Derivation of an Applied Nonlinear Schroedinger Equation.
Energy Technology Data Exchange (ETDEWEB)
Pitts, Todd Alan; Laine, Mark Richard; Schwarz, Jens; Rambo, Patrick K.; Karelitz, David B.
2015-01-01
We derive from first principles a mathematical physics model useful for understanding nonlinear optical propagation (including filamentation). All assumptions necessary for the development are clearly explained. We include the Kerr effect, Raman scattering, and ionization (as well as linear and nonlinear shock, diffraction and dispersion). We explain the phenomenological sub-models and each assumption required to arrive at a complete and consistent theoretical description. The development includes the relationship between shock and ionization and demonstrates why inclusion of Drude model impedance effects alters the nature of the shock operator. Unclassified Unlimited Release
Derivation of an applied nonlinear Schroedinger equation
Energy Technology Data Exchange (ETDEWEB)
Pitts, Todd Alan [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Laine, Mark Richard [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Schwarz, Jens [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Rambo, Patrick K. [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Karelitz, David B. [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
2015-01-01
We derive from first principles a mathematical physics model useful for understanding nonlinear optical propagation (including filamentation). All assumptions necessary for the development are clearly explained. We include the Kerr effect, Raman scattering, and ionization (as well as linear and nonlinear shock, diffraction and dispersion). We explain the phenomenological sub-models and each assumption required to arrive at a complete and consistent theoretical description. The development includes the relationship between shock and ionization and demonstrates why inclusion of Drude model impedance effects alters the nature of the shock operator. Unclassified Unlimited Release
The exact solutions for a nonisospectral nonlinear Schroedinger equation
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Ning Tongke [Finance College, Shanghai Normal University, Shanghai 200234 (China)], E-mail: tkning@shnu.edu.cn; Zhang Weiguo; Jia Gao [Science College, University of Shanghai for Science and Technology, Shanghai 200093 (China)
2009-10-30
In this paper, lax pair for the nonisospectral nonlinear Schroedinger hierarchy is given, the time dependence of nonisospectral scattering data is derived and exact solutions for the nonisospectral nonlinear Schroedinger hierarchy are obtained through the inverse scattering transform.
The Homoclinic Orbits in Nonlinear Schroedinger Equation
Institute of Scientific and Technical Information of China (English)
PengchengXU; BolingGUO; 等
1998-01-01
The persistence of Homoclinic orbits for perturbed nonlinear Schroedinger equation with five degree term under een periodic boundary conditions is considered.The exstences of the homoclinic orbits for the truncation equation is established by Melnikov's analysis and geometric singular perturbation theory.
Generalized dromions of the （2＋1）—dimensional nonlinear Schroedinger equations
Institute of Scientific and Technical Information of China (English)
JiefangZHANG
2001-01-01
We derive the generalized dromions of the (2+1)-dimensional nonlinear Schroedinger equations besides the basic dromion solutions by sutably ustilising the arbitrary function in the bilinearized equatins.The rich dromion structures for this system are revealed.
A nonlinear Schroedinger wave equation with linear quantum behavior
Energy Technology Data Exchange (ETDEWEB)
Richardson, Chris D.; Schlagheck, Peter; Martin, John; Vandewalle, Nicolas; Bastin, Thierry [Departement de Physique, University of Liege, 4000 Liege (Belgium)
2014-07-01
We show that a nonlinear Schroedinger wave equation can reproduce all the features of linear quantum mechanics. This nonlinear wave equation is obtained by exploring, in a uniform language, the transition from fully classical theory governed by a nonlinear classical wave equation to quantum theory. The classical wave equation includes a nonlinear classicality enforcing potential which when eliminated transforms the wave equation into the linear Schroedinger equation. We show that it is not necessary to completely cancel this nonlinearity to recover the linear behavior of quantum mechanics. Scaling the classicality enforcing potential is sufficient to have quantum-like features appear and is equivalent to scaling Planck's constant.
The nonlinear Schroedinger equation on a disordered chain
Energy Technology Data Exchange (ETDEWEB)
Scharf, R.; Bishop, A.R.
