming Rao
2001-01-01
In this paper we will show that the Richardson extrapolation can be used to enhance the numerical solution generated by a Petrov-Galerkin finite element method for the initialvalue problem for a nonlinear Volterra integro-differential equation. As by-products, we will also show that these enhanced approximations can be used to form a class of aposteriori estimators for this Petrov-Galerkin finite element method. Numerical examples are supplied to illustrate the theoretical results.
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Omar Abu Arqub
2012-01-01
Full Text Available This paper investigates the numerical solution of nonlinear Fredholm-Volterra integro-differential equations using reproducing kernel Hilbert space method. The solution ( is represented in the form of series in the reproducing kernel space. In the mean time, the n-term approximate solution ( is obtained and it is proved to converge to the exact solution (. Furthermore, the proposed method has an advantage that it is possible to pick any point in the interval of integration and as well the approximate solution and its derivative will be applicable. Numerical examples are included to demonstrate the accuracy and applicability of the presented technique. The results reveal that the method is very effective and simple.
Institute of Scientific and Technical Information of China (English)
Xingqiu ZHANG
2012-01-01
The existence of positive solutions to a boundary value problem of second-order impulsive singular integro-differential equation with integral boundary conditions in a Banach space is obtained by means of fixed point theory.Moreover,an application is also given to illustrate the main result.
A DELAY-DEPENDENT STABILITY CRITERION FOR NONLINEAR STOCHASTIC DELAY-INTEGRO-DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
Niu Yuanling; Zhang Chengjian; Duan Jinqiao
2011-01-01
A type of complex systems under both random influence and memory effects is considered.The systems are modeled by a class of nonlinear stochastic delay-integrodifferential equations.A delay-dependent stability criterion for such equations is derived under the condition that the time lags are small enough.Numerical simulations are presented to illustrate the theoretical result.
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
The comparison principle is first established,and then the lower and upper solution method and the monotone iterative technique are employed to the study of terminal value problems for the first order nonlinear impulsive integro-differential equations in Banach spaces.Finally,the existence theorem on the maximal and minimal solutions is obtained.
Directory of Open Access Journals (Sweden)
Zhinan Xia
2015-07-01
Full Text Available In this article, we show sufficient conditions for the existence, uniqueness and attractivity of piecewise weighted pseudo almost periodic classical solution of nonlinear impulsive integro-differential equations. The working tools are based on the fixed point theorem and fractional powers of operators. An application to impulsive integro-differential equations is presented.
Lipschitz Regularity of Solutions for Mixed Integro-Differential Equations
Barles, Guy; Ciomaga, Adina; Imbert, Cyril
2011-01-01
We establish new Hoelder and Lipschitz estimates for viscosity solutions of a large class of elliptic and parabolic nonlinear integro-differential equations, by the classical Ishii-Lions's method. We thus extend the Hoelder regularity results recently obtained by Barles, Chasseigne and Imbert (2011). In addition, we deal with a new class of nonlocal equations that we term mixed integro-differential equations. These equations are particularly interesting, as they are degenerate both in the local and nonlocal term, but their overall behavior is driven by the local-nonlocal interaction, e.g. the fractional diffusion may give the ellipticity in one direction and the classical diffusion in the complementary one.
Splitting methods for partial Volterra integro-differential equations
Brunner, H.; Houwen, P.J. van der; Sommeijer, B.P.
1999-01-01
The spatial discretization of initial-value problems for (nonlinear) parabolic or hyperbolic PDEs with memory terms leads to (large) systems of Volterra integro-differential equations (VIDEs). In this paper we study the efficient numerical solution of such systems by methods based on linear multiste
Institute of Scientific and Technical Information of China (English)
俞卫琴; 陈芳启
2008-01-01
By the use of Monch fixed point theorem and a new comparison result, the solutions of initial value problems for nonlinear second order impulsive integro-differential equations of mixed type in Banach spaces are investigated and the existence theorem is obtained.
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Shadan Sadigh Behzadi
2011-12-01
Full Text Available In this paper, Adomian decomposition method (ADM and homotopy analysis method (HAM are proposed to solving the fuzzy nonlinear Volterra-Fredholm integral equation of the second kind$(FVFIE-2$. we convert a fuzzy nonlinear Volterra-Fredholm integral equation to a nonlinear system of Volterra-Fredholm integral equation in crisp case. we use ADM , HAM and find the approximate solution of this system and hence obtain an approximation for fuzzy solution of the nonlinear fuzzy Volterra-Fredholm integral equation. Also, the existence and uniqueness of the solution and convergence of the proposed methods are proved. Examples is given and the results reveal that homotopy analysis method is very effective and simple compared with the Adomian decomposition method.
Xu, Run; Ma, Xiangting
2017-01-01
In this paper, we establish some new retarded nonlinear Volterra-Fredholm type integral inequalities with maxima in two independent variables, and we present the applications to research the boundedness of solutions to retarded nonlinear Volterra-Fredholm type integral equations.
Khairullin, Ermek
2016-08-01
In this paper we consider a special boundary value problem for multidimensional parabolic integro-differential equation with boundary conditions that contains as a boundary condition containing derivatives of order higher than the order of the equation. The solution is sought in the form of a thermal potential of a double layer. Shows lemma of finding the limits of the derivatives of the unknown function in the neighborhood of the hyperplane. Using the boundary condition and lemma obtained integral-differential equation (IDE) of parabolic operators, whĐţre an unknown function under the integral contains higher-order space variables derivatives. IDE is reduced to a singular integral equation (SIE), when an unknown function in the spatial variables satisfies the Holder. The characteristic part is solved in the class of distribution function using method of transformation of Fourier-Laplace. Found an algebraic condition for the transition to the classical generalized solution. Integral equation of the resolvent for the characteristic part of SIE is obtained. Integro-differential equation is reduced to the Volterra-Fredholm type integral equation of the second kind by method of regularization. It is shown that the solution of SIE is a solution of IDE. Obtain a theorem on the solvability of the boundary value problem of multidimensional parabolic integro-differential equation, when a known function of the spatial variables belongs to the Holder class and satisfies the solvability conditions.
Terminal value problems of impulsive integro-differential equations in Banach spaces
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Dajun Guo
1997-01-01
Full Text Available This paper uses cone theory and the monotone iterative technique to investigate the existence of minimal nonnegative solutions of terminal value problems for first order nonlinear impulsive integro-differential equations of mixed type in a Banach space.
N-th order impulsive integro-differential equations in Banach spaces
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Manfeng Hu
2004-03-01
Full Text Available We investigate the maximal and minimal solutions of initial value problem for N-th order nonlinear impulsive integro-differential equation in Banach space by establishing a comparison result and using the upper and lower solutions methods.
A RANK THEOREM FOR NONLINEAR SEMI-FREDHOLM OPERATORS BETWEEN TWO BANACH MANIFOLDS
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
In this article the concept of local conjugation of a C1 mapping between two Banach manifolds is introduced. Then a rank theorem for nonlinear semi-Fredholm operators between two Banach manifolds and a finite rank theorem are established in global analysis.
Institute of Scientific and Technical Information of China (English)
王芬玲; 石东洋; 陈金环
2012-01-01
在半离散和全离散格式下讨论非线性抛物积分微分方程的类Wilson非协调有限元逼近.当问题的精确解u∈H3(Ω)/H4(Ω)时,利用该元的相容误差在能量模意义下可以达到O(h2 )/O(h3)比其插值误差高一阶和二阶的特殊性质,再结合协调部分的高精度分析及插值后处理技术,并借助于双线性插值代替传统有限元分析中不可缺少的Ritz-Volterra投影导出了半离散格式下的O(h2)阶超逼近和超收敛结果.同时分别得到了向后Euler全离散格式下的超逼近性和Crank-Nicolson全离散格式下的最优误差估计.%A nonconforming quasi-Wilson finite element approximation for nonlinear parabolic integro-differential equation is discussed under the semi-discrete and fully-discrete schemes. By use of the special property of the element,i. e. , the consistence error estimate in energy norm when the exact solution u of the problem belongs to H3(Ω)/ H4(Ω) can reach to O(h2)/O(h3), one/two order higher than the interpolation error, then combination it with the higher accuracy analysis of its conforming part and the interpolated postprocessing technique, the superclose and superconvergence results with order O(h2) are obtained for semi-discrete scheme through interpolation instead of the Ritz-Volterra projection which is an indispensable tool in traditional finite element analysis. The superclose property and the optimal error estimate for backward Euler and Crank-Nicolson fully-discrete schemes are derived , respectively.
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Behzad Ghanbari
2014-01-01
Full Text Available We aim to study the convergence of the homotopy analysis method (HAM in short for solving special nonlinear Volterra-Fredholm integrodifferential equations. The sufficient condition for the convergence of the method is briefly addressed. Some illustrative examples are also presented to demonstrate the validity and applicability of the technique. Comparison of the obtained results HAM with exact solution shows that the method is reliable and capable of providing analytic treatment for solving such equations.
An oscillation criterion for inhomogeneous Stieltjes integro-differential equations
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M. A. El-Sayed
1994-01-01
Full Text Available The aim of the paper is to give an oscillation theorem for inhomogeneous Stieltjes integro-differential equation of the form p(tx′+∫atx(sdσ=f(t. The paper generalizes the author's work [2].
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Diem Dang Huan
2015-12-01
Full Text Available The current paper is concerned with the controllability of nonlocal second-order impulsive neutral stochastic functional integro-differential equations with infinite delay and Poisson jumps in Hilbert spaces. Using the theory of a strongly continuous cosine family of bounded linear operators, stochastic analysis theory and with the help of the Banach fixed point theorem, we derive a new set of sufficient conditions for the controllability of nonlocal second-order impulsive neutral stochastic functional integro-differential equations with infinite delay and Poisson jumps. Finally, an application to the stochastic nonlinear wave equation with infinite delay and Poisson jumps is given.
Aleksandrov-Bakelman-Pucci Type Estimates For Integro-Differential Equations
Guillen, Nestor
2011-01-01
In this work we provide an Aleksandrov-Bakelman-Pucci type estimate for a certain class of fully nonlinear elliptic integro-differential equations and generalizations of both the Monge-Amp\\`ere operator and the convex envelope to a nonlocal, fractional-order setting. This particular elliptic family under consideration is large enough to capture the second order theory as the order of the integro-differential equations tends to 2. Moreover, our estimate is uniform in the order of the equations, resulting in a genuine generalization of the existing ABP estimate. This result also gives a new comparison theorem for viscosity solutions of such equations which only depends on the $L^\\infty$ and $L^n$ norms of the right hand side, in contrast to previous comparison results which utilize the continuity of the right hand side for their conclusions. These results appear to be new even for the linear case of the relevant equations.
Compactness for an integro-differential equation with measures
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Gabriela Grosu
2010-01-01
Full Text Available In this paper, using some compactness arguments, we prove some local or even global existence results for the essentially bounded solution to an integro-differential Cauchy problem with distributed measures in a real Banach space. An example involving the Dirac measure concentrated at point is included.
Extrapolation of Nystrom solution for two dimensional nonlinear Fredholm integral equations
Guoqiang, Han; Jiong, Wang
2001-09-01
In this paper, we analyze the existence of asymptotic error expansion of the Nystrom solution for two-dimensional nonlinear Fredholm integral equations of the second kind. We show that the Nystrom solution admits an error expansion in powers of the step-size h and the step-size k. For a special choice of the numerical quadrature, the leading terms in the error expansion for the Nystrom solution contain only even powers of h and k, beginning with terms h2p and k2q. These expansions are useful for the application of Richardson extrapolation and for obtaining sharper error bounds. Numerical examples show that how Richardson extrapolation gives a remarkable increase of precision, in addition to faster convergence.
A Simple Quantum Integro-Differential Solver (SQuIDS)
Delgado, Carlos Alberto Arguelles; Weaver, Christopher N
2014-01-01
Simple Quantum Integro-Differential Solver (SQuIDS) is a C++ code designed to solve semi-analytically the evolution of a set of density matrices and scalar functions. This is done efficiently by expressing all operators in an SU(N) basis. SQuIDS provides a base class from which users can derive new classes to include new non-trivial terms from the right hand sides of density matrix equations. The code was designed in the context of solving neutrino oscillation problems, but can be applied to any problem that involves solving the quantum evolution of a collection of particles with Hilbert space of dimension up to six.
Analytic solution to a class of integro-differential equations
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Xuming Xie
2003-03-01
Full Text Available In this paper, we consider the integro-differential equation $$ epsilon^2 y''(x+L(xmathcal{H}(y=N(epsilon,x,y,mathcal{H}(y, $$ where $mathcal{H}(y[x]=frac{1}{pi}(Pint_{-infty}^{infty} frac{y(t}{t-x}dt$ is the Hilbert transform. The existence and uniqueness of analytic solution in appropriately chosen space is proved. Our method consists of extending the equation to an appropriately chosen region in the complex plane, then use the Contraction Mapping Theorem.
Barles, Guy; Ley, Olivier; Topp, Erwin
2017-02-01
In this paper, we provide suitable adaptations of the ‘weak version of Bernstein method’ introduced by the first author in 1991, in order to obtain Lipschitz regularity results and Lipschitz estimates for nonlinear integro-differential elliptic and parabolic equations set in the whole space. Our interest is to obtain such Lipschitz results to possibly degenerate equations, or to equations which are indeed ‘uniformly elliptic’ (maybe in the nonlocal sense) but which do not satisfy the usual ‘growth condition’ on the gradient term allowing to use (for example) the Ishii-Lions’ method. We treat the case of a model equation with a superlinear coercivity on the gradient term which has a leading role in the equation. This regularity result together with comparison principle provided for the problem allow to obtain the ergodic large time behavior of the evolution problem in the periodic setting.
Altürk, Ahmet
2016-01-01
Mean value theorems for both derivatives and integrals are very useful tools in mathematics. They can be used to obtain very important inequalities and to prove basic theorems of mathematical analysis. In this article, a semi-analytical method that is based on weighted mean-value theorem for obtaining solutions for a wide class of Fredholm integral equations of the second kind is introduced. Illustrative examples are provided to show the significant advantage of the proposed method over some ...
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1 Taiwo O. A
2013-01-01
Full Text Available The problem of solving special nth-order linear integro-differential equations has special importance in engineering and sciences that constitutes a good model for many systems in various fields. In this paper, we construct canonical polynomial from the differential parts of special nth-order integro-differential equations and use it as our basis function for the numerical solutions of special nth-order integro-differential equations. The results obtained by this method are compared with those obtained by Adomian Decomposition method. It is also observed that the new method is an effective method with high accuracy. Some examples are given to illustrate the method.
Method for solving the periodic problem for integro-differential equations
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Snezhana G. Hristova
1989-05-01
Full Text Available In the paper a monotone-iterative method for approximate finding a couple of minimal and maximal quasisolutions of the periodic problem for a system of integro-differential equations of Volterra type is justified.
Ullah, Saif; Farooq, Muhammad; Ahmad, Latif; Abdullah, Saleem
2014-01-01
Fuzzy partial integro-differential equations have a major role in the fields of science and engineering. In this paper, we propose the solution of fuzzy partial Volterra integro-differential equation with convolution type kernel using fuzzy Laplace transform method (FLTM) under Hukuhara differentiability. It is shown that FLTM is a simple and reliable approach for solving such equations analytically. Finally, the method is illustrated with few examples to show the ability of the proposed method.
Özen, Kemal
2016-12-01
One of the little-known techniques for ordinary integro-differential equations in literature is Green's functional method, the origin of which dates back to Azerbaijani scientist Seyidali S. Akhiev. According to this method, Green's functional concepts for some simple forms of such equations have been introduced in the several studies. In this study, we extend Green's functional concept to a higher order ordinary integro-differential equation involving generally nonlocal conditions. A novel kind of adjoint problem and Green's functional are constructed for completely nonhomogeneous problem. By means of the obtained Green's functional, the solution to the problem is identified.
THE NUMERICAL SOLUTION FOR A PARTIAL INTEGRO-DIFFERENTIAL EQUATION WITH A WEAKLY SINGULAR KERNEL
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
In this paper, a first order semi-discrete method of a partial integro-differential equation with a weakly singular kernel is considered. We apply Galerkin spectral method in one direction, and the inversion technique for the Laplace transform in another direction, the result of the numerical experiment proves the accuracy of this method.
Indian Academy of Sciences (India)
Syed Abbas; V Kavitha; R Murugesu
2015-08-01
In this article, we study the concept of Stepanov-like weighted pseudo almost automorphic solutions to fractional order abstract integro-differential equations. We establish the results with Lipschitz condition and without Lipschitz condition on the forcing term. An interesting example is presented to illustrate the main findings. The results proven are new and complement the existing ones.
Controllability of Fractional Neutral Stochastic Integro-Differential Systems with Infinite Delay
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Xichao Sun
2013-01-01
Full Text Available This paper is concerned with the controllability of a class of fractional neutral stochastic integro-differential systems with infinite delay in an abstract space. By employing fractional calculus and Sadovskii's fixed point principle without assuming severe compactness condition on the semigroup, a set of sufficient conditions are derived for achieving the controllability result.
EXISTENCE OF MULTIPLE POSITIVE PERIODIC SOLUTIONS TO A CLASS OF INTEGRO-DIFFERENTIAL EQUATION
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
In this paper,by the Avery-Henderson fixed point theorem,we investigate the existence of multiple positive periodic solutions to a class of integro-differential equation. Some suficient conditions are obtained for the existence of multiple positive periodic solutions.
Analytical lie group approach for solving fractional integro-differential equations
Pashayi, S.; Hashemi, M. S.; Shahmorad, S.
2017-10-01
This study is concerned with the Lie symmetry group analysis of Fractional Integro-Differential Equations (FIDEs) with nonlocal structures based on a new development of prolongation formula. A new prolongation for FIDEs is extracted and invariant solutions are finally presented for some illustrative examples.
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Yan-Tao Bian
2014-04-01
Full Text Available In this article, we study weighted asymptotic behavior of solutions to the semilinear integro-differential equation $$ u'(t=Au(t+\\alpha\\int_{-\\infty}^{t}e^{-\\beta(t-s}Au(sds+f(t,u(t, \\quad t\\in \\mathbb{R}, $$ where $\\alpha, \\beta \\in \\mathbb{R}$, with $\\beta > 0, \\alpha \
Error estimates for finite element solution for parabolic integro-differential equations
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Hasan N. Ymeri
1993-05-01
Full Text Available In this paper we first study the stability of Ritz-Volterra projection and its maximum norm estimates, and then we use these results to derive some L\\infty error estimates for finite element methods for parabolic partial integro-differential equations.
Mehdiyeva, Galina; Imanova, Mehriban; Ibrahimov, Vagif
2012-11-01
As is well known investigation of many processes of natural sciences reduce to the solving of initial value problem for integro-differential equations which are one of the priority areas of modern mathematics. To define the exact solution of such problems is not always possible. Therefore the scientists constructed approximate methods for solving them. There are a number of papers devoted to finding approximate solutions of integro-differential equations. Unlike at papers investigated, here the numerical solution of initial value problem for Volterra integro-differential equations by the hybrid methods, constructed concrete methods with the degree p ≤ 6 and suggested algorithm for using them.
Zhou, Long-Qiao; Meleshko, Sergey V.
2017-01-01
A linear thermoviscoelastic model for homogeneous, aging materials with memory is established. A system of integro-differential equations is obtained by using two motions (a one-dimensional motion and a shearing motion) for this model. Applying the group analysis method to the system of integro-differential equations, the admitted Lie group is determined. Using this admitted Lie group, invariant and partially invariant solutions are found. The present paper gives a first example of application of partially invariant solutions to integro-differential equations.
Abstract fractional integro-differential equations involving nonlocal initial conditions in α-norm
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Wang Rong-Nian
2011-01-01
Full Text Available Abstract In the present paper, we deal with the Cauchy problems of abstract fractional integro-differential equations involving nonlocal initial conditions in α-norm, where the operator A in the linear part is the generator of a compact analytic semigroup. New criterions, ensuring the existence of mild solutions, are established. The results are obtained by using the theory of operator families associated with the function of Wright type and the semigroup generated by A, Krasnoselkii's fixed point theorem and Schauder's fixed point theorem. An application to a fractional partial integro-differential equation with nonlocal initial condition is also considered. Mathematics subject classification (2000 26A33, 34G10, 34G20
Mikhailov, SE
2006-01-01
Copyright @ 2006 Tech Science Press A quasi-static mixed boundary value problem of elastic damage mechanics for a continuously inhomogeneous body is considered. Using the two-operator Green-Betti formula and the fundamental solution of an auxiliary homogeneous linear elasticity with frozen initial, secant or tangent elastic coe±cients, a boundary-domain integro-differential formulation of the elasto-plastic problem with respect to the displacement rates and their gradients is derived. Usin...
Stability Analysis of Runge-Kutta Methods for Delay Integro-Differential Equations
Institute of Scientific and Technical Information of China (English)
甘四清; 郑纬民
2004-01-01
Considering a linear system of delay integro-differential equations with a constant delay whose zero solution is asympototically stable, this paper discusses the stability of numerical methods for the system. The adaptation of Runge-Kutta methods with a Lagrange interpolation procedure was focused on inheriting the asymptotic stability of underlying linear systems. The results show that an A-stable Runge-Kutta method preserves the asympototic stability of underlying linear systems whenever an unconstrained grid is used.
Institute of Scientific and Technical Information of China (English)
CHEN Fang-qi; TIAN Rui-lan; CHEN Yu-shu
2006-01-01
Under loose conditions, the existence of solutions to initial value problem are studied for second order impulsive integro-differential equation with infinite moments of impulse effect on the positive half real axis in Banach spaces. By the use of recurrence method, Tonelii sequence and the locally convex topology, the new existence theorems are achieved, which improve the related results obtained by Guo Da-jun.
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Salih Yalcinbas
2016-01-01
Full Text Available In this paper, a new collocation method based on the Fibonacci polynomials is introduced to solve the high-order linear Volterra integro-differential equations under the conditions. Numerical examples are included to demonstrate the applicability and validity of the proposed method and comparisons are made with the existing results. In addition, an error estimation based on the residual functions is presented for this method. The approximate solutions are improved by using this error estimation.
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Ammar Ali Neamah
2014-01-01
Full Text Available The paper uses the Local fractional variational Iteration Method for solving the second kind Volterra integro-differential equations within the local fractional integral operators. The analytical solutions within the non-differential terms are discussed. Some illustrative examples will be discussed. The obtained results show the simplicity and efficiency of the present technique with application to the problems for the integral equations.
Chen, J.; Lee, Y. C.
1985-01-01
In the present investigation, a general integro-differential formalism is derived for the study of the collisionless tearing mode in a highly non-Maxwellian neutral sheet in which both electrons and ions are treated kinetically. The obtained formalism is applied to a specific non-Maxwellian distribution. The dispersion relation for the considered system is determined, taking into account the fundamental harmonic of the orbital frequency. It is found that the dispersion relation is dominated by the electrons. The results are presented in a number of graphs. The growth rates of non-Maxwellian distributions are generally much greater than the growth rate of the conventional isotropic tearing instability.
Stability of Runge-Kutta-Pouzet methods for Volterra integro-differential equations with delays
Institute of Scientific and Technical Information of China (English)
Chengming HUANG; Stefan VANDEWALLE
2009-01-01
This paper is concerned with the study of the stability of Runge Kutta-Pouzet methods for Volterra integro-differential equations with delays.We are interested in the comparison between the analytical and numerical stability regions.First,we focus on scalar equations with real coefficients.It is proved that all Gauss-Pouzet methods can retain the asymptotic stability of the analytical solution.Then,we consider the multidimensional case.A new stability condition for the stability of the analytical solution is given.Under this condition,the asymptotic stability of Gauss-Pouzet methods is investigated.
One-step block method for solving Volterra integro-differential equations
Mohamed, Nurul Atikah binti; Majid, Zanariah Abdul
2015-10-01
One-step block method for solving linear Volterra integro-differential equations (VIDEs) is presented in this paper. In VIDEs, the unknown function appears in the form of derivative and under the integral sign. The popular methods for solving VIDEs are the method of quadrature or quadrature method combined with numerical method. The proposed block method will solve the ordinary differential equations (ODEs) part and Newton-Cotes quadrature rule is applied to calculate the integral part of VIDEs. Numerical problems are presented to illustrate the performance of the proposed method.
Constructing conservation laws for fractional-order integro-differential equations
Lukashchuk, S. Yu.
2015-08-01
In a class of functions depending on linear integro-differential fractional-order variables, we prove an analogue of the fundamental operator identity relating the infinitesimal operator of a point transformation group, the Euler-Lagrange differential operator, and Noether operators. Using this identity, we prove fractional-differential analogues of the Noether theorem and its generalizations applicable to equations with fractional-order integrals and derivatives of various types that are Euler-Lagrange equations. In explicit form, we give fractional-differential generalizations of Noether operators that gives an efficient way to construct conservation laws, which we illustrate with three examples.
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Z. Denton
2017-01-01
Full Text Available In this work we investigate integro-differential initial value problems with Riemann Liouville fractional derivatives where the forcing function is a sum of an increasing function and a decreasing function. We will apply the method of lower and upper solutions and develop two monotone iterative techniques by constructing two sequences that converge uniformly and monotonically to minimal and maximal solutions. In the first theorem we will construct two natural sequences and in the second theorem we will construct two intertwined sequences. Finally, we illustrate our results with an example.
Relativistic integro-differential form of the Lorentz-Dirac equation in 3D without runaways
Ibison, Michael; Puthoff, Harold E.
2001-04-01
It is well known that the third-order Lorentz-Dirac equation admits runaway solutions wherein the energy of the particle grows without limit, even when there is no external force. These solutions can be denied simply on physical grounds, and on the basis of careful analysis of the correspondence between classical and quantum theory. Nonetheless, one would prefer an equation that did not admit unphysical behavior at the outset. Such an equation - an integro-differential version of the Lorentz-Dirac equation - is currently available either in 1 dimension only, or in 3 dimensions only in the non-relativistic limit. It is shown herein how the Lorentz-Dirac equation may be integrated without approximation, and is thereby converted to a second-order integro-differential equation in 3D satisfying the above requirement. I.E., as a result, no additional constraints on the solutions are required because runaway solutions are intrinsically absent. The derivation is placed within the historical context established by standard works on classical electrodynamics by Rohrlich, and by Jackson.
Gou, Haide; Li, Baolin
2017-01-01
In this paper, we study local and global existence of mild solution for an impulsive fractional functional integro differential equation with non-compact semi-group in Banach spaces. We establish a general framework to find the mild solutions for impulsive fractional integro-differential equations, which will provide an effective way to deal with such problems. The theorems proved in this paper improve and extend some related conclusions on this topic. Finally, two applications are given to illustrate that our results are valuable.
GOSWAMI, DEEPJYOTI
2014-01-01
AWe propose and analyse an alternate approach to a priori error estimates for the semidiscrete Galerkin approximation to a time-dependent parabolic integro-differential equation with nonsmooth initial data. The method is based on energy arguments combined with repeated use of time integration, but without using parabolic-type duality techniques. An optimal L2-error estimate is derived for the semidiscrete approximation when the initial data is in L2. A superconvergence result is obtained and then used to prove a maximum norm estimate for parabolic integro-differential equations defined on a two-dimensional bounded domain. © 2014 Australian Mathematical Society.
An hp-local Discontinuous Galerkin Method for Parabolic Integro-Differential Equations
Pani, Amiya K.
2010-06-06
In this article, a priori error bounds are derived for an hp-local discontinuous Galerkin (LDG) approximation to a parabolic integro-differential equation. It is shown that error estimates in L 2-norm of the gradient as well as of the potential are optimal in the discretizing parameter h and suboptimal in the degree of polynomial p. Due to the presence of the integral term, an introduction of an expanded mixed type Ritz-Volterra projection helps us to achieve optimal estimates. Further, it is observed that a negative norm estimate of the gradient plays a crucial role in our convergence analysis. As in the elliptic case, similar results on order of convergence are established for the semidiscrete method after suitably modifying the numerical fluxes. The optimality of these theoretical results is tested in a series of numerical experiments on two dimensional domains. © 2010 Springer Science+Business Media, LLC.
Institute of Scientific and Technical Information of China (English)
石东洋; 廖歆; 唐启立
2014-01-01
A highly effcient H 1-Galerkin mixed finite element method (MFEM) is presented with linear triangular element for the parabolic integro-differential equation. Firstly, some new results about the integral estimation and asymptotic expansions are studied. Then, the superconvergence of order O(h2) for both the original variable u in H1(Ω) norm and the flux p=∇u in H(div,Ω) norm is derived through the interpolation post processing technique. Furthermore, with the help of the asymptotic expansions and a suitable auxiliary problem, the extrapolation solutions with accuracy O(h3) are obtained for the above two variables. Finally, some numerical results are provided to confirm validity of the theoretical analysis and excellent performance of the proposed method.
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Bashir Ahmad
2013-02-01
Full Text Available In this article, we discuss the existence of solutions for a boundary-value problem of integro-differential equations of fractional order with nonlocal fractional boundary conditions by means of some standard tools of fixed point theory. Our problem describes a more general form of fractional stochastic dynamic model for financial asset. An illustrative example is also presented.
On the spectra of certain integro-differential-delay problems with applications in neurodynamics
Grindrod, P.; Pinotsis, D. A.
2011-01-01
We investigate the spectrum of certain integro-differential-delay equations (IDDEs) which arise naturally within spatially distributed, nonlocal, pattern formation problems. Our approach is based on the reformulation of the relevant dispersion relations with the use of the Lambert function. As a particular application of this approach, we consider the case of the Amari delay neural field equation which describes the local activity of a population of neurons taking into consideration the finite propagation speed of the electric signal. We show that if the kernel appearing in this equation is symmetric around some point a≠0 or consists of a sum of such terms, then the relevant dispersion relation yields spectra with an infinite number of branches, as opposed to finite sets of eigenvalues considered in previous works. Also, in earlier works the focus has been on the most rightward part of the spectrum and the possibility of an instability driven pattern formation. Here, we numerically survey the structure of the entire spectra and argue that a detailed knowledge of this structure is important within neurodynamical applications. Indeed, the Amari IDDE acts as a filter with the ability to recognise and respond whenever it is excited in such a way so as to resonate with one of its rightward modes, thereby amplifying such inputs and dampening others. Finally, we discuss how these results can be generalised to the case of systems of IDDEs.
Institute of Scientific and Technical Information of China (English)
娄梅枝
2003-01-01
In this paper, A.B.Mingarelli's result is generalized to General Volterra-Stieltjes Integro-differential Equations. Comparison theorem and equivalence condition of non-oscillation are obtained. Classical Sturm comparison theorem and some conclusions are generalized.
Institute of Scientific and Technical Information of China (English)
Chun-hui XU; Tai-yan QIN; Li YUAN; NaoAki Noda
2009-01-01
By using the concept of finite-part integral, a set of hypersingular integro-differential equations for multiple interracial cracks in a three-dimensional infinite hi-material subjected to arbitrary loads is derived. In the numerical analysis, unknown displacement discontinuities are approximated with the products of the fundamental den-sity functions and power series. The fundamental functions are chosen to express a two-dimensional interface crack rigorously. As illustrative examples, the stress intensity factors for two rectangular interface cracks are calculated for various spacing, crack shape and elastic constants. It is shown that the stress intensity factors decrease with the crack spacing.
Arisawa, M
2010-01-01
A comparison principle for the integro-differential equation with the L{\\'e}vy operator corresponding to the spacial depending jump process is presented in this paper. The jump $\\beta(x,z)$ at a point $x$ and the L{\\'e}vy measure $dq(z)$ satisfy conditions given independently for each of them, which is a major difference from other works. Moreover, a useful form of the viscosity solution is presented, which is equivalent to more "classical" definitions, and is used to prove the comparison principle easily.
Alvarez, Gustavo; Kniehl, Bernd A; Kondrashuk, Igor; Parra-Ferrada, Ivan
2016-01-01
We consider a simple model for QCD dynamics in which DGLAP integro-differential equation may be solved analytically. This is a gauge model which possesses dominant evolution of gauge boson (gluon) distribution and in which the gauge coupling does not run. This may be ${\\cal N} =4$ supersymmetric gauge theory with softly broken supersymmetry, other finite supersymmetric gauge theory with lower level of supersymmetry, or topological Chern-Simons field theories. We maintain only one term in the splitting function of unintegrated gluon distribution and solve DGLAP analytically for this simplified splitting function. The solution is found by use of the Cauchy integral formula. The solution restricts form of the unintegrated gluon distribution as function of transfer momentum and of Bjorken $x$. Then we consider an almost realistic splitting function of unintegrated gluon distribution as an input to DGLAP equation and solve it by the same method which we have developed to solve DGLAP equation for the toy-model. We ...
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Zhang Xinhua
2011-01-01
Full Text Available Abstract In this paper, a class of impulsive bidirectional associative memory (BAM fuzzy cellular neural networks (FCNNs with time delays in the leakage terms and distributed delays is formulated and investigated. By establishing an integro-differential inequality with impulsive initial conditions and employing M-matrix theory, some sufficient conditions ensuring the existence, uniqueness and global exponential stability of equilibrium point for impulsive BAM FCNNs with time delays in the leakage terms and distributed delays are obtained. In particular, the estimate of the exponential convergence rate is also provided, which depends on the delay kernel functions and system parameters. It is believed that these results are significant and useful for the design and applications of BAM FCNNs. An example is given to show the effectiveness of the results obtained here.
Fredholm Composition Operators on Riemann Surfaces
Institute of Scientific and Technical Information of China (English)
Guang Fu CAO
2005-01-01
It is proved that the invertibility of a composition operator on the differential form space for a Riemann surface is equivalent to its Fredholmness. In addition, the Fredholmness of weighted composition operators is discussed.
Goswami, Deepjyoti
2013-05-01
In the first part of this article, a new mixed method is proposed and analyzed for parabolic integro-differential equations (PIDE) with nonsmooth initial data. Compared to the standard mixed method for PIDE, the present method does not bank on a reformulation using a resolvent operator. Based on energy arguments combined with a repeated use of an integral operator and without using parabolic type duality technique, optimal L2 L2-error estimates are derived for semidiscrete approximations, when the initial condition is in L2 L2. Due to the presence of the integral term, it is, further, observed that a negative norm estimate plays a crucial role in our error analysis. Moreover, the proposed analysis follows the spirit of the proof techniques used in deriving optimal error estimates for finite element approximations to PIDE with smooth data and therefore, it unifies both the theories, i.e., one for smooth data and other for nonsmooth data. Finally, we extend the proposed analysis to the standard mixed method for PIDE with rough initial data and provide an optimal error estimate in L2, L 2, which improves upon the results available in the literature. © 2013 Springer Science+Business Media New York.
Energy Technology Data Exchange (ETDEWEB)
Alvarez, Gustavo [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Concepcion Univ. (Chile). Dept. de Fisica; Cvetic, Gorazd [Univ. Tecnica Federico Santa Maria, Valparaiso (Chile). Dept. de Fisica; Kniehl, Bernd A. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Kondrashuk, Igor [Univ. del Bio-Bio, Chillan (Chile). Grupo de Matematica Aplicada; Univ. del Bio-Bio, Chillan (Chile). Grupo de Fisica de Altas Energias; Parra-Ferrada, Ivan [Talca Univ. (Chile). Inst. de Matematica y Fisica
2016-11-15
We consider a simple model for QCD dynamics in which DGLAP integro-differential equation may be solved analytically. This is a gauge model which possesses dominant evolution of gauge boson (gluon) distribution and in which the gauge coupling does not run. This may be N=4 supersymmetric gauge theory with softly broken supersymmetry, other finite supersymmetric gauge theory with lower level of supersymmetry, or topological Chern-Simons field theories. We maintain only one term in the splitting function of unintegrated gluon distribution and solve DGLAP analytically for this simplified splitting function. The solution is found by use of the Cauchy integral formula. The solution restricts form of the unintegrated gluon distribution as function of transfer momentum and of Bjorken x. Then we consider an almost realistic splitting function of unintegrated gluon distribution as an input to DGLAP equation and solve it by the same method which we have developed to solve DGLAP equation for the toy-model. We study a result obtained for the realistic gluon distribution and find a singular Bessel-like behaviour in the vicinity of the point x=0 and a smooth behaviour in the vicinity of the point x=1.
A degree theory for a class of perturbed Fredholm maps II
Directory of Open Access Journals (Sweden)
Calamai Alessandro
2006-01-01
Full Text Available In a recent paper we gave a notion of degree for a class of perturbations of nonlinear Fredholm maps of index zero between real infinite dimensional Banach spaces. Our purpose here is to extend that notion in order to include the degree introduced by Nussbaum for local -condensing perturbations of the identity, as well as the degree for locally compact perturbations of Fredholm maps of index zero recently defined by the first and third authors.
A semigroup approach to an integro-differential equation modeling slow erosion
Bressan, Alberto; Shen, Wen
2014-10-01
The paper is concerned with a scalar conservation law with nonlocal flux, providing a model for granular flow with slow erosion and deposition. While the solution u=u(t,x) can have jumps, the inverse function x=x(t,u) is always Lipschitz continuous; its derivative has bounded variation and satisfies a balance law with measure-valued sources. Using a backward Euler approximation scheme combined with a nonlinear projection operator, we construct a continuous semigroup whose trajectories are the unique entropy weak solutions to this balance law. Going back to the original variables, this yields the global well-posedness of the Cauchy problem for the granular flow model.
Fredholm's equations for subwavelength focusing
Velázquez-Arcos, J. M.
2012-10-01
Subwavelength focusing (SF) is a very useful tool that can be carried out with the use of left hand materials for optics that involve the range of the microwaves. Many recent works have described a successful alternative procedure using time reversal methods. The advantage is that we do not need devices which require the complicated manufacture of left-hand materials; nevertheless, the theoretical mathematical bases are far from complete because before now we lacked an adequate easy-to-apply frame. In this work we give, for a broad class of discrete systems, a solid support for the theory of electromagnetic SF that can be applied to communications and nanotechnology. The very central procedure is the development of vector-matrix formalism (VMF) based on exploiting both the inhomogeneous and homogeneous Fredholm's integral equations in cases where the last two kinds of integral equations are applied to some selected discrete systems. To this end, we first establish a generalized Newmann series for the Fourier transform of the Green's function in the inhomogeneous Fredholm's equation of the problem. Then we go from an integral operator equation to a vector-matrix algebraic one. In this way we explore the inhomogeneous case and later on also the very interesting one about the homogeneous equation. Thus, on the one hand we can relate in a simple manner the arriving electromagnetic signals with those at their sources and we can use them to perform a SF. On the other hand, we analyze the homogeneous version of the equations, finding resonant solutions that have analogous properties to their counterparts in quantum mechanical scattering, that can be used in a proposed very powerful way in communications. Also we recover quantum mechanical operator relations that are identical for classical electromagnetics. Finally, we prove two theorems that formalize the relation between the theory of Fredholm's integral equations and the VMF we present here.
Stability of waves using the Fredholm determinant
Karambal, Issa
2011-01-01
We present a new method for reducing the Fredholm determinant associated with an underlying Birman-Schwinger operator to a finite dimensional determinant. Moreover, we compute explicitly the connection between the Fredholm determinant and the Evans function for travelling wave problems of all orders, in one dimension
Sarsenbi, Abdisalam A.; Zhumanova, Lyazzat K.
2016-12-01
The present work is devoted to calculating a first regularized trace of one integro-differential operator with the main part of the Sturm-Liouville type on a segment with punctured points at integral perturbation of "transmission" conditions. The integro-differential Sturm-Liouville operator -y″(x )+q (x )y (x )+γ ∫0πy (t )d t =λ y (x ) given on the segments π/n (k -1 )type: y(0) = 0, y(π) = 0 are given on the left-hand and right-hand ends of the segment [0, π]. The functions continuous on [0, π], the first derivatives of which have jumps at the points x =π/n k , are solutions. The value of jumps is expressed by the formula y'(π/k n -0 )=y'(π/k n +0 )-βk∫0πy (t )d t , k =1 ,n -1 ¯ . The basic result of the paper is the exact formula of the first regularized trace of the considered differential operator.
Bobodzhanov, A. A.; Safonov, V. F.
2016-04-01
We consider an algorithm for constructing asymptotic solutions regularized in the sense of Lomov (see [1], [2]). We show that such problems can be reduced to integro-differential equations with inverse time. But in contrast to known papers devoted to this topic (see, for example, [3]), in this paper we study a fundamentally new case, which is characterized by the absence, in the differential part, of a linear operator that isolates, in the asymptotics of the solution, constituents described by boundary functions and by the fact that the integral operator has kernel with diagonal degeneration of high order. Furthermore, the spectrum of the regularization operator A(t) (see below) may contain purely imaginary eigenvalues, which causes difficulties in the application of the methods of construction of asymptotic solutions proposed in the monograph [3]. Based on an analysis of the principal term of the asymptotics, we isolate a class of inhomogeneities and initial data for which the exact solution of the original problem tends to the limit solution (as \\varepsilon\\to+0) on the entire time interval under consideration, also including a boundary-layer zone (that is, we solve the so-called initialization problem). The paper is of a theoretical nature and is designed to lead to a greater understanding of the problems in the theory of singular perturbations. There may be applications in various applied areas where models described by integro-differential equations are used (for example, in elasticity theory, the theory of electrical circuits, and so on).