1990-01-01
The integrable lattice nonlinear Schroedinger equation is a unique model with which to investigate the effects of disorder on a discrete integrable dynamics, and its interplay with nonlinearity. We first review some features of the lattice nonlinear Schroedinger equation in the absence of disorder and introduce a 1- and 2-soliton collective variable approximation. Then we describe the effect of different types of disorder: attractive and repulsive isolated impurities, spatially periodic potentials, random potentials, and time dependent (kicked) long wavelength perturbations. 18 refs., 15 figs.
Analytical exact solution of the non-linear Schroedinger equation
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Martins, Alisson Xavier; Rocha Filho, Tarcisio Marciano da [Universidade de Brasilia (UnB), DF (Brazil). Inst. de Fisica. Grupo de Fisica e Matematica
2011-07-01
Full text: In this work we present how to classify and obtain analytical solutions of the Schroedinger equation with a generic non-linearity in 1+1 dimensions. Our approach is based on the determination of Lie symmetry transformation mapping solutions into solutions, and non-classical symmetry transformations, mapping a given solution into itself. From these symmetries it is then possible to reduce the equation to a system of ordinary differential equations which can then be solved using standard methods. The generic non-linearity is handled by considering it as an additional unknown in the determining equations for the symmetry transformations. This results in an over-determined system of non-linear partial differential equations. Its solution can then be determined in some cases by reducing it to the so called involutive (triangular) form, and then solved. This reduction is very tedious and can only performed using a computer algebra system. Once the determining system is solved, we obtain the explicit form for the non-linearity admitting a Lie or non-classical symmetry. The analytical solutions are then derived by solving the reduced ordinary differential equations. The non-linear determining system for the non-classical symmetry transformations and Lie symmetry generators are obtaining using the computer algebra package SADE (symmetry analysis of differential equations), developed at our group. (author)
Exact solutions for the cubic-quintic nonlinear Schroedinger equation
Energy Technology Data Exchange (ETDEWEB)
Zhu Jiamin [Department of Physics, Zhejiang Lishui University, Lishui 323000 (China)]. E-mail: zjm64@163.com; Ma Zhengyi [Department of Physics, Zhejiang Lishui University, Lishui 323000 (China); Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072 (China)
2007-08-15
In this paper, the cubic-quintic nonlinear Schroedinger equation is solved through the extended elliptic sub-equation method. As a consequence, many types of exact travelling wave solutions are obtained which including bell and kink profile solitary wave solutions, triangular periodic wave solutions and singular solutions.
On the recovering of a coupled nonlinear Schroedinger potential
Energy Technology Data Exchange (ETDEWEB)
Corona, Gulmaro Corona [Area de Analisis Matematico y sus Aplicaciones, Universidad Autonoma Metropolitana, Atzcapotzalco, DF (Mexico)]. E-mail: ccg@hp9000a1.uam.mx
2000-04-28
We establish a priori conditions for a Gel'fand-Levitan (GL) integral using some results of the Fredholm theory. As consequence, we obtain a recovering formula for the potential of the coupled nonlinear Schroedinger equations. The remarkable fact is that the recovering formula is given in terms of the solutions of a classical GL-integral equation. (author)
Stochasticity in numerical solutions of the nonlinear Schroedinger equation
Shen, Mei-Mei; Nicholson, D. R.
1987-01-01
The cubically nonlinear Schroedinger equation is an important model of nonlinear phenomena in fluids and plasmas. Numerical solutions in a spatially periodic system commonly involve truncation to a finite number of Fourier modes. These solutions are found to be stochastic in the sense that the largest Liapunov exponent is positive. As the number of modes is increased, the size of this exponent appears to converge to zero, in agreement with the recent demonstration of the integrability of the spatially periodic case.
Defects in the discrete non-linear Schroedinger model
Energy Technology Data Exchange (ETDEWEB)
Doikou, Anastasia, E-mail: adoikou@upatras.gr [University of Patras, Department of Engineering Sciences, Physics Division, GR-26500 Patras (Greece)
2012-01-01
The discrete non-linear Schroedinger (NLS) model in the presence of an integrable defect is examined. The problem is viewed from a purely algebraic point of view, starting from the fundamental algebraic relations that rule the model. The first charges in involution are explicitly constructed, as well as the corresponding Lax pairs. These lead to sets of difference equations, which include particular terms corresponding to the impurity point. A first glimpse regarding the corresponding continuum limit is also provided.