Uniform Stability of Damped Nonlinear Vibrations of an Elastic String
Indian Academy of Sciences (India)
Ganesh C Gorain; Sujit K Bose
2003-11-01
Here we are concerned about uniform stability of damped nonlinear transverse vibrations of an elastic string fixed at its two ends. The vibrations governed by nonlinear integro-differential equation of Kirchoff type, is shown to possess energy uniformly bounded by exponentially decaying function of time. The result is achieved by considering an energy-like Lyapunov functional for the system.
Aimakhanova, Aizat Sh.; Shalginbayeva, Saltanat Kh.; Zhumanova, Lyazzat K.
2016-08-01
The paper is devoted to calculation of a first regularized trace of one integro-differential operator with the main part of the Sturm-Liouville type on a segment with punctured points at integral perturbation of "transmission" conditions. The Sturm-Liouville operator -y″(x )+q (x )y (x )+γ ∫0πy (t ) d t =λ y (x ) given on the segments π/n (k -1 )right-hand ends of the segment [0, π]. The functions are continuous on [0, π], the first derivatives of which have jumps at the points x =π/n k are solutions. The value of jumps is expressed by the formula y'(π/k n -0 ) =y'(π/k n +0 ) -βk∫0πy (t )d t , k =1 , n -1 ¯. The basic result of the paper is the exact formula of the first regularized trace of the considered differential operator.
Transversality and Lipschitz-Fredholm maps
2015-01-01
We study transversality for Lipschitz-Fredholm maps in the context of bounded Fr\\'{e}chet manifolds. We show that the set of all Lipschitz-Fredholm maps of a fixed index between Fr\\'{e}chet spaces has the transverse stability property. We give a straightforward extension of the Smale transversality theorem by using the generalized Sard's theorem for this category of manifolds. We also provide an answer to the well known problem concerning the existence of a submanifold structure on the preima...
Adomian Method for Solving Fuzzy Fredholm-Volterra Integral Equations
Directory of Open Access Journals (Sweden)
M. Barkhordari Ahmadi
2013-09-01
Full Text Available In this paper, Adomian method has been applied to approximate the solution of fuzzy volterra-fredholm integral equation. That, by using parametric form of fuzzy numbers, a fuzzy volterra-fredholm integral equation has been converted to a system of volterra-fredholm integral equation in crisp case. Finally, the method is explained with illustrative examples.
NONLOCAL INITIAL PROBLEM FOR NONLINEAR NONAUTONOMOUS DIFFERENTIAL EQUATIONS IN A BANACH SPACE
Institute of Scientific and Technical Information of China (English)
M.I.Gil＇
2004-01-01
The nonlocal initial problem for nonlinear nonautonomous evolution equations in a Banach space is considered. It is assumed that the nonlinearities have the local Lipschitz properties. The existence and uniqueness of mild solutions are proved. Applications to integro-differential equations are discussed. The main tool in the paper is the normalizing mapping (the generalized norm).
Institute of Scientific and Technical Information of China (English)
张铁; 李长军
2001-01-01
The object of this paper is to investigate the superconvergence properties of finite element approximations to parabolic and hyperbolic integro-differential equations. The quasi projection technique introduced earlier by Douglas et al. is developed to derive the O(h2r) order knot superconvergence in the case of a single space variable, and to show the optimal order negative norm estimates in the case of several space variables.
Relations between asymptotic and Fredholm representations
Manuilov, V M
1997-01-01
We prove that for matrix algebras $M_n$ there exists a monomorphism $(\\prod_n M_n/\\oplus_n M_n)\\otimes C(S^1) \\to {\\cal Q} $ into the Calkin algebra which induces an isomorphism of the $K_1$-groups. As a consequence we show that every vector bundle over a classifying space $B\\pi$ which can be obtained from an asymptotic representation of a discrete group $\\pi$ can be obtained also from a representation of the group $\\pi\\times Z$ into the Calkin algebra. We give also a generalization of the notion of Fredholm representation and show that asymptotic representations can be viewed as asymptotic Fredholm representations.
Fast Solvers of Fredholm Optimal Control Problems
Institute of Scientific and Technical Information of China (English)
Mario; Borzì
2010-01-01
The formulation of optimal control problems governed by Fredholm integral equations of second kind and an efficient computational framework for solving these control problems is presented. Existence and uniqueness of optimal solutions is proved.A collective Gauss-Seidel scheme and a multigrid scheme are discussed. Optimal computational performance of these iterative schemes is proved by local Fourier analysis and demonstrated by results of numerical experiments.
Evans Functions, Jost Functions, and Fredholm Determinants
Gesztesy, Fritz; Latushkin, Yuri; Makarov, Konstantin A.
2007-12-01
The principal results of this paper consist of an intrinsic definition of the Evans function in terms of newly introduced generalized matrix-valued Jost solutions for general first-order matrix-valued differential equations on the real line, and a proof of the fact that the Evans function, a finite-dimensional determinant by construction, coincides with a modified Fredholm determinant associated with a Birman-Schwinger-type integral operator up to an explicitly computable nonvanishing factor.
Yan, Zuomao; Lu, Fangxia
2016-08-01
In this paper, we introduce the optimal control problems governed by a new class of impulsive stochastic partial neutral evolution equations with infinite delay in Hilbert spaces. First, by using stochastic analysis, the analytic semigroup theory, fractional powers of closed operators, and suitable fixed point theorems, we prove an existence result of mild solutions for the control systems in the α-norm without the assumptions of compactness. Next, we derive the existence conditions of optimal pairs of these systems. Finally, application to a nonlinear impulsive stochastic parabolic optimal control system is considered.
Periodic Solutions of Scalar Neutral Integro-Differential Equation%中立型标量积分微分方程的周期解
Institute of Scientific and Technical Information of China (English)
陈凤德; 孙德献; 陈晓星
2003-01-01
本文考虑中立型标量方程x′(t)=a(t)x(t)+∫t-∞g(t,s,x(s))ds+∫t-∞h(t,s,x′(s))ds+f(t,x(t))的周期的存在唯一性问题. 其中a是连续函数,f是R×R上的连续函数,g(t,s,x)和h(t,s,x)是R×R×R上的连续函数,以及a(t+T)=a(t), g(t+T, s+T, x)=g(t,s,x), h(t+T, s+T, x)=h(t,s,x), f(t+T, x)=f(t,x). 通过利用线性系统解的估计式和泛函分析的方法,我们得到保证上述系统周期解存在和唯一的充分性条件.%This paper deals with the existence and uniqueness of periodic solutions of scalar neutral integro-differential equation with infinite delay of the form x′(t)=a(t)x(t)+∫t-∞g(t,s,x(s))ds+∫t-∞h(t,s,x′(s))ds+f(t,x(t))where a is continuous function, f is continuous function on R×R, g(t,s,x) and h(t,s,x) are continuous functions on R×R×R, also a(t+T)=a(t), g(t+T, s+T, x)=g(t,s,x), h(t+T, s+T, x)=h(t,s,x), f(t+T, x)=f(t,x). The sufficient conditions for the existing unique periodic solution of the equation are obtained by using functional analysis method and the estimated formulas of solutions of the linear scalar system.
On the Cellular Indecomposable Property of Semi-Fredholm Operators
Institute of Scientific and Technical Information of China (English)
Guozheng CHENG; Xiang FANG
2012-01-01
The authors prove that an operator with the cellular indecomposable property has no singular points in the semi-Fredholm domain,by applying the 4 × 4 matrix model of semi-Fredholm operators due to Fang in 2004. This result fills a gap in the result of Olin and Thomson in 1984.
Institute of Scientific and Technical Information of China (English)
孙文兵; 杨立君
2012-01-01
文章讨论了带时滞项的积微分系统最优参数选择问题，并利用变分法推导出目标函数的梯度公式，将最优参数选择问题当成最优化问题利用逐步二次规划法（SQP）进行数值求解，并给出具体的算法．%In this paper, an optimal parameter selection problem with delay integro-differential systems was considered.Gradient formulae for the objective function was derived by using variational calculus. With the gradient formulae, the optimal parameter selec- tion problem can be treated as mathematical programming problem applying sequential quadratic programming algorithm (SQP), and a unified computational approach to the problem was given.
Institute of Scientific and Technical Information of China (English)
石东洋; 王海红
2009-01-01
H1-Galerkin nonconforming mixed finite element methods are analyzed for integro-differential equation of parabolic type.By use of the typical characteristic of the elements,we obtain that the Galerkin mixed approximations have the same rates of convergence as in the classical mixed method,but without LBB stability condition.
Institute of Scientific and Technical Information of China (English)
LI Shoufu
2005-01-01
A series of stability, contractivity and asymptotic stability results of the solutions to nonlinear stiff Volterra functional differential equations (VFDEs) in Banach spaces is obtained, which provides the unified theoretical foundation for the stability analysis of solutions to nonlinear stiff problems in ordinary differential equations(ODEs), delay differential equations(DDEs), integro-differential equations(IDEs) and VFDEs of other type which appear in practice.
基于微积分算子的彩色虹膜图像定位算法%Location Algorithm of RGB Iris Image Based on Integro-Differential Operators
Institute of Scientific and Technical Information of China (English)
张祥德; 董晓鹏; 王琪; 孙艳蕊
2011-01-01
针对NICE：Ⅱ中的彩色噪声虹膜图像难于精确定位问题,提出了一种基于微积分算子的彩色虹膜图像定位算法.首先选择RGB虹膜图像的R层,结合Gabor滤波器和图像梯度信息检测图像中的光斑区域;然后利用Adaboost算法检测虹膜区域,并使用抛物线形微积分算子定位上下眼睑;再利用基于微积分算子的模板,通过局部极值的逐步迭代和对虹膜边界点的聚类分析,定位虹膜外边界;最后使用同态滤波对虹膜区域进行增强处理,检测虹膜内边界.在NICE：Ⅱ彩色虹膜图像库上的实验表明,该方法的定位准确率为98.22%.%A location algorithm based on integro-differential operators was presented for solving the difficulty of precise segmentation in NICE：Ⅱ.The R layer of RGB iris image is chosen first,and the Gabor filter and gradient information are used to detect the reflection area.Moreover,Adaboost algorithm is used to detect iris area in the whole image,then the upper and lower eyelids are detected.A center template based on integro-differential operators was adopted to search the outer boundary of iris through iteration step by step,and cluster analysis was used to remove the noise on iris boundaries.Because the inner boundary of iris is weak,the homomorphic filtering is adopted to enhance the iris area,then the inner boundary is located.The proposed algorithm was tested under NICE：Ⅱ,and the accuracy of the new method is 98.22%.
On a Mixed Nonlinear One Point Boundary Value Problem for an Integrodifferential Equation
Directory of Open Access Journals (Sweden)
Said Mesloub
2008-03-01
Full Text Available This paper is devoted to the study of a mixed problem for a nonlinear parabolic integro-differential equation which mainly arise from a one dimensional quasistatic contact problem. We prove the existence and uniqueness of solutions in a weighted Sobolev space. Proofs are based on some a priori estimates and on the Schauder fixed point theorem. we also give a result which helps to establish the regularity of a solution.
On a Mixed Nonlinear One Point Boundary Value Problem for an Integrodifferential Equation
Directory of Open Access Journals (Sweden)
Mesloub Said
2008-01-01
Full Text Available This paper is devoted to the study of a mixed problem for a nonlinear parabolic integro-differential equation which mainly arise from a one dimensional quasistatic contact problem. We prove the existence and uniqueness of solutions in a weighted Sobolev space. Proofs are based on some a priori estimates and on the Schauder fixed point theorem. we also give a result which helps to establish the regularity of a solution.
Fredholm determinant and Nekrasov sum representations of isomonodromic tau functions
Gavrylenko, P
2016-01-01
We derive Fredholm determinant representation for isomonodromic tau functions of Fuchsian systems with $n$ regular singular points on the Riemann sphere and generic monodromy in $\\mathrm{GL}(N,\\mathbb C)$. The corresponding operator acts in the direct sum of $N(n-3)$ copies of $L^2(S^1)$. Its kernel has a block integrable form and is expressed in terms of fundamental solutions of $n-2$ elementary 3-point Fuchsian systems whose monodromy is determined by monodromy of the relevant $n$-point system via a decomposition of the punctured sphere into pairs of pants. For $N=2$ these building blocks have hypergeometric representations, the kernel becomes completely explicit and has Cauchy type. In this case Fredholm determinant expansion yields multivariate series representation for the tau function of the Garnier system, obtained earlier via its identification with Fourier transform of Liouville conformal block (or a dual Nekrasov-Okounkov partition function). Further specialization to $n=4$ gives a series representa...
The nonlinear evolution of modes on unstable stratified shear layers
Blackaby, Nicholas; Dando, Andrew; Hall, Philip
1993-06-01
The nonlinear development of disturbances in stratified shear flows (having a local Richardson number of value less than one quarter) is considered. Such modes are initially fast growing but, like related studies, we assume that the viscous, non-parallel spreading of the shear layer results in them evolving in a linear fashion until they reach a position where their amplitudes are large enough and their growth rates have diminished sufficiently so that amplitude equations can be derived using weakly nonlinear and non-equilibrium critical-layer theories. Four different basic integro-differential amplitude equations are possible, including one due to a novel mechanism; the relevant choice of amplitude equation, at a particular instance, being dependent on the relative sizes of the disturbance amplitude, the growth rate of the disturbance, its wavenumber, and the viscosity of the fluid. This richness of choice of possible nonlinearities arises mathematically from the indicial Frobenius roots of the governing linear inviscid equation (the Taylor-Goldstein equation) not, in general, differing by an integer. The initial nonlinear evolution of a mode will be governed by an integro-differential amplitude equations with a cubic nonlinearity but the resulting significant increase in the size of the disturbance's amplitude leads on to the next stage of the evolution process where the evolution of the mode is governed by an integro-differential amplitude equations with a quintic nonlinearity. Continued growth of the disturbance amplitude is expected during this stage, resulting in the effects of nonlinearity spreading to outside the critical level, by which time the flow has become fully nonlinear.
Perturbation Results on Semi-Fredholm Operators and Applications
Directory of Open Access Journals (Sweden)
Abdelmoumen Boulbeba
2009-01-01
Full Text Available We give some results concerning stability in the Fredholm operators and Browder operators set, via the concept of measure of noncompactness. Moreover, we prove some localization results on the essential spectra of bounded operators on Banach space. As application, we describe the essential spectra of weighted shift operators. Finally, we describe the spectra of polynomially compact operators, and we use the obtained results to study the solvability for operator equations in Banach spaces.
Fredholm Operators and Einstein Metrics on Conformally Compact Manifolds
2001-01-01
The main purpose of this monograph is to give an elementary and self-contained account of the existence of asymptotically hyperbolic Einstein metrics with prescribed conformal infinities sufficiently close to that of a given asymptotically hyperbolic Einstein metric with nonpositive curvature. The proof is based on an elementary derivation of sharp Fredholm theorems for self-adjoint geometric linear elliptic operators on asymptotically hyperbolic manifolds.
NEW ALTERNATING DIRECTION FINITE ELEMENT SCHEME FOR NONLINEAR PARABOLIC EQUATION
Institute of Scientific and Technical Information of China (English)
崔霞
2002-01-01
A new alternating direction (AD) finite element (FE) scheme for 3-dimensional nonlinear parabolic equation and parabolic integro-differential equation is studied. By using AD,the 3-dimensional problem is reduced to a family of single space variable problems, calculation work is simplified; by using FE, high accuracy is kept; by using various techniques for priori estimate for differential equations such as inductive hypothesis reasoning, the difficulty arising from the nonlinearity is treated. For both FE and ADFE schemes, the convergence properties are rigorously demonstrated, the optimal H1- and L2-norm space estimates and the O((△t)2) estimate for time variable are obtained.
On nulls of perturbed Fredholm operators and degenerate homoclinic bifurcations
Institute of Scientific and Technical Information of China (English)
无
2004-01-01
It is known that small perturbations of a Fredholm operator L have nulls of dimension not larger than dirnN(L). In this paper for any given positive integer κ≤ dimN(L)we prove that there is a perturbation of L which has an exactlyκ-dimensional null. Actually,our proof gives a construction of the perturbation. We further apply our result to concrete examples of differential equations with degenerate homoclinic orbits, showing how many independent homoclinic orbits can be bifurcated from a perturbation.
Construction of Spectral Triples Starting from Fredholm Modules
Schrohe, E.; Walze, M.; Warzecha, J. -M.
1998-01-01
Let (A,H,F) be a p-summable Fredholm module where the algebra A= C \\Gamma is generated by a discrete group of unitaries in L(H) which is of polynomial growth r. Then we construct a spectral triple (A,H,D) with F= sign D which is q-summable for each q > p+r+1. In case (A,H,F) is (p,\\infty)-summable we obtain (q,\\infty)-summability of (A,H,D) for each q > p+r+1.
Nonlinear waves on the free surface of a dielectric liquid in an oblique electric field
Energy Technology Data Exchange (ETDEWEB)
Gashkov, M. A.; Zubarev, N. M., E-mail: nick@iep.uran.ru; Kochurin, E. A., E-mail: kochurin@iep.uran.ru [Ural Branch, Russian Academy of Sciences, Institute of Electrophysics (Russian Federation)
2015-09-15
The nonlinear dynamics of the free surface of an ideal dielectric liquid that is exposed to an external oblique electric field has been studied theoretically. In the framework of the Hamiltonian formalism, a system of nonlinear integro-differential equations has been derived that describes the dynamics of nonlinear waves in the small-angle approximation. It is established that for a liquid with high dielectric permittivity, these equations have a solution in the form of plane waves of arbitrary shape that propagate without distortion in the direction of the horizontal component of the external field.
A multilevel finite element method for Fredholm integral eigenvalue problems
Xie, Hehu; Zhou, Tao
2015-12-01
In this work, we proposed a multigrid finite element (MFE) method for solving the Fredholm integral eigenvalue problems. The main motivation for such studies is to compute the Karhunen-Loève expansions of random fields, which play an important role in the applications of uncertainty quantification. In our MFE framework, solving the eigenvalue problem is converted to doing a series of integral iterations and eigenvalue solving in the coarsest mesh. Then, any existing efficient integration scheme can be used for the associated integration process. The error estimates are provided, and the computational complexity is analyzed. It is noticed that the total computational work of our method is comparable with a single integration step in the finest mesh. Several numerical experiments are presented to validate the efficiency of the proposed numerical method.
Shayma Adil Murad; Hussein Jebrail Zekri; Samir Hadid
2011-01-01
We study the existence and uniqueness of the solutions of mixed Volterra-Fredholm type integral equations with integral boundary condition in Banach space. Our analysis is based on an application of the Krasnosel'skii fixed-point theorem.
Directory of Open Access Journals (Sweden)
Mohammad Almousa
2013-01-01
Full Text Available The aim of this study is to present the use of a semi analytical method called the optimal homotopy asymptotic method (OHAM for solving the linear Fredholm integral equations of the first kind. Three examples are discussed to show the ability of the method to solve the linear Fredholm integral equations of the first kind. The results indicated that the method is very effective and simple.
Gesztesy, Fritz; Makarov, Konstantin A.
2003-01-01
We revisit the computation of (2-modified) Fredholm determinants for operators with matrix-valued semi-separable integral kernels. The latter occur, for instance, in the form of Green's functions associated with closed ordinary differential operators on arbitrary intervals on the real line. Our approach determines the (2-modified) Fredholm determinants in terms of solutions of closely associated Volterra integral equations, and as a result offers a natural way to compute such determinants. We...
非线性粘弹性梁的混沌运动%Chaotic Motions of Nonlinear Viscoelastic Beams
Institute of Scientific and Technical Information of China (English)
陈立群; 程昌; 张能辉
2000-01-01
The integro-partial-differential equation that governs the dynamical behavior of homogeneous viscoelastic beams with geometric and material nonlinearities is established. The material of the beams obeys the Leaderman nonlinear constitutive relation. In the case of simple supported ends, the Galerkin method is applied to simplify the integro-partial-differential equation to a integro -differential equation. The equation is further simplified to a set of ordinary differential equations by introducing an additional variable. Finally, the numerical method is applied to investigate the dynamical behavior of the beam, and results show that chaos occurs in the motion of the beam.
非线性粘弹性梁的混沌运动%Chaotic Motions of Nonlinear Viscoelastic Beams
Institute of Scientific and Technical Information of China (English)
陈立群; 程昌; 张能辉
2001-01-01
The integro-partial-differential equation that governs the dynamical behavior of homogeneous viscoelastic beams with geometric and material nonlinearities is established. The material of the beams obeys the Leaderman nonlinear constitutive relation. In the case of simple supported ends, the Galerkin method is applied to simplify the integro-partial-differential equation to a integro -differential equation. The equation is further simplified to a set of ordinary differential equations by introducing an additional variable. Finally, the numerical method is applied to investigate the dynamical behavior of the beam, and results show that chaos occurs in the motion of the beam.
Institute of Scientific and Technical Information of China (English)
李永献; 李先枝
2015-01-01
将非协调三角形类Carey元应用于非线性伪双曲积分微分方程进行了超收敛分析.利用该元在能量模意义下非协调误差比插值误差高一阶的特殊性质,线性三角形元的高精度分析结果及平均值技巧,在抛弃传统的Ritz-Volterra投影的情形下,得到了半离散格式能量模意义下的超逼近性质.进一步地,借助插值后处理技术,导出了相应的整体超收敛结果.
The nonlinear evolution of inviscid Goertler vortices in three-dimensional boundary layers
Blackaby, Nicholas; Dando, Andrew; Hall, Philip
1995-09-01
The nonlinear development of inviscid Gortler vortices in a three-dimensional boundary layer is considered. We do not follow the classical approach of weakly nonlinear stability problems and consider a mode which has just become unstable. Instead we extend the method of Blackaby, Dando, and Hall (1992), which considered the closely related nonlinear development of disturbances in stratified shear flows. The Gortler modes we consider are initially fast growing and we assume, following others, that boundary-layer spreading results in them evolving in a linear fashion until they reach a stage where their amplitudes are large enough and their growth rates have diminished sufficiently so that amplitude equations can be derived using weakly nonlinear and non-equilibrium critical-layer theories. From the work of Blackaby, Dando and Hall (1993) is apparent, given the range of parameters for the Gortler problem, that there are three possible nonlinear integro-differential evolution equations for the disturbance amplitude. These are a cubic due to viscous effects, a cubic which corresponds to the novel mechanism investigated in this previous paper, and a quintic. In this paper we shall concentrate on the two cubic integro-differential equations and in particular, on the one due to the novel mechanism as this will be the first to affect a disturbance. It is found that the consideration of a spatial evolution problem as opposed to temporal (as was considered in Blackaby, Dando, and Hall, 1992) causes a number of significant changes to the evolution equations.
Institute of Scientific and Technical Information of China (English)
王海红; 郭城
2012-01-01
针对双曲型积分微分方程问题,研究了非协调任意四边形H1-Galerkin混合有限元方法.在半离散格式下,利用所选单元本身的特点,在不需要Ritz-Volterra投影的情况下得到了与传统协调混合有限元方法相同的误差估计.%A nonconforming arbitrary quadrilateral H1 -Galerkin mixed finite element method for hyperbolic type integro-differential equations problem was studied. By use of the characteristic of the chosen finite elements, the same error estimates as in the traditional conforming mixed finite elements methods were derived in semi-discrete formulation without using Ritz-Volterra projection.
Nonlinear wave propagation through a ferromagnet with damping in (2+1) dimensions
Indian Academy of Sciences (India)
S G Bindu; V C Kuriakose
2000-02-01
We investigate how dissipation and nonlinearity can affect the electromagnetic wave propagating through a saturated ferromagnet in the presence of an external magnetic ﬁeld in (2+1) dimensions. The propagation of electromagnetic waves through a ferromagnet under an external magnetic ﬁeld in the presence of dissipative effect has been studied using reductive perturbation method. It is found that to the lowest order of perturbation the system of equations for the electromagnetic waves in a ferromagnet can be reduced to an integro-differential equation.
Directory of Open Access Journals (Sweden)
Yange Huang
2014-01-01
Full Text Available We discuss a class of Volterra-Fredholm type difference inequalities with weakly singular. The upper bounds of the embedded unknown functions are estimated explicitly by analysis techniques. An application of the obtained inequalities to the estimation of Volterra-Fredholm type difference equations is given.
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Boulbeba Abdelmoumen
2008-03-01
Full Text Available The theory of measures of noncompactness has many applications on topology, functional analysis, and operator theory. In this paper, we consider one axiomatic approach to this notion which includes the most important classical definitions. We give some results concerning a certain class of semi-Fredholm and Fredholm operators via the concept of measures of noncompactness. Moreover, we establish a fine description of the Schechter essential spectrum of a closed densely defined operators. These results are exploited to investigate the Schechter essential spectrum of a multidimensional neutron transport operator.
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Dehici Abdelkader
2008-01-01
Full Text Available Abstract The theory of measures of noncompactness has many applications on topology, functional analysis, and operator theory. In this paper, we consider one axiomatic approach to this notion which includes the most important classical definitions. We give some results concerning a certain class of semi-Fredholm and Fredholm operators via the concept of measures of noncompactness. Moreover, we establish a fine description of the Schechter essential spectrum of a closed densely defined operators. These results are exploited to investigate the Schechter essential spectrum of a multidimensional neutron transport operator.
Saaty, Thomas L
1981-01-01
Covers major types of classical equations: operator, functional, difference, integro-differential, and more. Suitable for graduate students as well as scientists, technologists, and mathematicians. "A welcome contribution." - Math Reviews. 1964 edition.
Introducing Differential Equations Students to the Fredholm Alternative--In Staggered Doses
Savoye, Philippe
2011-01-01
The development, in an introductory differential equations course, of boundary value problems in parallel with initial value problems and the Fredholm Alternative. Examples are provided of pairs of homogeneous and nonhomogeneous boundary value problems for which existence and uniqueness issues are considered jointly. How this heightens students'…
Directory of Open Access Journals (Sweden)
Shayma Adil Murad
2011-01-01
Full Text Available We study the existence and uniqueness of the solutions of mixed Volterra-Fredholm type integral equations with integral boundary condition in Banach space. Our analysis is based on an application of the Krasnosel'skii fixed-point theorem.
Trace formulas for a class of non-Fredholm operators: A review
Carey, Alan; Gesztesy, Fritz; Grosse, Harald; Levitina, Galina; Potapov, Denis; Sukochev, Fedor; Zanin, Dmitriy
2016-11-01
Take a one-parameter family of self-adjoint Fredholm operators {A(t)}t∈ℝ on a Hilbert space ℋ, joining endpoints A±. There is a long history of work on the question of whether the spectral flow along this path is given by the index of the operator DA = (d/dt) + A acting in L2(ℝ; ℋ), where A denotes the multiplication operator (Af)(t) = A(t)f(t) for f ∈dom(A). Most results are about the case where the operators A(ṡ) have compact resolvent. In this article, we review what is known when these operators have some essential spectrum and describe some new results. Using the operators H1 = DA∗D A, H2 = DADA∗, an abstract trace formula for Fredholm operators with essential spectrum was proved in [23], extending a result of Pushnitski [35], although, still under strong hypotheses on A(ṡ): trL2(ℝ;ℋ)((H2 - zI)-1 - (H 1 - zI)-1) = 1 2ztrL2(ℋ)(gz(A+) - gz(A-)), where gz(x) = x(x2 - z)-1/2, x ∈ ℝ, z ∈ ℂ\\[0,∞). Associated to the pairs (H2,H1) and (A+,A-) are Krein spectral shift functions ξ(ṡ; H2,H1) and ξ(ṡ; A+,A-), respectively. From the trace formula, it was shown that there is a second, Pushnitski-type, formula: ξ(λ; H2,H1) = 1 π∫-λ1/2λ1/2 ξ(ν; A+,A-)dν (λ - ν2)1/2 for a.e. λ > 0. This can be employed to establish the desired equality, Fredholm index = ξ(0; A+,A-) = spectral flow. This equality was generalized to non-Fredholm operators in [14] in the form Witten index = [ξR(0; A+,A-) + ξL(0; A+,A-)]/2, replacing the Fredholm index on the left-hand side by the Witten index of DA and ξ(0; A+,A-) on the right-hand side by an appropriate arithmetic mean (assuming 0 is a right and left Lebesgue point for ξ(ṡ; A+,A-) denoted by ξR(0; A+,A-) and ξL(0; A+,A-), respectively). But this applies only under the restrictive assumption that the endpoint A+ is a relatively trace class perturbation of A- (ruling out general differential operators). In addition to reviewing this previous work, we describe in this article some
Institute of Scientific and Technical Information of China (English)
王波; 王强
2009-01-01
The Finite volume backward Euler difference method is established to discuss two-dimensional parabolic integro-differential equations.These results are new for finite volume element methods for parabolic integro-differential equations.
Strong Metrizability for Closed Operators and the Semi-Fredholm Operators between Two Hilbert Spaces
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Mohammed Benharrat
2015-08-01
Full Text Available To be able to refine the completion of C(H1, H2, the of set all closed densely defined linear operators between two Hilbert spaces H1 and H2, we define in this paper some new strictly stronger metrics than the gap metric g and we characterize the closure with respect to theses metrics of the subset L(H1, H2 of bounded elements of C(H1, H2. In addition, several operator norm inequalities concerning the equivalence of some metrics on L(H1, H2 are presented. We also establish the semi-Fredholmness and Fredholmness of unbounded in terms of bounded pure contractions.
Strong Metrizability for Closed Operators and the Semi-Fredholm Operators between Two Hilbert Spaces
Directory of Open Access Journals (Sweden)
Mohammed Benharrat
2015-08-01
Full Text Available To be able to refine the completion of C(H1, H2, the of set all closed densely defined linear operators between two Hilbert spaces H1 and H2, we define in this paper some new strictly stronger metrics than the gap metric g and we characterize the closure with respect to theses metrics of the subset L(H1, H2 of bounded elements of C(H1, H2. In addition, several operator norm inequalities concerning the equivalence of some metrics on L(H1, H2 are presented. We also establish the semi-Fredholmness and Fredholmness of unbounded in terms of bounded pure contractions.
Transversality problems in symplectic field theory and a new Fredholm theory
Fabert, Oliver
2010-01-01
This survey wants to give a short introduction to the transversality problem in symplectic field theory and motivate to approach it using the new Fredholm theory by Hofer, Wysocki and Zehnder. With this it should serve as a lead-in for the user's guide to polyfolds, which will appear soon and is the result of a working group organized by J. Fish, R. Golovko and the author at MSRI Berkeley in fall 2009.
Solvability in the sense of sequences to some non-Fredholm operators
Directory of Open Access Journals (Sweden)
Vitaly Volpert
2013-07-01
Full Text Available We study the solvability of certain linear nonhomogeneous elliptic problems and show that under reasonable technical conditions the convergence in $L^2(mathbb{R}^d$ of their right sides implies the existence and the convergence in $H^2(mathbb{R}^d$ of the solutions. The equations involve second order differential operators without Fredholm property and we use the methods of spectral and scattering theory for Schrodinger type operators analogously to our preceding work [17].
On the Convergence of the Homotopy Analysis Method for Solving Fredholm Integral Equations
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Behzad GHANBARI
2013-07-01
Full Text Available The aim of this paper is to study the convergence of the Homotopy analysis method (HAM for solving Fredholm integral equations. A sufficient condition for convergence of the method is illustrated. The validity of the presented condition for convergence of the HAM is studied for two examples. The comparison of the obtained results by the method with an exact solution shows that the method is reliable and capable of providing analytic treatment for solving such equations.
Solution of two-dimensional Fredholm integral equation via RBF-triangular method
Directory of Open Access Journals (Sweden)
Amir Fallahzadeh
2012-04-01
Full Text Available In this paper, a new method is introduced to solve a two-dimensional Fredholm integral equation. The method is based on the approximation by Gaussian radial basis functions and triangular nodes and weights. Also, a new quadrature is introduced to approximate the two dimensional integrals which is called the triangular method. The results of the example illustrate the accuracy of the proposed method increases.
Institute of Scientific and Technical Information of China (English)
Qiumei Huang; Yidu Yang
2008-01-01
In this paper,we introduce a new extrapolation formula by combining Richardson extrapolation and Sloan iteration algorithms.Using this extrapolation formula,we obtain some asymptotic expansions of the Galerkin finite element method for semi-simple eigenvalue problems of Fredholm integral equations of the second kind and improve the accuracy of the numerical approximations of the corresponding eigenvalues.Some numerical experiments are carried out to demonstrate the effectiveness of OUr new method and to confirm our theoretical results.
Hybrid function method for solving Fredholm and Volterra integral equations of the second kind
Hsiao, Chun-Hui
2009-08-01
Numerical solutions of Fredholm and Volterra integral equations of the second kind via hybrid functions, are proposed in this paper. Based upon some useful properties of hybrid functions, integration of the cross product, a special product matrix and a related coefficient matrix with optimal order, are applied to solve these integral equations. The main characteristic of this technique is to convert an integral equation into an algebraic; hence, the solution procedures are either reduced or simplified accordingly. The advantages of hybrid functions are that the values of n and m are adjustable as well as being able to yield more accurate numerical solutions than the piecewise constant orthogonal function, for the solutions of integral equations. We propose that the available optimal values of n and m can minimize the relative errors of the numerical solutions. The high accuracy and the wide applicability of the hybrid function approach will be demonstrated with numerical examples. The hybrid function method is superior to other piecewise constant orthogonal functions [W.F. Blyth, R.L. May, P. Widyaningsih, Volterra integral equations solved in Fredholm form using Walsh functions, Anziam J. 45 (E) (2004) C269-C282; M.H. Reihani, Z. Abadi, Rationalized Haar functions method for solving Fredholm and Volterra integral equations, J. Comp. Appl. Math. 200 (2007) 12-20] for these problems.
Dimensions of subspaces of a Hilbert space and index of the semi-Fredholm operator
Institute of Scientific and Technical Information of China (English)
马吉溥
1996-01-01
Let 2" denote the set of all closed subspaces of the Hilbert space H. The generalized dimension, dim gH0 for any , is introduced. Then an order is defined in [2H], the set of generalized dimensions of 2H. It makes [2H] totally ordered such that 0
Directory of Open Access Journals (Sweden)
Vrkoč Ivo
2001-01-01
Full Text Available The notions of lower and upper functions of the second order differential equations take their beginning from the classical work by C. Scorza-Dragoni and have been investigated till now because they play an important role in the theory of nonlinear boundary value problems. Most of them define lower and upper functions as solutions of the corresponding second order differential inequalities. The aim of this paper is to compare two more general approaches. One is due to Rachůnková and Tvrdý (Nonlinear systems of differential inequalities and solvability of certain boundary value problems (J. of Inequal. & Appl. (to appear who defined the lower and upper functions of the given equation as solutions of associated systems of two differential inequalities with solutions possibly not absolutely continuous. The second belongs to Fabry and Habets (Nonlinear Analysis, TMA 10 (1986, 985–1007 and requires the monotonicity of certain integro-differential expressions.
Topological Analysis From the Basics to the Triple Degree for Nonlinear Fredholm Inclusions
Väth, Martin
2012-01-01
This monograph is an introduction to some special aspects of topology, functional analysis, and analysis for the advanced reader. It also wants to develop a degree theory for function triples which unifies and extends most known degree theories. The book aims to be self-contained and many chapters could even serve as a basis of a course on the covered topics. Only knowledge in basic calculus and of linear algebra is assumed.
Fredholm and Wronskian representations of solutions to the KPI equation and multi-rogue waves
Gaillard, Pierre
2016-06-01
We construct solutions to the Kadomtsev-Petviashvili equation (KPI) in terms of Fredholm determinants. We deduce solutions written as a quotient of Wronskians of order 2N. These solutions, called solutions of order N, depend on 2N - 1 parameters. When one of these parameters tends to zero, we obtain N order rational solutions expressed as a quotient of two polynomials of degree 2N(N + 1) in x, y, and t depending on 2N - 2 parameters. So we get with this method an infinite hierarchy of solutions to the KPI equation.
An iterative method for solving Fredholm integral equations of the first kind
Indratno, Sapto W.; Ramm, A. G.
2009-01-01
The purpose of this paper is to give a convergence analysis of the iterative scheme: \\bee u_n^\\dl=qu_{n-1}^\\dl+(1-q)T_{a_n}^{-1}K^*f_\\dl,\\quad u_0^\\dl=0,\\eee where $T:=K^*K,\\quad T_a:=T+aI,\\quad q\\in(0,1),\\quad a_n:=\\alpha_0q^n, \\alpha_0>0,$ with finite-dimensional approximations of $T$ and $K^*$ for solving stably Fredholm integral equations of the first kind with noisy data.
On the recovering of a coupled nonlinear Schroedinger potential
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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)
Nonlocal Cauchy problem for nonlinear mixed integrodifferential equations
Directory of Open Access Journals (Sweden)
H.L. Tidke
2010-12-01
Full Text Available The present paper investigates the existence and uniqueness of mild and strong solutions of a nonlinear mixed Volterra-Fredholm integrodifferential equation with nonlocal condition. The results obtained by using Schauder fixed point theorem and the theory of semigroups.
Approximate self-similar solutions to a nonlinear diffusion equation with time-fractional derivative
Płociniczak, Łukasz; Okrasińska, Hanna
2013-10-01
In this paper, we consider a fractional nonlinear problem for anomalous diffusion. The diffusion coefficient we use is of power type, and hence the investigated problem generalizes the porous-medium equation. A generalization is made by introducing a fractional time derivative. We look for self-similar solutions for which the fractional setting introduces other than classical space-time scaling. The resulting similarity equations are of nonlinear integro-differential type. We approximate these equations by an expansion of the integral operator and by looking for solutions in a power function form. Our method can be easily adapted to solve various problems in self-similar diffusion. The approximations obtained give very good results in numerical analysis. Their simplicity allows for easy use in applications, as our fitting with experimental data shows. Moreover, our derivation justifies theoretically some previously used empirical models for anomalous diffusion.
Nonlinear static and dynamic responses of an electrically actuated viscoelastic microbeam
Institute of Scientific and Technical Information of China (English)
Y. M. Fu; J. Zhang
2009-01-01
On the basis of the Euler-Bernoulli hypothesis,nonlinear static and dynamic responses of a viscoelastic microbeam under two kinds of electric forces [a purely direct current (DC) and a combined current composed of a DC and an alternating current] are studied. By using Taylor series expansion, a governing equation of nonlinear integro-differential type is derived, and numerical analyses are performed.When a purely DC is applied, there exist an instantaneous pull-in voltage and a durable pull-in voltage of which the physical meanings are also given, whereas under an applied combined current, the effect of the element relaxation coefficient on the dynamic pull-in phenomenon is observed where the largest Lyapunov exponent is taken as a criterion for the dynamic pull-in instability of viscoelastic microbeams.
Solution of stochastic nonlinear PDEs using Wiener-Hermite expansion of high orders
El Beltagy, Mohamed
2016-01-06
In this work, the Wiener-Hermite Expansion (WHE) is used to solve stochastic nonlinear PDEs excited with noise. The generation of the equivalent set of deterministic integro-differential equations is automated and hence allows for high order terms of WHE. The automation difficulties are discussed, solved and implemented to output the final system to be solved. A numerical Pikard-like algorithm is suggested to solve the resulting deterministic system. The automated WHE is applied to the 1D diffusion equation and to the heat equation. The results are compared with previous solutions obtained with WHEP (WHE with perturbation) technique. The solution obtained using the suggested WHE technique is shown to be the limit of the WHEP solutions with infinite number of corrections. The automation is extended easily to account for white-noise of higher dimension and for general nonlinear PDEs.
Institute of Scientific and Technical Information of China (English)
Shoufu LI
2009-01-01
In this review,we present the recent work of the author in comparison with various related results obtained by other authors in literature.We first recall the stability,contractivity and asymptotic stability results of the true solution to nonlinear stiff Volterra functional differential equations (VFDEs),then a series of stability,contractivity,asymptotic stability and B-convergence results of Runge-Kutta methods for VFDEs is presented in detail.This work provides a unified theoretical foundation for the theoretical and numerical analysis of nonlinear stiff problems in delay differential equations (DDEs),integro-differential equations (IDEs),delayintegro-differential equations (DIDEs) and VFDEs of other type which appear in practice.
Generic Properties of an Integro-Differential Equation.
1980-06-01
Let T (t): C * C, t > 0, be the semigroup operatora,g by (1.1); that is, T a,g(t)o(e) x(o)(t+0), -1 < o < 0. 2. Nongeneric Hopf bifurcation. To prove...in a sufficiently small neigtborhood V of a0 (s) - 492(1-s). From the results in Cooperman [11 (see also Hale (14]), the semigroup T t) has aag
Euler-Chebyshev methods for integro-differential equations
Houwen, P.J. van der; Sommeijer, B.P.
1996-01-01
We construct and analyse explicit methods for solving initial value problems for systems of differential equations with expensive righthand side functions whose Jacobian has its stiff eigenvalues along the negative axis. Such equations arise after spatial discretization of parabolic integro-differen
PERIODIC SOLUTIONS OF LINEAR NEUTRAL INTEGRO-DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
马世旺; 王志成; 许强
2004-01-01
Consider the linear neutral FDEd/dt[x(t)+ Ax(t -7)] =∫R[dL(8)]x(t+s)+f(t)where x and f are n-dimensional vectors;A is an n×n constant matrix and L(s) is an n×n matrix function with bounded total variation. Some necessary and sufficient conditions are given which guarantee the existence and uniqueness of periodic solutions to the above equation.
Integral and integrable algorithms for a nonlinear shallow-water wave equation
Camassa, Roberto; Huang, Jingfang; Lee, Long
2006-08-01
An asymptotic higher-order model of wave dynamics in shallow water is examined in a combined analytical and numerical study, with the aim of establishing robust and efficient numerical solution methods. Based on the Hamiltonian structure of the nonlinear equation, an algorithm corresponding to a completely integrable particle lattice is implemented first. Each "particle" in the particle method travels along a characteristic curve. The resulting system of nonlinear ordinary differential equations can have solutions that blow-up in finite time. We isolate the conditions for global existence and prove l1-norm convergence of the method in the limit of zero spatial step size and infinite particles. The numerical results show that this method captures the essence of the solution without using an overly large number of particles. A fast summation algorithm is introduced to evaluate the integrals of the particle method so that the computational cost is reduced from O( N2) to O( N), where N is the number of particles. The method possesses some analogies with point vortex methods for 2D Euler equations. In particular, near singular solutions exist and singularities are prevented from occurring in finite time by mechanisms akin to those in the evolution of vortex patches. The second method is based on integro-differential formulations of the equation. Two different algorithms are proposed, based on different ways of extracting the time derivative of the dependent variable by an appropriately defined inverse operator. The integro-differential formulations reduce the order of spatial derivatives, thereby relaxing the stability constraint and allowing large time steps in an explicit numerical scheme. In addition to the Cauchy problem on the infinite line, we include results on the study of the nonlinear equation posed in the quarter (space-time) plane. We discuss the minimum number of boundary conditions required for solution uniqueness and illustrate this with numerical
Spectra originated from semi-B-Fredholm theory and commuting perturbations
Zeng, Qingping; Zhong, Huaijie
2012-01-01
Burgos, Kaidi, Mbekhta and Oudghiri provided an affirmative answer to a question of Kaashoek and Lay and proved that an operator $F$ is power finite rank if and only if $\\sigma_{dsc}(T+F) =\\sigma_{dsc}(T)$ for every operator $T$ commuting with $F$. Later, several authors extended this result to the essential descent spectrum, the left Drazin spectrum and the left essentially Drazin spectrum. In this paper, using the theory of operator with eventual topological uniform descent and the technique used in Burgos, Kaidi, Mbekhta, and Oudghiri, we generalize this result to various spectra originated from seni-B-Fredholm theory. As immediate consequences, we give affirmative answers to several questions posed by Berkani, Amouch and Zariouh. Besides, we provide a general framework which allows us to derive in a unify way commuting perturbational results of Weyl-Browder type theorems and properties (generalized or not). These commuting perturbational results, in particular, improve many recent results of Berkani and A...
Probabilistic density function method for nonlinear dynamical systems driven by colored noise
Energy Technology Data Exchange (ETDEWEB)
Barajas-Solano, David A.; Tartakovsky, Alexandre M.
2016-05-01
We present a probability density function (PDF) method for a system of nonlinear stochastic ordinary differential equations driven by colored noise. The method provides an integro-differential equation for the temporal evolution of the joint PDF of the system's state, which we close by means of a modified Large-Eddy-Diffusivity-type closure. Additionally, we introduce the generalized local linearization (LL) approximation for deriving a computable PDF equation in the form of the second-order partial differential equation (PDE). We demonstrate the proposed closure and localization accurately describe the dynamics of the PDF in phase space for systems driven by noise with arbitrary auto-correlation time. We apply the proposed PDF method to the analysis of a set of Kramers equations driven by exponentially auto-correlated Gaussian colored noise to study the dynamics and stability of a power grid.
Padovan, Joe
1986-01-01
In a three part series of papers, a generalized finite element analysis scheme is developed to handle the steady and transient response of moving/rolling nonlinear viscoelastic structure. This paper considers the development of the moving/rolling element strategy, including the effects of large deformation kinematics and viscoelasticity modelled by fractional integro-differential operators. To improve the solution strategy, a special hierarchical constraint procedure is developed for the case of steady rolling/translating as well as a transient scheme involving the use of a Grunwaldian representation of the fractional operator. In the second and third parts of the paper, 3-D extensions are developed along with transient contact strategies enabling the handling of impacts with obstructions. Overall, the various developments are benchmarked via comprehensive 2- and 3-D simulations. These are correlated with experimental data to define modelling capabilities.
Nonlinear propagation and decay of intense regular and random waves in relaxing media
Gurbatov, S. N.; Rudenko, O. V.; Demin, I. Yu.
2015-10-01
An integro-differential equation is written down that contains terms responsible for nonlinear absorption, visco-heat-conducting dissipation, and relaxation processes in a medium. A general integral expression is obtained for calculating energy losses of the wave with arbitrary characteristics—intensity, profile (frequency spectrum), and kernel describing the internal dynamics of the medium. Profiles of stationary solutions are constructed both for an exponential relaxation kernel and for other types of kernels. Energy losses at the front of week shock waves are calculated. General integral formulas are obtained for energy losses of intense noise, which are determined by the form of the kernel, the structure of the noise correlation function, and the mean square of the derivative of realization of a random process.
Banach代数A=A上左(右)乘子的Fredholm定理%Fredholm Theory of Left (Right) Multipliers on Banach AlgebrasA={ A
Institute of Scientific and Technical Information of China (English)
代正贵
2000-01-01
n this paper, Fredholm theory of left (right) multipliers on certainnon- commutative Banach algebras are obtained. As an application,Fredholm Left (right) multipliers of compact group are characterized.%本文得到了某些不可换Banach代数上左(右)乘子的Fredholm定理.作为应用,我们刻划了紧群上的Fredholm左(右)乘子.
Existence of solutions for nonlinear mixed type integrodifferential equation of second order
Directory of Open Access Journals (Sweden)
Haribhau Laxman Tidke
2010-04-01
Full Text Available In this paper, we investigate the existence of solutions for nonlinear mixed Volterra-Fredholm integrodifferential equation of second order with nonlocal conditions in Banach spaces. Our analysis is based on Leray-Schauder alternative, rely on a priori bounds of solutions and the inequality established by B. G. Pachpatte.
On form factors of the conjugated field in the non-linear Schroedinger model
Energy Technology Data Exchange (ETDEWEB)
Kozlowski, K.K.
2011-05-15
Izergin-Korepin's lattice discretization of the non-linear Schroedinger model along with Oota's inverse problem provides one with determinant representations for the form factors of the lattice discretized conjugated field operator. We prove that these form factors converge, in the zero lattice spacing limit, to those of the conjugated field operator in the continuous model. We also compute the large-volume asymptotic behavior of such form factors in the continuous model. These are in particular characterized by Fredholm determinants of operators acting on closed contours. We provide a way of defining these Fredholm determinants in the case of generic paramaters. (orig.)
On form factors of the conjugated field in the non-linear Schroedinger model
Energy Technology Data Exchange (ETDEWEB)
Kozlowski, K.K.
2011-05-15
Izergin-Korepin's lattice discretization of the non-linear Schroedinger model along with Oota's inverse problem provides one with determinant representations for the form factors of the lattice discretized conjugated field operator. We prove that these form factors converge, in the zero lattice spacing limit, to those of the conjugated field operator in the continuous model. We also compute the large-volume asymptotic behavior of such form factors in the continuous model. These are in particular characterized by Fredholm determinants of operators acting on closed contours. We provide a way of defining these Fredholm determinants in the case of generic paramaters. (orig.)
Numerical treatments for solving nonlinear mixed integral equation
Directory of Open Access Journals (Sweden)
M.A. Abdou
2016-12-01
Full Text Available We consider a mixed type of nonlinear integral equation (MNLIE of the second kind in the space C[0,T]×L2(Ω,T<1. The Volterra integral terms (VITs are considered in time with continuous kernels, while the Fredholm integral term (FIT is considered in position with singular general kernel. Using the quadratic method and separation of variables method, we obtain a nonlinear system of Fredholm integral equations (NLSFIEs with singular kernel. A Toeplitz matrix method, in each case, is then used to obtain a nonlinear algebraic system. Numerical results are calculated when the kernels take a logarithmic form or Carleman function. Moreover, the error estimates, in each case, are then computed.
Nonlinear physics of shear Alfvén waves
Energy Technology Data Exchange (ETDEWEB)
Zonca, Fulvio [Associazione EURATOM-ENEA sulla Fusione, C.P. 65-00044 Frascati, Italy and Institute for Fusion Theory and Simulation, Zhejiang University, Hangzhou 31007 (China); Chen, Liu [Institute for Fusion Theory and Simulation, Zhejiang University, Hangzhou 31007, P.R.C. and Department of Physics and Astronomy, University of California, Irvine, CA 92697 (United States)
2014-02-12
Shear Alfvén waves (SAW) play fundamental roles in thermonuclear plasmas of fusion interest, since they are readily excited by energetic particles in the MeV range as well as by the thermal plasma components. Thus, understanding fluctuation induced transport in burning plasmas requires understanding nonlinear SAW physics. There exist two possible routes to nonlinear SAW physics: (i) wave-wave interactions and the resultant spectral energy transfer; (ii) nonlinear wave-particle interactions of SAW instabilities with energetic particles. Within the first route, it is advantageous to understand and describe nonlinear processes in term of proximity of the system to the Alfvénic state, where wave-wave interactions are minimized due to the cancellation of Reynolds and Maxwell stresses. Here, various wave-wave nonlinear dynamics are elucidated in terms of how they break the Alfvénic state. In particular, we discuss the qualitative and quantitative modification of the SAW parametric decay process due to finite ion compressibility and finite ion Larmor radius. We also show that toroidal geometry plays a crucial role in the nonlinear excitation of zonal structures by Alfvén eigenmodes. Within the second route, the coherent nonlinear dynamics of structures in the energetic particle phase space, by which secular resonant particle transport can occur on meso- and macro-scales, must be addressed and understood. These 'nonlinear equilibria' or 'phase-space zonal structures' dynamically evolve on characteristic (fluctuation induced) turbulent transport time scales, which are generally of the same order of the nonlinear time scale of the underlying fluctuations. In this work, we introduce the general structure of nonlinear Schrödinger equations with complex integro-differential nonlinear terms, which govern these physical processes. To elucidate all these aspects, theoretical analyses are presented together with numerical simulation results.
Simulating propagation of coherent light in random media using the Fredholm type integral equation
Kraszewski, Maciej; Pluciński, Jerzy
2017-06-01
Studying propagation of light in random scattering materials is important for both basic and applied research. Such studies often require usage of numerical method for simulating behavior of light beams in random media. However, if such simulations require consideration of coherence properties of light, they may become a complex numerical problems. There are well established methods for simulating multiple scattering of light (e.g. Radiative Transfer Theory and Monte Carlo methods) but they do not treat coherence properties of light directly. Some variations of these methods allows to predict behavior of coherent light but only for an averaged realization of the scattering medium. This limits their application in studying many physical phenomena connected to a specific distribution of scattering particles (e.g. laser speckle). In general, numerical simulation of coherent light propagation in a specific realization of random medium is a time- and memory-consuming problem. The goal of the presented research was to develop new efficient method for solving this problem. The method, presented in our earlier works, is based on solving the Fredholm type integral equation, which describes multiple light scattering process. This equation can be discretized and solved numerically using various algorithms e.g. by direct solving the corresponding linear equations system, as well as by using iterative or Monte Carlo solvers. Here we present recent development of this method including its comparison with well-known analytical results and a finite-difference type simulations. We also present extension of the method for problems of multiple scattering of a polarized light on large spherical particles that joins presented mathematical formalism with Mie theory.
Directory of Open Access Journals (Sweden)
Mohammed M. Matar
2009-12-01
Full Text Available In this article we study the fractional semilinear mixed Volterra-Fredholm integrodifferential equation $$ frac{d^{alpha }x(t}{dt^{alpha }} =Ax(t+fBig(t,x(t, int_{t_0}^tk(t,s,x(sds,int_{t_0}^{T}h(t,s,x(sdsBig , $$ where $tin [t_0,T]$, $t_0geq 0$, $0
Cieslinski, Jan L.; Ferapontov, Eugene V.; Kitaev, Alexander V.; Nimmo, Jonathan J. C.
2009-10-01
-component dispersionless Boussinesq-type system. T E Kouloukas and V G Papageorgiou introduce a family of nonparametric Yang-Baxter maps obtained by re-factorization of matrix polynomials of first degree. These maps are Poisson with respect to the Sklyanin bracket, and their degenerations are connected to known integrable systems on quad-graphs. S V Manakov and P M Santini apply a novel version of the inverse scattering transform based on Lax pairs in multidimensional commuting vector fields to the heavenly and Pavlov equations, establishing that their localized solutions evolve without breaking, and constructing the long-time behaviour of the corresponding Cauchy problems. Discretizations of integrable geometric models depend heavily on the coordinates used. M Nieszporski and A Sym show how to discretize Bianchi surfaces (associated with an elliptic version of the Ernst equation) in arbitrary parametrization. C Rogers and A Szereszewski study the Bäcklund transformation for L-isothermic surfaces in the original Bianchi formulation. They establish a connection between this transformation and a nonhomogeneous linear Schrödinger equation and construct a class of generalized Dupin cyclides. W K Schief, A Szereszewski and C Rogers study a classical system of equilibrium equations for shell membranes. Various examples of viable membrane geometries lead to remarkable geometric configurations such as generalized Dupin cyclides and L-minimal surfaces. A Sergyeyev constructs infinite hierarchies of nonlocal higher symmetries for the oriented associativity equations using the spectral problem. The hierarchies in question generalize those constructed by Chen, Kontsevich and Schwarz for the WDVV equations. J Shiraishi and Y Tutiya study an integro-differential equation which generalizes the periodic intermediate long wave equation. The kernel of the singular integral involved is a second order difference of the Weierstrass ζ-function. Using Sato's formulation, the authors
Benhammouda, Brahim
2016-01-01
Since 1980, the Adomian decomposition method (ADM) has been extensively used as a simple powerful tool that applies directly to solve different kinds of nonlinear equations including functional, differential, integro-differential and algebraic equations. However, for differential-algebraic equations (DAEs) the ADM is applied only in four earlier works. There, the DAEs are first pre-processed by some transformations like index reductions before applying the ADM. The drawback of such transformations is that they can involve complex algorithms, can be computationally expensive and may lead to non-physical solutions. The purpose of this paper is to propose a novel technique that applies the ADM directly to solve a class of nonlinear higher-index Hessenberg DAEs systems efficiently. The main advantage of this technique is that; firstly it avoids complex transformations like index reductions and leads to a simple general algorithm. Secondly, it reduces the computational work by solving only linear algebraic systems with a constant coefficient matrix at each iteration, except for the first iteration where the algebraic system is nonlinear (if the DAE is nonlinear with respect to the algebraic variable). To demonstrate the effectiveness of the proposed technique, we apply it to a nonlinear index-three Hessenberg DAEs system with nonlinear algebraic constraints. This technique is straightforward and can be programmed in Maple or Mathematica to simulate real application problems.
Bifurcation of Fredholm Maps II; The Dimension of the Set of Bifurcation Points
Pejsachowicz, Jacobo
2010-01-01
We obtain an estimate for the covering dimension of the set of bifurcation points for solutions of nonlinear elliptic boundary value problems from the principal symbol of the linearization of the problem along the trivial branch of solutions.
Ansari, R.; Faraji Oskouie, M.; Gholami, R.
2016-01-01
In recent decades, mathematical modeling and engineering applications of fractional-order calculus have been extensively utilized to provide efficient simulation tools in the field of solid mechanics. In this paper, a nonlinear fractional nonlocal Euler-Bernoulli beam model is established using the concept of fractional derivative and nonlocal elasticity theory to investigate the size-dependent geometrically nonlinear free vibration of fractional viscoelastic nanobeams. The non-classical fractional integro-differential Euler-Bernoulli beam model contains the nonlocal parameter, viscoelasticity coefficient and order of the fractional derivative to interpret the size effect, viscoelastic material and fractional behavior in the nanoscale fractional viscoelastic structures, respectively. In the solution procedure, the Galerkin method is employed to reduce the fractional integro-partial differential governing equation to a fractional ordinary differential equation in the time domain. Afterwards, the predictor-corrector method is used to solve the nonlinear fractional time-dependent equation. Finally, the influences of nonlocal parameter, order of fractional derivative and viscoelasticity coefficient on the nonlinear time response of fractional viscoelastic nanobeams are discussed in detail. Moreover, comparisons are made between the time responses of linear and nonlinear models.
Jacobian-free Newton-Krylov methods with GPU acceleration for computing nonlinear ship wave patterns
Pethiyagoda, Ravindra; Moroney, Timothy J; Back, Julian M
2014-01-01
The nonlinear problem of steady free-surface flow past a submerged source is considered as a case study for three-dimensional ship wave problems. Of particular interest is the distinctive wedge-shaped wave pattern that forms on the surface of the fluid. By reformulating the governing equations with a standard boundary-integral method, we derive a system of nonlinear algebraic equations that enforce a singular integro-differential equation at each midpoint on a two-dimensional mesh. Our contribution is to solve the system of equations with a Jacobian-free Newton-Krylov method together with a banded preconditioner that is carefully constructed with entries taken from the Jacobian of the linearised problem. Further, we are able to utilise graphics processing unit acceleration to significantly increase the grid refinement and decrease the run-time of our solutions in comparison to schemes that are presently employed in the literature. Our approach provides opportunities to explore the nonlinear features of three-...
Gajjar, J. S. B.
1995-01-01
We consider the nonlinear stability of a fully three-dimensional boundary layer flow in an incompressible fluid and derive an equation governing the nonlinear development of a stationary cross-flow vortex. The amplitude equation is a novel integro-differential equation which has spatial derivatives of the amplitude occurring in the kernal function. It is shown that the evolution of the cross-flow vortex is strongly coupled to the properties of an unsteady wall layer which is in fact driven by an unknown slip velocity, proportional to the amplitude of the cross-flow vortex. The work is extended to obtain the corresponding equation for rotating disk flow. A number of special cases are examined and the numerical solution for one of cases, and further analysis, demonstrates the existence of finite-distance as well as focussing type singularities. The numerical solutions also indicate the presence of a new type of nonlinear wave solution for a certain set of parameter values.
Solutions to systems of partial differential equations with weighted self-reference and heredity
Directory of Open Access Journals (Sweden)
Pham Ky Anh
2012-07-01
Full Text Available This article studies the existence of solutions to systems of nonlinear integro-differential self-referred and heredity equations. We show the existence of a global solution and the uniqueness of a local solution to a system of integro-differential equations with given initial conditions.
SINGULAR SOLUTIONS OF AN INTEGRO-DIFFERENTIAL EQUATION IN RADIATIVE TRANSFER
infinite for finite values of the parameter T. Some of these singular solutions first come close to the desired solution and then diverge to infinity...The nearness of approach of these singular solutions is proportional to a quantity which measures the nearness of local scattering to the conservative
Directory of Open Access Journals (Sweden)
Roberts Jason A
2006-01-01
Full Text Available We consider the reliability of some numerical methods in preserving the stability properties of the linear stochastic functional differential equation , where α, β, σ, τ ≥ 0 are real constants, and W(t is a standard Wiener process. The areas of the regions of asymptotic stability for the class of methods considered, indicated by the sufficient conditions for the discrete system, are shown to be equal in size to each other and we show that an upper bound can be put on the time-step parameter for the numerical method for which the system is asymptotically mean-square stable. We illustrate our results by means of numerical experiments and various stability diagrams. We examine the extent to which the continuous system can tolerate stochastic perturbations before losing its stability properties and we illustrate how one may accurately choose a numerical method to preserve the stability properties of the original problem in the numerical solution. Our numerical experiments also indicate that the quality of the sufficient conditions is very high.
Qualitative analysis of an integro-differential equation model of periodic chemotherapy
Jain, Harsh Vardhan
2012-12-01
An existing model of tumor growth that accounts for cell cycle arrest and cell death induced by chemotherapy is extended to simulate the response to treatment of a tumor growing in vivo. The tumor is assumed to undergo logistic growth in the absence of therapy, and treatment is administered periodically rather than continuously. Necessary and sufficient conditions for the global stability of the cancer-free equilibrium are derived and conditions under which the system evolves to periodic solutions are determined. © 2012 Elsevier Ltd. All rights reserved.
Spreading fronts in a partially degenerate integro-differential reaction–diffusion system
Li, Wan-Tong; Zhao, Meng; Wang, Jie
2017-10-01
This paper is concerned with the spreading and vanishing of an epidemic disease, which is described by a partially degenerate reaction-diffusion system with the nonlocal term and double free boundaries. We first consider the sign of the corresponding principal eigenvalue, which is determined by some given conditions. Then, we get the sufficient conditions that ensure the disease spreading or vanishing. At last, when spreading occurs, some rough estimates of the asymptotic spreading speed are given under some conditions.
Energy Technology Data Exchange (ETDEWEB)
Besse, Nicolas, E-mail: Nicolas.Besse@oca.eu [Laboratoire J.-L. Lagrange, UMR CNRS/OCA/UCA 7293, Université Côte d’Azur, Observatoire de la Côte d’Azur, Bd de l’Observatoire CS 34229, 06304 Nice Cedex 4 (France); Institut Jean Lamour, UMR CNRS/UL 7198, Université de Lorraine, BP 70239 54506 Vandoeuvre-lès-Nancy Cedex (France); Coulette, David, E-mail: David.Coulette@ipcms.unistra.fr [Institut Jean Lamour, UMR CNRS/UL 7198, Université de Lorraine, BP 70239 54506 Vandoeuvre-lès-Nancy Cedex (France); Institut de Physique et Chimie des Matériaux de Strasbourg, UMR CNRS/US 7504, Université de Strasbourg, 23 Rue du Loess, 67034 Strasbourg (France)
2016-08-15
Achieving plasmas with good stability and confinement properties is a key research goal for magnetic fusion devices. The underlying equations are the Vlasov–Poisson and Vlasov–Maxwell (VPM) equations in three space variables, three velocity variables, and one time variable. Even in those somewhat academic cases where global equilibrium solutions are known, studying their stability requires the analysis of the spectral properties of the linearized operator, a daunting task. We have identified a model, for which not only equilibrium solutions can be constructed, but many of their stability properties are amenable to rigorous analysis. It uses a class of solution to the VPM equations (or to their gyrokinetic approximations) known as waterbag solutions which, in particular, are piecewise constant in phase-space. It also uses, not only the gyrokinetic approximation of fast cyclotronic motion around magnetic field lines, but also an asymptotic approximation regarding the magnetic-field-induced anisotropy: the spatial variation along the field lines is taken much slower than across them. Together, these assumptions result in a drastic reduction in the dimensionality of the linearized problem, which becomes a set of two nested one-dimensional problems: an integral equation in the poloidal variable, followed by a one-dimensional complex Schrödinger equation in the radial variable. We show here that the operator associated to the poloidal variable is meromorphic in the eigenparameter, the pulsation frequency. We also prove that, for all but a countable set of real pulsation frequencies, the operator is compact and thus behaves mostly as a finite-dimensional one. The numerical algorithms based on such ideas have been implemented in a companion paper [D. Coulette and N. Besse, “Numerical resolution of the global eigenvalue problem for gyrokinetic-waterbag model in toroidal geometry” (submitted)] and were found to be surprisingly close to those for the original gyrokinetic-Vlasov equations. The purpose of the present paper is to make these new ideas accessible to two readerships: applied mathematicians and plasma physicists.
Besse, Nicolas; Coulette, David
2016-08-01
Achieving plasmas with good stability and confinement properties is a key research goal for magnetic fusion devices. The underlying equations are the Vlasov-Poisson and Vlasov-Maxwell (VPM) equations in three space variables, three velocity variables, and one time variable. Even in those somewhat academic cases where global equilibrium solutions are known, studying their stability requires the analysis of the spectral properties of the linearized operator, a daunting task. We have identified a model, for which not only equilibrium solutions can be constructed, but many of their stability properties are amenable to rigorous analysis. It uses a class of solution to the VPM equations (or to their gyrokinetic approximations) known as waterbag solutions which, in particular, are piecewise constant in phase-space. It also uses, not only the gyrokinetic approximation of fast cyclotronic motion around magnetic field lines, but also an asymptotic approximation regarding the magnetic-field-induced anisotropy: the spatial variation along the field lines is taken much slower than across them. Together, these assumptions result in a drastic reduction in the dimensionality of the linearized problem, which becomes a set of two nested one-dimensional problems: an integral equation in the poloidal variable, followed by a one-dimensional complex Schrödinger equation in the radial variable. We show here that the operator associated to the poloidal variable is meromorphic in the eigenparameter, the pulsation frequency. We also prove that, for all but a countable set of real pulsation frequencies, the operator is compact and thus behaves mostly as a finite-dimensional one. The numerical algorithms based on such ideas have been implemented in a companion paper [D. Coulette and N. Besse, "Numerical resolution of the global eigenvalue problem for gyrokinetic-waterbag model in toroidal geometry" (submitted)] and were found to be surprisingly close to those for the original gyrokinetic-Vlasov equations. The purpose of the present paper is to make these new ideas accessible to two readerships: applied mathematicians and plasma physicists.
A New Numerical Method for Fast Solution of Partial Integro-Differential Equations
Dourbal, Pavel; Pekker, Mikhail
2016-01-01
A new method of numerical solution for partial differential equations is proposed. The method is based on a fast matrix multiplication algorithm. Two-dimensional Poison equation is used for comparison of the proposed method with conventional numerical methods. It was shown that the new method allows for linear growth in the number of elementary addition and multiplication operations with the growth of grid size, as contrasted with quadratic growth necessitated by the standard numerical method...
Energy Technology Data Exchange (ETDEWEB)
Picozzi, A., E-mail: Antonio.Picozzi@u-bourgogne.fr [Laboratoire Interdisciplinaire Carnot de Bourgogne, Université de Bourgogne, CNRS-UMR 5027, Dijon (France); Garnier, J. [Laboratoire de Probabilités et Modèles Aléatoires and Laboratoire Jacques-Louis Lions, Université Paris VII, 75205 Paris Cedex 13 (France); Hansson, T. [Department of Information Engineering, Università di Brescia, Brescia 25123 (Italy); Suret, P.; Randoux, S. [Laboratoire de Physique des Lasers, Atomes et Molécules, CNRS, Université de Lille (France); Millot, G. [Laboratoire Interdisciplinaire Carnot de Bourgogne, Université de Bourgogne, CNRS-UMR 5027, Dijon (France); Christodoulides, D.N. [College of Optics/CREOL, University of Central Florida, Orlando, FL 32816 (United States)
2014-09-01
The nonlinear propagation of coherent optical fields has been extensively explored in the framework of nonlinear optics, while the linear propagation of incoherent fields has been widely studied in the framework of statistical optics. However, these two fundamental fields of optics have been mostly developed independently of each other, so that a satisfactory understanding of statistical nonlinear optics is still lacking. This article is aimed at reviewing a unified theoretical formulation of statistical nonlinear optics on the basis of the wave turbulence theory, which provides a nonequilibrium thermodynamic description of the system of incoherent nonlinear waves. We consider the nonlinear Schrödinger equation as a representative model accounting either for a nonlocal or a noninstantaneous nonlinearity, as well as higher-order dispersion effects. Depending on the amount of nonlocal (noninstantaneous) nonlinear interaction and the amount of inhomogeneous (nonstationary) statistics of the incoherent wave, different types of kinetic equations are derived and discussed. In the spatial domain, when the incoherent wave exhibits inhomogeneous statistical fluctuations, different forms of the (Hamiltonian) Vlasov equation are obtained depending on the amount of nonlocality. This Vlasov approach describes the processes of incoherent modulational instability and localized incoherent soliton structures. In the temporal domain, the causality property inherent to the response function leads to a kinetic formulation analogous to the weak Langmuir turbulence equation, which describes nonlocalized spectral incoherent solitons. In the presence of a highly noninstantaneous response, this formulation reduces to a family of singular integro-differential kinetic equations (e.g., Benjamin–Ono equation), which describe incoherent dispersive shock waves. Conversely, a non-stationary statistics leads to a (non-Hamiltonian) long-range Vlasov formulation, whose self-consistent potential
Camporeale, E.; Pezzi, O.; Valentini, F.
2015-12-01
The longstanding problem of collisions in plasmas is a very fascinating and huge topic in plasma physics. The 'natural' operator that describes the Coulombian interactions between charged particles is the Landau (LAN) integral operator. The LAN operator is a nonlinear, integro-differential and Fokker-Planck type operator which satisfies the H theorem for the entropy growth. Due to its nonlinear nature and multi-dimensionality, any approach to the solution of the Landau integral is almost prohibitive. Therefore collisions are usually modeled by simplified collisional operators. Here collisional effects are modeled by i) the one-dimensional Lenard-Bernstein (LB) operator and ii) the three-dimensional Dougherty (DG) operator. In the first case i), by focusing on a 1D-1V phase space, we study recurrence effects in a weakly collisional plasma, being collisions modeled by the LB operator. By decomposing the linear Vlasov-Poisson system in the Fourier-Hermite space, the recurrence problem is investigated in the linear regime of the damping of a Langmuir wave and of the onset of the bump-on-tail instability. The analysis is then confirmed and extended to the nonlinear regime through a Eulerian collisional Vlasov-Poisson code. Despite being routinely used, an artificial collisionality is not in general a viable way of preventing recurrence in numerical simulations. Moreover, recursive phenomena affect both the linear exponential growth and the nonlinear saturation of a linear instability by producing a fake growth in the electric field, thus showing that, although the filamentation is usually associated with low amplitude fluctuations contexts, it can occur also in nonlinear phenomena. On the other hand ii), the effects of electron-electron collisions on the propagation of nonlinear electrostatic waves are shown by means of Eulerian simulations in a 1D-3V (one dimension in physical space, three dimensions in velocity space) phase space. The nonlinear regime of the symmetric
Normalized RBF networks: application to a system of integral equations
Energy Technology Data Exchange (ETDEWEB)
Golbabai, A; Seifollahi, S; Javidi, M [Department of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16844 (Iran, Islamic Republic of)], E-mail: golbabai@iust.ac.ir, E-mail: seif@iust.ac.ir, E-mail: mojavidi@yahoo.com
2008-07-15
Linear integral and integro-differential equations of Fredholm and Volterra types have been successfully treated using radial basis function (RBF) networks in previous works. This paper deals with the case of a system of integral equations of Fredholm and Volterra types with a normalized radial basis function (NRBF) network. A novel learning algorithm is developed for the training of NRBF networks in which the BFGS backpropagation (BFGS-BP) least-squares optimization method as a recursive model is used. In the approach presented here, a trial solution is given by an NRBF network of incremental architecture with a set of unknown parameters. Detailed learning algorithms and concrete examples are also included.
Nonlinear Instability of Liquid Layers.
Newhouse, Lori Ann
The nonlinear instability of two superposed viscous liquid layers in planar and axisymmetric configurations is investigated. In the planar configuration, the light layer fluid is bounded below by a wall and above by a heavy semiinfinite fluid. Gravity drives the instability. In the first axisymmetric configuration, the layer is confined between a cylindrical wall and a core of another fluid. In the second, a thread is suspended in an infinite fluid. Surface tension forces drive the instability in the axisymmetric configurations. The nonlinear evolution of the fluid-fluid interface is computed for layers of arbitrary thickness when their dynamics are fully coupled to those of the second fluid. Under the assumption of creeping flow, the flow field is represented by an interfacial distribution of Green's functions. A Fredholm integral equation of the second kind for the strength of the distribution is derived and then solved using an iterative technique. The Green's functions produce flow fields which are periodic in the direction parallel to the wall and have zero velocity on the wall. For small and moderate surface tension, planar layers evolve into a periodic array of viscous plumes which penetrate into the overlying fluid. The morphology of the plumes depends on the surface tension and the ratio of the fluid viscosities. As the viscosity of the layer increases, the plumes change from a well defined drop on top of a narrow stem to a compact column of rising fluid. The capillary instability of cylindrical interfaces and interfaces in which the core thickness varies in the axial direction are investigated. In both the unbounded and wall bounded configurations, the core evolves into a periodic array of elongated fluid drops connected by thin, almost cylindrical fluid links. The characteristics of the drop-link structure depend on the core thickness, the ratio of the core radius to the wall radius, and the ratio of the fluid viscosities. The factors controlling the
Energy Technology Data Exchange (ETDEWEB)
Hart, H.
1976-03-09
Design modifications of a five-probe focusing collimator coincidence radioisotope scanning system are described. Clinical applications of the system were tested in phantoms using radioisotopes with short biological half-lives, including /sup 75/Se, /sup 192/Ir, /sup 43/K, /sup 130/I, and /sup 82/Br. Data processing methods are also described. (CH)
Directory of Open Access Journals (Sweden)
Hongwei Yang
2013-01-01
solitary waves generated by topography, especially in the resonant case; a large amplitude nonstationary disturbance is generated in the forcing region. This condition may explain the blocking phenomenon which exists in the atmosphere and ocean and generated by topographic forcing.
Bloembergen, Nicolaas
1996-01-01
Nicolaas Bloembergen, recipient of the Nobel Prize for Physics (1981), wrote Nonlinear Optics in 1964, when the field of nonlinear optics was only three years old. The available literature has since grown by at least three orders of magnitude.The vitality of Nonlinear Optics is evident from the still-growing number of scientists and engineers engaged in the study of new nonlinear phenomena and in the development of new nonlinear devices in the field of opto-electronics. This monograph should be helpful in providing a historical introduction and a general background of basic ideas both for expe
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Geniet, F; Leon, J [Physique Mathematique et Theorique, CNRS-UMR 5825, 34095 Montpellier (France)
2003-05-07
A nonlinear system possessing a natural forbidden band gap can transmit energy of a signal with a frequency in the gap, as recently shown for a nonlinear chain of coupled pendulums (Geniet and Leon 2002 Phys. Rev. Lett. 89 134102). This process of nonlinear supratransmission, occurring at a threshold that is exactly predictable in many cases, is shown to have a simple experimental realization with a mechanical chain of pendulums coupled by a coil spring. It is then analysed in more detail. First we go to different (nonintegrable) systems which do sustain nonlinear supratransmission. Then a Josephson transmission line (a one-dimensional array of short Josephson junctions coupled through superconducting wires) is shown to also sustain nonlinear supratransmission, though being related to a different class of boundary conditions, and despite the presence of damping, finiteness, and discreteness. Finally, the mechanism at the origin of nonlinear supratransmission is found to be a nonlinear instability, and this is briefly discussed here.
2016-07-01
Advanced Research Projects Agency (DARPA) Dynamics-Enabled Frequency Sources (DEFYS) program is focused on the convergence of nonlinear dynamics and...Early work in this program has shown that nonlinear dynamics can provide performance advantages. However, the pathway from initial results to...dependent nonlinear stiffness observed in these devices. This work is ongoing, and will continue through the final period of this program . Reference 9
Nayfeh, Ali Hasan
1995-01-01
Nonlinear Oscillations is a self-contained and thorough treatment of the vigorous research that has occurred in nonlinear mechanics since 1970. The book begins with fundamental concepts and techniques of analysis and progresses through recent developments and provides an overview that abstracts and introduces main nonlinear phenomena. It treats systems having a single degree of freedom, introducing basic concepts and analytical methods, and extends concepts and methods to systems having degrees of freedom. Most of this material cannot be found in any other text. Nonlinear Oscillations uses sim
Yoshida, Zensho
2010-01-01
This book gives a general, basic understanding of the mathematical structure "nonlinearity" that lies in the depths of complex systems. Analyzing the heterogeneity that the prefix "non" represents with respect to notions such as the linear space, integrability and scale hierarchy, "nonlinear science" is explained as a challenge of deconstruction of the modern sciences. This book is not a technical guide to teach mathematical tools of nonlinear analysis, nor a zoology of so-called nonlinear phenomena. By critically analyzing the structure of linear theories, and cl
Nanda, Sudarsan
2013-01-01
"Nonlinear analysis" presents recent developments in calculus in Banach space, convex sets, convex functions, best approximation, fixed point theorems, nonlinear operators, variational inequality, complementary problem and semi-inner-product spaces. Nonlinear Analysis has become important and useful in the present days because many real world problems are nonlinear, nonconvex and nonsmooth in nature. Although basic concepts have been presented here but many results presented have not appeared in any book till now. The book could be used as a text for graduate students and also it will be useful for researchers working in this field.
Zhu, Hong-Ming; Pen, Ue-Li; Chen, Xuelei; Yu, Hao-Ran
2016-01-01
We present a direct approach to non-parametrically reconstruct the linear density field from an observed non-linear map. We solve for the unique displacement potential consistent with the non-linear density and positive definite coordinate transformation using a multigrid algorithm. We show that we recover the linear initial conditions up to $k\\sim 1\\ h/\\mathrm{Mpc}$ with minimal computational cost. This reconstruction approach generalizes the linear displacement theory to fully non-linear fields, potentially substantially expanding the BAO and RSD information content of dense large scale structure surveys, including for example SDSS main sample and 21cm intensity mapping.
Boyd, Robert W
2013-01-01
Nonlinear Optics is an advanced textbook for courses dealing with nonlinear optics, quantum electronics, laser physics, contemporary and quantum optics, and electrooptics. Its pedagogical emphasis is on fundamentals rather than particular, transitory applications. As a result, this textbook will have lasting appeal to a wide audience of electrical engineering, physics, and optics students, as well as those in related fields such as materials science and chemistry.Key Features* The origin of optical nonlinearities, including dependence on the polarization of light* A detailed treatment of the q
Ruszczynski, Andrzej
2011-01-01
Optimization is one of the most important areas of modern applied mathematics, with applications in fields from engineering and economics to finance, statistics, management science, and medicine. While many books have addressed its various aspects, Nonlinear Optimization is the first comprehensive treatment that will allow graduate students and researchers to understand its modern ideas, principles, and methods within a reasonable time, but without sacrificing mathematical precision. Andrzej Ruszczynski, a leading expert in the optimization of nonlinear stochastic systems, integrates t
Zemlyanova, A. Y.
2013-03-08
A problem of an interface crack between two semi-planes made out of different materials under an action of an in-plane loading of general tensile-shear type is treated in a semi-analytical manner with the help of Dirichlet-to-Neumann mappings. The boundaries of the crack and the interface between semi-planes are subjected to a curvature-dependent surface tension. The resulting system of six singular integro-differential equations is reduced to the system of three Fredholm equations. It is shown that the introduction of the curvature-dependent surface tension eliminates both classical integrable power singularity of the order 1/2 and an oscillating singularity present in a classical linear elasticity solutions. The numerical results are obtained by solving the original system of singular integro-differential equations by approximating unknown functions with Taylor polynomials. © 2013 The Author.
Abdikarimov, R.; Bykovtsev, A.; Khodzhaev, D.; Research Team Of Geotechnical; Structural Engineers
2010-12-01
system of nonlinear integro-differential equations (NIDE) with variable coefficients concerning a deflection w=w(x,y) and displacements u=u(x,y), v=v(x,y) was used for construction mathematical model of the problem. The Kichhoff-Love hypothesis was used as basis for description physical and geometrical relations and construction of a discrete model of nonlinear problems dynamic theory of viscoelasticity. The most effective variational Bubnov-Galerkin method was used for obtaining Volterra type system of NIDE. The integration of the obtained equations system was carried out with the help of the numerical method based on quadrature formula. The computer codes on algorithmic language Delphi were created for investigation amplitude-time, deflected mode and torque-time characteristic of vibrations of the viscoelastic shells. For real composite materials at wide ranges of change of physical-mechanical and geometrical parameters the behavior of shells were investigated. Calculations were carried out at different laws of change of thickness. Results will be presented as graphs and tables.