Intermittency and solitons in the driven dissipative nonlinear Schroedinger equation
Moon, H. T.; Goldman, M. V.
1984-01-01
The cubic nonlinear Schroedinger equation, in the presence of driving and Landau damping, is studied numerically. As the pump intensity is increased, the system exhibits a transition from intermittency to a two-torus to chaos. The laminar phase of the intermittency is also a two-torus motion which corresponds in physical space to two identical solitons of amplitude determined by a power-balance equation.
Properties of some nonlinear Schroedinger equations motivated through information theory
Energy Technology Data Exchange (ETDEWEB)
Yuan, Liew Ding; Parwani, Rajesh R, E-mail: parwani@nus.edu.s [Department of Physics, National University of Singapore, Kent Ridge (Singapore)
2009-06-01
We update our understanding of nonlinear Schroedinger equations motivated through information theory. In particular we show that a q-deformation of the basic nonlinear equation leads to a perturbative increase in the energy of a system, thus favouring the simplest q = 1 case. Furthermore the energy minimisation criterion is shown to be equivalent, at leading order, to an uncertainty maximisation argument. The special value eta = 1/4 for the interpolation parameter, where leading order energy shifts vanish, implies the preservation of existing supersymmetry in nonlinearised supersymmetric quantum mechanics. Physically, eta might be encoding relativistic effects.
Energy Technology Data Exchange (ETDEWEB)
Belmonte-Beitia, Juan [Departamento de Matematicas, E.T.S. de Ingenieros Industriales and Instituto de Matematica Aplicada a la Ciencia y la Ingenieria (IMACI), Avda. Camilo Jose Cela 3, Universidad de Castilla-La Mancha, 13071 Ciudad Real (Spain)], E-mail: juan.belmonte@uclm.es; Calvo, Gabriel F. [Departamento de Matematicas, E.T.S. de Ingenieros Industriales and Instituto de Matematica Aplicada a la Ciencia y la Ingenieria (IMACI), Avda. Camilo Jose Cela 3, Universidad de Castilla-La Mancha, 13071 Ciudad Real (Spain)], E-mail: gabriel.fernandez@uclm.es
2009-01-19
In this Letter, by means of similarity transformations, we construct explicit solutions to the quintic nonlinear Schroedinger equation with potentials and nonlinearities depending both on time and on the spatial coordinates. We present the general approach and use it to study some examples and find nontrivial explicit solutions such as periodic (breathers), quasiperiodic and bright and dark soliton solutions.
Energy Technology Data Exchange (ETDEWEB)
Belmonte-Beitia, Juan [Departamento de Matematicas, E. T. S. de Ingenieros Industriales and Instituto de Matematica Aplicada a la Ciencia y la IngenierIa (IMACI), E. T. S. I. Industriales, Avda. Camilo Jose Cela, s/n Universidad de Castilla-La Mancha 13071 Ciudad Real (Spain)
2009-01-23
We introduce a model of a Bose-Einstein condensate based on the one-dimensional nonlinear Schroedinger equation, in which the nonlinear term depends on the domain. The nonlinear term changes a cubic term into a quintic term, according to the domain considered. We study the existence, stability and bifurcation of solutions, and use the qualitative theory of dynamical systems to study certain properties of such solutions.
Explicit and exact travelling wave solutions for the generalized derivative Schroedinger equation
Energy Technology Data Exchange (ETDEWEB)
Huang Dingjiang [Department of Applied Mathematics, Dalian University of Technology, Dalian 116024 (China)]. E-mail: hdj8116@163.com; Li Desheng [Department of Applied Mathematics, Dalian University of Technology, Dalian 116024 (China); Department of Mathematics, Shenyang Normal University, Shenyang 110034 (China); Zhang Hongqing [Department of Applied Mathematics, Dalian University of Technology, Dalian 116024 (China)
2007-02-15
In this paper, a new auxiliary equation expansion method and its algorithm is proposed by studying a first order nonlinear ordinary differential equation with a sixth-degree nonlinear term. Being concise and straightforward, the method is applied to the generalized derivative Schroedinger equation. As a result, some new exact travelling wave solutions are obtained which include bright and dark solitary wave solutions, triangular periodic wave solutions and singular solutions. This algorithm can also be applied to other nonlinear wave equations in mathematical physics.