In, Visarath; Longhini, Patrick; Kho, Andy; Neff, Joseph D.; Leung, Daniel; Liu, Norman; Meadows, Brian K.; Gordon, Frank; Bulsara, Adi R.; Palacios, Antonio
2012-12-01
The nonlinear channelizer is an integrated circuit made up of large parallel arrays of analog nonlinear oscillators, which, collectively, serve as a broad-spectrum analyzer with the ability to receive complex signals containing multiple frequencies and instantaneously lock-on or respond to a received signal in a few oscillation cycles. The concept is based on the generation of internal oscillations in coupled nonlinear systems that do not normally oscillate in the absence of coupling. In particular, the system consists of unidirectionally coupled bistable nonlinear elements, where the frequency and other dynamical characteristics of the emergent oscillations depend on the system's internal parameters and the received signal. These properties and characteristics are being employed to develop a system capable of locking onto any arbitrary input radio frequency signal. The system is efficient by eliminating the need for high-speed, high-accuracy analog-to-digital converters, and compact by making use of nonlinear coupled systems to act as a channelizer (frequency binning and channeling), a low noise amplifier, and a frequency down-converter in a single step which, in turn, will reduce the size, weight, power, and cost of the entire communication system. This paper covers the theory, numerical simulations, and some engineering details that validate the concept at the frequency band of 1-4 GHz.
Energy Technology Data Exchange (ETDEWEB)
Turchetti, G. (Bologna Univ. (Italy). Dipt. di Fisica)
1989-01-01
Research in nonlinear dynamics is rapidly expanding and its range of applications is extending beyond the traditional areas of science where it was first developed. Indeed while linear analysis and modelling, which has been very successful in mathematical physics and engineering, has become a mature science, many elementary phenomena of intrinsic nonlinear nature were recently experimentally detected and investigated, suggesting new theoretical work. Complex systems, as turbulent fluids, were known to be governed by intrinsically nonlinear laws since a long time ago, but received purely phenomenological descriptions. The pioneering works of Boltzmann and Poincare, probably because of their intrinsic difficulty, did not have a revolutionary impact at their time; it is only very recently that their message is reaching a significant number of mathematicians and physicists. Certainly the development of computers and computer graphics played an important role in developing geometric intuition of complex phenomena through simple numerical experiments, while a new mathematical framework to understand them was being developed.
Microscopic tunneling theory of long Josephson junctions
DEFF Research Database (Denmark)
Grønbech-Jensen, N.; Hattel, Søren A.; Samuelsen, Mogens Rugholm
1992-01-01
We present a numerical scheme for solving a nonlinear partial integro-differential equation with nonlocal time dependence. The equation describes the dynamics in a long Josephson junction modeled by use of the microscopic theory for tunneling between superconductors. We demonstrate that the detai......We present a numerical scheme for solving a nonlinear partial integro-differential equation with nonlocal time dependence. The equation describes the dynamics in a long Josephson junction modeled by use of the microscopic theory for tunneling between superconductors. We demonstrate...
Approximate and renormgroup symmetries
Energy Technology Data Exchange (ETDEWEB)
Ibragimov, Nail H. [Blekinge Institute of Technology, Karlskrona (Sweden). Dept. of Mathematics Science; Kovalev, Vladimir F. [Russian Academy of Sciences, Moscow (Russian Federation). Inst. of Mathematical Modeling
2009-07-01
''Approximate and Renormgroup Symmetries'' deals with approximate transformation groups, symmetries of integro-differential equations and renormgroup symmetries. It includes a concise and self-contained introduction to basic concepts and methods of Lie group analysis, and provides an easy-to-follow introduction to the theory of approximate transformation groups and symmetries of integro-differential equations. The book is designed for specialists in nonlinear physics - mathematicians and non-mathematicians - interested in methods of applied group analysis for investigating nonlinear problems in physical science and engineering. (orig.)
Seider, Warren D.; Ungar, Lyle H.
1987-01-01
Describes a course in nonlinear mathematics courses offered at the University of Pennsylvania which provides an opportunity for students to examine the complex solution spaces that chemical engineers encounter. Topics include modeling many chemical processes, especially those involving reaction and diffusion, auto catalytic reactions, phase…
2015-01-01
From the Back Cover: The emphasis throughout the present volume is on the practical application of theoretical mathematical models helping to unravel the underlying mechanisms involved in processes from mathematical physics and biosciences. It has been conceived as a unique collection of abstract methods dealing especially with nonlinear partial differential equations (either stationary or evolutionary) that are applied to understand concrete processes involving some important applications re...
Regularity for solutions of non local, non symmetric equations
Lara, Hector Chang
2011-01-01
We study the regularity for solutions of fully nonlinear integro differential equations with respect to nonsymmetric kernels. More precisely, we assume that our operator is elliptic with respect to a family of integro differential linear operators where the symmetric part of the kernels have a fixed homogeneity $\\sigma$ and the skew symmetric part have strictly smaller homogeneity $\\tau$. We prove a weak ABP estimate and $C^{1,\\alpha}$ regularity. Our estimates remain uniform as we take $\\sigma \\to 2$ and $\\tau \\to 1$ so that this extends the regularity theory for elliptic differential equations with dependence on the gradient.
PREFACE Integrability and nonlinear phenomena Integrability and nonlinear phenomena
Gómez-Ullate, David; Lombardo, Sara; Mañas, Manuel; Mazzocco, Marta; Nijhoff, Frank; Sommacal, Matteo
2010-10-01
one can generalize or adapt this construction to different settings like the integro-differential, discrete or super-symmetric ones. The emphasis is usually to find auxiliary linear systems defining an infinite set of linear commuting flows whose solutions, if some asymptotic conditions are imposed, are named wave or Baker-Akhiezer functions. These linear flows determine the so called Lax equations, another infinite set of commuting equations whose compatibility leads to the so called Zakharov-Shabat system. An alternative description of the hierarchies is achieved with the use of the bilinear equations directly linked with the tau-function description of the hierarchy. There are two paradigmatic integrable hierarchies, namely the KP and 2-dimensional Toda lattice (2DTL). These hierarchies are treated within this volume in three contributions. In particular, Takasaki [5] reconsiders the extended Toda hierarchy of Carlet, Dubrovin and Zhang in the light of Ogawa's 2 + 1D extension of the 1D Toda hierarchy. It turns out that the former may be thought of as some sort of dimensional reduction of the latter. This explains the structure of the bilinear formalism proposed by Milanov. Carlet and Manas [6] study the 2-component KP and 2D Toda hierarchies and solve explicitly several implicit constraints present in the usual Lax formulation of the hierarchy, thus identifying a set of free dependent variables for such hierarchies. Finally, the KP hierarchy is considered in the paper by Lin et al [7], which explores the extended flows of a q-deformed modified KP hierarchy leading to the introduction of self-consistent sources. By a combination of the dressing method and the method of variation of constants, the authors are able through a dressing approach to find a scheme for the construction of solutions of the corresponding integrable equations with self-consistent sources. The study of dispersionless integrable hierarchies is an active field of research, and this special issue
Rajasekar, Shanmuganathan
2016-01-01
This introductory text presents the basic aspects and most important features of various types of resonances and anti-resonances in dynamical systems. In particular, for each resonance, it covers the theoretical concepts, illustrates them with case studies, and reviews the available information on mechanisms, characterization, numerical simulations, experimental realizations, possible quantum analogues, applications and significant advances made over the years. Resonances are one of the most fundamental phenomena exhibited by nonlinear systems and refer to specific realizations of maximum response of a system due to the ability of that system to store and transfer energy received from an external forcing source. Resonances are of particular importance in physical, engineering and biological systems - they can prove to be advantageous in many applications, while leading to instability and even disasters in others. The book is self-contained, providing the details of mathematical derivations and techniques invo...
Institute of Scientific and Technical Information of China (English)
1996-01-01
3.1 A Unified Nonlinear Feedback Functional Method for Study Both Control and Synchronization of Spatiotemporal Chaos Fang Jinqing Ali M. K. (Department of Physics, The University of Lethbridge,Lethbridge, Alberta T1K 3M4,Canada) Two fundamental questions dominate future chaos control theories.The first is the problem of controlling hyperchaos in higher dimensional systems.The second question has yet to be addressed:the problem of controlling spatiotemporal chaos in a spatiotemporal system.In recent years, control and synchronization of spatiotemporal chaos and hyperchaos have became a much more important and challenging subject. The reason for this is the control and synchronism of such behaviours have extensive and great potential of interdisciplinary applications, such as security communication, information processing, medicine and so on. However, this subject is not much known and remains an outstanding open.
Nonlinear Materials Characterization Facility
Federal Laboratory Consortium — The Nonlinear Materials Characterization Facility conducts photophysical research and development of nonlinear materials operating in the visible spectrum to protect...
Lu, Yanfei; Lekszycki, Tomasz
2016-10-01
During fracture healing, a series of complex coupled biological and mechanical phenomena occurs. They include: (i) growth and remodelling of bone, whose Young's modulus varies in space and time; (ii) nutrients' diffusion and consumption by living cells. In this paper, we newly propose to model these evolution phenomena. The considered features include: (i) a new constitutive equation for growth simulation involving the number of sensor cells; (ii) an improved equation for nutrient concentration accounting for the switch between Michaelis-Menten kinetics and linear consumption regime; (iii) a new constitutive equation for Young's modulus evolution accounting for its dependence on nutrient concentration and variable number of active cells. The effectiveness of the model and its predictive capability are qualitatively verified by numerical simulations (using COMSOL) describing the healing of bone in the presence of damaged tissue between fractured parts.
Energy Technology Data Exchange (ETDEWEB)
Frankel, J.I.
1997-09-01
This investigation used sysmbolic manipulation in developing analytical methods and general computational strategies for solving both linear and nonlinear, regular and singular integral and integro-differential equations which appear in radiative and mixed-mode energy transport. Contained in this report are seven papers which present the technical results as individual modules.
Directory of Open Access Journals (Sweden)
І.С. Клюс
2007-01-01
Full Text Available The correctness of a problem with multi–point conditions on temporary variable of linear partial differential equations not solved as to the highest derivative with respect to time, perturbed by the nonlinear integro-differential operator is investigated
Nonlinear singular vectors and nonlinear singular values
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
A novel concept of nonlinear singular vector and nonlinear singular value is introduced, which is a natural generalization of the classical linear singular vector and linear singular value to the nonlinear category. The optimization problem related to the determination of nonlinear singular vectors and singular values is formulated. The general idea of this approach is demonstrated by a simple two-dimensional quasigeostrophic model in the atmospheric and oceanic sciences. The advantage and its applications of the new method to the predictability, ensemble forecast and finite-time nonlinear instability are discussed. This paper makes a necessary preparation for further theoretical and numerical investigations.
NONLINEAR EXPECTATIONS AND NONLINEAR MARKOV CHAINS
Institute of Scientific and Technical Information of China (English)
PENG SHIGE
2005-01-01
This paper deals with nonlinear expectations. The author obtains a nonlinear generalization of the well-known Kolmogorov's consistent theorem and then use it to construct filtration-consistent nonlinear expectations via nonlinear Markov chains. Compared to the author's previous results, i.e., the theory of g-expectations introduced via BSDE on a probability space, the present framework is not based on a given probability measure. Many fully nonlinear and singular situations are covered. The induced topology is a natural generalization of Lp-norms and L∞-norm in linear situations.The author also obtains the existence and uniqueness result of BSDE under this new framework and develops a nonlinear type of von Neumann-Morgenstern representation theorem to utilities and present dynamic risk measures.
Chen, Xianfeng; Zeng, Heping; Guo, Qi; She, Weilong
2015-01-01
This book presents an overview of the state of the art of nonlinear optics from weak light nonlinear optics, ultrafast nonlinear optics to electro-optical theory and applications. Topics range from the fundamental studies of the interaction between matter and radiation to the development of devices, components, and systems of tremendous commercial interest for widespread applications in optical telecommunications, medicine, and biotechnology.
Distributed nonlinear optical response
DEFF Research Database (Denmark)
Nikolov, Nikola Ivanov
2005-01-01
The purpose of the research presented here is to investigate basic physical properties in nonlinear optical materials with delayed or nonlocal nonlinearity. Soliton propagation, spectral broadening and the influence of the nonlocality or delay of the nonlinearity are the main focusses in the work...
Noncommutative Nonlinear Supersymmetry
Nishino, H; Nishino, Hitoshi; Rajpoot, Subhash
2002-01-01
We present noncommutative nonlinear supersymmetric theories. The first example is a non-polynomial Akulov-Volkov-type lagrangian with noncommutative nonlinear global supersymmetry in arbitrary space-time dimensions. The second example is the generalization of this lagrangian to Dirac-Born-Infeld lagrangian with nonlinear supersymmetry realized in dimensions D=2,3,4 and 6 (mod 8).
Fiber Nonlinearities: A Tutorial
Institute of Scientific and Technical Information of China (English)
Govind P. Agrawal
2003-01-01
Fiber nonlinearities have long been regarded as being mostly harmful for fiber-optic communication systems. Over the last few years, however, the nonlinear effects are increasingly being used for practical telecommunications applications,the Raman amplification being only one of the recent examples. In this tutorial I review the vario us nonlinear effects occurring in optical fibers from both standpoints..
Fiber Nonlinearities: A Tutorial
Institute of Scientific and Technical Information of China (English)
Govind; P.; Agrawal
2003-01-01
Fiber nonlinearities have long been regarded as being mostly harmful for fiber-optic communication systems. Over the last few years, however, the nonlinear effects are increasingly being used for practical telecommunications applications, the Raman amplification being only one of the recent examples. In this tutorial I review the various nonlinear effects occurring in optical fibers from both standpoints..
PBH tests for nonlinear systems
Kawano, Yu; Ohtsuka, Toshiyuki
2017-01-01
Recently, concepts of nonlinear eigenvalues and eigenvectors are introduced. In this paper, we establish connections between the nonlinear eigenvalues and nonlinear accessibility/observability. In particular, we provide a generalization of Popov- Belevitch-Hautus (PBH) test to nonlinear accessibilit
Nonlinear dynamics and complexity
Luo, Albert; Fu, Xilin
2014-01-01
This important collection presents recent advances in nonlinear dynamics including analytical solutions, chaos in Hamiltonian systems, time-delay, uncertainty, and bio-network dynamics. Nonlinear Dynamics and Complexity equips readers to appreciate this increasingly main-stream approach to understanding complex phenomena in nonlinear systems as they are examined in a broad array of disciplines. The book facilitates a better understanding of the mechanisms and phenomena in nonlinear dynamics and develops the corresponding mathematical theory to apply nonlinear design to practical engineering.
Nonlinear Elliptic Differential Equations with Multivalued Nonlinearities
Indian Academy of Sciences (India)
Antonella Fiacca; Nikolaos Matzakos; Nikolaos S Papageorgiou; Raffaella Servadei
2001-11-01
In this paper we study nonlinear elliptic boundary value problems with monotone and nonmonotone multivalued nonlinearities. First we consider the case of monotone nonlinearities. In the first result we assume that the multivalued nonlinearity is defined on all $\\mathbb{R}$. Assuming the existence of an upper and of a lower solution, we prove the existence of a solution between them. Also for a special version of the problem, we prove the existence of extremal solutions in the order interval formed by the upper and lower solutions. Then we drop the requirement that the monotone nonlinearity is defined on all of $\\mathbb{R}$. This case is important because it covers variational inequalities. Using the theory of operators of monotone type we show that the problem has a solution. Finally in the last part we consider an eigenvalue problem with a nonmonotone multivalued nonlinearity. Using the critical point theory for nonsmooth locally Lipschitz functionals we prove the existence of at least two nontrivial solutions (multiplicity theorem).
Directory of Open Access Journals (Sweden)
Wei Khim Ng
2009-02-01
Full Text Available We construct nonlinear extensions of Dirac's relativistic electron equation that preserve its other desirable properties such as locality, separability, conservation of probability and Poincaré invariance. We determine the constraints that the nonlinear term must obey and classify the resultant non-polynomial nonlinearities in a double expansion in the degree of nonlinearity and number of derivatives. We give explicit examples of such nonlinear equations, studying their discrete symmetries and other properties. Motivated by some previously suggested applications we then consider nonlinear terms that simultaneously violate Lorentz covariance and again study various explicit examples. We contrast our equations and construction procedure with others in the literature and also show that our equations are not gauge equivalent to the linear Dirac equation. Finally we outline various physical applications for these equations.
Ionescu, Tudor C.; Scherpen, Jacquelien M. A.
We study the notion of cross Gramians for nonlinear gradient systems, using the characterization in terms of prolongation and gradient extension associated to the system. The cross Gramian is given for the variational system associated to the original nonlinear gradient system. We obtain linearization results that correspond to the notion of a cross Gramian for symmetric linear systems. Furthermore, first steps towards relations with the singular value functions of the nonlinear Hankel operator are studied and yield promising results.
Directory of Open Access Journals (Sweden)
W. L. Fouché
1983-03-01
Full Text Available In this article we discuss some aspects of nonlinear functional analysis. It included reviews of Banach’s contraction theorem, Schauder’s fixed point theorem, globalising techniques and applications of homotopy theory to nonlinear functional analysis. The author emphasises that fundamentally new ideas are required in order to achieve a better understanding of phenomena which contain both nonlinear and definite infinite dimensional features.
Nonlinear Electrodynamics and QED
2003-01-01
The limits of linear electrodynamics are reviewed, and possible directions of nonlinear extension are explored. The central theme is that the qualitative character of the empirical successes of quantum electrodynamics must be used as a guide for understanding the nature of the nonlinearity of electrodynamics at the subatomic level. Some established theories of nonlinear electrodynamics, namely, those of Mie, Born, and Infeld are presented in the language of the modern geometrical and topologi...
Kono, Mitsuo
2010-01-01
A nonlinearity is one of the most important notions in modern physics. A plasma is rich in nonlinearities and provides a variety of behaviors inherent to instabilities, coherent wave structures and turbulence. The book covers the basic concepts and mathematical methods, necessary to comprehend nonlinear problems widely encountered in contemporary plasmas, but also in other fields of physics and current research on self-organized structures and magnetized plasma turbulence. The analyses make use of strongly nonlinear models solved by analytical techniques backed by extensive simulations and available experiments. The text is written for senior undergraduates, graduate students, lecturers and researchers in laboratory, space and fusion plasmas.
Nonlinear magnetic metamaterials.
Shadrivov, Ilya V; Kozyrev, Alexander B; van der Weide, Daniel W; Kivshar, Yuri S
2008-12-08
We study experimentally nonlinear tunable magnetic metamaterials operating at microwave frequencies. We fabricate the nonlinear metamaterial composed of double split-ring resonators where a varactor diode is introduced into each resonator so that the magnetic resonance can be tuned dynamically by varying the input power. We demonstrate that at higher powers the transmission of the metamaterial becomes power-dependent and, as a result, such metamaterial can demonstrate various nonlinear properties. In particular, we study experimentally the power-dependent shift of the transmission band and demonstrate nonlinearity-induced enhancement (or suppression) of wave transmission. (c) 2008 Optical Society of America
Organic nonlinear optical materials
Umegaki, S.
1987-01-01
Recently, it became clear that organic compounds with delocalized pi electrons show a great nonlinear optical response. Especially, secondary nonlinear optical constants of more than 2 digits were often seen in the molecular level compared to the existing inorganic crystals such as LiNbO3. The crystallization was continuously tried. Organic nonlinear optical crystals have a new future as materials for use in the applied physics such as photomodulation, optical frequency transformation, opto-bistabilization, and phase conjugation optics. Organic nonlinear optical materials, e.g., urea, O2NC6H4NH2, I, II, are reviewed with 50 references.
Nonlinearity-reduced interferometer
Wu, Chien-ming
2007-12-01
Periodic nonlinearity is a systematic error limiting the accuracy of displacement measurements at the nanometer level. It results from many causes such as the frequency mixing, polarization mixing, polarization-frequency mixing, and the ghost reflections. An interferometer having accuracy in displacement measurement of less than one-nanometer is necessary in nanometrology. To meet the requirement, the periodic nonlinearity should be less than deep sub-nanometer. In this paper, a nonlinearity-reduced interferometry has been proposed. Both the linear- and straightness-interferometer were tested. The developed interferometer demonstrated of a residual nonlinearity less than 25 pm.
Lasers for nonlinear microscopy.
Wise, Frank
2013-03-01
Various versions of nonlinear microscopy are revolutionizing the life sciences, almost all of which are made possible because of the development of ultrafast lasers. In this article, the main properties and technical features of short-pulse lasers used in nonlinear microscopy are summarized. Recent research results on fiber lasers that will impact future instruments are also discussed.
Eaton, D F
1991-07-19
The current state of materials development in nonlinear optics is summarized, and the promise of these materials is critically evaluated. Properties and important materials constants of current commercial materials and of new, promising, inorganic and organic molecular and polymeric materials with potential in second- and third-order nonlinear optical applications are presented.
Billings, S. A.
1988-03-01
Time and frequency domain identification methods for nonlinear systems are reviewed. Parametric methods, prediction error methods, structure detection, model validation, and experiment design are discussed. Identification of a liquid level system, a heat exchanger, and a turbocharge automotive diesel engine are illustrated. Rational models are introduced. Spectral analysis for nonlinear systems is treated. Recursive estimation is mentioned.
Ionescu, T. C.; Scherpen, J. M. A.; Korytowski, A; Malanowski, K; Mitkowski, W; Szymkat, M
2009-01-01
We study the notion of cross Gramians for nonlinear gradient systems, using the characterization in terms of prolongation and gradient extension associated to the system. The cross Gramian is given for the variational system associated to the original nonlinear gradient system. We obtain
DEFF Research Database (Denmark)
Clausen, Carl A. Balslev; Christiansen, Peter Leth; Torner, L.
1999-01-01
We show that with the quasi-phase-matching technique it is possible to fabricate stripes of nonlinearity that trap and guide light like waveguides. We investigate an array of such stripes and find that when the stripes are sufficiently narrow, the beam dynamics is governed by a quadratic nonlinear...
Controllability in nonlinear systems
Hirschorn, R. M.
1975-01-01
An explicit expression for the reachable set is obtained for a class of nonlinear systems. This class is described by a chain condition on the Lie algebra of vector fields associated with each nonlinear system. These ideas are used to obtain a generalization of a controllability result for linear systems in the case where multiplicative controls are present.
Menon, P. K. A.; Badgett, M. E.; Walker, R. A.
1992-01-01
Trajectory-control laws based on singular-perturbation theory and nonlinear dynamical modeling. Nonlinear maneuver autopilot commands flight-test trajectories of F-15 airplane. Underlying theory of controller enables separation of variables processed in fast and slow control loops, reducing amount of computation required.
Nonlinear optics and photonics
He, Guang S
2015-01-01
This book provides a comprehensive presentation on most of the major topics in nonlinear optics and photonics, with equal emphasis on principles, experiments, techniques, and applications. It covers many major new topics including optical solitons, multi-photon effects, nonlinear photoelectric effects, fast and slow light , and Terahertz photonics. Chapters 1-10 present the fundamentals of modern nonlinear optics, and could be used as a textbook with problems provided at the end of each chapter. Chapters 11-17 cover the more advanced topics of techniques and applications of nonlinear optics and photonics, serving as a highly informative reference for researchers and experts working in related areas. There are also 16 pages of color photographs to illustrate the visual appearances of some typical nonlinear optical effects and phenomena. The book could be adopted as a textbook for both undergraduates and graduate students, and serve as a useful reference work for researchers and experts in the fields of physics...
Lugiato, Luigi; Brambilla, Massimo
2015-01-01
Guiding graduate students and researchers through the complex world of laser physics and nonlinear optics, this book provides an in-depth exploration of the dynamics of lasers and other relevant optical systems, under the umbrella of a unitary spatio-temporal vision. Adopting a balanced approach, the book covers traditional as well as special topics in laser physics, quantum electronics and nonlinear optics, treating them from the viewpoint of nonlinear dynamical systems. These include laser emission, frequency generation, solitons, optically bistable systems, pulsations and chaos and optical pattern formation. It also provides a coherent and up-to-date treatment of the hierarchy of nonlinear optical models and of the rich variety of phenomena they describe, helping readers to understand the limits of validity of each model and the connections among the phenomena. It is ideal for graduate students and researchers in nonlinear optics, quantum electronics, laser physics and photonics.
B-Theory of Runge-Kutta methods for stiff Volterra functional differential equations
Institute of Scientific and Technical Information of China (English)
LI; Shoufu(李寿佛)
2003-01-01
B-stability and B-convergence theories of Runge-Kutta methods for nonlinear stiff Volterra func-tional differential equations (VFDEs) are established which provide unified theoretical foundation for the studyof Runge-Kutta methods when applied to nonlinear stiff initial value problems (IVPs) in ordinary differentialequations (ODEs), delay differential equations (DDEs), integro-differential equations (IDEs) and VFDEs ofother type which appear in practice.
On kinetic Boltzmann equations and related hydrodynamic flows with dry viscosity
Directory of Open Access Journals (Sweden)
Nikolai N. Bogoliubov (Jr.
2007-01-01
Full Text Available A two-component particle model of Boltzmann-Vlasov type kinetic equations in the form of special nonlinear integro-differential hydrodynamic systems on an infinite-dimensional functional manifold is discussed. We show that such systems are naturally connected with the nonlinear kinetic Boltzmann-Vlasov equations for some one-dimensional particle flows with pointwise interaction potential between particles. A new type of hydrodynamic two-component Benney equations is constructed and their Hamiltonian structure is analyzed.
Zweig, George
2016-05-01
An earlier paper characterizing the linear mechanical response of the organ of Corti [J. Acoust. Soc. Am. 138, 1102-1121 (2015)] is extended to the nonlinear domain. Assuming the existence of nonlinear oscillators nonlocally coupled through the pressure they help create, the oscillator equations are derived and examined when the stimuli are modulated tones and clicks. The nonlinearities are constrained by the requirements of oscillator stability and the invariance of zero crossings in the click response to changes in click amplitude. The nonlinear oscillator equations for tones are solved in terms of the fluid pressure that drives them, and its time derivative, presumably a proxy for forces created by outer hair cells. The pressure equation is reduced to quadrature, the integrand depending on the oscillators' responses. The resulting nonlocally coupled nonlinear equations for the pressure, and oscillator amplitudes and phases, are solved numerically in terms of the fluid pressure at the stapes. Methods for determining the nonlinear damping directly from measurements are described. Once the oscillators have been characterized from their tone and click responses, the mechanical response of the cochlea to natural sounds may be computed numerically. Signal processing inspired by cochlear mechanics opens up a new area of nonlocal nonlinear time-frequency analysis.
Agrawal, Govind P
2001-01-01
The Optical Society of America (OSA) and SPIE - The International Society for Optical Engineering have awarded Govind Agrawal with an honorable mention for the Joseph W. Goodman Book Writing Award for his work on Nonlinear Fiber Optics, 3rd edition.Nonlinear Fiber Optics, 3rd Edition, provides a comprehensive and up-to-date account of the nonlinear phenomena occurring inside optical fibers. It retains most of the material that appeared in the first edition, with the exception of Chapter 6, which is now devoted to the polarization effects relevant for light propagation in optical
Will Nonlinear Backcalculation Help?
DEFF Research Database (Denmark)
Ullidtz, Per
2000-01-01
demonstrates, that treating the subgrade as a nonlinear elastic material, can result in more realistic moduli and a much better agreement between measured and calculated stresses and strains.The response of nonlinear elastic materials can be calculated using the Finite Element Method (FEM). A much simpler...... approach is to use the Method of Equivalent Thicknesses (MET), modified for a nonlinear subgrade. The paper includes an example where moduli backcalculated using FEM, linear elastic theory and MET are compared. Stresses and strains predicted by the three methods are also compared to measured values...
Nonlinear graphene metamaterial
Nikolaenko, Andrey E; Atmatzakis, Evangelos; Luo, Zhiqiang; Shen, Ze Xiang; De Angelis, Francesco; Boden, Stuart A; Di Fabrizio, Enzo; Zheludev, Nikolay I
2012-01-01
We demonstrate that the broadband nonlinear optical response of graphene can be resonantly enhanced by more than an order of magnitude through hybridization with a plasmonic metamaterial,while retaining an ultrafast nonlinear response time of ~1 ps. Transmission modulation close to ~1% is seen at a pump uence of ~0.03 mJ/cm^2 at the wavelength of ~1600 nm. This approach allows to engineer and enhance graphene's nonlinearity within a broad wavelength range enabling applications in optical switching, mode-locking and pulse shaping.
Multipolar nonlinear nanophotonics
Smirnova, Daria
2016-01-01
Nonlinear nanophotonics is a rapidly developing field with many useful applications for a design of nonlinear nanoantennas, light sources, nanolasers, sensors, and ultrafast miniature metadevices. A tight confinement of the local electromagnetic fields in resonant photonic nanostructures can boost nonlinear optical effects, thus offering versatile opportunities for subwavelength control of light. To achieve the desired functionalities, it is essential to gain flexible control over the near- and far-field properties of nanostructures. Thus, both modal and multipolar analyses are widely exploited for engineering nonlinear scattering from resonant nanoscale elements, in particular for enhancing the near-field interaction, tailoring the far-field multipolar interference, and optimization of the radiation directionality. Here, we review the recent advances in this recently emerged research field ranging from metallic structures exhibiting localized plasmonic resonances to hybrid metal-dielectric and all-dielectric...
Solitons in nonlinear lattices
Kartashov, Yaroslav V; Torner, Lluis
2010-01-01
This article offers a comprehensive survey of results obtained for solitons and complex nonlinear wave patterns supported by purely nonlinear lattices (NLs), which represent a spatially periodic modulation of the local strength and sign of the nonlinearity, and their combinations with linear lattices. A majority of the results obtained, thus far, in this field and reviewed in this article are theoretical. Nevertheless, relevant experimental settings are surveyed too, with emphasis on perspectives for implementation of the theoretical predictions in the experiment. Physical systems discussed in the review belong to the realms of nonlinear optics (including artificial optical media, such as photonic crystals, and plasmonics) and Bose-Einstein condensation (BEC). The solitons are considered in one, two, and three dimensions (1D, 2D, and 3D). Basic properties of the solitons presented in the review are their existence, stability, and mobility. Although the field is still far from completion, general conclusions c...
Directory of Open Access Journals (Sweden)
Shakeeb Bin Hasan
2014-12-01
Full Text Available Contrary to traditional optical elements, plasmonic antennas made from nanostructured metals permit the localization of electromagnetic fields on length scales much smaller than the wavelength of light. This results in huge amplitudes for the electromagnetic field close to the antenna being conducive for the observation of nonlinear effects already at moderate pump powers. Thus, these antennas exhibit a promising potential to achieve optical frequency conversion and all-optical control of light at the nano-scale. This opens unprecedented opportunities for ultrafast nonlinear spectroscopy, sensing devices, on-chip optical frequency conversion, nonlinear optical metamaterials, and novel photon sources. Here, we review some of the recent advances in exploiting the potential of plasmonic antennas to realize robust nonlinear applications.
Leburn, Christopher; Reid, Derryck
2013-01-01
The field of ultrafast nonlinear optics is broad and multidisciplinary, and encompasses areas concerned with both the generation and measurement of ultrashort pulses of light, as well as those concerned with the applications of such pulses. Ultrashort pulses are extreme events – both in terms of their durations, and also the high peak powers which their short durations can facilitate. These extreme properties make them powerful experiment tools. On one hand, their ultrashort durations facilitate the probing and manipulation of matter on incredibly short timescales. On the other, their ultrashort durations can facilitate high peak powers which can drive highly nonlinear light-matter interaction processes. Ultrafast Nonlinear Optics covers a complete range of topics, both applied and fundamental in nature, within the area of ultrafast nonlinear optics. Chapters 1 to 4 are concerned with the generation and measurement of ultrashort pulses. Chapters 5 to 7 are concerned with fundamental applications of ultrasho...
DEFF Research Database (Denmark)
Nguyen-Duy, Khiem
and remains the prime source of energy in non-terrestrial applications such as those in sky-explorers. However, a renewable energy source is expensive, bulky, and its performance is weather dependent, which make testing of downstream converters very difficult. As a result, a nonlinear source emulator (NSE......) is a good solution to solve the problems associated with the use of real nonlinear sources in testing phases. However, a recent technical survey conducted during this work shows that most existing NSEs have only been concerned with simulating nonlinear systems in terrestrial applications. Furthermore......, their dynamic performance were not fast enough in order to imitate how a real nonlinear energy source would react under extreme conditions and operation modes. Particularly, a system in the sky can experience a step change of sunlight irradiation. Moreover, operation modes may include load step between nominal...
Introduction to nonlinear science
Nicolis, G
1995-01-01
One of the most unexpected results in science in recent years is that quite ordinary systems obeying simple laws can give rise to complex, nonlinear or chaotic, behavior. In this book, the author presents a unified treatment of the concepts and tools needed to analyze nonlinear phenomena and to outline some representative applications drawn from the physical, engineering, and biological sciences. Some of the interesting topics covered include: dynamical systems with a finite number of degrees of freedom, linear stability analysis of fixed points, nonlinear behavior of fixed points, bifurcation analysis, spatially distributed systems, broken symmetries, pattern formation, and chaotic dynamics. The author makes a special effort to provide a logical connection between ordinary dynamical systems and spatially extended systems, and to balance the emphasis on chaotic behavior and more classical nonlinear behavior. He also develops a statistical approach to complex systems and compares it to traditional deterministi...
Nonlinear magnetoinductive transmission lines
Lazarides, Nikos; Tsironis, G P
2011-01-01
Power transmission in one-dimensional nonlinear magnetic metamaterials driven at one end is investigated numerically and analytically in a wide frequency range. The nonlinear magnetic metamaterials are composed of varactor-loaded split-ring resonators which are coupled magnetically through their mutual inductances, forming thus a magnetoiductive transmission line. In the linear limit, significant power transmission along the array only appears for frequencies inside the linear magnetoinductive wave band. We present analytical, closed form solutions for the magnetoinductive waves transmitting the power in this regime, and their discrete frequency dispersion. When nonlinearity is important, more frequency bands with significant power transmission along the array may appear. In the equivalent circuit picture, the nonlinear magnetoiductive transmission line driven at one end by a relatively weak electromotive force, can be modeled by coupled resistive-inductive-capacitive (RLC) circuits with voltage-dependent cap...
Optimization under Nonlinear Constraints
1982-01-01
In this paper a timesaving method is proposed for maximizing likelihood functions when the parameter space is subject to nonlinear constraints, expressible as second order polynomials. The suggested approach is especially attractive when dealing with systems with many parameters.
Nonlinearity in nanomechanical cantilevers
DEFF Research Database (Denmark)
Villanueva Torrijo, Luis Guillermo; Karabalin, R. B.; Matheny, M. H.
2013-01-01
Euler-Bernoulli beam theory is widely used to successfully predict the linear dynamics of micro-and nanocantilever beams. However, its capacity to characterize the nonlinear dynamics of these devices has not yet been rigorously assessed, despite its use in nanoelectromechanical systems development....... These findings underscore the delicate balance between inertial and geometric nonlinear effects in the fundamental mode, and strongly motivate further work to develop theories beyond the Euler-Bernoulli approximation. DOI: 10.1103/PhysRevB.87.024304....... In this article, we report the first highly controlled measurements of the nonlinear response of nanomechanical cantilevers using an ultralinear detection system. This is performed for an extensive range of devices to probe the validity of Euler-Bernoulli theory in the nonlinear regime. We find that its...
Nonlinear Stokes Mueller Polarimetry
Samim, Masood; Barzda, Virginijus
2015-01-01
The Stokes Mueller polarimetry is generalized to include nonlinear optical processes such as second- and third-harmonic generation, sum- and difference-frequency generations. The overall algebraic form of the polarimetry is preserved, where the incoming and outgoing radiations are represented by column vectors and the intervening medium is represented by a matrix. Expressions for the generalized nonlinear Stokes vector and the Mueller matrix are provided in terms of coherency and correlation matrices, expanded by higher-dimensional analogues of Pauli matrices. In all cases, the outgoing radiation is represented by the conventional $4\\times 1$ Stokes vector, while dimensions of the incoming radiation Stokes vector and Mueller matrix depend on the order of the process being examined. In addition, relation between nonlinear susceptibilities and the measured Mueller matrices are explicitly provided. Finally, the approach of combining linear and nonlinear optical elements is discussed within the context of polarim...
Adaptive and Nonlinear Control
1992-02-29
in [22], we also applied the concept of zero dynamics to the problem of exact linearization of a nonlinear control system by dynamic feedback. Exact ...nonlinear systems, although it was well-known that the conditions for exact linearization are very stringent and consequently do not apply to a broad...29th IEEE Conference n Decision and Control, Invited Paper delivered by Dr. Gilliam. Exact Linearization of Zero Dynamics, 29th IEEE Conference on
Nonlinear Optics and Turbulence
1992-10-01
currently at Queen Mary College, London Patrick Dunne, (Ph.D., 1987, M.I.T., Hydrodynamic Stability, Nonlinear Waves), 1987-1988. Alecsander Dyachenko...U I I I U I I 3 9 3 V. BIOGRAPHIES A. FACULTY BRUCE BAYLY, 31, Ph.D. 1986, Princeton University. Postdoctoral visiting member 1986-88 at Courant...Caputo, A. C. Newell, and M. Shelley , "Nonlinear Wave Propagation Through a Random Medium and Soliton Tunneling", Integrable Systems and
Yang, Qianli; Pitkow, Xaq
2015-03-01
Most interesting natural sensory stimuli are encoded in the brain in a form that can only be decoded nonlinearly. But despite being a core function of the brain, nonlinear population codes are rarely studied and poorly understood. Interestingly, the few existing models of nonlinear codes are inconsistent with known architectural features of the brain. In particular, these codes have information content that scales with the size of the cortical population, even if that violates the data processing inequality by exceeding the amount of information entering the sensory system. Here we provide a valid theory of nonlinear population codes by generalizing recent work on information-limiting correlations in linear population codes. Although these generalized, nonlinear information-limiting correlations bound the performance of any decoder, they also make decoding more robust to suboptimal computation, allowing many suboptimal decoders to achieve nearly the same efficiency as an optimal decoder. Although these correlations are extremely difficult to measure directly, particularly for nonlinear codes, we provide a simple, practical test by which one can use choice-related activity in small populations of neurons to determine whether decoding is suboptimal or optimal and limited by correlated noise. We conclude by describing an example computation in the vestibular system where this theory applies. QY and XP was supported by a grant from the McNair foundation.
Nonlinear Multiantenna Detection Methods
Directory of Open Access Journals (Sweden)
Chen Sheng
2004-01-01
Full Text Available A nonlinear detection technique designed for multiple-antenna assisted receivers employed in space-division multiple-access systems is investigated. We derive the optimal solution of the nonlinear spatial-processing assisted receiver for binary phase shift keying signalling, which we refer to as the Bayesian detector. It is shown that this optimal Bayesian receiver significantly outperforms the standard linear beamforming assisted receiver in terms of a reduced bit error rate, at the expense of an increased complexity, while the achievable system capacity is substantially enhanced with the advent of employing nonlinear detection. Specifically, when the spatial separation expressed in terms of the angle of arrival between the desired and interfering signals is below a certain threshold, a linear beamformer would fail to separate them, while a nonlinear detection assisted receiver is still capable of performing adequately. The adaptive implementation of the optimal Bayesian detector can be realized using a radial basis function network. Two techniques are presented for constructing block-data-based adaptive nonlinear multiple-antenna assisted receivers. One of them is based on the relevance vector machine invoked for classification, while the other on the orthogonal forward selection procedure combined with the Fisher ratio class-separability measure. A recursive sample-by-sample adaptation procedure is also proposed for training nonlinear detectors based on an amalgam of enhanced -means clustering techniques and the recursive least squares algorithm.
Nonlinear systems in medicine.
Higgins, John P
2002-01-01
Many achievements in medicine have come from applying linear theory to problems. Most current methods of data analysis use linear models, which are based on proportionality between two variables and/or relationships described by linear differential equations. However, nonlinear behavior commonly occurs within human systems due to their complex dynamic nature; this cannot be described adequately by linear models. Nonlinear thinking has grown among physiologists and physicians over the past century, and non-linear system theories are beginning to be applied to assist in interpreting, explaining, and predicting biological phenomena. Chaos theory describes elements manifesting behavior that is extremely sensitive to initial conditions, does not repeat itself and yet is deterministic. Complexity theory goes one step beyond chaos and is attempting to explain complex behavior that emerges within dynamic nonlinear systems. Nonlinear modeling still has not been able to explain all of the complexity present in human systems, and further models still need to be refined and developed. However, nonlinear modeling is helping to explain some system behaviors that linear systems cannot and thus will augment our understanding of the nature of complex dynamic systems within the human body in health and in disease states.
Handbook of nonlinear optical crystals
Dmitriev, Valentin G; Nikogosyan, David N
1991-01-01
This Handbook of Nonlinear Optical Crystals provides a complete description of the properties and applications of nonlinear crystals In addition, it presents the most important equations for calculating the main parameters of nonlinear frequency converters This comprehensive reference work will be of great value to all scientists and engineers working in nonlinear optics, quantum electronics and laser physics
Nonlinear Approaches in Engineering Applications
Jazar, Reza
2012-01-01
Nonlinear Approaches in Engineering Applications focuses on nonlinear phenomena that are common in the engineering field. The nonlinear approaches described in this book provide a sound theoretical base and practical tools to design and analyze engineering systems with high efficiency and accuracy and with less energy and downtime. Presented here are nonlinear approaches in areas such as dynamic systems, optimal control and approaches in nonlinear dynamics and acoustics. Coverage encompasses a wide range of applications and fields including mathematical modeling and nonlinear behavior as applied to microresonators, nanotechnologies, nonlinear behavior in soil erosion,nonlinear population dynamics, and optimization in reducing vibration and noise as well as vibration in triple-walled carbon nanotubes. This book also: Provides a complete introduction to nonlinear behavior of systems and the advantages of nonlinearity as a tool for solving engineering problems Includes applications and examples drawn from the el...
Energy Technology Data Exchange (ETDEWEB)
Davis, C.G.
1990-01-01
The advent of nonlinear pulsation theory really coincides with the development of the large computers after the second world war. Christy and Stobbie were the first to make use of finite difference techniques on computers to model the bumps'' observed in the classical Cepheid light and velocity curves, the so-called Hertzsprung'' sequence. Following this work a more sophisticated analysis of the light and velocity curves from the models was made by Simon and Davis using Fourier techniques. Recently a simpler amplitude equation formalism has been developed that helps explain this resonance mechanism. The determination of Population I Cepheid masses by nonlinear methods will be discussed. For the lower mass objects, such as RR Lyrae and BL Her. stars, we find general agreement using evolutionary masses and nonlinear pulsation theory. An apparent difficulty of nonlinear pulsation theory occurs in the understanding of double'' mode pulsation, which will also be discussed. Recent studies in nonlinear pulsation theory have dealt with the question of mode selection, period doubling and the trends towards chaotic behavior such as is observed in the transition from W Virginis to RV Tauri-like stars. 10 refs., 1 fig., 2 tabs.
Nonlinear elastic waves in materials
Rushchitsky, Jeremiah J
2014-01-01
The main goal of the book is a coherent treatment of the theory of propagation in materials of nonlinearly elastic waves of displacements, which corresponds to one modern line of development of the nonlinear theory of elastic waves. The book is divided on five basic parts: the necessary information on waves and materials; the necessary information on nonlinear theory of elasticity and elastic materials; analysis of one-dimensional nonlinear elastic waves of displacement – longitudinal, vertically and horizontally polarized transverse plane nonlinear elastic waves of displacement; analysis of one-dimensional nonlinear elastic waves of displacement – cylindrical and torsional nonlinear elastic waves of displacement; analysis of two-dimensional nonlinear elastic waves of displacement – Rayleigh and Love nonlinear elastic surface waves. The book is addressed first of all to people working in solid mechanics – from the students at an advanced undergraduate and graduate level to the scientists, professional...
Nonlinear Dynamic Force Spectroscopy
Björnham, Oscar
2016-01-01
Dynamic force spectroscopy (DFS) is an experimental technique that is commonly used to assess information of the strength, energy landscape, and lifetime of noncovalent bio-molecular interactions. DFS traditionally requires an applied force that increases linearly with time so that the bio-complex under investigation is exposed to a constant loading rate. However, tethers or polymers can modulate the applied force in a nonlinear regime. For example, bacterial adhesion pili and polymers with worm-like chain properties are examples of structures that show nonlinear force responses. In these situations, the theory for traditional DFS cannot be readily applied. In this work we expand the theory for DFS to also include nonlinear external forces while still maintaining compatibility with the linear DFS theory. To validate the theory we modeled a bio-complex expressed on a stiff, an elastic and a worm-like chain polymer, using Monte Carlo methods, and assessed the corresponding rupture force spectra. It was found th...
Nonlinear optomechanical paddle nanocavities
Kaviani, Hamidreza; Wu, Marcelo; Ghobadi, Roohollah; Barclay, Paul E
2014-01-01
A photonic crystal optomechanical system combining strong nonlinear optomechanical coupling, low effective mass and large optical mode spacing is introduced. This nanoscale "paddle nanocavity" device supports mechanical resonances with effective mass of 300--600 fg which couple nonlinearly to co-localized optical modes with a quadratic optomechanical coupling coefficient $g^{(2)} > 2\\pi\\times400$ MHz/nm$^2$, and a two phonon to single photon optomechanical coupling rate $\\Delta \\omega_0 > 2\\pi\\times 16$ Hz. This coupling relies on strong phonon-photon interactions in a structure whose optical mode spectrum is highly non--degenerate. Simulations indicate that nonlinear optomechanical readout of thermally driven motion in these devices should be observable for T $> 50 $ mK, and that measurement of phonon shot noise is achievable.
Nonlinear dynamics of structures
Oller, Sergio
2014-01-01
This book lays the foundation of knowledge that will allow a better understanding of nonlinear phenomena that occur in structural dynamics. This work is intended for graduate engineering students who want to expand their knowledge on the dynamic behavior of structures, specifically in the nonlinear field, by presenting the basis of dynamic balance in non‐linear behavior structures due to the material and kinematics mechanical effects. Particularly, this publication shows the solution of the equation of dynamic equilibrium for structure with nonlinear time‐independent materials (plasticity, damage and frequencies evolution), as well as those time dependent non‐linear behavior materials (viscoelasticity and viscoplasticity). The convergence conditions for the non‐linear dynamic structure solution are studied, and the theoretical concepts and its programming algorithms are presented.
Nonlinear Photonic Crystal Fibers
DEFF Research Database (Denmark)
Hansen, Kim Per
2004-01-01
, leading to reduced mode confinement and dispersion flexibility. In this thesis, we treat the nonlinear photonic crystal fiber – a special sub-class of photonic crystal fibers, the core of which has a diameter comparable to the wavelength of the light guided in the fiber. The small core results in a large...... nonlinear coefficient and in various applications, it is therefore possible to reduce the required fiber lengths quite dramatically, leading to increased stability and efficiency. Furthermore, it is possible to design these fibers with zero-dispersion at previously unreachable wavelengths, paving the way...... for completely new applications, especially in and near the visible wavelength region. One such application is supercontinuum generation. Supercontinuum generation is extreme broadening of pulses in a nonlinear medium (in this case a small-core fiber), and depending on the dispersion of the fiber, it is possible...
Schmidt, Bruno E; Ernotte, Guilmot; Clerici, Matteo; Morandotti, Roberto; Ibrahim, Heide; Legare, Francois
2016-01-01
In the framework of linear optics, light fields do not interact with each other in a medium. Yet, when their field amplitude becomes comparable to the electron binding energies of matter, the nonlinear motion of these electrons emits new dipole radiation whose amplitude, frequency and phase differ from the incoming fields. Such high fields are typically achieved with ultra-short, femtosecond (1fs = 10-15 sec.) laser pulses containing very broad frequency spectra. Here, the matter not only couples incoming and outgoing fields but also causes different spectral components to interact and mix through a convolution process. In this contribution, we describe how frequency domain nonlinear optics overcomes the shortcomings arising from this convolution in conventional time domain nonlinear optics1. We generate light fields with previously inaccessible properties because the uncontrolled coupling of amplitudes and phases is turned off. For example, arbitrary phase functions are transferred linearly to the second har...
Nonlinear optomechanics with graphene
Shaffer, Airlia; Patil, Yogesh Sharad; Cheung, Hil F. H.; Wang, Ke; Vengalattore, Mukund
2016-05-01
To date, studies of cavity optomechanics have been limited to exploiting the linear interactions between the light and mechanics. However, investigations of quantum signal transduction, quantum enhanced metrology and manybody physics with optomechanics each require strong, nonlinear interactions. Graphene nanomembranes are an exciting prospect for realizing such studies due to their inherently nonlinear nature and low mass. We fabricate large graphene nanomembranes and study their mechanical and optical properties. By using dark ground imaging techniques, we correlate their eigenmode shapes with the measured dissipation. We study their hysteretic response present even at low driving amplitudes, and their nonlinear dissipation. Finally, we discuss ongoing efforts to use these resonators for studies of quantum optomechanics and force sensing. This work is supported by the DARPA QuASAR program through a Grant from the ARO.
Nonlinear Analysis of Buckling
Directory of Open Access Journals (Sweden)
Psotný Martin
2014-06-01
Full Text Available The stability analysis of slender web loaded in compression was presented. To solve this problem, a specialized computer program based on FEM was created. The nonlinear finite element method equations were derived from the variational principle of minimum of potential energy. To obtain the nonlinear equilibrium paths, the Newton-Raphson iteration algorithm was used. Corresponding levels of the total potential energy were defined. The peculiarities of the effects of the initial imperfections were investigated. Special attention was focused on the influence of imperfections on the post-critical buckling mode. The stable and unstable paths of the nonlinear solution were separated. Obtained results were compared with those gained using ANSYS system.
Nonlinear Metamaterials for Holography
Almeida, Euclides; Prior, Yehiam
2015-01-01
A hologram is an optical element storing phase and possibly amplitude information enabling the reconstruction of a three dimensional image of an object by illumination and scattering of a coherent beam of light, and the image is generated at the same wavelength as the input laser beam. In recent years it was shown that information can be stored in nanometric antennas giving rise to ultrathin components. Here we demonstrate nonlinear multi-layer metamaterial holograms where by the nonlinear process of Third Harmonic Generation, a background free image is formed at a new frequency which is the third harmonic of the illuminating beam. Using e-beam lithography of multilayer plasmonic nanoantennas, we fabricate polarization-sensitive nonlinear elements such as blazed gratings, lenses and other computer-generated holograms. These holograms are analyzed and prospects for future device applications are discussed.
Multidimensional nonlinear descriptive analysis
Nishisato, Shizuhiko
2006-01-01
Quantification of categorical, or non-numerical, data is a problem that scientists face across a wide range of disciplines. Exploring data analysis in various areas of research, such as the social sciences and biology, Multidimensional Nonlinear Descriptive Analysis presents methods for analyzing categorical data that are not necessarily sampled randomly from a normal population and often involve nonlinear relations. This reference not only provides an overview of multidimensional nonlinear descriptive analysis (MUNDA) of discrete data, it also offers new results in a variety of fields. The first part of the book covers conceptual and technical preliminaries needed to understand the data analysis in subsequent chapters. The next two parts contain applications of MUNDA to diverse data types, with each chapter devoted to one type of categorical data, a brief historical comment, and basic skills peculiar to the data types. The final part examines several problems and then concludes with suggestions for futu...
Nonlinear airship aeroelasticity
Bessert, N.; Frederich, O.
2005-12-01
The aeroelastic derivatives for today's aircraft are calculated in the concept phase using a standard procedure. This scheme has to be extended for large airships, due to various nonlinearities in structural and aerodynamic behaviour. In general, the structural model of an airship is physically as well as geometrically nonlinear. The main sources of nonlinearity are large deformations and the nonlinear material behaviour of membranes. The aerodynamic solution is also included in the nonlinear problem, because the deformed airship influences the surrounding flow. Due to these nonlinearities, the aeroelastic problem for airships can only be solved by an iterative procedure. As one possibility, the coupled aerodynamic and structural dynamic problem was handled using linked standard solvers. On the structural side, the Finite-Element program package ABAQUS was extended with an interface to the aerodynamic solver VSAERO. VSAERO is based on the aerodynamic panel method using potential flow theory. The equilibrium of the internal structural and the external aerodynamic forces leads to the structural response and a trimmed flight state for the specified flight conditions (e.g. speed, altitude). The application of small perturbations around a trimmed state produces reaction forces and moments. These constraint forces are then transferred into translational and rotational acceleration fields by performing an inertia relief analysis of the disturbed structural model. The change between the trimmed flight state and the disturbed one yields the respective aeroelastic derivatives. By including the calculated derivatives in the linearised equation of motion system, it is possible to judge the stability and controllability of the investigated airship.
Agrawal, Govind
2012-01-01
Since the 4e appeared, a fast evolution of the field has occurred. The 5e of this classic work provides an up-to-date account of the nonlinear phenomena occurring inside optical fibers, the basis of all our telecommunications infastructure as well as being used in the medical field. Reflecting the big developments in research, this new edition includes major new content: slow light effects, which offers a reduction in noise and power consumption and more ordered network traffic-stimulated Brillouin scattering; vectorial treatment of highly nonlinear fibers; and a brand new chapter o
DEFF Research Database (Denmark)
Mosegaard, Klaus
2012-01-01
For non-linear inverse problems, the mathematical structure of the mapping from model parameters to data is usually unknown or partly unknown. Absence of information about the mathematical structure of this function prevents us from presenting an analytical solution, so our solution depends on our......-heuristics are inefficient for large-scale, non-linear inverse problems, and that the 'no-free-lunch' theorem holds. We discuss typical objections to the relevance of this theorem. A consequence of the no-free-lunch theorem is that algorithms adapted to the mathematical structure of the problem perform more efficiently than...
Fundamentals of nonlinear optics
Powers, Peter E
2011-01-01
Peter Powers's rigorous but simple description of a difficult field keeps the reader's attention throughout. … All chapters contain a list of references and large numbers of practice examples to be worked through. … By carefully working through the proposed problems, students will develop a sound understanding of the fundamental principles and applications. … the book serves perfectly for an introductory-level course for second- and third-order nonlinear optical phenomena. The author's writing style is refreshing and original. I expect that Fundamentals of Nonlinear Optics will fast become pop
Tunable nonlinear graphene metasurfaces
Smirnova, Daria A; Kivshar, Yuri S; Khanikaev, Alexander B
2015-01-01
We introduce the concept of nonlinear graphene metasurfaces employing the controllable interaction between a graphene layer and a planar metamaterial. Such hybrid metasurfaces support two types of subradiant resonant modes, asymmetric modes of structured metamaterial elements ("metamolecules") and graphene plasmons exhibiting strong mutual coupling and avoided dispersion crossing. High tunability of graphene plasmons facilitates strong interaction between the subradiant modes, modifying the spectral position and lifetime of the associated Fano resonances. We demonstrate that strong resonant interaction, combined with the subwavelength localization of plasmons, leads to the enhanced nonlinear response and high efficiency of the second-harmonic generation.
Nonlinear effects in optical fibers
Ferreira, Mario F
2011-01-01
Cutting-edge coverage of nonlinear phenomena occurring inside optical fibers Nonlinear fiber optics is a specialized part of fiber optics dealing with optical nonlinearities and their applications. As fiber-optic communication systems have become more advanced and complex, the nonlinear effects in optical fibers have increased in importance, as they adversely affect system performance. Paradoxically, the same nonlinear phenomena also offer the promise of addressing the bandwidth bottleneck for signal processing for future ultra-high speed optical networks. Nonlinear Effects in Optical Fiber
Energy Technology Data Exchange (ETDEWEB)
Santos, Marcio Bueno dos; Saboya, Sergio Mourao [Instituto Nacional de Pesquisas Espaciais (INPE), S Jose dos Campos, SP (Brazil). Lab. de Integracao e Testes]. E-mail: bueno@lit.inpe.br; saboya@mec.ita.cta.br
1997-07-01
The entropy generation minimization method is applied to tube and fin radiative systems. The mathematical modeling of the systems lead to a non-linear integro-differential systems of equations, which is solved numerically. The entropy generation in the fin is computed. This is obtained as result of the thermal analysis of the system which gives the fin temperature distributions and the radiative heat transfer rates. Examples of optimized design are considered and discussed. (author)
Nonlinear elliptic systems with exponential nonlinearities
Directory of Open Access Journals (Sweden)
Said El Manouni
2002-12-01
Full Text Available In this paper we investigate the existence of solutions for {gather*} -mathop{m div}( a(| abla u | ^N| abla u |^{N-2}u = f(x,u,v quad mbox{in } Omega -mathop{m div}(a(| abla v| ^N| abla v |^{N-2}v = g(x,u,v quad mbox{in } Omega u(x = v(x = 0 quad mbox{on }partial Omega. end{gather*} Where $Omega$ is a bounded domain in ${mathbb{R}}^N$, $Ngeq 2$, $f$ and $g$ are nonlinearities having an exponential growth on $Omega$ and $a$ is a continuous function satisfying some conditions which ensure the existence of solutions.
Nonlinearity and disorder: Classification and stability of nonlinear impurity modes
DEFF Research Database (Denmark)
Sukhorukov, Andrey A.; Kivshar, Yuri S.; Bang, Ole
2001-01-01
We study the effects produced by competition of two physical mechanisms of energy localization in inhomogeneous nonlinear systems. As an example, we analyze spatially localized modes supported by a nonlinear impurity in the generalized nonlinear Schrödinger equation and describe three types of no...
Generalized Nonlinear Yule Models
Lansky, Petr; Polito, Federico; Sacerdote, Laura
2016-10-01
With the aim of considering models related to random graphs growth exhibiting persistent memory, we propose a fractional nonlinear modification of the classical Yule model often studied in the context of macroevolution. Here the model is analyzed and interpreted in the framework of the development of networks such as the World Wide Web. Nonlinearity is introduced by replacing the linear birth process governing the growth of the in-links of each specific webpage with a fractional nonlinear birth process with completely general birth rates. Among the main results we derive the explicit distribution of the number of in-links of a webpage chosen uniformly at random recognizing the contribution to the asymptotics and the finite time correction. The mean value of the latter distribution is also calculated explicitly in the most general case. Furthermore, in order to show the usefulness of our results, we particularize them in the case of specific birth rates giving rise to a saturating behaviour, a property that is often observed in nature. The further specialization to the non-fractional case allows us to extend the Yule model accounting for a nonlinear growth.
Ritz, Christian; Parmigiani, Giovanni
2009-01-01
R is a rapidly evolving lingua franca of graphical display and statistical analysis of experiments from the applied sciences. This book provides a coherent treatment of nonlinear regression with R by means of examples from a diversity of applied sciences such as biology, chemistry, engineering, medicine and toxicology.
Gorban, A. N.; Karlin, I.V.
2003-01-01
Nonlinear kinetic equations are reviewed for a wide audience of specialists and postgraduate students in physics, mathematical physics, material science, chemical engineering and interdisciplinary research. Contents: The Boltzmann equation, Phenomenology and Quasi-chemical representation of the Boltzmann equation, Kinetic models, Discrete velocity models, Direct simulation, Lattice Gas and Lattice Boltzmann models, Minimal Boltzmann models for flows at low Knudsen number, Other kinetic equati...
Intramolecular and nonlinear dynamics
Energy Technology Data Exchange (ETDEWEB)
Davis, M.J. [Argonne National Laboratory, IL (United States)
1993-12-01
Research in this program focuses on three interconnected areas. The first involves the study of intramolecular dynamics, particularly of highly excited systems. The second area involves the use of nonlinear dynamics as a tool for the study of molecular dynamics and complex kinetics. The third area is the study of the classical/quantum correspondence for highly excited systems, particularly systems exhibiting classical chaos.
DEFF Research Database (Denmark)
Jørgensen, Michael Finn
1995-01-01
It is generally very difficult to solve nonlinear systems, and such systems often possess chaotic solutions. In the rare event that a system is completely solvable, it is said to integrable. Such systems never have chaotic solutions. Using the Inverse Scattering Transform Method (ISTM) two...
Nonlinear phased array imaging
Croxford, Anthony J.; Cheng, Jingwei; Potter, Jack N.
2016-04-01
A technique is presented for imaging acoustic nonlinearity within a specimen using ultrasonic phased arrays. Acoustic nonlinearity is measured by evaluating the difference in energy of the transmission bandwidth within the diffuse field produced through different focusing modes. The two different modes being classical beam forming, where delays are applied to different element of a phased array to physically focus the energy at a single location (parallel firing) and focusing in post processing, whereby one element at a time is fired and a focused image produced in post processing (sequential firing). Although these two approaches are linearly equivalent the difference in physical displacement within the specimen leads to differences in nonlinear effects. These differences are localized to the areas where the amplitude is different, essentially confining the differences to the focal point. Direct measurement at the focal point are however difficult to make. In order to measure this the diffuse field is used. It is a statistical property of the diffuse field that it represents the total energy in the system. If the energy in the diffuse field for both the sequential and parallel firing case is measured then the difference between these, within the input signal bandwidth, is largely due to differences at the focal spot. This difference therefore gives a localized measurement of where energy is moving out of the transmission bandwidth due to nonlinear effects. This technique is used to image fatigue cracks and other damage types undetectable with conventional linear ultrasonic measurements.
Generalized Nonlinear Yule Models
Lansky, Petr; Polito, Federico; Sacerdote, Laura
2016-11-01
With the aim of considering models related to random graphs growth exhibiting persistent memory, we propose a fractional nonlinear modification of the classical Yule model often studied in the context of macroevolution. Here the model is analyzed and interpreted in the framework of the development of networks such as the World Wide Web. Nonlinearity is introduced by replacing the linear birth process governing the growth of the in-links of each specific webpage with a fractional nonlinear birth process with completely general birth rates. Among the main results we derive the explicit distribution of the number of in-links of a webpage chosen uniformly at random recognizing the contribution to the asymptotics and the finite time correction. The mean value of the latter distribution is also calculated explicitly in the most general case. Furthermore, in order to show the usefulness of our results, we particularize them in the case of specific birth rates giving rise to a saturating behaviour, a property that is often observed in nature. The further specialization to the non-fractional case allows us to extend the Yule model accounting for a nonlinear growth.
Trirefringence in nonlinear metamaterials
De Lorenci, Vitorio A
2012-01-01
We study the propagation of electromagnetic waves in the limit of geometrical optics for a class of nearly transparent nonlinear uniaxial metamaterials for which their permittivity tensors present a negative principal component. Their permeability are assumed positive and dependent on the electric field. We show that light waves experience triple refraction -- trirefringence. Additionally to the ordinary wave, two extraordinary waves propagate in such media.
Borghi, M.; Castellan, C.; Signorini, S.; Trenti, A.; Pavesi, L.
2017-09-01
Silicon photonics is a technology based on fabricating integrated optical circuits by using the same paradigms as the dominant electronics industry. After twenty years of fervid development, silicon photonics is entering the market with low cost, high performance and mass-manufacturable optical devices. Until now, most silicon photonic devices have been based on linear optical effects, despite the many phenomenologies associated with nonlinear optics in both bulk materials and integrated waveguides. Silicon and silicon-based materials have strong optical nonlinearities which are enhanced in integrated devices by the small cross-section of the high-index contrast silicon waveguides or photonic crystals. Here the photons are made to strongly interact with the medium where they propagate. This is the central argument of nonlinear silicon photonics. It is the aim of this review to describe the state-of-the-art in the field. Starting from the basic nonlinearities in a silicon waveguide or in optical resonator geometries, many phenomena and applications are described—including frequency generation, frequency conversion, frequency-comb generation, supercontinuum generation, soliton formation, temporal imaging and time lensing, Raman lasing, and comb spectroscopy. Emerging quantum photonics applications, such as entangled photon sources, heralded single-photon sources and integrated quantum photonic circuits are also addressed at the end of this review.
Nonlinear fibre optics overview
DEFF Research Database (Denmark)
Travers, J. C.; Frosz, Michael Henoch; Dudley, J. M.
2010-01-01
, provides a background to the associated nonlinear optical processes, treats the generation mechanisms from continuous wave to femtosecond pulse pump regimes and highlights the diverse applications. A full discussion of numerical methods and comprehensive computer code are also provided, enabling readers...
Tsia, Kevin K.; Jalali, Bahram
2010-05-01
An intriguing optical property of silicon is that it exhibits a large third-order optical nonlinearity, with orders-ofmagnitude larger than that of silica glass in the telecommunication band. This allows efficient nonlinear optical interaction at relatively low power levels in a small footprint. Indeed, we have witnessed a stunning progress in harnessing the Raman and Kerr effects in silicon as the mechanisms for enabling chip-scale optical amplification, lasing, and wavelength conversion - functions that until recently were perceived to be beyond the reach of silicon. With all the continuous efforts developing novel techniques, nonlinear silicon photonics is expected to be able to reach even beyond the prior achievements. Instead of providing a comprehensive overview of this field, this manuscript highlights a number of new branches of nonlinear silicon photonics, which have not been fully recognized in the past. In particular, they are two-photon photovoltaic effect, mid-wave infrared (MWIR) silicon photonics, broadband Raman effects, inverse Raman scattering, and periodically-poled silicon (PePSi). These novel effects and techniques could create a new paradigm for silicon photonics and extend its utility beyond the traditionally anticipated applications.
Leitao, J C; Gerlach, M; Altmann, E G
2016-01-01
One of the most celebrated findings in complex systems in the last decade is that different indexes y (e.g., patents) scale nonlinearly with the population~x of the cities in which they appear, i.e., $y\\sim x^\\beta, \\beta \
Nonlinear Gravitational Lagrangians revisited
Magnano, Guido
2016-01-01
The Legendre transformation method, applied in 1987 to deal with purely metric gravitational Lagrangians with nonlinear dependence on the Ricci tensor, is extended to metric-affine models and is shown to provide a concise and insightful comparison of the dynamical content of the two variational frameworks.
Nonlinearities in Microwave Superconductivity
Ledenyov, Dimitri O.; Ledenyov, Viktor O.
2012-01-01
The research is focused on the modeling of nonlinear properties of High Temperature Superconducting (HTS) thin films, using Bardeen, Cooper, Schrieffer and Lumped Element Circuit theories, with purpose to enhance microwave power handling capabilities of microwave filters and optimize design of microwave circuits in micro- and nano- electronics.
Nonlinear tsunami generation mechanism
Directory of Open Access Journals (Sweden)
M. A. Nosov
2001-01-01
Full Text Available The nonlinear mechanism of long gravitational surface water wave generation by high-frequency bottom oscillations in a water layer of constant depth is investigated analytically. The connection between the surface wave amplitude and the parameters of bottom oscillations and source length is investigated.
DEFF Research Database (Denmark)
Mosekilde, Erik
Through a significant number of detailed and realistic examples this book illustrates how the insights gained over the past couple of decades in the fields of nonlinear dynamics and chaos theory can be applied in practice. Aomng the topics considered are microbiological reaction systems, ecological...
Terahertz semiconductor nonlinear optics
DEFF Research Database (Denmark)
Turchinovich, Dmitry; Hvam, Jørn Märcher; Hoffmann, Matthias
2013-01-01
nonlinearity in doped semiconductors originates from the near-instantaneous heating of free electrons in the ponderomotive potential created by electric field of the THz pulse, leading to ultrafast increase of electron effective mass by intervalley scattering. Modification of effective mass in turn leads...
Nonlinear Optical Terahertz Technology Project
National Aeronautics and Space Administration — Our approach is based on high-Q optical WGM resonators made with a nonlinear crystal. Such resonators have been demonstrated to dramatically enhance nonlinear...
Phase retrieval using nonlinear diversity.
Lu, Chien-Hung; Barsi, Christopher; Williams, Matthew O; Kutz, J Nathan; Fleischer, Jason W
2013-04-01
We extend the Gerchberg-Saxton algorithm to phase retrieval in a nonlinear system. Using a tunable photorefractive crystal, we experimentally demonstrate the noninterferometric technique by reconstructing an unknown phase object from optical intensity measurements taken at different nonlinear strengths.
Strong nonlinear oscillators analytical solutions
Cveticanin, Livija
2017-01-01
This book outlines an analytical solution procedure of the pure nonlinear oscillator system, offering a solution for free and forced vibrations of the one-degree-of-freedom strong nonlinear system with constant and time variable parameter. Includes exercises.
Cubication of Conservative Nonlinear Oscillators
Belendez, Augusto; Alvarez, Mariela L.; Fernandez, Elena; Pascual, Immaculada
2009-01-01
A cubication procedure of the nonlinear differential equation for conservative nonlinear oscillators is analysed and discussed. This scheme is based on the Chebyshev series expansion of the restoring force, and this allows us to approximate the original nonlinear differential equation by a Duffing equation in which the coefficients for the linear…
Terahertz Nonlinear Optics in Semiconductors
DEFF Research Database (Denmark)
Turchinovich, Dmitry; Hvam, Jørn Märcher; Hoffmann, Matthias C.
2013-01-01
We demonstrate the nonlinear optical effects – selfphase modulation and saturable absorption of a single-cycle THz pulse in a semiconductor. Resulting from THz-induced modulation of Drude plasma, these nonlinear optical effects, in particular, lead to self-shortening and nonlinear spectral...
Fault Detection for Nonlinear Systems
DEFF Research Database (Denmark)
Stoustrup, Jakob; Niemann, H.H.
1998-01-01
The paper describes a general method for designing fault detection and isolation (FDI) systems for nonlinear processes. For a rich class of nonlinear systems, a nonlinear FDI system can be designed using convex optimization procedures. The proposed method is a natural extension of methods based...
Nonlinear electrostatic drift Kelvin-Helmholtz instability
Sharma, Avadhesh C.; Srivastava, Krishna M.
1993-01-01
Nonlinear analysis of electrostatic drift Kelvin-Helmholtz instability is performed. It is shown that the analysis leads to the propagation of the weakly nonlinear dispersive waves, and the nonlinear behavior is governed by the nonlinear Burger's equation.
Optothermal nonlinearity of silica aerogel
Braidotti, Maria Chiara; Fleming, Adam; Samuels, Michiel C; Di Falco, Andrea; Conti, Claudio
2016-01-01
We report on the characterization of silica aerogel thermal optical nonlinearity, obtained by z-scan technique. The results show that typical silica aerogels have nonlinear optical coefficient similar to that of glass $(\\simeq 10^{-12} $m$^2/$W), with negligible optical nonlinear absorption. The non\\-li\\-near coefficient can be increased to values in the range of $10^{-10} $m$^2/$W by embedding an absorbing dye in the aerogel. This value is one order of magnitude higher than that observed in the pure dye and in typical highly nonlinear materials like liquid crystals.
Essentials of nonlinear optics
Murti, Y V G S
2014-01-01
Current literature on Nonlinear Optics varies widely in terms of content, style, and coverage of specific topics, relative emphasis of areas and the depth of treatment. While most of these books are excellent resources for the researchers, there is a strong need for books appropriate for presenting the subject at the undergraduate or postgraduate levels in Universities. The need for such a book to serve as a textbook at the level of the bachelors and masters courses was felt by the authors while teaching courses on nonlinear optics to students of both science and engineering during the past two decades. This book has emerged from an attempt to address the requirement of presenting the subject at college level. A one-semester course covering the essentials can effectively be designed based on this.
Nonlinear metamaterials for holography
Almeida, Euclides; Bitton, Ora; Prior, Yehiam
2016-08-01
A hologram is an optical element storing phase and possibly amplitude information enabling the reconstruction of a three-dimensional image of an object by illumination and scattering of a coherent beam of light, and the image is generated at the same wavelength as the input laser beam. In recent years, it was shown that information can be stored in nanometric antennas giving rise to ultrathin components. Here we demonstrate nonlinear multilayer metamaterial holograms. A background free image is formed at a new frequency--the third harmonic of the illuminating beam. Using e-beam lithography of multilayer plasmonic nanoantennas, we fabricate polarization-sensitive nonlinear elements such as blazed gratings, lenses and other computer-generated holograms. These holograms are analysed and prospects for future device applications are discussed.
Nonlinear metamaterials for holography
Almeida, Euclides; Bitton, Ora
2016-01-01
A hologram is an optical element storing phase and possibly amplitude information enabling the reconstruction of a three-dimensional image of an object by illumination and scattering of a coherent beam of light, and the image is generated at the same wavelength as the input laser beam. In recent years, it was shown that information can be stored in nanometric antennas giving rise to ultrathin components. Here we demonstrate nonlinear multilayer metamaterial holograms. A background free image is formed at a new frequency—the third harmonic of the illuminating beam. Using e-beam lithography of multilayer plasmonic nanoantennas, we fabricate polarization-sensitive nonlinear elements such as blazed gratings, lenses and other computer-generated holograms. These holograms are analysed and prospects for future device applications are discussed. PMID:27545581
Van Leeuwen, Peter Jan; Reich, Sebastian
2015-01-01
This book contains two review articles on nonlinear data assimilation that deal with closely related topics but were written and can be read independently. Both contributions focus on so-called particle filters. The first contribution by Jan van Leeuwen focuses on the potential of proposal densities. It discusses the issues with present-day particle filters and explorers new ideas for proposal densities to solve them, converging to particle filters that work well in systems of any dimension, closing the contribution with a high-dimensional example. The second contribution by Cheng and Reich discusses a unified framework for ensemble-transform particle filters. This allows one to bridge successful ensemble Kalman filters with fully nonlinear particle filters, and allows a proper introduction of localization in particle filters, which has been lacking up to now.
Nonlinearity without Superluminality
Kent, A
2002-01-01
Quantum theory is compatible with special relativity. In particular, though measurements on entangled systems are correlated in a way that cannot be reproduced by local hidden variables, they cannot be used for superluminal signalling. As Gisin and Polchinski first pointed out, this is not true for general nonlinear modifications of the Schroedinger equation. Excluding superluminal signalling has thus been taken to rule out most nonlinear versions of quantum theory. The no superluminal signalling constraint has also been used for alternative derivations of the optimal fidelities attainable for imperfect quantum cloning and other operations. These results apply to theories satisfying the rule that their predictions for widely separated and slowly moving entangled systems can be approximated by non-relativistic equations of motion with respect to a preferred time coordinate. This paper describes a natural way in which this rule might fail to hold. In particular, it is shown that quantum readout devices which di...
Monte Carlo and nonlinearities
Dauchet, Jérémi; Blanco, Stéphane; Caliot, Cyril; Charon, Julien; Coustet, Christophe; Hafi, Mouna El; Eymet, Vincent; Farges, Olivier; Forest, Vincent; Fournier, Richard; Galtier, Mathieu; Gautrais, Jacques; Khuong, Anaïs; Pelissier, Lionel; Piaud, Benjamin; Roger, Maxime; Terrée, Guillaume; Weitz, Sebastian
2016-01-01
The Monte Carlo method is widely used to numerically predict systems behaviour. However, its powerful incremental design assumes a strong premise which has severely limited application so far: the estimation process must combine linearly over dimensions. Here we show that this premise can be alleviated by projecting nonlinearities on a polynomial basis and increasing the configuration-space dimension. Considering phytoplankton growth in light-limited environments, radiative transfer in planetary atmospheres, electromagnetic scattering by particles and concentrated-solar-power-plant productions, we prove the real world usability of this advance on four test-cases that were so far regarded as impracticable by Monte Carlo approaches. We also illustrate an outstanding feature of our method when applied to sharp problems with interacting particles: handling rare events is now straightforward. Overall, our extension preserves the features that made the method popular: addressing nonlinearities does not compromise o...
Nonlinear Photonics 2014: introduction.
Akhmediev, N; Kartashov, Yaroslav
2015-01-12
International Conference "Nonlinear Photonics-2014" took place in Barcelona, Spain on July 27-31, 2014. It was a part of the "Advanced Photonics Congress" which is becoming a traditional notable event in the world of photonics. The current focus issue of Optics Express contains contributions from the participants of the Conference and the Congress. The articles in this focus issue by no means represent the total number of the congress contributions (around 400). However, it demonstrates wide range of topics covered at the event. The next conference of this series is to be held in 2016 in Australia, which is the home of many researchers working in the field of photonics in general and nonlinear photonics in particular.
Nonlinear fractional relaxation
Indian Academy of Sciences (India)
A Tofighi
2012-04-01
We deﬁne a nonlinear model for fractional relaxation phenomena. We use -expansion method to analyse this model. By studying the fundamental solutions of this model we ﬁnd that when → 0 the model exhibits a fast decay rate and when → ∞ the model exhibits a power-law decay. By analysing the frequency response we ﬁnd a logarithmic enhancement for the relative ratio of susceptibility.
Indian Academy of Sciences (India)
Ramaswamy Jaganathan; Sudeshna Sinha
2005-03-01
Motivated by studies on -deformed physical systems related to quantum group structures, and by the elements of Tsallis statistical mechanics, the concept of -deformed nonlinear maps is introduced. As a specific example, a -deformation procedure is applied to the logistic map. Compared to the canonical logistic map, the resulting family of -logistic maps is shown to have a wider spectrum of interesting behaviours, including the co-existence of attractors – a phenomenon rare in one-dimensional maps.
Controllability of nonlinear systems.
Sussmann, H. J.; Jurdjevic, V.
1972-01-01
Discussion of the controllability of nonlinear systems described by the equation dx/dt - F(x,u). Concepts formulated by Chow (1939) and Lobry (1970) are applied to establish criteria for F and its derivatives to obtain qualitative information on sets which can be obtained from x which denotes a variable of state in an arbitrary, real, analytical manifold. It is shown that controllability implies strong accessibility for a large class of manifolds including Euclidean spaces.-
Stochastic Nonlinear Aeroelasticity
2009-01-01
STOCHASTIC NONLINEAR AEROELASTICITY 5a. CONTRACT NUMBER In- house 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 0601102 6. AUTHOR(S) Philip S...ABSTRACT This report documents the culmination of in- house work in the area of uncertainty quantification and probabilistic techniques for... coff U∞ cs ea lw cw Figure 6: Wing and store geometry (left), wing box structural model (middle), flutter distribution (right
2007-03-01
IEEE Transactions on Automatic Control , AC- 48, pp. 1712-1723, (2003). [14] C.I. Byrnes, A. Isidori...Nonlinear internal models for output regulation,” IEEE Transactions on Automatic Control , AC-49, pp. 2244-2247, (2004). [15] C.I. Byrnes, F. Celani, A...approach,” IEEE Transactions on Automatic Control , 48 (Dec. 2003), 2172–2190. 2. C. I. Byrnes, “Differential Forms and Dynamical Systems,” to appear
Filamentation with nonlinear Bessel vortices.
Jukna, V; Milián, C; Xie, C; Itina, T; Dudley, J; Courvoisier, F; Couairon, A
2014-10-20
We present a new type of ring-shaped filaments featured by stationary nonlinear high-order Bessel solutions to the laser beam propagation equation. Two different regimes are identified by direct numerical simulations of the nonlinear propagation of axicon focused Gaussian beams carrying helicity in a Kerr medium with multiphoton absorption: the stable nonlinear propagation regime corresponds to a slow beam reshaping into one of the stationary nonlinear high-order Bessel solutions, called nonlinear Bessel vortices. The region of existence of nonlinear Bessel vortices is found semi-analytically. The influence of the Kerr nonlinearity and nonlinear losses on the beam shape is presented. Direct numerical simulations highlight the role of attractors played by nonlinear Bessel vortices in the stable propagation regime. Large input powers or small cone angles lead to the unstable propagation regime where nonlinear Bessel vortices break up into an helical multiple filament pattern or a more irregular structure. Nonlinear Bessel vortices are shown to be sufficiently intense to generate a ring-shaped filamentary ionized channel in the medium which is foreseen as opening the way to novel applications in laser material processing of transparent dielectrics.
Strongly nonlinear oscillators analytical solutions
Cveticanin, Livija
2014-01-01
This book provides the presentation of the motion of pure nonlinear oscillatory systems and various solution procedures which give the approximate solutions of the strong nonlinear oscillator equations. The book presents the original author’s method for the analytical solution procedure of the pure nonlinear oscillator system. After an introduction, the physical explanation of the pure nonlinearity and of the pure nonlinear oscillator is given. The analytical solution for free and forced vibrations of the one-degree-of-freedom strong nonlinear system with constant and time variable parameter is considered. Special attention is given to the one and two mass oscillatory systems with two-degrees-of-freedom. The criteria for the deterministic chaos in ideal and non-ideal pure nonlinear oscillators are derived analytically. The method for suppressing chaos is developed. Important problems are discussed in didactic exercises. The book is self-consistent and suitable as a textbook for students and also for profess...
Quantum well nonlinear microcavities
Oudar, J. L.; Kuszelewicz, R.; Sfez, B.; Pellat, D.; Azoulay, R.
We report on recent progress in reducing the power threshold of all-optical bistable quantum well vertical microcavities. Significant improvements are achieved through an increase of the cavity finesse, together with a reduction of the device active layer thickness. A critical intensity of 5 μW/μm 2 has been observed on a microcavity of finesse 250, with a nonlinear medium of only 18 GaAs quantum wells of 10 nm thickness. Further improvements of the Bragg mirror quality resulted in a finesse of 700 and a power-lifetime product of 15 fJ/μm 2. Microresonator pixellation allows to obtain 2-dimensional arrays. A thermally-induced alloy-mixing technique is described, which produced a 110 meV carrier confinement energy, together with a refractive index change of -.012, averaged over the 2.6 μm nonlinear medium thickness. The resulting electrical and optical confinement is shown to improve the nonlinear characteristics, by limiting lateral carrier diffusion and light diffraction.
Nonlinear robust hierarchical control for nonlinear uncertain systems
Directory of Open Access Journals (Sweden)
Leonessa Alexander
1999-01-01
Full Text Available A nonlinear robust control-system design framework predicated on a hierarchical switching controller architecture parameterized over a set of moving nominal system equilibria is developed. Specifically, using equilibria-dependent Lyapunov functions, a hierarchical nonlinear robust control strategy is developed that robustly stabilizes a given nonlinear system over a prescribed range of system uncertainty by robustly stabilizing a collection of nonlinear controlled uncertain subsystems. The robust switching nonlinear controller architecture is designed based on a generalized (lower semicontinuous Lyapunov function obtained by minimizing a potential function over a given switching set induced by the parameterized nominal system equilibria. The proposed framework robustly stabilizes a compact positively invariant set of a given nonlinear uncertain dynamical system with structured parametric uncertainty. Finally, the efficacy of the proposed approach is demonstrated on a jet engine propulsion control problem with uncertain pressure-flow map data.
Nonlinear scattering in plasmonic nanostructures
Chu, Shi-Wei
2016-09-01
Nonlinear phenomena provide novel light manipulation capabilities and innovative applications. Recently, we discovered nonlinear saturation on single-particle scattering of gold nanospheres by continuous-wave laser excitation and innovatively applied to improve microscopic resolution down to λ/8. However, the nonlinearity was limited to the green-orange plasmonic band of gold nanosphere, and the underlying mechanism has not yet been fully understood. In this work, we demonstrated that nonlinear scattering exists for various material/geometry combinations, thus expanding the applicable wavelength range. For near-infrared, gold nanorod is used, while for blue-violet, silver nanospheres are adopted. In terms of mechanism, the nonlinearity may originate from interband/intraband absorption, hot electron, or hot lattice, which are spectrally mixed in the case of gold nanosphere. For gold nanorod and silver nanosphere, nonlinear scattering occurs at plasmonic resonances, which are spectrally far from interband/intraband absorptions, so they are excluded. We found that the nonlinear index is much larger than possible contributions from hot electrons in literature. Therefore, we conclude that hot lattice is the major mechanism. In addition, we propose that similar to z-scan, which is the standard method to characterize nonlinearity of a thin sample, laser scanning microscopy should be adopted as the standard method to characterize nonlinearity from a nanostructure. Our work not only provides the physical mechanism of the nonlinear scattering, but also paves the way toward multi-color superresolution imaging based on non-bleaching plasmonic scattering.
Discrete nonlinear Schrodinger equations with arbitrarily high-order nonlinearities
DEFF Research Database (Denmark)
Khare, A.; Rasmussen, Kim Ø; Salerno, M.
2006-01-01
A class of discrete nonlinear Schrodinger equations with arbitrarily high-order nonlinearities is introduced. These equations are derived from the same Hamiltonian using different Poisson brackets and include as particular cases the saturable discrete nonlinear Schrodinger equation and the Ablowi......-Ladik equation. As a common property, these equations possess three kinds of exact analytical stationary solutions for which the Peierls-Nabarro barrier is zero. Several properties of these solutions, including stability, discrete breathers, and moving solutions, are investigated....
Dichromatic nonlinear eigenmodes in slab waveguide with chi(2) nonlinearity.
Darmanyan, S A; Nevière, M
2001-03-01
The existence of purely nonlinear eigenmodes in a waveguiding structure composed of a slab with quadratic nonlinearity surrounded by (non)linear claddings is reported. Modes having bright and dark solitonlike shapes and consisting of two mutually locked harmonics are identified. Asymmetrical modes are shown to exist in symmetrical environments. Constraints for the existence of the modes are derived in terms of parameters of guiding structure materials.
Nonlinear Schrodinger equation with chaotic, random, and nonperiodic nonlinearity
Cardoso, W B; Avelar, A T; Bazeia, D; Hussein, M S
2009-01-01
In this paper we deal with a nonlinear Schr\\"{o}dinger equation with chaotic, random, and nonperiodic cubic nonlinearity. Our goal is to study the soliton evolution, with the strength of the nonlinearity perturbed in the space and time coordinates and to check its robustness under these conditions. Comparing with a real system, the perturbation can be related to, e.g., impurities in crystalline structures, or coupling to a thermal reservoir which, on the average, enhances the nonlinearity. We also discuss the relevance of such random perturbations to the dynamics of Bose-Einstein Condensates and their collective excitations and transport.
Stolz, A; Markey, L; Francs, G Colas des; Bouhelier, A
2013-01-01
We introduce strongly-coupled optical gap antennas to interface optical radiation with current-carrying electrons at the nanoscale. The transducer relies on the nonlinear optical and electrical properties of an optical antenna operating in the tunneling regime. We discuss the underlying physical mechanisms controlling the conversion and demonstrate that a two-wire optical antenna can provide advanced optoelectronic functionalities beyond tailoring the electromagnetic response of a single emitter. Interfacing an electronic command layer with a nanoscale optical device may thus be facilitated by the optical rectennas discussed here.
Nonlinear surface electromagnetic phenomena
Ponath, H-E
1991-01-01
In recent years the physics of electromagnetic surface phenomena has developed rapidly, evolving into technologies for communications and industry, such as fiber and integrated optics. The variety of phenomena based on electromagnetism at surfaces is rich and this book was written with the aim of summarizing the available knowledge in selected areas of the field. The book contains reviews written by solid state and optical physicists on the nonlinear interaction of electromagnetic waves at and with surfaces and films. Both the physical phenomena and some potential applications are
Nonlinear electrodynamics with birefringence
Kruglov, S I
2015-01-01
A new model of nonlinear electrodynamics with three parameters is suggested. The phenomena of vacuum birefringence takes place when there is the external constant magnetic field. We calculate the indices of refraction for two polarizations of electromagnetic waves, parallel and perpendicular to the magnetic induction field. From the Bir\\'{e}fringence Magn\\'{e}tique du Vide (BMV) experiment one of the coefficients, $\\gamma\\approx 10^{-20}$ T$^{-2}$, was estimated. The canonical, symmetrical Belinfante energy-momentum tensors and dilatation current were obtained. The dilatation symmetry and the dual symmetry are broken in the model considered.
Wu Zhuo Qun; Li Hui Lai; Zhao Jun Ning
2001-01-01
Nonlinear diffusion equations, an important class of parabolic equations, come from a variety of diffusion phenomena which appear widely in nature. They are suggested as mathematical models of physical problems in many fields, such as filtration, phase transition, biochemistry and dynamics of biological groups. In many cases, the equations possess degeneracy or singularity. The appearance of degeneracy or singularity makes the study more involved and challenging. Many new ideas and methods have been developed to overcome the special difficulties caused by the degeneracy and singularity, which
Nonlinear dynamics in psychology
Directory of Open Access Journals (Sweden)
Stephen J. Guastello
2001-01-01
Full Text Available This article provides a survey of the applications of nonlinear dynamical systems theory to substantive problems encountered in the full scope of psychological science. Applications are organized into three topical areas – cognitive science, social and organizational psychology, and personality and clinical psychology. Both theoretical and empirical studies are considered with an emphasis on works that capture the broadest scope of issues that are of substantive interest to psychological theory. A budding literature on the implications of NDS principles in professional practice is reported also.
2009-11-18
analytic semigroup T(t) ~ eAl is exponentially stable (Notice that it is also a contraction semigroup ). 3. Be 3(U, Z) and P e £(W, 2) are bounded. 4. Ce...quite often in practice, .4 is self-adjoint. We also note that, since we assume (—A) is sectorial, we work with the semigroup exp(.4f) rather than...Uniform Output Regulation of Nonlinear Sys- tems: A convergent Dynamics Approach, Birkhauser, Boston, 2006. 23 135] A. Pazy, Semigroups of Linear
Directory of Open Access Journals (Sweden)
DJAIRO G. DEFIGUEIREDO
2000-12-01
Full Text Available In this paper we treat the question of the existence of solutions of boundary value problems for systems of nonlinear elliptic equations of the form - deltau = f (x, u, v,Ñu,Ñv, - deltav = g(x, u, v, Ñu, Ñv, in omega, We discuss several classes of such systems using both variational and topological methods. The notion of criticality takes into consideration the coupling, which plays important roles in both a priori estimates for the solutions and Palais-Smale conditions for the associated functional in the variational case.
Global Analysis of Nonlinear Dynamics
Luo, Albert
2012-01-01
Global Analysis of Nonlinear Dynamics collects chapters on recent developments in global analysis of non-linear dynamical systems with a particular emphasis on cell mapping methods developed by Professor C.S. Hsu of the University of California, Berkeley. This collection of contributions prepared by a diverse group of internationally recognized researchers is intended to stimulate interests in global analysis of complex and high-dimensional nonlinear dynamical systems, whose global properties are largely unexplored at this time. This book also: Presents recent developments in global analysis of non-linear dynamical systems Provides in-depth considerations and extensions of cell mapping methods Adopts an inclusive style accessible to non-specialists and graduate students Global Analysis of Nonlinear Dynamics is an ideal reference for the community of nonlinear dynamics in different disciplines including engineering, applied mathematics, meteorology, life science, computational science, and medicine.
Nonlinear evolution of drift instabilities
Energy Technology Data Exchange (ETDEWEB)
Lee, W.W.; Krommes, J.A.; Oberman, C.R.; Smith, R.A.
1984-01-01
The nonlinear evolution of collisionless drift instabilities in a shear-free magnetic field has been studied by means of gyrokinetic particle simulation as well as numerical integration of model mode-coupling equations. The purpose of the investigation is to identify relevant nonlinear mechanisms responsible for the steady-state drift wave fluctuations. It is found that the saturation of the instability is mainly caused by the nonlinear E x B convection of the resonant electrons and their associated velocity space nonlinearity. The latter also induces energy exchange between the competing modes, which, in turn, gives rise to enhanced diffusion. The nonlinear E x B convection of the ions, which contributes to the nonlinear frequency shift, is also an important ingredient for the saturation.
Rashidian Vaziri, Mohammad Reza
2013-07-10
In this paper, the Z-scan theory for nonlocal nonlinear media has been further developed when nonlinear absorption and nonlinear refraction appear simultaneously. To this end, the nonlinear photoinduced phase shift between the impinging and outgoing Gaussian beams from a nonlocal nonlinear sample has been generalized. It is shown that this kind of phase shift will reduce correctly to its known counterpart for the case of pure refractive nonlinearity. Using this generalized form of phase shift, the basic formulas for closed- and open-aperture beam transmittances in the far field have been provided, and a simple procedure for interpreting the Z-scan results has been proposed. In this procedure, by separately performing open- and closed-aperture Z-scan experiments and using the represented relations for the far-field transmittances, one can measure the nonlinear absorption coefficient and nonlinear index of refraction as well as the order of nonlocality. Theoretically, it is shown that when the absorptive nonlinearity is present in addition to the refractive nonlinearity, the sample nonlocal response can noticeably suppress the peak and enhance the valley of the Z-scan closed-aperture transmittance curves, which is due to the nonlocal action's ability to change the beam transverse dimensions.
Topics on nonlinear generalized functions
Colombeau, J F
2011-01-01
The aim of this paper is to give the text of a recent introduction to nonlinear generalized functions exposed in my talk in the congress gf2011, which was asked by several participants. Three representative topics were presented: two recalls "Nonlinear generalized functions and their connections with distribution theory", "Examples of applications", and a recent development: "Locally convex topologies and compactness: a functional analysis of nonlinear generalized functions".
Nonlinear Ultrasonic Phased Array Imaging
Potter, J. N.; Croxford, A. J.; Wilcox, P. D.
2014-10-01
This Letter reports a technique for the imaging of acoustic nonlinearity. By contrasting the energy of the diffuse field produced through the focusing of an ultrasonic array by delayed parallel element transmission with that produced by postprocessing of sequential transmission data, acoustic nonlinearity local to the focal point is measured. Spatially isolated wave distortion is inferred without requiring interrogation of the wave at the inspection point, thereby allowing nonlinear imaging through depth.
Nonlinear ultrasonic phased array imaging
Potter, J N; Croxford, A.J.; Wilcox, P. D.
2014-01-01
This Letter reports a technique for the imaging of acoustic nonlinearity. By contrasting the energy of the diffuse field produced through the focusing of an ultrasonic array by delayed parallel element transmission with that produced by postprocessing of sequential transmission data, acoustic nonlinearity local to the focal point is measured. Spatially isolated wave distortion is inferred without requiring interrogation of the wave at the inspection point, thereby allowing nonlinear imaging t...
Research on Nonlinear Dynamical Systems.
1983-01-10
investigated fundamental aspects of functional differential equations, including qualitative questions (stability, nonlinear oscillations ), in 142,45,47,52...Bifurcation in the Duffing equation with several parameters, II. Proc. of the Royal Society of Edinburgh, Series A, 79A (1977), pp.317-326. 1I.J (with ;Ibtoas...Lecture Notes in Mathematics, Vol. 730 (1979). [54] Nonlinear oscillations in equations with delays. Proc. at A.M.S. 10th Summer Seminar on Nonlinear
Nonlinear ultrasonic phased array imaging.
Potter, J N; Croxford, A J; Wilcox, P D
2014-10-03
This Letter reports a technique for the imaging of acoustic nonlinearity. By contrasting the energy of the diffuse field produced through the focusing of an ultrasonic array by delayed parallel element transmission with that produced by postprocessing of sequential transmission data, acoustic nonlinearity local to the focal point is measured. Spatially isolated wave distortion is inferred without requiring interrogation of the wave at the inspection point, thereby allowing nonlinear imaging through depth.
Remote Atmospheric Nonlinear Optical Magnetometry
2014-04-28
Boyd , Nonlinear Optics (Elsevier, Burlington, MA, 2008). [13] M. Scully and S. Zubairy, Quantum Optics (Cambridge U. Press, Cambridge, UK, 1997...Naval Research Laboratory Washington, DC 20375-5320 NRL/MR/6703--14-9548 Remote Atmospheric Nonlinear Optical Magnetometry PhilliP SPrangle...b. ABSTRACT c. THIS PAGE 18. NUMBER OF PAGES 17. LIMITATION OF ABSTRACT Remote Atmospheric Nonlinear Optical Magnetometry Phillip Sprangle, Luke
Applications of nonlinear fiber optics
Agrawal, Govind
2008-01-01
* The only book describing applications of nonlinear fiber optics * Two new chapters on the latest developments: highly nonlinear fibers and quantum applications* Coverage of biomedical applications* Problems provided at the end of each chapterThe development of new highly nonlinear fibers - referred to as microstructured fibers, holey fibers and photonic crystal fibers - is the next generation technology for all-optical signal processing and biomedical applications. This new edition has been thoroughly updated to incorporate these key technology developments.The bo
Linearization of conservative nonlinear oscillators
Energy Technology Data Exchange (ETDEWEB)
Belendez, A; Alvarez, M L [Departamento de Fisica, IngenierIa de Sistemas y TeorIa de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Fernandez, E; Pascual, I [Departamento de Optica, FarmacologIa y AnatomIa, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)], E-mail: a.belendez@ua.es
2009-03-11
A linearization method of the nonlinear differential equation for conservative nonlinear oscillators is analysed and discussed. This scheme is based on the Chebyshev series expansion of the restoring force which allows us to obtain a frequency-amplitude relation which is valid not only for small but also for large amplitudes and, sometimes, for the complete range of oscillation amplitudes. Some conservative nonlinear oscillators are analysed to illustrate the usefulness and effectiveness of the technique.
Problems in nonlinear resistive MHD
Energy Technology Data Exchange (ETDEWEB)
Turnbull, A.D.; Strait, E.J.; La Haye, R.J.; Chu, M.S.; Miller, R.L. [General Atomics, San Diego, CA (United States)
1998-12-31
Two experimentally relevant problems can relatively easily be tackled by nonlinear MHD codes. Both problems require plasma rotation in addition to the nonlinear mode coupling and full geometry already incorporated into the codes, but no additional physics seems to be crucial. These problems discussed here are: (1) nonlinear coupling and interaction of multiple MHD modes near the B limit and (2) nonlinear coupling of the m/n = 1/1 sawtooth mode with higher n gongs and development of seed islands outside q = 1.
Asymptotics for dissipative nonlinear equations
Hayashi, Nakao; Kaikina, Elena I; Shishmarev, Ilya A
2006-01-01
Many of problems of the natural sciences lead to nonlinear partial differential equations. However, only a few of them have succeeded in being solved explicitly. Therefore different methods of qualitative analysis such as the asymptotic methods play a very important role. This is the first book in the world literature giving a systematic development of a general asymptotic theory for nonlinear partial differential equations with dissipation. Many typical well-known equations are considered as examples, such as: nonlinear heat equation, KdVB equation, nonlinear damped wave equation, Landau-Ginzburg equation, Sobolev type equations, systems of equations of Boussinesq, Navier-Stokes and others.
Focus issue introduction: nonlinear optics.
Boulanger, Benoît; Cundiff, Steven T; Gauthier, Daniel J; Karlsson, Magnus; Lu, Yan-Qing; Norwood, Robert A; Skryabin, Dmitry; Taira, Takunori
2011-11-07
It is now fifty years since the original observation of second harmonic generation ushered in the field of nonlinear optics, close on the heels of the invention of the laser. This feature issue celebrates this anniversary with papers that span the range from new nonlinear optical materials, through the increasingly novel methods that have been developed for phase matching, to emerging areas such as nonlinear metamaterials and plasmonic enhancement of optical properties. It is clear that the next fifty years of nonlinear optics will witness a proliferation of new applications with increasing technological impact.
Nonlocal homogenization for nonlinear metamaterials
Gorlach, Maxim A; Lapine, Mikhail; Kivshar, Yuri S; Belov, Pavel A
2016-01-01
We present a consistent theoretical approach for calculating effective nonlinear susceptibilities of metamaterials taking into account both frequency and spatial dispersion. Employing the discrete dipole model, we demonstrate that effects of spatial dispersion become especially pronounced in the vicinity of effective permittivity resonance where nonlinear susceptibilities reach their maxima. In that case spatial dispersion may enable simultaneous generation of two harmonic signals with the same frequency and polarization but different wave vectors. We also prove that the derived expressions for nonlinear susceptibilities transform into the known form when spatial dispersion effects are negligible. In addition to revealing new physical phenomena, our results provide useful theoretical tools for analysing resonant nonlinear metamaterials.
Nonlinear Peltier effect in semiconductors
Zebarjadi, Mona; Esfarjani, Keivan; Shakouri, Ali
2007-09-01
Nonlinear Peltier coefficient of a doped InGaAs semiconductor is calculated numerically using the Monte Carlo technique. The Peltier coefficient is also obtained analytically for single parabolic band semiconductors assuming a shifted Fermi-Dirac electronic distribution under an applied bias. Analytical results are in agreement with numerical simulations. Key material parameters affecting the nonlinear behavior are doping concentration, effective mass, and electron-phonon coupling. Current density thresholds at which nonlinear behavior is observable are extracted from numerical data. It is shown that the nonlinear Peltier effect can be used to enhance cooling of thin film microrefrigerator devices especially at low temperatures.
Nonlinearities in Behavioral Macroeconomics.
Gomes, Orlando
2017-07-01
This article undertakes a journey across the literature on behavioral macroeconomics, with attention concentrated on the nonlinearities that the behavioral approach typically suggests or implies. The emphasis is placed on thinking the macro economy as a living organism, composed of many interacting parts, each one having a will of its own, which is in sharp contrast with the mechanism of the orthodox view (well represented by the neoclassical or new Keynesian dynamic stochastic general equilibrium - DSGE - model). The paper advocates that a thorough understanding of individual behavior in collective contexts is the only possible avenue to further explore macroeconomic phenomena and the often observed 'anomalies' that the benchmark DSGE macro framework is unable to explain or justify. After a reflection on the role of behavioral traits as a fundamental component of a new way of thinking the economy, the article proceeds with a debate on some of the most relevant frameworks in the literature that somehow link macro behavior and nonlinearities; covered subjects include macro models with disequilibrium rules, agent-based models that highlight interaction and complexity, evolutionary switching frameworks, and inattention based decision problems. These subjects have, as a fundamental point in common, the use of behavioral elements to transform existing interpretations of the economic reality, making it more evident how irregular fluctuations emerge and unfold on the aggregate.
Improved nonlinear prediction method
Adenan, Nur Hamiza; Md Noorani, Mohd Salmi
2014-06-01
The analysis and prediction of time series data have been addressed by researchers. Many techniques have been developed to be applied in various areas, such as weather forecasting, financial markets and hydrological phenomena involving data that are contaminated by noise. Therefore, various techniques to improve the method have been introduced to analyze and predict time series data. In respect of the importance of analysis and the accuracy of the prediction result, a study was undertaken to test the effectiveness of the improved nonlinear prediction method for data that contain noise. The improved nonlinear prediction method involves the formation of composite serial data based on the successive differences of the time series. Then, the phase space reconstruction was performed on the composite data (one-dimensional) to reconstruct a number of space dimensions. Finally the local linear approximation method was employed to make a prediction based on the phase space. This improved method was tested with data series Logistics that contain 0%, 5%, 10%, 20% and 30% of noise. The results show that by using the improved method, the predictions were found to be in close agreement with the observed ones. The correlation coefficient was close to one when the improved method was applied on data with up to 10% noise. Thus, an improvement to analyze data with noise without involving any noise reduction method was introduced to predict the time series data.
Institute of Scientific and Technical Information of China (English)
马戈; 石东洋
2010-01-01
将各向异性三角形非协调类Carey元应用于二维空间中的双曲积分微分方程,在不引入广义椭圆投影的情况下,通过一些新技巧,获得解的超逼近性质和整体超收敛结果.
Nonlinear Response of Strong Nonlinear System Arisen in Polymer Cushion
Directory of Open Access Journals (Sweden)
Jun Wang
2013-01-01
Full Text Available A dynamic model is proposed for a polymer foam-based nonlinear cushioning system. An accurate analytical solution for the nonlinear free vibration of the system is derived by applying He's variational iteration method, and conditions for resonance are obtained, which should be avoided in the cushioning design.
A Fredholm Determinant for Semi-classical Quantization
Cvitanovic, P; Vattay, G; Rugh, H H; Cvitanovi\\'c, Predrag; Rosenqvist, Per E.; Rugh, Hans Henrik
1993-01-01
We investigate a new type of approximation to quantum determinants, the ``\\qFd", and test numerically the conjecture that for Axiom A hyperbolic flows such determinants have a larger domain of analyticity and better convergence than the \\qS s derived from the \\Gt. The conjecture is supported by numerical investigations of the 3-disk repeller, a normal-form model of a flow, and a model 2-$d$ map.
Nonlinear Evolution of Ferroelectric Domains
Institute of Scientific and Technical Information of China (English)
WeiLU; Dai－NingFANG; 等
1997-01-01
The nonlinear evolution of ferroelectric domains is investigated in the paper and amodel is proposed which can be applied to numerical computation.Numerical results show that the model can accurately predict some nonlinear behavior and consist with those experimental results.
Nonlinear Electrodynamics and black holes
Breton, N; Breton, Nora; Garcia-Salcedo, Ricardo
2007-01-01
It is addressed the issue of black holes with nonlinear electromagnetic field, focussing mainly in the Born-Infeld case. The main features of these systems are described, for instance, geodesics, energy conditions, thermodynamics and isolated horizon aspects. Also are revised some black hole solutions of alternative nonlinear electrodynamics and its inconveniences.
Space curves, anholonomy and nonlinearity
Indian Academy of Sciences (India)
Radha Balakrishnan
2005-04-01
Using classical differential geometry, we discuss the phenomenon of anholonomy that gets associated with a static and a moving curve. We obtain the expressions for the respective geometric phases in the two cases and interpret them. We show that there is a close connection between anholonomy and nonlinearity in a wide class of nonlinear systems.
Balancing for unstable nonlinear systems
Scherpen, J.M.A.
1993-01-01
A previously obtained method of balancing for stable nonlinear systems is extended to unstable nonlinear systems. The similarity invariants obtained by the concept of LQG balancing for an unstable linear system can also be obtained by considering a past and future energy function of the system. By c
Nonlinear diffusion and superconducting hysteresis
Energy Technology Data Exchange (ETDEWEB)
Mayergoyz, I.D. [Univ. of Maryland, College Park, MD (United States)
1996-12-31
Nonlinear diffusion of electromagnetic fields in superconductors with ideal and gradual resistive transitions is studied. Analytical results obtained for linear and nonlinear polarizations of electromagnetic fields are reported. These results lead to various extensions of the critical state model for superconducting hysteresis.
Energy Technology Data Exchange (ETDEWEB)
Lallart, Mickael; Guyomar, Daniel, E-mail: mickael.lallart@insa-lyon.fr [LGEF, INSA-Lyon, Universite de Lyon, 8 rue de la Physique, F-69621 (France)
2011-10-29
The proliferation of wearable and left-behind devices has raised the issue of powering such systems. While primary batteries have been widely used in order to address this issue, recent trends have focused on energy harvesting products that feature high reliability and low maintenance issues. Among all the ambient sources available for energy harvesting, vibrations and heat have been of significant interest among the research community for small-scale devices. However, the conversion abilities of materials are still limited when dealing with systems featuring small dimensions. The purpose of this paper is to presents an up-to-date view of nonlinear approaches for increasing the efficiency of electromechanical and electrocaloric conversion mechanisms. From the modeling of the operation principles of the different architectures, a comparative analysis will be exposed, emphasizing the advantages and drawbacks of the presented concepts, in terms of maximal output power (under constant vibration magnitude or taking into account the damping effect), load independence, and implementation easiness.
Fainberg, B D
2015-01-01
Purely organic materials with negative and near-zero dielectric permittivity can be easily fabricated. Here we develop a theory of nonlinear non-steady-state organic plasmonics with strong laser pulses. The bistability response of the electron-vibrational model of organic materials in the condensed phase has been demonstrated. Non-steady-state organic plasmonics enable us to obtain near-zero dielectric permittivity during a short time. We have proposed to use non-steady-state organic plasmonics for the enhancement of intersite dipolar energy-transfer interaction in the quantum dot wire that influences on electron transport through nanojunctions. Such interactions can compensate Coulomb repulsions for particular conditions. We propose the exciton control of Coulomb blocking in the quantum dot wire based on the non-steady-state near-zero dielectric permittivity of the organic host medium.
2016-01-01
This volume brings together four lecture courses on modern aspects of water waves. The intention, through the lectures, is to present quite a range of mathematical ideas, primarily to show what is possible and what, currently, is of particular interest. Water waves of large amplitude can only be fully understood in terms of nonlinear effects, linear theory being not adequate for their description. Taking advantage of insights from physical observation, experimental evidence and numerical simulations, classical and modern mathematical approaches can be used to gain insight into their dynamics. The book presents several avenues and offers a wide range of material of current interest. Due to the interdisciplinary nature of the subject, the book should be of interest to mathematicians (pure and applied), physicists and engineers. The lectures provide a useful source for those who want to begin to investigate how mathematics can be used to improve our understanding of water wave phenomena. In addition, some of the...
Nonlinear estimation and classification
Hansen, Mark; Holmes, Christopher; Mallick, Bani; Yu, Bin
2003-01-01
Researchers in many disciplines face the formidable task of analyzing massive amounts of high-dimensional and highly-structured data This is due in part to recent advances in data collection and computing technologies As a result, fundamental statistical research is being undertaken in a variety of different fields Driven by the complexity of these new problems, and fueled by the explosion of available computer power, highly adaptive, non-linear procedures are now essential components of modern "data analysis," a term that we liberally interpret to include speech and pattern recognition, classification, data compression and signal processing The development of new, flexible methods combines advances from many sources, including approximation theory, numerical analysis, machine learning, signal processing and statistics The proposed workshop intends to bring together eminent experts from these fields in order to exchange ideas and forge directions for the future
Nonlinear transmission sputtering
Bitensky, I. S.; Sigmund, P.
1996-05-01
General expressions have been derived for the nonlinear yield of transmission sputtering for an incident polyatomic ion under the assumption that the molecule breaks up on entering the target and that sputter yields are enhanced due to proximity of atomic trajectories. Special attention is given to the case of negligible Coulomb explosion where projectile atoms penetrate independently. For weakly overlapping trajectories, the yield enhancement factor of a polyatomic molecule can be expressed by that of a diatom, amended with a correction for triple correlations if necessary. This expression is in good agreement with recent experimental findings on phenylalanine targets. Pertinent results on multiple scattering of atomic ions are reviewed and applied to independently-moving fragment atoms. The merits of measurements at variable layer thickness in addition to variable projectile energy are mentioned.
Perspectives on Nonlinear Filtering
Law, Kody
2015-01-07
The solution to the problem of nonlinear filtering may be given either as an estimate of the signal (and ideally some measure of concentration), or as a full posterior distribution. Similarly, one may evaluate the fidelity of the filter either by its ability to track the signal or its proximity to the posterior filtering distribution. Hence, the field enjoys a lively symbiosis between probability and control theory, and there are plenty of applications which benefit from algorithmic advances, from signal processing, to econometrics, to large-scale ocean, atmosphere, and climate modeling. This talk will survey some recent theoretical results involving accurate signal tracking with noise-free (degenerate) dynamics in high-dimensions (infinite, in principle, but say d between 103 and 108 , depending on the size of your application and your computer), and high-fidelity approximations of the filtering distribution in low dimensions (say d between 1 and several 10s).
Nonlinear rotordynamics analysis
Day, W. B.; Zalik, R. A.
1986-01-01
Three analytic consequences of the nonlinear Jeffcott equations are examined. The primary application of these analyses is directed toward understanding the excessive vibrations recorded in the Liquid Oxygen (LOX) pump of the Space Shuttle Main Engine (SSME) during hot firing ground testing. The first task is to provide bounds on the coefficients of the equations which delimit the two cases of numerical solution as a circle or an annulus. The second task examines the mathematical generalization to multiple forcing functions, which includes the special problems of mass imbalance, side force, rubbing, and combination of these forces. Finally, stability and boundedness of the steady-state solutions is discussed and related to the corresponding linear problem.
Nonlinearities in vegetation functioning
Ceballos-Núñez, Verónika; Müller, Markus; Metzler, Holger; Sierra, Carlos
2016-04-01
Given the current drastic changes in climate and atmospheric CO2 concentrations, and the role of vegetation in the global carbon cycle, there is increasing attention to the carbon allocation component in biosphere terrestrial models. Improving the representation of C allocation in models could be the key to having better predictions of the fate of C once it enters the vegetation and is partitioned to C pools of different residence times. C allocation has often been modeled using systems of ordinary differential equations, and it has been hypothesized that most models can be generalized with a specific form of a linear dynamical system. However, several studies have highlighted discrepancies between empirical observations and model predictions, attributing these differences to problems with model structure. Although efforts have been made to compare different models, the outcome of these qualitative assessments has been a conceptual categorization of them. In this contribution, we introduce a new effort to identify the main properties of groups of models by studying their mathematical structure. For this purpose, we performed a literature research of the relevant models of carbon allocation in vegetation and developed a database with their representation in symbolic mathematics. We used the Python package SymPy for symbolic mathematics as a common language and manipulated the models to calculate their Jacobian matrix at fixed points and their eigenvalues, among other mathematical analyses. Our preliminary results show a tendency of inverse proportionality between model complexity and size of time/space scale; complex interactions between the variables controlling carbon allocation in vegetation tend to operate at shorter time/space scales, and vice-versa. Most importantly, we found that although the linear structure is common, other structures with non-linearities have been also proposed. We, therefore, propose a new General Model that can accommodate these
Nonlinear field space cosmology
Mielczarek, Jakub; Trześniewski, Tomasz
2017-08-01
We consider the FRW cosmological model in which the matter content of the Universe (playing the role of an inflaton or quintessence) is given by a novel generalization of the massive scalar field. The latter is a scalar version of the recently introduced nonlinear field space theory, where the physical phase space of a given field is assumed to be compactified at large energies. For our analysis, we choose the simple case of a field with the spherical phase space and endow it with the generalized Hamiltonian analogous to the XXZ Heisenberg model, normally describing a system of spins in condensed matter physics. Subsequently, we study both the homogenous cosmological sector and linear perturbations of such a test field. In the homogenous sector, we find that nonlinearity of the field phase space is becoming relevant for large volumes of the Universe and can lead to a recollapse, and possibly also at very high energies, leading to the phase of a bounce. Quantization of the field is performed in the limit where the nontrivial nature of its phase space can be neglected, while there is a nonvanishing contribution from the Lorentz symmetry breaking term of the Hamiltonian. As a result, in the leading order of the XXZ anisotropy parameter, we find that the inflationary spectral index remains unmodified with respect to the standard case but the total amplitude of perturbations is subject to a correction. The Bunch-Davies vacuum state also becomes appropriately corrected. The proposed new approach is bringing cosmology and condensed matter physics closer together, which may turn out to be beneficial for both disciplines.
NONLINEAR STABILITY FOR EADY'S MODEL
Institute of Scientific and Technical Information of China (English)
LIU Yong-ming; QIU Ling-cun
2005-01-01
Poincaré type integral inequality plays an important role in the study of nonlinear stability ( in the sense of Arnold's second theorem) for three-dimensional quasigeostophic flow. The nonlinear stability of Eady's model is one of the most important cases in the application of the method. But the best nonlinear stability criterion obtained so far and the linear stability criterion are not coincident. The two criteria coincide only when the period of the channel is infinite.additional conservation law of momentum and by rigorous estimate of integral inequality. So the new nonlinear stability criterion was obtained, which shows that for Eady 's model in the periodic channel, the linear stable implies the nonlinear stable.
Nonlinear Waves in Complex Systems
DEFF Research Database (Denmark)
2007-01-01
The study of nonlinear waves has exploded due to the combination of analysis and computations, since the discovery of the famous recurrence phenomenon on a chain of nonlinearly coupled oscillators by Fermi-Pasta-Ulam fifty years ago. More than the discovery of new integrable equations, it is the ......The study of nonlinear waves has exploded due to the combination of analysis and computations, since the discovery of the famous recurrence phenomenon on a chain of nonlinearly coupled oscillators by Fermi-Pasta-Ulam fifty years ago. More than the discovery of new integrable equations......, it is the universality and robustness of the main models with respect to perturbations that developped the field. This is true for both continuous and discrete equations. In this volume we keep this broad view and draw new perspectives for nonlinear waves in complex systems. In particular we address energy flow...
Terahertz Nonlinearity in Graphene Plasmons
Jadidi, Mohammad M; Winnerl, Stephan; Sushkov, Andrei B; Drew, H Dennis; Murphy, Thomas E; Mittendorff, Martin
2015-01-01
Sub-wavelength graphene structures support localized plasmonic resonances in the terahertz and mid-infrared spectral regimes. The strong field confinement at the resonant frequency is predicted to significantly enhance the light-graphene interaction, which could enable nonlinear optics at low intensity in atomically thin, sub-wavelength devices. To date, the nonlinear response of graphene plasmons and their energy loss dynamics have not been experimentally studied. We measure and theoretically model the terahertz nonlinear response and energy relaxation dynamics of plasmons in graphene nanoribbons. We employ a THz pump-THz probe technique at the plasmon frequency and observe a strong saturation of plasmon absorption followed by a 10 ps relaxation time. The observed nonlinearity is enhanced by two orders of magnitude compared to unpatterned graphene with no plasmon resonance. We further present a thermal model for the nonlinear plasmonic absorption that supports the experimental results.
Fast Numerical Nonlinear Fourier Transforms
Wahls, Sander
2014-01-01
The nonlinear Fourier transform, which is also known as the forward scattering transform, decomposes a periodic signal into nonlinearly interacting waves. In contrast to the common Fourier transform, these waves no longer have to be sinusoidal. Physically relevant waveforms are often available for the analysis instead. The details of the transform depend on the waveforms underlying the analysis, which in turn are specified through the implicit assumption that the signal is governed by a certain evolution equation. For example, water waves generated by the Korteweg-de Vries equation can be expressed in terms of cnoidal waves. Light waves in optical fiber governed by the nonlinear Schr\\"dinger equation (NSE) are another example. Nonlinear analogs of classic problems such as spectral analysis and filtering arise in many applications, with information transmission in optical fiber, as proposed by Yousefi and Kschischang, being a very recent one. The nonlinear Fourier transform is eminently suited to address them ...
Properties of Nonlinear Dynamo Waves
Tobias, S. M.
1997-01-01
Dynamo theory offers the most promising explanation of the generation of the sun's magnetic cycle. Mean field electrodynamics has provided the platform for linear and nonlinear models of solar dynamos. However, the nonlinearities included are (necessarily) arbitrarily imposed in these models. This paper conducts a systematic survey of the role of nonlinearities in the dynamo process, by considering the behaviour of dynamo waves in the nonlinear regime. It is demonstrated that only by considering realistic nonlinearities that are non-local in space and time can modulation of the basic dynamo wave he achieved. Moreover, this modulation is greatest when there is a large separation of timescales provided by including a low magnetic Prandtl number in the equation for the velocity perturbations.
Cubication of conservative nonlinear oscillators
Energy Technology Data Exchange (ETDEWEB)
Belendez, Augusto; Alvarez, Mariela L [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Fernandez, Elena; Pascual, Inmaculada [Departamento de Optica, FarmacologIa y Anatomia, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)], E-mail: a.belendez@ua.es
2009-09-15
A cubication procedure of the nonlinear differential equation for conservative nonlinear oscillators is analysed and discussed. This scheme is based on the Chebyshev series expansion of the restoring force, and this allows us to approximate the original nonlinear differential equation by a Duffing equation in which the coefficients for the linear and cubic terms depend on the initial amplitude, A, while in a Taylor expansion of the restoring force these coefficients are independent of A. The replacement of the original nonlinear equation by an approximate Duffing equation allows us to obtain an approximate frequency-amplitude relation as a function of the complete elliptic integral of the first kind. Some conservative nonlinear oscillators are analysed to illustrate the usefulness and effectiveness of this scheme.
Nonlinear Oscillators in Space Physics
Lester,Daniel; Thronson, Harley
2011-01-01
We discuss dynamical systems that produce an oscillation without an external time dependent source. Numerical results are presented for nonlinear oscillators in the Em1h's atmosphere, foremost the quasi-biennial oscillation (QBOl. These fluid dynamical oscillators, like the solar dynamo, have in common that one of the variables in a governing equation is strongly nonlinear and that the nonlinearity, to first order, has particular form. of 3rd or odd power. It is shown that this form of nonlinearity can produce the fundamental li'equency of the internal oscillation. which has a period that is favored by the dynamical condition of the fluid. The fundamental frequency maintains the oscillation, with no energy input to the system at that particular frequency. Nonlinearities of 2nd or even power could not maintain the oscillation.
Asymptotic expansions in nonlinear rotordynamics
Day, William B.
1987-01-01
This paper is an examination of special nonlinearities of the Jeffcott equations in rotordynamics. The immediate application of this analysis is directed toward understanding the excessive vibrations recorded in the LOX pump of the SSME during hot-firing ground testing. Deadband, side force, and rubbing are three possible sources of inducing nonlinearity in the Jeffcott equations. The present analysis initially reduces these problems to the same mathematical description. A special frequency, named the nonlinear natural frequency, is defined and used to develop the solutions of the nonlinear Jeffcott equations as singular asymptotic expansions. This nonlinear natural frequency, which is the ratio of the cross-stiffness and the damping, plays a major role in determining response frequencies.
Nonlinear hyperbolic waves in multidimensions
Prasad, Phoolan
2001-01-01
The propagation of curved, nonlinear wavefronts and shock fronts are very complex phenomena. Since the 1993 publication of his work Propagation of a Curved Shock and Nonlinear Ray Theory, author Phoolan Prasad and his research group have made significant advances in the underlying theory of these phenomena. This volume presents their results and provides a self-contained account and gradual development of mathematical methods for studying successive positions of these fronts.Nonlinear Hyperbolic Waves in Multidimensions includes all introductory material on nonlinear hyperbolic waves and the theory of shock waves. The author derives the ray theory for a nonlinear wavefront, discusses kink phenomena, and develops a new theory for plane and curved shock propagation. He also derives a full set of conservation laws for a front propagating in two space dimensions, and uses these laws to obtain successive positions of a front with kinks. The treatment includes examples of the theory applied to converging wavefronts...
Analysis of Nonlinear Electromagnetic Metamaterials
Poutrina, Ekaterina; Smith, David R
2010-01-01
We analyze the properties of a nonlinear metamaterial formed by integrating nonlinear components or materials into the capacitive regions of metamaterial elements. A straightforward homogenization procedure leads to general expressions for the nonlinear susceptibilities of the composite metamaterial medium. The expressions are convenient, as they enable inhomogeneous system of scattering elements to be described as a continuous medium using the standard notation of nonlinear optics. We illustrate the validity and accuracy of our theoretical framework by performing measurements on a fabricated metamaterial sample composed of an array of split ring resonators (SRRs) with packaged varactors embedded in the capacitive gaps in a manner similar to that of Wang et al. [Opt. Express 16, 16058 (2008)]. Because the SRRs exhibit a predominant magnetic response to electromagnetic fields, the varactor-loaded SRR composite can be described as a magnetic material with nonlinear terms in its effective magnetic susceptibility...
The Nonlinear Analytical Envelope Equation in quadratic nonlinear crystals
Bache, Morten
2016-01-01
We here derive the so-called Nonlinear Analytical Envelope Equation (NAEE) inspired by the work of Conforti et al. [M. Conforti, A. Marini, T. X. Tran, D. Faccio, and F. Biancalana, "Interaction between optical fields and their conjugates in nonlinear media," Opt. Express 21, 31239-31252 (2013)], whose notation we follow. We present a complete model that includes $\\chi^{(2)}$ terms [M. Conforti, F. Baronio, and C. De Angelis, "Nonlinear envelope equation for broadband optical pulses in quadratic media," Phys. Rev. A 81, 053841 (2010)], $\\chi^{(3)}$ terms, and then extend the model to delayed Raman effects in the $\\chi^{(3)}$ term. We therefore get a complete model for ultrafast pulse propagation in quadratic nonlinear crystals similar to the Nonlinear Wave Equation in Frequency domain [H. Guo, X. Zeng, B. Zhou, and M. Bache, "Nonlinear wave equation in frequency domain: accurate modeling of ultrafast interaction in anisotropic nonlinear media," J. Opt. Soc. Am. B 30, 494-504 (2013)], but where the envelope is...
Breatherlike impurity modes in discrete nonlinear lattices
DEFF Research Database (Denmark)
Hennig, D.; Rasmussen, Kim; Tsironis, G. P.
1995-01-01
We investigate the properties of a disordered generalized discrete nonlinear Schrodinger equation, containing both diagonal and nondiagonal nonlinear terms. The equation models a Linear host lattice doped with nonlinear impurities. We find different types of impurity states that form itinerant...
Spatial solitons in nonlinear photonic crystals
DEFF Research Database (Denmark)
Corney, Joel Frederick; Bang, Ole
2000-01-01
We study solitons in one-dimensional quadratic nonlinear photonic crystals with periodic linear and nonlinear susceptibilities. We show that such crystals support stable bright and dark solitons, even when the effective quadratic nonlinearity is zero.......We study solitons in one-dimensional quadratic nonlinear photonic crystals with periodic linear and nonlinear susceptibilities. We show that such crystals support stable bright and dark solitons, even when the effective quadratic nonlinearity is zero....
Resource Letter NO-1: Nonlinear Optics
Garmire, Elsa
2011-03-01
This Resource Letter provides a guide to the literature on nonlinear optics. Books, journals, and websites are introduced that cover the general subject. Journal articles and websites are cited covering the following topics: second-order nonlinearities in transparent media including second-harmonic generation and optical parametric oscillation, third-order and higher nonlinearities, nonlinear refractive index, absorptive nonlinearities such as saturable absorption and multiphoton absorption, and scattering nonlinearities such as stimulated Raman scattering and stimulated Brillouin scattering. Steady-state and transient phenomena, fiber optics, solitons, nonlinear wave mixing, optical phase conjugation, nonlinear spectroscopy, and multiphoton microscopy are all outlined.
Neurodynamics: nonlinear dynamics and neurobiology.
Abarbanel, H D; Rabinovich, M I
2001-08-01
The use of methods from contemporary nonlinear dynamics in studying neurobiology has been rather limited.Yet, nonlinear dynamics has become a practical tool for analyzing data and verifying models. This has led to productive coupling of nonlinear dynamics with experiments in neurobiology in which the neural circuits are forced with constant stimuli, with slowly varying stimuli, with periodic stimuli, and with more complex information-bearing stimuli. Analysis of these more complex stimuli of neural circuits goes to the heart of how one is to understand the encoding and transmission of information by nervous systems.
Dissipative Nonlinear Dynamics in Holography
Basu, Pallab
2013-01-01
We look at the response of a nonlinearly coupled scalar field in an asymptotically AdS black brane geometry and find a behaviour very similar to that of known dissipative nonlinear systems like the chaotic pendulum. Transition to chaos proceeds through a series of period-doubling bifurcations. The presence of dissipation, crucial to this behaviour, arises naturally in a black hole background from the ingoing conditions imposed at the horizon. AdS/CFT translates our solution to a chaotic response of the operator dual to the scalar field. Our setup can also be used to study quench-like behaviour in strongly coupled nonlinear systems.
Acoustic-gravity nonlinear structures
Directory of Open Access Journals (Sweden)
D. Jovanović
2002-01-01
Full Text Available A catalogue of nonlinear vortex structures associated with acoustic-gravity perturbations in the Earth's atmosphere is presented. Besides the previously known Kelvin-Stewart cat's eyes, dipolar and tripolar structures, new solutions having the form of a row of counter-rotating vortices, and several weakly two-dimensional vortex chains are given. The existence conditions for these nonlinear structures are discussed with respect to the presence of inhomogeneities of the shear flows. The mode-coupling mechanism for the nonlinear generation of shear flows in the presence of linearly unstable acoustic-gravity waves, possibly also leading to intermittency and chaos, is presented.
Nonlinear effects in Thomson backscattering
Maroli, C.; Petrillo, V.; Tomassini, P.; Serafini, L.
2013-03-01
We analyze the nonlinear classical effects of the X/γ radiation produced by Thomson/Compton sources. We confirm the development of spectral fringes of the radiation on axis, which comports broadening, shift, and deformation of the spectrum. For the nominal parameters of the SPARC-LAB Thomson scattering and of the European Proposal for the gamma source ELI-NP, however, the radiation, when collected in the suitable acceptance angle, does not reveal many differences from that predicted by the linear model and the nonlinear redshift is subdominant with respect to the quantum recoil. An experiment aimed to the study of the nonlinearities is proposed on the SPARC-LAB source.
Nonlinear Dynamic Phenomena in Mechanics
Warminski, Jerzy; Cartmell, Matthew P
2012-01-01
Nonlinear phenomena should play a crucial role in the design and control of engineering systems and structures as they can drastically change the prevailing dynamical responses. This book covers theoretical and applications-based problems of nonlinear dynamics concerned with both discrete and continuous systems of interest in civil and mechanical engineering. They include pendulum-like systems, slender footbridges, shape memory alloys, sagged elastic cables and non-smooth problems. Pendulums can be used as a dynamic absorber mounted in high buildings, bridges or chimneys. Geometrical nonlinear
Nonlinear Optics: Principles and Applications
DEFF Research Database (Denmark)
Rottwitt, Karsten; Tidemand-Lichtenberg, Peter
As nonlinear optics further develops as a field of research in electromagnetic wave propagation, its state-of-the-art technologies will continue to strongly impact real-world applications in a variety of fields useful to the practicing scientist and engineer. From basic principles to examples...... of applications, Nonlinear Optics: Principles and Applications effectively bridges physics and mathematics with relevant applied material for real-world use. The book progresses naturally from fundamental aspects to illustrative examples, and presents a strong theoretical foundation that equips the reader...... and matter, this text focuses on the physical understanding of nonlinear optics, and explores optical material response functions in the time and frequency domain....
Oscillating solitons in nonlinear optics
Indian Academy of Sciences (India)
Lin Xiao-Gang; Liu Wen-Jun; Lei Ming
2016-03-01
Oscillating solitons are obtained in nonlinear optics. Analytical study of the variable coefficient nonlinear Schrödinger equation, which is used to describe the soliton propagation in those systems, is carried out using the Hirota’s bilinear method. The bilinear forms and analytic soliton solutions are derived, and the relevant properties and features of oscillating solitons are illustrated. Oscillating solitons are controlled by the reciprocal of the group velocity and Kerr nonlinearity. Results of this paper will be valuable to the study of dispersion-managed optical communication system and mode-locked fibre lasers.
Nonlinear dynamics: Challenges and perspectives
Indian Academy of Sciences (India)
M Lakshmanan
2005-04-01
The study of nonlinear dynamics has been an active area of research since 1960s, after certain path-breaking discoveries, leading to the concepts of solitons, integrability, bifurcations, chaos and spatio-temporal patterns, to name a few. Several new techniques and methods have been developed to understand nonlinear systems at different levels. Along with these, a multitude of potential applications of nonlinear dynamics have also been enunciated. In spite of these developments, several challenges, some of them fundamental and others on the efficacy of these methods in developing cutting edge technologies, remain to be tackled. In this article, a brief personal perspective of these issues is presented.
Femtosecond nonlinear polarization evolution based on cascade quadratic nonlinearities.
Liu, X; Ilday, F O; Beckwitt, K; Wise, F W
2000-09-15
We experimentally demonstrate that one can exploit nonlinear phase shifts produced in type I phase-mismatched second-harmonic generation to produce intensity-dependent polarization evolution with 100-fs pulses. An amplitude modulator based on nonlinear polarization rotation provides passive amplitude-modulation depth of up to ~50%. Applications of the amplitude and phase modulations to mode locking of femtosecond bulk and fiber lasers are promising and are discussed.
Intrinsic nonlinear response of surface plasmon polaritons
Im, Song-Jin; Kim, Gum-Hyok
2015-01-01
We offer a model to describe the intrinsic nonlinear response of surface plasmon polaritons (SPPs). Relation of the complex nonlinear coefficient of SPPs to the third-order nonlinear susceptibility of the metal is provided. As reported in a recent study, gold is highly lossy and simultaneously highly nonlinear due to interband absorption and interband thermo-modulation at a wavelength shorter than 700 nm. The effect of the high loss of the metal on the SPP nonlinear propagation is taken into account in our model. With the model we show difference in sign of real and imaginary parts between the nonlinear propagation coefficient and the nonlinear susceptibility of component material for the first time to our knowledge. Our model could have practical importance in studying plasmonic devices utilizing the nonlinear phase modulation and the nonlinear absorption of SPPs. For example, it allows one to extract the complex nonlinear susceptibility of gold through a measurement of SPP nonlinear propagation at the visib...
Deimling, Klaus
1985-01-01
topics. However, only a modest preliminary knowledge is needed. In the first chapter, where we introduce an important topological concept, the so-called topological degree for continuous maps from subsets ofRn into Rn, you need not know anything about functional analysis. Starting with Chapter 2, where infinite dimensions first appear, one should be familiar with the essential step of consider ing a sequence or a function of some sort as a point in the corresponding vector space of all such sequences or functions, whenever this abstraction is worthwhile. One should also work out the things which are proved in § 7 and accept certain basic principles of linear functional analysis quoted there for easier references, until they are applied in later chapters. In other words, even the 'completely linear' sections which we have included for your convenience serve only as a vehicle for progress in nonlinearity. Another point that makes the text introductory is the use of an essentially uniform mathematical languag...
Meyer, George
1997-01-01
The paper describes a method for guiding a dynamic system through a given set of points. The paradigm is a fully automatic aircraft subject to air traffic control (ATC). The ATC provides a sequence of way points through which the aircraft trajectory must pass. The way points typically specify time, position, and velocity. The guidance problem is to synthesize a system state trajectory which satisfies both the ATC and aircraft constraints. Complications arise because the controlled process is multi-dimensional, multi-axis, nonlinear, highly coupled, and the state space is not flat. In addition, there is a multitude of possible operating modes, which may number in the hundreds. Each such mode defines a distinct state space model of the process by specifying the state space coordinatization, the partition of the controls into active controls and configuration controls, and the output map. Furthermore, mode transitions must be smooth. The guidance algorithm is based on the inversion of the pure feedback approximations, which is followed by iterative corrections for the effects of zero dynamics. The paper describes the structure and modules of the algorithm, and the performance is illustrated by several example aircraft maneuvers.
Whittam, A J
2001-01-01
susceptibility from 26 pm/V (same film without octadecanoic acid) to 40 pm/V. This increase in the second-order susceptibility occurred even though the amount of NLO-active dye was effectively diluted by the addition of the inactive octadecanoic acid. The wavelength of the absorption maximum ranged from 346-440 nm and there was direct correlation between the susceptibilities and the transparency of the films at the harmonic wavelength. Hemicyanine dyes were synthesised, with the general formulae: - (a) C sub 1 sub 8 H sub 3 sub 7 -A sup + -[CH=CH-C sub 6 H sub 4] sub x -N(CH sub 3) sub 2 I (b) C sub 1 sub 8 H sub 3 sub 7 -A sup + -[CH=CH] sub y -C sub 6 H sub 4 -N(CH sub 3) sub 2 I where A sup + is a pyridinium or isoquinolinium acceptor, and x = 1 or 2, and y = 1 or 2. The optically nonlinear dyes were investigated via the Langmuir-Blodgett (LB) technique. The dyes all produced isotherm data, with molecular areas of 22-60 A sup 2 per molecule, which are consistent with the cross-sectional areas of the chromo...
Nonlinear helical MHD instability
Energy Technology Data Exchange (ETDEWEB)
Zueva, N.M.; Solov' ev, L.S.
1977-07-01
An examination is made of the boundary problem on the development of MHD instability in a toroidal plasma. Two types of local helical instability are noted - Alfven and thermal, and the corresponding criteria of instability are cited. An evaluation is made of the maximum attainable kinetic energy, limited by the degree to which the law of conservation is fulfilled. An examination is made of a precise solution to a kinematic problem on the helical evolution of a cylindrical magnetic configuration at a given velocity distribution in a plasma. A numerical computation of the development of MHD instability in a plasma cylinder by a computerized solution of MHD equations is made where the process's helical symmetry is conserved. The development of instability is of a resonance nature. The instability involves the entire cross section of the plasma and leads to an inside-out reversal of the magnetic surfaces when there is a maximum unstable equilibrium configuration in the nonlinear stage. The examined instability in the tore is apparently stabilized by a magnetic hole when certain limitations are placed on the distribution of flows in the plasma. 29 references, 8 figures.
Design with Nonlinear Constraints
Tang, Chengcheng
2015-12-10
Most modern industrial and architectural designs need to satisfy the requirements of their targeted performance and respect the limitations of available fabrication technologies. At the same time, they should reflect the artistic considerations and personal taste of the designers, which cannot be simply formulated as optimization goals with single best solutions. This thesis aims at a general, flexible yet e cient computational framework for interactive creation, exploration and discovery of serviceable, constructible, and stylish designs. By formulating nonlinear engineering considerations as linear or quadratic expressions by introducing auxiliary variables, the constrained space could be e ciently accessed by the proposed algorithm Guided Projection, with the guidance of aesthetic formulations. The approach is introduced through applications in different scenarios, its effectiveness is demonstrated by examples that were difficult or even impossible to be computationally designed before. The first application is the design of meshes under both geometric and static constraints, including self-supporting polyhedral meshes that are not height fields. Then, with a formulation bridging mesh based and spline based representations, the application is extended to developable surfaces including origami with curved creases. Finally, general approaches to extend hard constraints and soft energies are discussed, followed by a concluding remark outlooking possible future studies.
Nonlinear plasmonics at high temperatures
Directory of Open Access Journals (Sweden)
Sivan Yonatan
2017-01-01
Full Text Available We solve the Maxwell and heat equations self-consistently for metal nanoparticles under intense continuous wave (CW illumination. Unlike previous studies, we rely on experimentally-measured data for metal permittivity for increasing temperature and for the visible spectral range. We show that the thermal nonlinearity of the metal can lead to substantial deviations from the predictions of the linear model for the temperature and field distribution and, thus, can explain qualitatively the strong nonlinear scattering from such configurations observed experimentally. We also show that the incompleteness of existing data of the temperature dependence of the thermal properties of the system prevents reaching a quantitative agreement between the measured and calculated scattering data. This modeling approach is essential for the identification of the underlying physical mechanism responsible for the thermo-optical nonlinearity of the metal and should be adopted in all applications of high-temperature nonlinear plasmonics, especially for refractory metals, for both CW and pulsed illumination.
Nonlinear optics and organic materials
Energy Technology Data Exchange (ETDEWEB)
Shen, Y.R.
1994-07-01
We shall consider an interesting topic relating nonlinear optics and organic materials: how nonlinear optics can be used to study organic materials. One of the main differences between linear and nonlinear responses of a medium to incoming radiation is in their symmetries. It leads to the possibility that some properties of the medium could be more sensitively probed by nonlinear, rather than linear, optical means, or vise versa. A well-known example is that some vibrational modes of a medium could be Raman-active but infrared-inactive, and would be more readily observed by Raman scattering, which is a two-photon transition process. In this paper, we shall discuss, with the help of three examples, how we can use second harmonic generation (SHG) and sum frequency generation (SFG) to obtain unique information about a material. We shall focus on thin films, surfaces, and interfaces.
Nonlinear plasmonics at high temperatures
Sivan, Yonatan; Chu, Shi-Wei
2017-01-01
We solve the Maxwell and heat equations self-consistently for metal nanoparticles under intense continuous wave (CW) illumination. Unlike previous studies, we rely on experimentally-measured data for metal permittivity for increasing temperature and for the visible spectral range. We show that the thermal nonlinearity of the metal can lead to substantial deviations from the predictions of the linear model for the temperature and field distribution and, thus, can explain qualitatively the strong nonlinear scattering from such configurations observed experimentally. We also show that the incompleteness of existing data of the temperature dependence of the thermal properties of the system prevents reaching a quantitative agreement between the measured and calculated scattering data. This modeling approach is essential for the identification of the underlying physical mechanism responsible for the thermo-optical nonlinearity of the metal and should be adopted in all applications of high-temperature nonlinear plasmonics, especially for refractory metals, for both CW and pulsed illumination.
Nonlinear microstructured polymer optical fibres
DEFF Research Database (Denmark)
Frosz, Michael Henoch
. The combination of a small core size and zero-dispersion wavelength at the operating wavelength of widely available femtosecond Ti:sapphire lasers led to an extensive research in supercontinuum generation and other nonlinear effects in PCFs. It is crucial for the efficiency of many nonlinear mechanisms...... that the pump laser wavelength is close to the zero-dispersion wavelength and that the core size is small. Recently, work in fabricating PCFs from materials other than silica has intensified. One of the advantages of using alternative materials can be a higher inherent material nonlinearity, which...... to accurately obtain a small core size while maintaining small structural variations during fibre drawing. This talk will give a presentation of how the mPOFs are fabricated and the route to obtaining nonlinear effects in them....
Device Applications of Nonlinear Dynamics
Baglio, Salvatore
2006-01-01
This edited book is devoted specifically to the applications of complex nonlinear dynamic phenomena to real systems and device applications. While in the past decades there has been significant progress in the theory of nonlinear phenomena under an assortment of system boundary conditions and preparations, there exist comparatively few devices that actually take this rich behavior into account. "Device Applications of Nonlinear Dynamics" applies and exploits this knowledge to make devices which operate more efficiently and cheaply, while affording the promise of much better performance. Given the current explosion of ideas in areas as diverse as molecular motors, nonlinear filtering theory, noise-enhanced propagation, stochastic resonance and networked systems, the time is right to integrate the progress of complex systems research into real devices.
Nonlinear Inflaton Fragmentation after Preheating
Felder, G N; Felder, Gary N.; Kofman, Lev
2007-01-01
We consider the nonlinear dynamics of inflaton fragmentation during and after preheating in the simplest model of chaotic inflation. While the earlier regime of parametric resonant particle production and the later turbulent regime of interacting fields evolving towards equilibrium are well identified and understood, the short intermediate stage of violent nonlinear dynamics remains less explored. Lattice simulations of fully nonlinear preheating dynamics show specific features of this intermediate stage: occupation numbers of the scalar particles are peaked, scalar fields become significantly non-gaussian and the field dynamics become chaotic and irreversible. Visualization of the field dynamics in configuration space reveals that nonlinear interactions generate non-gaussian inflaton inhomogeneities with very fast growing amplitudes. The peaks of the inflaton inhomogeneities coincide with the peaks of the scalar field(s) produced by parametric resonance. When the inflaton peaks reach their maxima, they stop ...
Reconstruction of nonlinear wave propagation
Fleischer, Jason W; Barsi, Christopher; Wan, Wenjie
2013-04-23
Disclosed are systems and methods for characterizing a nonlinear propagation environment by numerically propagating a measured output waveform resulting from a known input waveform. The numerical propagation reconstructs the input waveform, and in the process, the nonlinear environment is characterized. In certain embodiments, knowledge of the characterized nonlinear environment facilitates determination of an unknown input based on a measured output. Similarly, knowledge of the characterized nonlinear environment also facilitates formation of a desired output based on a configurable input. In both situations, the input thus characterized and the output thus obtained include features that would normally be lost in linear propagations. Such features can include evanescent waves and peripheral waves, such that an image thus obtained are inherently wide-angle, farfield form of microscopy.
BRST charge for nonlinear algebras
Buchbinder, I L
2007-01-01
We study the construction of the classical nilpotent canonical BRST charge for the nonlinear gauge algebras where a commutator (in terms of Poisson brackets) of the constraints is a finite order polynomial of the constraints.
Nonlinear optics: the next decade.
Kivshar, Yuri S
2008-12-22
This paper concludes the Focus Serial assembled of invited papers in key areas of nonlinear optics (Editors: J.M. Dudley and R.W. Boyd), and it discusses new directions for future research in this field.
Nonlinear opto-mechanical pressure
Conti, Claudio
2014-01-01
A transparent material exhibits ultra-fast optical nonlinearity and is subject to optical pressure if irradiated by a laser beam. However, the effect of nonlinearity on optical pressure is often overlooked, even if a nonlinear optical pressure may be potentially employed in many applications, as optical manipulation, biophysics, cavity optomechanics, quantum optics, optical tractors, and is relevant in fundamental problems as the Abraham-Minkoswky dilemma, or the Casimir effect. Here we show that an ultra-fast nonlinear polarization gives indeed a contribution to the optical pressure that also is negative in certain spectral ranges; the theoretical analysis is confirmed by first-principles simulations. An order of magnitude estimate shows that the effect can be observable by measuring the deflection of a membrane made by graphene.
Nonlinear programming analysis and methods
Avriel, Mordecai
2012-01-01
This text provides an excellent bridge between principal theories and concepts and their practical implementation. Topics include convex programming, duality, generalized convexity, analysis of selected nonlinear programs, techniques for numerical solutions, and unconstrained optimization methods.
Nonlinear optics principles and applications
Li, Chunfei
2017-01-01
This book reflects the latest advances in nonlinear optics. Besides the simple, strict mathematical deduction, it also discusses the experimental verification and possible future applications, such as the all-optical switches. It consistently uses the practical unit system throughout. It employs simple physical images, such as "light waves" and "photons" to systematically explain the main principles of nonlinear optical effects. It uses the first-order nonlinear wave equation in frequency domain under the condition of “slowly varying amplitude approximation" and the classical model of the interaction between the light and electric dipole. At the same time, it also uses the rate equations based on the energy-level transition of particle systems excited by photons and the energy and momentum conservation principles to explain the nonlinear optical phenomenon. The book is intended for researchers, engineers and graduate students in the field of the optics, optoelectronics, fiber communication, information tech...
Hilbert complexes of nonlinear elasticity
Angoshtari, Arzhang; Yavari, Arash
2016-12-01
We introduce some Hilbert complexes involving second-order tensors on flat compact manifolds with boundary that describe the kinematics and the kinetics of motion in nonlinear elasticity. We then use the general framework of Hilbert complexes to write Hodge-type and Helmholtz-type orthogonal decompositions for second-order tensors. As some applications of these decompositions in nonlinear elasticity, we study the strain compatibility equations of linear and nonlinear elasticity in the presence of Dirichlet boundary conditions and the existence of stress functions on non-contractible bodies. As an application of these Hilbert complexes in computational mechanics, we briefly discuss the derivation of a new class of mixed finite element methods for nonlinear elasticity.
Studies of Nonlinear Problems. I
Fermi, E.; Pasta, J.; Ulam, S.
1955-05-01
A one-dimensional dynamical system of 64 particles with forces between neighbors containing nonlinear terms has been studied on the Los Alamos computer MANIAC I. The nonlinear terms considered are quadratic, cubic, and broken linear types. The results are analyzed into Fourier components and plotted as a function of time. The results show very little, if any, tendency toward equipartition of energy among the degrees of freedom.
Nonlinear magnetization dynamics in nanosystems
Mayergoyz, Isaak D; Serpico, Claudio
2014-01-01
As data transfer rates increase within the magnetic recording industry, improvements in device performance and reliability crucially depend on the thorough understanding of nonlinear magnetization dynamics at a sub-nanoscale level. This book offers a modern, stimulating approach to the subject of nonlinear magnetization dynamics by discussing important aspects such as the Landau-Lifshitz-Gilbert (LLG) equation, analytical solutions, and the connection between the general topological and structural aspects of dynamics. An advanced reference for the study and understanding of non
Nonlinear Observers for Gyro Calibration
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 convergence properties of all three 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.
Nonlinear dynamics in atom optics
Energy Technology Data Exchange (ETDEWEB)
Chen Wenyu; Dyrting, S.; Milburn, G.J. [Queensland Univ., St. Lucia, QLD (Australia). Dept. of Physics
1996-12-31
In this paper theoretical work on classical and quantum nonlinear dynamics of cold atoms is reported. The basic concepts in nonlinear dynamics are reviewed and then applied to the motion of atoms in time-dependent standing waves and to the atomic bouncer. The quantum dynamics for the cases of regular and chaotic classical dynamics is described. The effect of spontaneous emission and external noise is also discussed. 104 refs., 1 tab., 21 figs.
A Nonlinear Transfer Operator Theorem
Pollicott, Mark
2017-02-01
In recent papers, Kenyon et al. (Ergod Theory Dyn Syst 32:1567-1584 2012), and Fan et al. (C R Math Acad Sci Paris 349:961-964 2011, Adv Math 295:271-333 2016) introduced a form of non-linear thermodynamic formalism based on solutions to a non-linear equation using matrices. In this note we consider the more general setting of Hölder continuous functions.
Nonlinear programming analysis and methods
Avriel, Mordecai
2003-01-01
Comprehensive and complete, this overview provides a single-volume treatment of key algorithms and theories. The author provides clear explanations of all theoretical aspects, with rigorous proof of most results. The two-part treatment begins with the derivation of optimality conditions and discussions of convex programming, duality, generalized convexity, and analysis of selected nonlinear programs. The second part concerns techniques for numerical solutions and unconstrained optimization methods, and it presents commonly used algorithms for constrained nonlinear optimization problems. This g
Nonlinear acoustics in biomedical ultrasound
Cleveland, Robin O.
2015-10-01
Ultrasound is widely used to image inside the body; it is also used therapeutically to treat certain medical conditions. In both imaging and therapy applications the amplitudes employed in biomedical ultrasound are often high enough that nonlinear acoustic effects are present in the propagation: the effects have the potential to be advantageous in some scenarios but a hindrance in others. In the case of ultrasound imaging the nonlinearity produces higher harmonics that result in images of greater quality. However, nonlinear effects interfere with the imaging of ultrasound contrast agents (typically micron sized bubbles with a strong nonlinear response of their own) and nonlinear effects also result in complications when derating of pressure measurements in water to in situ values in tissue. High intensity focused ultrasound (HIFU) is emerging as a non-invasive therapeutic modality which can result in thermal ablation of tissue. For thermal ablation, the extra effective attenuation resulting from nonlinear effects can result in enhanced heating of tissue if shock formation occurs in the target region for ablation - a highly desirable effect. However, if nonlinearity is too strong it can also result in undesired near-field heating and reduced ablation in the target region. The disruption of tissue (histotripsy) and fragmentation of kidney stones (lithotripsy) exploits shock waves to produce mechanically based effects, with minimal heating present. In these scenarios it is necessary for the waves to be of sufficient amplitude that a shock exists when the waveform reaches the target region. This talk will discuss how underlying nonlinear phenomenon act in all the diagnostic and therapeutic applications described above.
Nonlinear evolution equations in QCD
Stasto, A. M.
2004-01-01
The following lectures are an introduction to the phenomena of partonic saturation and nonlinear evolution equations in Quantum Chromodynamics. After a short introduction to the linear evolution, the problems of unitarity bound and parton saturation are discussed. The nonlinear Balitsky-Kovchegov evolution equation in the high energy limit is introduced, and the progress towards the understanding of the properties of its solution is reviewed. We discuss the concepts of the saturation scale, g...
Predictive simulation of nonlinear ultrasonics
Shen, Yanfeng; Giurgiutiu, Victor
2012-04-01
Most of the nonlinear ultrasonic studies to date have been experimental, but few theoretical predictive studies exist, especially for Lamb wave ultrasonic. Compared with nonlinear bulk waves and Rayleigh waves, nonlinear Lamb waves for structural health monitoring become more challenging due to their multi-mode dispersive features. In this paper, predictive study of nonlinear Lamb waves is done with finite element simulation. A pitch-catch method is used to interrogate a plate with a "breathing crack" which opens and closes under tension and compression. Piezoelectric wafer active sensors (PWAS) used as transmitter and receiver are modeled with coupled field elements. The "breathing crack" is simulated via "element birth and death" technique. The ultrasonic waves generated by the transmitter PWAS propagate into the structure, interact with the "breathing crack", acquire nonlinear features, and are picked up by the receiver PWAS. The features of the wave packets at the receiver PWAS are studied and discussed. The received signal is processed with Fast Fourier Transform to show the higher harmonics nonlinear characteristics. A baseline free damage index is introduced to assess the presence and the severity of the crack. The paper finishes with summary, conclusions, and suggestions for future work.
Leslie, Thomas M.
1993-01-01
A focused approach to development and evaluation of organic polymer films for use in optoelectronics is presented. The issues and challenges that are addressed include: (1) material synthesis, purification, and the tailoring of the material properties; (2) deposition of uniform thin films by a variety of methods; (3) characterization of material physical properties (thermal, electrical, optical, and electro-optical); and (4) device fabrication and testing. Photonic materials, devices, and systems were identified as critical technology areas by the Department of Commerce and the Department of Defense. This approach offers strong integration of basic material issues through engineering applications by the development of materials that can be exploited as the active unit in a variety of polymeric thin film devices. Improved materials were developed with unprecedented purity and stability. The absorptive properties can be tailored and controlled to provide significant improvement in propagation losses and nonlinear performance. Furthermore, the materials were incorporated into polymers that are highly compatible with fabrication and patterning processes for integrated optical devices and circuits. By simultaneously addressing the issues of materials development and characterization, keeping device design and fabrication in mind, many obstacles were overcome for implementation of these polymeric materials and devices into systems. We intend to considerably improve the upper use temperature, poling stability, and compatibility with silicon based devices. The principal device application that was targeted is a linear electro-optic modulation etalon. Organic polymers need to be properly designed and coupled with existing integrated circuit technology to create new photonic devices for optical communication, image processing, other laser applications such as harmonic generation, and eventually optical computing. The progression from microscopic sample to a suitable film
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...
New nonlinear optical materials based on ferrofluids
Energy Technology Data Exchange (ETDEWEB)
Huang, J P [Department of Physics, Fudan University, Shanghai 200433 (China); Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz (Germany); Institute of Theoretical Physics, Chinese University of Hong Kong, Shatin, NT, Hong Kong (China); Yu, K W [Department of Physics, Chinese University of Hong Kong, Shatin, NT, Hong Kong (China); Institute of Theoretical Physics, Chinese University of Hong Kong, Shatin, NT, Hong Kong (China)
2006-01-01
We exploit theoretically a new class of magneto-controlled nonlinear optical material based on ferrofluids in which ferromagnetic nanoparticles are coated with a nonmagnetic metallic nonlinear shell. Such an optical material can have anisotropic nonlinear optical properties and a giant enhancement of nonlinearity, as well as an attractive figure of merit.
Graphene - a rather ordinary nonlinear optical material
khurgin, Jacob B
2014-01-01
An analytical expression for the nonlinear refractive index of graphene has been derived and used to obtain the performance metrics of third order nonlinear devices using graphene as a nonlinear medium. None of the metrics is found to be superior to the existing nonlinear optical materials.
Nonlinear models for autoregressive conditional heteroskedasticity
DEFF Research Database (Denmark)
Teräsvirta, Timo
This paper contains a brief survey of nonlinear models of autore- gressive conditional heteroskedasticity. The models in question are parametric nonlinear extensions of the original model by Engle (1982). After presenting the individual models, linearity testing and parameter estimation...... are discussed. Forecasting volatility with nonlinear models is considered. Finally, parametric nonlinear models based on multi- plicative decomposition of the variance receive attention....
Focus issue introduction: nonlinear optics 2013.
Dadap, Jerry I; Karlsson, Magnus; Panoiu, Nicolae C
2013-12-16
Nonlinear Optics has continued to develop over the last few years at an extremely fast pace, with significant advances being reported in nonlinear optical metamaterials, optical signal processing, quantum optics, nonlinear optics at subwavelength scale, and biophotonics. These exciting new developments have generated significant potential for a broad spectrum of technological applications in which nonlinear-optical processes play a central role.
Standing waves for discrete nonlinear Schrodinger equations
Ming Jia
2016-01-01
The discrete nonlinear Schrodinger equation is a nonlinear lattice system that appears in many areas of physics such as nonlinear optics, biomolecular chains and Bose-Einstein condensates. By using critical point theory, we establish some new sufficient conditions on the existence results of standing waves for the discrete nonlinear Schrodinger equations. We give an appropriate example to illustrate the conclusion obtained.
BOOK REVIEW: Nonlinear Magnetohydrodynamics
Shafranov, V.
1998-08-01
Nonlinear magnetohydrodynamics by Dieter Biskamp is a thorough introduction to the physics of the most impressive non-linear phenomena that occur in conducting magnetoplasmas. The basic systems, in which non-trivial dynamic processes are observed, accompanied by changes of geometry of the magnetic field and the effects of energy transformation (magnetic energy into kinetic energy or the opposite effect in magnetic dynamos), are the plasma magnetic confinement systems for nuclear fusion and space plasmas, mainly the solar plasma. A significant number of the examples of the dynamic processes considered are taken from laboratory plasmas, for which an experimental check of the theory is possible. Therefore, though the book is intended for researchers and students interested in both laboratory, including nuclear fusion, and astrophysical plasmas, it is most probably closer to the first category of reader. In the Introduction the author notes that unlike the hydrodynamics of non-conducting fluids, where the phenomena caused by rapid fluid motions are the most interesting, for plasmas in a strong magnetic field the quasi-static configurations inside which the local dynamic processes occur are often the most important. Therefore, the reader will also find in this book rather traditional material on the theory of plasma equilibrium and stability in magnetic fields. In addition, it is notable that, as opposed to a linear theory, the non-linear theory, as a rule, cannot give quite definite explanations or predictions of phenomena, and consequently there are in the book many results obtained by consideration of numerical models with the use of supercomputers. The treatment of non-linear dynamics is preceded by Chapters 2 to 4, in which the basics of MHD theory are presented with an emphasis on the role of integral invariants of the magnetic helicity type, a derivation of the reduced MHD equations is given, together with examples of the exact solutions of the equilibrium
Complex motions and chaos in nonlinear systems
Machado, José; Zhang, Jiazhong
2016-01-01
This book brings together 10 chapters on a new stream of research examining complex phenomena in nonlinear systems—including engineering, physics, and social science. Complex Motions and Chaos in Nonlinear Systems provides readers a particular vantage of the nature and nonlinear phenomena in nonlinear dynamics that can develop the corresponding mathematical theory and apply nonlinear design to practical engineering as well as the study of other complex phenomena including those investigated within social science.
Compressed Sensing with Nonlinear Observations and Related Nonlinear Optimisation Problems
Blumensath, Thomas
2012-01-01
Non-convex constraints have recently proven a valuable tool in many optimisation problems. In particular sparsity constraints have had a significant impact on sampling theory, where they are used in Compressed Sensing and allow structured signals to be sampled far below the rate traditionally prescribed. Nearly all of the theory developed for Compressed Sensing signal recovery assumes that samples are taken using linear measurements. In this paper we instead address the Compressed Sensing recovery problem in a setting where the observations are non-linear. We show that, under conditions similar to those required in the linear setting, the Iterative Hard Thresholding algorithm can be used to accurately recover sparse or structured signals from few non-linear observations. Similar ideas can also be developed in a more general non-linear optimisation framework. In the second part of this paper we therefore present related result that show how this can be done under sparsity and union of subspaces constraints, wh...
Input saturation in nonlinear multivariable processes resolved by nonlinear decoupling
Directory of Open Access Journals (Sweden)
Jens G. Balchen
1995-04-01
Full Text Available A new method is presented for the resolution of the problem of input saturation in nonlinear multivariable process control by means of elementary nonlinear decoupling (END. Input saturation can have serious consequences particularly in multivariable control because it may lead to very undesirable system behaviour and quite often system instability. Many authors have searched for systematic techniques for designing multivariable control systems in which saturation may occur in any of the control variables (inputs, manipulated variables. No generally accepted method seems to have been presented so far which gives a solution in closed form. The method of elementary nonlinear decoupling (END can be applied directly to the case of saturation control variables by deriving as many control strategies as there are combinations of saturating control variables. The method is demonstrated by the multivariable control of a simulated Fluidized Catalytic Cracker (FCC with very convincing results.
Nonlinear graphene plasmonics (Conference Presentation)
Cox, Joel D.; Marini, Andrea; Garcia de Abajo, Javier F.
2016-09-01
The combination of graphene's intrinsically-high nonlinear optical response with its ability to support long-lived, electrically tunable plasmons that couple strongly with light has generated great expectations for application of the atomically-thin material to nanophotonic devices. These expectations are mainly reinforced by classical analyses performed using the response derived from extended graphene, neglecting finite-size and nonlocal effects that become important when the carbon layer is structured on the nanometer scale in actual device designs. Based on a quantum-mechanical description of graphene using tight-binding electronic states combined with the random-phase approximation, we show that finite-size effects produce large contributions that increase the nonlinear response associated with plasmons in nanostructured graphene to significantly higher levels than previously thought, particularly in the case of Kerr-type optical nonlinearities. Motivated by this finding, we discuss and compare saturable absorption in extended and nanostructured graphene, with or without plasmonic enhancement, within the context of passive mode-locking for ultrafast lasers. We also explore the possibility of high-harmonic generation in doped graphene nanoribbons and nanoislands, where illumination by an infrared pulse of moderate intensity, tuned to a plasmon resonance, is predicted to generate light at harmonics of order 13 or higher, extending over the visible and UV regimes. Our atomistic description of graphene's nonlinear optical response reveals its complex nature in both extended and nanostructured systems, while further supporting the exceptional potential of this material for nonlinear nanophotonic devices.
Introduction to nonlinear dispersive equations
Linares, Felipe
2015-01-01
This textbook introduces the well-posedness theory for initial-value problems of nonlinear, dispersive partial differential equations, with special focus on two key models, the Korteweg–de Vries equation and the nonlinear Schrödinger equation. A concise and self-contained treatment of background material (the Fourier transform, interpolation theory, Sobolev spaces, and the linear Schrödinger equation) prepares the reader to understand the main topics covered: the initial-value problem for the nonlinear Schrödinger equation and the generalized Korteweg–de Vries equation, properties of their solutions, and a survey of general classes of nonlinear dispersive equations of physical and mathematical significance. Each chapter ends with an expert account of recent developments and open problems, as well as exercises. The final chapter gives a detailed exposition of local well-posedness for the nonlinear Schrödinger equation, taking the reader to the forefront of recent research. The second edition of Introdu...
Nonlinear plasmonics at high temperatures
Sivan, Yonatan
2016-01-01
We solve the Maxwell and heat equations self-consistently for metal nanoparticles under intense continuous wave (CW) illumination. Unlike previous studies, we rely on {\\em experimentally}-measured data for the metal permittivity for increasing temperature and for the visible spectral range. We show that the thermal nonlinearity of the metal can lead to substantial deviations from the predictions of the linear model for the temperature and field distribution, and thus, can explain qualitatively the strong nonlinear scattering from such configurations observed experimentally. We also show that the incompleteness of existing data of the temperature dependence of the thermal properties of the system prevents reaching a quantitative agreement between the measured and calculated scattering data. This modelling approach is essential for the identification of the underlying physical mechanism responsible for the thermo-optical nonlinearity of the metal and should be adopted in all applications of high temperature non...
Nonlinear Multigrid for Reservoir Simulation
DEFF Research Database (Denmark)
Christensen, Max la Cour; Eskildsen, Klaus Langgren; Engsig-Karup, Allan Peter
2016-01-01
A feasibility study is presented on the effectiveness of applying nonlinear multigrid methods for efficient reservoir simulation of subsurface flow in porous media. A conventional strategy modeled after global linearization by means of Newton’s method is compared with an alternative strategy...... modeled after local linearization, leading to a nonlinear multigrid method in the form of the full-approximation scheme (FAS). It is demonstrated through numerical experiments that, without loss of robustness, the FAS method can outperform the conventional techniques in terms of algorithmic and numerical...... efficiency for a black-oil model. Furthermore, the use of the FAS method enables a significant reduction in memory usage compared with conventional techniques, which suggests new possibilities for improved large-scale reservoir simulation and numerical efficiency. Last, nonlinear multilevel preconditioning...
Nonlinear photoacoustic spectroscopy of hemoglobin
Energy Technology Data Exchange (ETDEWEB)
Danielli, Amos; Maslov, Konstantin; Favazza, Christopher P.; Xia, Jun; Wang, Lihong V., E-mail: LHWANG@WUSTL.EDU [Optical Imaging Laboratory, Department of Biomedical Engineering, Washington University in St. Louis, One Brookings Drive, St. Louis, Missouri 63130 (United States)
2015-05-18
As light intensity increases in photoacoustic imaging, the saturation of optical absorption and the temperature dependence of the thermal expansion coefficient result in a measurable nonlinear dependence of the photoacoustic (PA) signal on the excitation pulse fluence. Here, under controlled conditions, we investigate the intensity-dependent photoacoustic signals from oxygenated and deoxygenated hemoglobin at varied optical wavelengths and molecular concentrations. The wavelength and concentration dependencies of the nonlinear PA spectrum are found to be significantly greater in oxygenated hemoglobin than in deoxygenated hemoglobin. These effects are further influenced by the hemoglobin concentration. These nonlinear phenomena provide insights into applications of photoacoustics, such as measurements of average inter-molecular distances on a nm scale or with a tuned selection of wavelengths, a more accurate quantitative PA tomography.
Nonlinear Waves in Complex Systems
DEFF Research Database (Denmark)
2007-01-01
The study of nonlinear waves has exploded due to the combination of analysis and computations, since the discovery of the famous recurrence phenomenon on a chain of nonlinearly coupled oscillators by Fermi-Pasta-Ulam fifty years ago. More than the discovery of new integrable equations......, it is the universality and robustness of the main models with respect to perturbations that developped the field. This is true for both continuous and discrete equations. In this volume we keep this broad view and draw new perspectives for nonlinear waves in complex systems. In particular we address energy flow...... in Fourier space and equipartition, the role of inhomogeneities and complex geometry and the importance of coupled systems....
Nonlinear dynamics in biological systems
Carballido-Landeira, Jorge
2016-01-01
This book presents recent research results relating to applications of nonlinear dynamics, focusing specifically on four topics of wide interest: heart dynamics, DNA/RNA, cell mobility, and proteins. The book derives from the First BCAM Workshop on Nonlinear Dynamics in Biological Systems, held in June 2014 at the Basque Center of Applied Mathematics (BCAM). At this international meeting, researchers from different but complementary backgrounds, including molecular dynamics, physical chemistry, bio-informatics and biophysics, presented their most recent results and discussed the future direction of their studies using theoretical, mathematical modeling and experimental approaches. Such was the level of interest stimulated that the decision was taken to produce this publication, with the organizers of the event acting as editors. All of the contributing authors are researchers working on diverse biological problems that can be approached using nonlinear dynamics. The book will appeal especially to applied math...
Nonlinear microrheology of living cells
Kollmannsberger, Philip; Fabry, Ben
2009-01-01
The linear rheology of adherent cells is characterized by a power-law creep or stress relaxation response, and proportionality between stiffness and internal prestress. It is unknown whether these observations hold in the physiologically relevant nonlinear regime. We used magnetic tweezers microrheology to measure the time- and force-dependent nonlinear creep response of adherent cells. Cell deformations in response to a stepwise increasing force applied to cytoskeletally bound magnetic beads were analyzed with a nonlinear superposition approach. The creep response followed a weak power law regardless of force. Stiffness and power law exponent both increased with force, indicating stress stiffening as well as fluidization of the cytoskeleton. Softer cells showed a more pronounced stress stiffening, which is quantitatively explained by their smaller internal prestress. Stiffer and more elastic cells showed a more pronounced force-induced fluidization, consistent with predictions from soft glassy rheology. Thes...
A NONLINEAR FEASIBILITY PROBLEM HEURISTIC
Directory of Open Access Journals (Sweden)
Sergio Drumond Ventura
2015-04-01
Full Text Available In this work we consider a region S ⊂ given by a finite number of nonlinear smooth convex inequalities and having nonempty interior. We assume a point x 0 is given, which is close in certain norm to the analytic center of S, and that a new nonlinear smooth convex inequality is added to those defining S (perturbed region. It is constructively shown how to obtain a shift of the right-hand side of this inequality such that the point x 0 is still close (in the same norm to the analytic center of this shifted region. Starting from this point and using the theoretical results shown, we develop a heuristic that allows us to obtain the approximate analytic center of the perturbed region. Then, we present a procedure to solve the problem of nonlinear feasibility. The procedure was implemented and we performed some numerical tests for the quadratic (random case.
Nonlinear Deformable-body Dynamics
Luo, Albert C J
2010-01-01
"Nonlinear Deformable-body Dynamics" mainly consists in a mathematical treatise of approximate theories for thin deformable bodies, including cables, beams, rods, webs, membranes, plates, and shells. The intent of the book is to stimulate more research in the area of nonlinear deformable-body dynamics not only because of the unsolved theoretical puzzles it presents but also because of its wide spectrum of applications. For instance, the theories for soft webs and rod-reinforced soft structures can be applied to biomechanics for DNA and living tissues, and the nonlinear theory of deformable bodies, based on the Kirchhoff assumptions, is a special case discussed. This book can serve as a reference work for researchers and a textbook for senior and postgraduate students in physics, mathematics, engineering and biophysics. Dr. Albert C.J. Luo is a Professor of Mechanical Engineering at Southern Illinois University, Edwardsville, IL, USA. Professor Luo is an internationally recognized scientist in the field of non...
Solving Volterra's Population Model Using New Second Derivative Multistep Methods
Directory of Open Access Journals (Sweden)
K. Parand
2008-01-01
Full Text Available In this study new second derivative multistep methods (denoted SDMM are used to solve Volterra's model for population growth of a species within a closed system. This model is a nonlinear integro-differential where the integral term represents the effect of toxin. This model is first converted to a nonlinear ordinary differential equation and then the new SDMM, which has good stability and accuracy properties, are applied to solve this equation. We compare this method with the others and show that new SDMM gives excellent results.
Approximate Controllability of Fractional Neutral Stochastic System with Infinite Delay
Sakthivel, R.; Ganesh, R.; Suganya, S.
2012-12-01
The concept of controllability plays an important role in analysis and design of linear and nonlinear control systems. Further, fractional differential equations have wide applications in engineering and science. In this paper, the approximate controllability of neutral stochastic fractional integro-differential equation with infinite delay in a Hilbert space is studied. By using Krasnoselskii's fixed point theorem with stochastic analysis theory, we derive a new set of sufficient conditions for the approximate controllability of nonlinear fractional stochastic system under the assumption that the corresponding linear system is approximately controllable. Finally, an example is provided to illustrate the obtained theory.
Pole solutions for flame front propagation
Kupervasser, Oleg
2015-01-01
This book deals with solving mathematically the unsteady flame propagation equations. New original mathematical methods for solving complex non-linear equations and investigating their properties are presented. Pole solutions for flame front propagation are developed. Premixed flames and filtration combustion have remarkable properties: the complex nonlinear integro-differential equations for these problems have exact analytical solutions described by the motion of poles in a complex plane. Instead of complex equations, a finite set of ordinary differential equations is applied. These solutions help to investigate analytically and numerically properties of the flame front propagation equations.
Schauder’s fixed-point theorem in approximate controllability problems
Directory of Open Access Journals (Sweden)
Babiarz Artur
2016-06-01
Full Text Available The main objective of this article is to present the state of the art concerning approximate controllability of dynamic systems in infinite-dimensional spaces. The presented investigation focuses on obtaining sufficient conditions for approximate controllability of various types of dynamic systems using Schauder’s fixed-point theorem. We describe the results of approximate controllability for nonlinear impulsive neutral fuzzy stochastic differential equations with nonlocal conditions, impulsive neutral functional evolution integro-differential systems, stochastic impulsive systems with control-dependent coefficients, nonlinear impulsive differential systems, and evolution systems with nonlocal conditions and semilinear evolution equation.
A multilevel method for conductive-radiative heat transfer
Energy Technology Data Exchange (ETDEWEB)
Banoczi, J.M.; Kelley, C.T. [North Carolina State Univ., Raleigh, NC (United States)
1996-12-31
We present a fast multilevel algorithm for the solution of a system of nonlinear integro-differential equations that model steady-state combined radiative-conductive heat transfer. The equations can be formulated as a compact fixed point problem with a fixed point map that requires both a solution of the linear transport equation and the linear heat equation for its evaluation. We use fast transport solvers developed by the second author, to construct an efficient evaluation of the fixed point map and then apply the Atkinson-Brakhage, method, with Newton-GMRES as the coarse mesh solver, to the full nonlinear system.
Nonlinear Resistivity for Magnetohydrodynamical Models
Lingam, Manasvi; Pfefferlé, David; Comisso, Luca; Bhattacharjee, Amitava
2016-01-01
A nonlinear current-dependent resistivity that accurately accounts for the collisional electron-ion momentum transfer rate is derived. It is shown that the Spitzer resistivity overestimates the resistivity in certain observationally relevant regimes. The nonlinear resistivity computed herein is a strictly decreasing function of the current, in contrast to some notable previous proposals. The relative importance of the new expression with respect to the well-established electron inertia and Hall terms is also examined. The subtle implications of this current-dependent resistivity are discussed in the context of plasma systems and phenomena such as magnetic reconnection.
Time Series with Tailored Nonlinearities
Raeth, C
2015-01-01
It is demonstrated how to generate time series with tailored nonlinearities by inducing well- defined constraints on the Fourier phases. Correlations between the phase information of adjacent phases and (static and dynamic) measures of nonlinearities are established and their origin is explained. By applying a set of simple constraints on the phases of an originally linear and uncor- related Gaussian time series, the observed scaling behavior of the intensity distribution of empirical time series can be reproduced. The power law character of the intensity distributions being typical for e.g. turbulence and financial data can thus be explained in terms of phase correlations.
Topics in nonlinear functional analysis
Nirenberg, Louis
2001-01-01
Since its first appearance as a set of lecture notes published by the Courant Institute in 1974, this book served as an introduction to various subjects in nonlinear functional analysis. The current edition is a reprint of these notes, with added bibliographic references. Topological and analytic methods are developed for treating nonlinear ordinary and partial differential equations. The first two chapters of the book introduce the notion of topological degree and develop its basic properties. These properties are used in later chapters in the discussion of bifurcation theory (the possible br
Finite elements of nonlinear continua
Oden, J T
2000-01-01
Geared toward undergraduate and graduate students, this text extends applications of the finite element method from linear problems in elastic structures to a broad class of practical, nonlinear problems in continuum mechanics. It treats both theory and applications from a general and unifying point of view.The text reviews the thermomechanical principles of continuous media and the properties of the finite element method, and then brings them together to produce discrete physical models of nonlinear continua. The mathematical properties of these models are analyzed, along with the numerical s
Nonlinear Control of Heartbeat Models
Directory of Open Access Journals (Sweden)
Witt Thanom
2011-02-01
Full Text Available This paper presents a novel application of nonlinear control theory to heartbeat models. Existing heartbeat models are investigated and modified by incorporating the control input as a pacemaker to provide the control channel. A nonlinear feedback linearization technique is applied to force the output of the systems to generate artificial electrocardiogram (ECG signal using discrete data as the reference inputs. The synthetic ECG may serve as a flexible signal source to assess the effectiveness of a diagnostic ECG signal-processing device.
Edge detection by nonlinear dynamics
Energy Technology Data Exchange (ETDEWEB)
Wong, Yiu-fai
1994-07-01
We demonstrate how the formulation of a nonlinear scale-space filter can be used for edge detection and junction analysis. By casting edge-preserving filtering in terms of maximizing information content subject to an average cost function, the computed cost at each pixel location becomes a local measure of edgeness. This computation depends on a single scale parameter and the given image data. Unlike previous approaches which require careful tuning of the filter kernels for various types of edges, our scheme is general enough to be able to handle different edges, such as lines, step-edges, corners and junctions. Anisotropy in the data is handled automatically by the nonlinear dynamics.
Generation of nonlinear vortex precursors
Chen, Yue-Yue; Liu, Chengpu
2016-01-01
We numerically study the propagation of a few-cycle pulse carrying orbital angular momentum (OAM) through a dense atomic system. Nonlinear precursors consisting of high-order vortex har- monics are generated in the transmitted field due to ultrafast Bloch oscillation. The nonlinear precursors survive to propagation effects and are well separated with the main pulse, which provide a straightforward way of measuring precursors. By the virtue of carrying high-order OAM, the obtained vortex precursors as information carriers have potential applications in optical informa- tion and communication fields where controllable loss, large information-carrying capacity and high speed communication are required.
Stability analysis of nonlinear systems
Lakshmikantham, Vangipuram; Martynyuk, Anatoly A
2015-01-01
The book investigates stability theory in terms of two different measure, exhibiting the advantage of employing families of Lyapunov functions and treats the theory of a variety of inequalities, clearly bringing out the underlying theme. It also demonstrates manifestations of the general Lyapunov method, showing how this technique can be adapted to various apparently diverse nonlinear problems. Furthermore it discusses the application of theoretical results to several different models chosen from real world phenomena, furnishing data that is particularly relevant for practitioners. Stability Analysis of Nonlinear Systems is an invaluable single-sourse reference for industrial and applied mathematicians, statisticians, engineers, researchers in the applied sciences, and graduate students studying differential equations.
Higher dimensional nonlinear massive gravity
Do, Tuan Q
2016-01-01
Inspired by a recent ghost-free nonlinear massive gravity in four-dimensional spacetime, we study its higher dimensional scenarios. As a result, we are able to show the constant-like behavior of massive graviton terms for some well-known metrics such as the Friedmann-Lemaitre-Robertson-Walker, Bianchi type I, and Schwarzschild-Tangherlini-(A)dS metrics in a specific five-dimensional nonlinear massive gravity under an assumption that its fiducial metrics are compatible with physical ones. In addition, some simple cosmological solutions of the five-dimensional massive gravity will be figured out consistently.
Wave equation with concentrated nonlinearities
Noja, Diego; Posilicano, Andrea
2004-01-01
In this paper we address the problem of wave dynamics in presence of concentrated nonlinearities. Given a vector field $V$ on an open subset of $\\CO^n$ and a discrete set $Y\\subset\\RE^3$ with $n$ elements, we define a nonlinear operator $\\Delta_{V,Y}$ on $L^2(\\RE^3)$ which coincides with the free Laplacian when restricted to regular functions vanishing at $Y$, and which reduces to the usual Laplacian with point interactions placed at $Y$ when $V$ is linear and is represented by an Hermitean m...
Field guide to nonlinear optics
Powers, Peter E
2013-01-01
Optomechanics is a field of mechanics that addresses the specific design challenges associated with optical systems. This [i]Field Guide [/i]describes how to mount optical components, as well as how to analyze a given design. It is intended for practicing optical and mechanical engineers whose work requires knowledge in both optics and mechanics. This Field Guide is designed for those looking for a condensed and concise source of key concepts, equations, and techniques for nonlinear optics. Topics covered include technologically important effects, recent developments in nonlinear optics
Stability analysis of nonlinear systems with slope restricted nonlinearities.
Liu, Xian; Du, Jiajia; Gao, Qing
2014-01-01
The problem of absolute stability of Lur'e systems with sector and slope restricted nonlinearities is revisited. Novel time-domain and frequency-domain criteria are established by using the Lyapunov method and the well-known Kalman-Yakubovich-Popov (KYP) lemma. The criteria strengthen some existing results. Simulations are given to illustrate the efficiency of the results.
Stability Analysis of Nonlinear Systems with Slope Restricted Nonlinearities
Directory of Open Access Journals (Sweden)
Xian Liu
2014-01-01
Full Text Available The problem of absolute stability of Lur’e systems with sector and slope restricted nonlinearities is revisited. Novel time-domain and frequency-domain criteria are established by using the Lyapunov method and the well-known Kalman-Yakubovich-Popov (KYP lemma. The criteria strengthen some existing results. Simulations are given to illustrate the efficiency of the results.
Nonlinearity and nonclassicality in a nanomechanical resonator
Energy Technology Data Exchange (ETDEWEB)
Teklu, Berihu [Clermont Universite, Blaise Pascal University, CNRS, PHOTON-N2, Institut Pascal, Aubiere Cedex (France); Universita degli Studi di Milano, Dipartimento di Fisica, Milano (Italy); Ferraro, Alessandro; Paternostro, Mauro [Queen' s University, Centre for Theoretical Atomic, Molecular, and Optical Physics, School of Mathematics and Physics, Belfast (United Kingdom); Paris, Matteo G.A. [Universita degli Studi di Milano, Dipartimento di Fisica, Milano (Italy)
2015-12-15
We address quantitatively the relationship between the nonlinearity of a mechanical resonator and the nonclassicality of its ground state. In particular, we analyze the nonclassical properties of the nonlinear Duffing oscillator (being driven or not) as a paradigmatic example of a nonlinear nanomechanical resonator. We first discuss how to quantify the nonlinearity of this system and then show that the nonclassicality of the ground state, as measured by the volume occupied by the negative part of the Wigner function, monotonically increases with the nonlinearity in all the working regimes addressed in our study. Our results show quantitatively that nonlinearity is a resource to create nonclassical states in mechanical systems. (orig.)
Analysis of Wave Nonlinear Dispersion Relation
Institute of Scientific and Technical Information of China (English)
LI Rui-jie; TAO Jian-fu
2005-01-01
The nonlinear dispersion relations and modified relations proposed by Kirby and Hedges have the limitation of intermediate minimum value. To overcome the shortcoming, a new nonlinear dispersion relation is proposed. Based on the summarization and comparison of existing nonlinear dispersion relations, it can be found that the new nonlinear dispersion relation not only keeps the advantages of other nonlinear dispersion relations, but also significantly reduces the relative errors of the nonlinear dispersion relations for a range of the relative water depth of 1＜kh＜1.5 and has sufficient accuracy for practical purposes.
Topology optimization of nonlinear optical devices
DEFF Research Database (Denmark)
Jensen, Jakob Søndergaard
2011-01-01
This paper considers the design of nonlinear photonic devices. The nonlinearity stems from a nonlinear material model with a permittivity that depends on the local time-averaged intensity of the electric field. A finite element model is developed for time-harmonic wave propagation and an incremen......This paper considers the design of nonlinear photonic devices. The nonlinearity stems from a nonlinear material model with a permittivity that depends on the local time-averaged intensity of the electric field. A finite element model is developed for time-harmonic wave propagation...
Non-linear canonical correlation
van der Burg, Eeke; de Leeuw, Jan
1983-01-01
Non-linear canonical correlation analysis is a method for canonical correlation analysis with optimal scaling features. The method fits many kinds of discrete data. The different parameters are solved for in an alternating least squares way and the corresponding program is called CANALS. An
DEFF Research Database (Denmark)
Andersen, Steffen; Harrison, Glenn W.; Hole, Arne Risa
2012-01-01
We develop an extension of the familiar linear mixed logit model to allow for the direct estimation of parametric non-linear functions defined over structural parameters. Classic applications include the estimation of coefficients of utility functions to characterize risk attitudes and discountin...
Impurity solitons with quadratic nonlinearities
DEFF Research Database (Denmark)
Clausen, Carl A. Balslev; Torres, Juan P-; Torner, Lluis
1998-01-01
We fmd families of solitary waves mediated by parametric mixing in quadratic nonlinear media that are localized at point-defect impurities. Solitons localized at attractive impurities are found to be dynamically stable. It is shown that localization at the impurity modifies strongly the soliton p...
Stochastic nonlinear differential equations. I
Heilmann, O.J.; Kampen, N.G. van
1974-01-01
A solution method is developed for nonlinear differential equations having the following two properties. Their coefficients are stochastic through their dependence on a Markov process. The magnitude of the fluctuations, multiplied with their auto-correlation time, is a small quantity. Under these co
Badikyan, Karen
2016-01-01
The nonlinear theory of relyativistic strophotron is developed. Classical equations of motion are averaged over fast oscillations. The slow motion phase and saturation parameter are found different from usual undulator oscillation parameters. In the strong field approximation the analytical expression of gain is found on higher harmonics of main resonance frequency.
Observation of Nonlinear Compton Scattering
Energy Technology Data Exchange (ETDEWEB)
Kotseroglou, T.
2003-12-19
This experiment tests Quantum Electrodynamics in the strong field regime. Nonlinear Compton scattering has been observed during the interaction of a 46.6 GeV electron beam with a 10{sup 18} W/cm{sup 2} laser beam. The strength of the field achieved was measured by the parameter {eta} = e{var_epsilon}{sub rms}/{omega}mc = 0.6. Data were collected with infrared and green laser photons and circularly polarized laser light. The timing stabilization achieved between the picosecond laser and electron pulses has {sigma}{sub rms} = 2 ps. A strong signal of electrons that absorbed up to 4 infrared photons (or up to 3 green photons) at the same point in space and time, while emitting a single gamma ray, was observed. The energy spectra of the scattered electrons and the nonlinear dependence of the electron yield on the field strength agreed with the simulation over 3 orders of magnitude. The detector could not resolve the nonlinear Compton scattering from the multiple single Compton scattering which produced rates of scattered electrons of the same order of magnitude. Nevertheless, a simulation has studied this difference and concluded that the scattered electron rates observed could not be accounted for only by multiple ordinary Compton scattering; nonlinear Compton scattering processes are dominant for n {ge} 3.
Nonlinear Optics of Hexaphenyl Nanofibers
DEFF Research Database (Denmark)
Balzer, Frank; Al-Shamery, Katharina; Neuendorf, Rolf
2003-01-01
measurements reveal that the nonlinear optical transition dipole moment is oriented with an angle of 75° with respect to the needles long axes. The absolute value of the macroscopic second-order susceptibility, averaged over a size distribution of p-6P nanoaggregates, is estimated to be of the order of 6...
Nonlinear intravascular ultrasound contrast imaging
Goertz, David E.; Frijlink, Martijn E.; de Jong, N.; van der Steen, Antonius F.W.
2006-01-01
Nonlinear contrast agent imaging with intravascular ultrasound (IVUS) is investigated using a prototype IVUS system and an experimental small bubble contrast agent. The IVUS system employed a mechanically scanned single element transducer and was operated at a 20 MHz transmit frequency (F20) for
Nonlinear wavetrains in viscous conduits
Maiden, Michelle; Hoefer, Mark
2016-11-01
Viscous fluid conduits provide an ideal system for the study of dissipationless, dispersive hydrodynamics. A dense, viscous fluid serves as the background medium through which a lighter, less viscous fluid buoyantly rises. If the interior fluid is continuously injected, a deformable pipe forms. The long wave interfacial dynamics are well-described by a dispersive nonlinear partial differential equation. In this talk, experiments, numerics, and asymptotics of the viscous fluid conduit system will be presented. Structures at multiple length scales are discussed, including solitons, dispersive shock waves, and periodic waves. Modulations of periodic waves will be explored in the weakly nonlinear regime with the Nonlinear Schrödinger (NLS) equation. Modulational instability (stability) is identified for sufficiently short (long) periodic waves due to a change in dispersion curvature. These asymptotic results are confirmed by numerical simulations of perturbed nonlinear periodic wave solutions. Also, numerically observed are envelope bright and dark solitons well approximated by NLS. This work was partially supported by NSF CAREER DMS-1255422 (M.A.H.) and NSF GRFP (M.D.M.).
Quantum nonlinear optics without photons
Stassi, Roberto; Macrı, Vincenzo; Kockum, Anton Frisk; Di Stefano, Omar; Miranowicz, Adam; Savasta, Salvatore; Nori, Franco
2017-08-01
Spontaneous parametric down-conversion is a well-known process in quantum nonlinear optics in which a photon incident on a nonlinear crystal spontaneously splits into two photons. Here we propose an analogous physical process where one excited atom directly transfers its excitation to a pair of spatially separated atoms with probability approaching 1. The interaction is mediated by the exchange of virtual rather than real photons. This nonlinear atomic process is coherent and reversible, so the pair of excited atoms can transfer the excitation back to the first one: the atomic analog of sum-frequency generation of light. The parameters used to investigate this process correspond to experimentally demonstrated values in ultrastrong circuit quantum electrodynamics. This approach can be extended to realize other nonlinear interatomic processes, such as four-atom mixing, and is an attractive architecture for the realization of quantum devices on a chip. We show that four-qubit mixing can efficiently implement quantum repetition codes and, thus, can be used for error-correction codes.
Cosmological effects of nonlinear electrodynamics
Energy Technology Data Exchange (ETDEWEB)
Novello, M [Instituto de Cosmologia Relatividade Astrofisica (ICRA-Brasil/CBPF), Rua Dr Xavier Sigaud, 150, CEP 22290-180, Rio de Janeiro (Brazil); Goulart, E [Instituto de Cosmologia Relatividade Astrofisica (ICRA-Brasil/CBPF), Rua Dr Xavier Sigaud, 150, CEP 22290-180, Rio de Janeiro (Brazil); Salim, J M [Instituto de Cosmologia Relatividade Astrofisica (ICRA-Brasil/CBPF), Rua Dr Xavier Sigaud, 150, CEP 22290-180, Rio de Janeiro (Brazil); Bergliaffa, S E Perez [Departamento de Fisica Teorica, Universidade do Estado do Rio de Janeiro, R. Sao Francisco Xavier, 524, Maracana, CEP 20559-900, Rio de Janeiro (Brazil)
2007-06-07
It will be shown that a given realization of nonlinear electrodynamics, used as a source of Einstein's equations, generates a cosmological model with interesting features, namely a phase of current cosmic acceleration, and the absence of an initial singularity, thus pointing to a way of solving two important problems in cosmology.
On Nonlinear Higher Spin Curvature
Manvelyan, Ruben(Yerevan Physics Institute, Alikhanian Br. St. 2, Yerevan, 0036, Armenia); Mkrtchyan, Karapet; Rühl, Werner; Tovmasyan, Murad
2011-01-01
We present the first nonlinear term of the higher spin curvature which is covariant with respect to deformed gauge transformations that are linear in the field. We consider in detail the case of spin 3 after presenting spin 2 as an example, and then construct the general spin s quadratic term of the deWit-Freedman curvature.
On nonlinear higher spin curvature
Energy Technology Data Exchange (ETDEWEB)
Manvelyan, Ruben, E-mail: manvel@physik.uni-kl.d [Department of Physics, Erwin Schroedinger Strasse, Technical University of Kaiserslautern, Postfach 3049, 67653 Kaiserslautern (Germany); Yerevan Physics Institute, Alikhanian Br. Str. 2, 0036 Yerevan (Armenia); Mkrtchyan, Karapet, E-mail: karapet@yerphi.a [Department of Physics, Erwin Schroedinger Strasse, Technical University of Kaiserslautern, Postfach 3049, 67653 Kaiserslautern (Germany); Yerevan Physics Institute, Alikhanian Br. Str. 2, 0036 Yerevan (Armenia); Ruehl, Werner, E-mail: ruehl@physik.uni-kl.d [Department of Physics, Erwin Schroedinger Strasse, Technical University of Kaiserslautern, Postfach 3049, 67653 Kaiserslautern (Germany); Tovmasyan, Murad, E-mail: mtovmasyan@ysu.a [Yerevan Physics Institute, Alikhanian Br. Str. 2, 0036 Yerevan (Armenia)
2011-05-09
We present the first nonlinear term of the higher spin curvature which is covariant with respect to deformed gauge transformations that are linear in the field. We consider the case of spin 3 after presenting spin 2 as an example, and then construct the general spin s quadratic term of the de Wit-Freedman curvature.
Nonlinear smoothing for random fields
Aihara, Shin Ichi; Bagchi, Arunabha
1995-01-01
Stochastic nonlinear elliptic partial differential equations with white noise disturbances are studied in the countably additive measure set up. Introducing the Onsager-Machlup function to the system model, the smoothing problem for maximizing the modified likelihood functional is solved and the exp
Practical stability of nonlinear systems
Lakshmikantham, Vangipuram; Martynyuk, Anatolii Andreevich
1990-01-01
This is the first book that deals with practical stability and its development. It presents a systematic study of the theory of practical stability in terms of two different measures and arbitrary sets and demonstrates the manifestations of general Lyapunov's method by showing how this effective technique can be adapted to investigate various apparently diverse nonlinear problems including control systems and multivalued differential equations.
The virial theorem for nonlinear problems
Energy Technology Data Exchange (ETDEWEB)
Amore, Paolo [Facultad de Ciencias, Universidad de Colima, Bernal DIaz del Castillo 340, Colima (Mexico); Fernandez, Francisco M [INIFTA (UNLP, CCT La Plata-CONICET), Division Quimica Teorica, Blvd 113 S/N, Sucursal 4, Casilla de Correo 16, 1900 La Plata (Argentina)], E-mail: paolo.amore@gmail.com, E-mail: fernande@quimica.unlp.edu.ar
2009-09-15
We show that the virial theorem provides a useful simple tool for approximating nonlinear problems. In particular, we consider conservative nonlinear oscillators and obtain the same main result derived earlier from the expansion in Chebyshev polynomials. (letters and comments)
Nonlinear rheological models for structured interfaces
Sagis, L.M.C.
2010-01-01
The GENERIC formalism is a formulation of nonequilibrium thermodynamics ideally suited to develop nonlinear constitutive equations for the stress–deformation behavior of complex interfaces. Here we develop a GENERIC model for multiphase systems with interfaces displaying nonlinear viscoelastic stres
International Conference on Applications in Nonlinear Dynamics
Longhini, Patrick; Palacios, Antonio
2017-01-01
This book presents collaborative research works carried out by experimentalists and theorists around the world in the field of nonlinear dynamical systems. It provides a forum for applications of nonlinear systems while solving practical problems in science and engineering. Topics include: Applied Nonlinear Optics, Sensor, Radar & Communication Signal Processing, Nano Devices, Nonlinear Biomedical Applications, Circuits & Systems, Coupled Nonlinear Oscillator, Precision Timing Devices, Networks, and other contemporary topics in the general field of Nonlinear Science. This book provides a comprehensive report of the various research projects presented at the International Conference on Applications in Nonlinear Dynamics (ICAND 2016) held in Denver, Colorado, 2016. It can be a valuable tool for scientists and engineering interested in connecting ideas and methods in nonlinear dynamics with actual design, fabrication and implementation of engineering applications or devices.
Hamiltonian realizations of nonlinear adjoint operators
Fujimoto, Kenji; Scherpen, Jacquelien M.A.; Gray, W. Steven
2002-01-01
This paper addresses the issue of state-space realizations for nonlinear adjoint operators. In particular, the relationships between nonlinear Hilbert adjoint operators, Hamiltonian extensions and port-controlled Hamiltonian systems are established. Then, characterizations of the adjoints of control
Hamiltonian Realizations of Nonlinear Adjoint Operators
Fujimoto, Kenji; Scherpen, Jacquelien M.A.; Gray, W. Steven
2000-01-01
This paper addresses state-space realizations for nonlinear adjoint operators. In particular the relationship among nonlinear Hilbert adjoint operators, Hamiltonian extensions and port-controlled Hamiltonian systems are clarified. The characterization of controllability, observability and Hankel ope
Nonlinear Least Squares for Inverse Problems
Chavent, Guy
2009-01-01
Presents an introduction into the least squares resolution of nonlinear inverse problems. This title intends to develop a geometrical theory to analyze nonlinear least square (NLS) problems with respect to their quadratic wellposedness, that is, both wellposedness and optimizability
Nonlinear dynamics by mode superposition
Energy Technology Data Exchange (ETDEWEB)
Nickell, R.E.
1976-01-01
A mode superposition technique for approximately solving nonlinear initial-boundary-value problems of structural dynamics is discussed, and results for examples involving large deformation are compared to those obtained with implicit direct integration methods such as the Newmark generalized acceleration and Houbolt backward-difference operators. The initial natural frequencies and mode shapes are found by inverse power iteration with the trial vectors for successively higher modes being swept by Gram-Schmidt orthonormalization at each iteration. The subsequent modal spectrum for nonlinear states is based upon the tangent stiffness of the structure and is calculated by a subspace iteration procedure that involves matrix multiplication only, using the most recently computed spectrum as an initial estimate. Then, a precise time integration algorithm that has no artificial damping or phase velocity error for linear problems is applied to the uncoupled modal equations of motion. Squared-frequency extrapolation is examined for nonlinear problems as a means by which these qualities of accuracy and precision can be maintained when the state of the system (and, thus, the modal spectrum) is changing rapidly. The results indicate that a number of important advantages accrue to nonlinear mode superposition: (a) there is no significant difference in total solution time between mode superposition and implicit direct integration analyses for problems having narrow matric half-bandwidth (in fact, as bandwidth increases, mode superposition becomes more economical), (b) solution accuracy is under better control since the analyst has ready access to modal participation factors and the ratios of time step size to modal period, and (c) physical understanding of nonlinear dynamic response is improved since the analyst is able to observe the changes in the modal spectrum as deformation proceeds.
Interaction nonlinearity in asphalt binders
Motamed, Arash; Bhasin, Amit; Liechti, Kenneth M.
2012-05-01
Asphalt mixtures are complex composites that comprise aggregate, asphalt binder, and air. Several research studies have shown that the mechanical behavior of the asphalt mixture is strongly influenced by the matrix, i.e. the asphalt binder. Characterization and a thorough understanding of the binder behavior is the first and crucial step towards developing an accurate constitutive model for the composite. Accurate constitutive models for the constituent materials are critical to ensure accurate performance predictions at a material and structural level using micromechanics. This paper presents the findings from a systematic investigation into the nature of the linear and nonlinear response of asphalt binders subjected to different types of loading using the Dynamic Shear Rheometer (DSR). Laboratory test data show that a compressive normal force is generated in an axially constrained specimen subjected to torsional shear. This paper investigates the source of this normal force and demonstrates that the asphalt binder can dilate when subjected to shear loads. This paper also presents the findings from a study conducted to investigate the source of the nonlinearity in the asphalt binder. Test results demonstrate that the application of cyclic shear loads results in the development of a normal force and a concomitant reduction in the dynamic shear modulus. This form of nonlinear response is referred to as an "interaction nonlinearity". A combination of experimental and analytical tools is used to demonstrate and verify the presence of this interaction nonlinearity in asphalt binders. The findings from this study highlight the importance of modeling the mechanical behavior of asphalt binders based on the overall stress state of the material.
Nonlinear Michelson interferometer for improved quantum metrology
Luis, Alfredo; Rivas, Ángel
2015-08-01
We examine quantum detection via a Michelson interferometer embedded in a gas with Kerr nonlinearity. This nonlinear interferometer is illuminated by pulses of classical light. This strategy combines the robustness against practical imperfections of classical light with the improvement provided by nonlinear processes. Regarding ultimate quantum limits, we stress that, as a difference with linear schemes, the nonlinearity introduces pulse duration as a new variable into play along with the energy resources.
Detecting the Nonlinearity of Fish Acoustic Signals
Institute of Scientific and Technical Information of China (English)
REN Xinmin; YIN Li
2006-01-01
This paper discusses the nonlinearity of fish acoustic signals by using the surrogate data method.We compare the difference of three test statistics - time-irreversibility Trey, correlation dimension D2 and auto mutual information function Ⅰbetween the original data and the surrogate data.We come to the conclusion that there exists nonlinearity in the fish acoustic signals and there exist deterministic nonlinear components; therefore nonlinear dynamic theory can be used to analyze fish acoustic signals.
Nonlinear Markov Control Processes and Games
2012-11-15
further research we indicated possible extensions to state spaces with nontrivial geometry, to the controlled nonlinear quantum dynamic semigroups and...space nonlinear Markov semigroup is a one-parameter semigroup of (possibly nonlinear) transformations of the unit simplex in n-dimensional Euclidean...certain mixing property of nonlinear transition probabilities. In case of the semigroup parametrized by continuous time one defines its generator as the
Nonlinear metrology with a quantum interface
Napolitano, M.; Mitchell, M. W.
2009-01-01
We describe nonlinear quantum atom-light interfaces and nonlinear quantum metrology in the collective continuous variable formalism. We develop a nonlinear effective Hamiltonian in terms of spin and polarization collective variables and show that model Hamiltonians of interest for nonlinear quantum metrology can be produced in $^{87}$Rb ensembles. With these Hamiltonians, metrologically relevant atomic properties, e.g. the collective spin, can be measured better than the "Heisenberg limit" $\\...
Nonlinear Michelson interferometer for improved quantum metrology
Luis Aina, Alfredo; Rivas Vargas, Ángel
2015-01-01
We examine quantum detection via a Michelson interferometer embedded in a gas with Kerr nonlinearity. This nonlinear interferometer is illuminated by pulses of classical light. This strategy combines the robustness against practical imperfections of classical light with the improvement provided by nonlinear processes. Regarding ultimate quantum limits, we stress that, as a difference with linear schemes, the nonlinearity introduces pulse duration as a new variable into play along with the ene...
Standing waves for discrete nonlinear Schrodinger equations
Directory of Open Access Journals (Sweden)
Ming Jia
2016-07-01
Full Text Available The discrete nonlinear Schrodinger equation is a nonlinear lattice system that appears in many areas of physics such as nonlinear optics, biomolecular chains and Bose-Einstein condensates. By using critical point theory, we establish some new sufficient conditions on the existence results of standing waves for the discrete nonlinear Schrodinger equations. We give an appropriate example to illustrate the conclusion obtained.
Nonlinear Young integrals via fractional calculus
Hu, Yaozhong (1961-); Le, Khoa
2015-01-01
For H\\"older continuous functions $W(t,x)$ and $\\varphi_t$, we define nonlinear integral $\\int_a^b W(dt, \\varphi_t)$ via fractional calculus. This nonlinear integral arises naturally in the Feynman-Kac formula for stochastic heat equations with random coefficients. We also define iterated nonlinear integrals.
Nonlinear approaches in engineering applications 2
Jazar, Reza N
2013-01-01
Provides updated principles and applications of the nonlinear approaches in solving engineering and physics problems Demonstrates how nonlinear approaches may open avenues to better, safer, cheaper systems with less energy consumption Has a strong emphasis on the application, physical meaning, and methodologies of nonlinear approaches in different engineering and science problems
Nonlinear quasimodes near elliptic periodic geodesics
Albin, Pierre; Marzuola, Jeremy L; Thomann, Laurent
2011-01-01
We consider the nonlinear Schr\\"odinger equation on a compact manifold near an elliptic periodic geodesic. Using a geometric optics construction, we construct quasimodes to a nonlinear stationary problem which are highly localized near the periodic geodesic. We show the nonlinear Schr\\"odinger evolution of such a quasimode remains localized near the geodesic, at least for short times.
Nonlinear time series modelling: an introduction
Simon M. Potter
1999-01-01
Recent developments in nonlinear time series modelling are reviewed. Three main types of nonlinear models are discussed: Markov Switching, Threshold Autoregression and Smooth Transition Autoregression. Classical and Bayesian estimation techniques are described for each model. Parametric tests for nonlinearity are reviewed with examples from the three types of models. Finally, forecasting and impulse response analysis is developed.
Variational principles for nonlinear piezoelectric materials
Energy Technology Data Exchange (ETDEWEB)
Rodriguez-Ramos, R.; Guinovart-Diaz, R. [Universidad de la Habana, Facultad de Matematica y Computacion, Vedado, Habana (Cuba); Pobedria, B.E. [Moscow State University M. V. Lomonosov, Composites Department, Moscow (Russian Federation); Padilla, P. [Universidad Nacional Autonoma de Mexico, Instituto de Investigaciones en Matematicas Aplicadas y en Sistemas (IIMAS), Cd. Universitaria, Mexico D.F. (Mexico); Bravo-Castillero, J. [Universidad de la Habana, Facultad de Matematica y Computacion, Vedado, Habana (Cuba); Campus Estado de Mexico. Division de Arquitectura e Ingenieria, Instituto Tecnologico de Estudios Superiores de Monterrey, Atizapan de Zaragoza, Estado de Mexico (Mexico); Maugin, G.A. [Universite Pierre et Marie Curie. Case 162, UMR 7607 CNRS, Laboratoire de Modelisation en Mecanique, Paris Cedex 05 (France)
2004-12-01
In the present paper, we consider the behavior of nonlinear piezoelectric materials by generalization for this case of the Hashin-Shtrikman variational principles. The new general formulation used here differs from others, because, it gives the possibility to evaluate the upper and lower Hashin-Shtrikman bounds for specific physical nonlinearities of piezoelectric materials. Geometrical nonlinearities are not considered. (orig.)
Unsymmetrical squaraines for nonlinear optical materials
Marder, Seth R. (Inventor); Chen, Chin-Ti (Inventor); Cheng, Lap-Tak (Inventor)
1996-01-01
Compositions for use in non-linear optical devices. The compositions have first molecular electronic hyperpolarizability (.beta.) either positive or negative in sign and therefore display second order non-linear optical properties when incorporated into non-linear optical devices.
Nonlinear parametric instability of wind turbine wings
DEFF Research Database (Denmark)
Larsen, Jesper Winther; Nielsen, Søren R.K.
2006-01-01
Nonlinear rotor dynamic is characterized by parametric excitation of both linear and nonlinear terms caused by centrifugal and Coriolis forces when formulated in a moving frame of reference. Assuming harmonically varying support point motions from the tower, the nonlinear parametric instability...