Energy Technology Data Exchange (ETDEWEB)
Belmonte-Beitia, J [Departamento de Matematicas, E T S de Ingenieros Industriales and Instituto de Matematica Aplicada a la Ciencia y la IngenierIa (IMACI), Avda Camilo Jose Cela, 3 Universidad de Castilla-La Mancha 13071 Ciudad Real (Spain); Cuevas, J [Grupo de Fisica No Lineal, Departamento de Fisica Aplicada I, Escuela Universitaria Politecnica, C/Virgen de Africa, 7, 41011 Sevilla (Spain)], E-mail: juan.belmonte@uclm.es, E-mail: jcuevas@us.es
2009-04-24
In this paper, we construct, by means of similarity transformations, explicit solutions to the cubic-quintic nonlinear Schroedinger equation with potentials and nonlinearities depending on both time and spatial coordinates. We present the general approach and use it to calculate bright and dark soliton solutions for nonlinearities and potentials of physical interest in applications to Bose-Einstein condensates and nonlinear optics.
Energy Technology Data Exchange (ETDEWEB)
Nguyen, Ba Phi [Central University of Construction, Tuy Hoa (Viet Nam); Kim, Ki Hong [Ajou University, Suwon (Korea, Republic of)
2014-02-15
We study numerically the dynamics of an initially localized wave packet in one-dimensional nonlinear Schroedinger lattices with both local and nonlocal nonlinearities. Using the discrete nonlinear Schroedinger equation generalized by including a nonlocal nonlinear term, we calculate four different physical quantities as a function of time, which are the return probability to the initial excitation site, the participation number, the root-mean-square displacement from the excitation site and the spatial probability distribution. We investigate the influence of the nonlocal nonlinearity on the delocalization to self-trapping transition induced by the local nonlinearity. In the non-self-trapping region, we find that the nonlocal nonlinearity compresses the soliton width and slows down the spreading of the wave packet. In the vicinity of the delocalization to self-trapping transition point and inside the self-trapping region, we find that a new kind of self-trapping phenomenon, which we call partial self-trapping, takes place when the nonlocal nonlinearity is sufficiently strong.
Institute of Scientific and Technical Information of China (English)
ZHENGChun-Long; ZHANGJie-Fang; CHENLi-Qun
2003-01-01
Starting from a special Baecklund transform and a variable separation approach, a quite general variable separation solution of the generalized ( 2 + 1 )-dimensional perturbed nonlinear Schroedinger system is obtained. In addition to the single-valued localized coherent soliron excitations like dromions, breathers, instantons, peakons, and previously revealed chaotic localized solution, a new type of multi-valued (folded) localized excitation is derived by introducing some appropriate lower-dimensional multiple valued functions.
Energy Technology Data Exchange (ETDEWEB)
Wang Dengshan [CEMA and CIAS, Central Univ. of Finance and Economics, BJ (China); BNLCMP, Inst. of Physics, Chinese Academy of Sciences, BJ (China); Liu Yifang [School of Economics, Central Univ. of Finance and Economics, BJ (China)
2010-01-15
In this paper, with the aid of symbolic computation the bright soliton solutions of two variable-coefficient coupled nonlinear Schroedinger equations are obtained by Hirota's method. Some figures are plotted to illustrate the properties of the obtained solutions. The properties are meaningful for the investigation on the stability of soliton propagation in the optical soliton communications. (orig.)
Blow-up in nonlinear Schroedinger equations. I. A general review
DEFF Research Database (Denmark)
Juul Rasmussen, Jens; Rypdal, K.
1986-01-01
The general properties of a class of nonlinear Schroedinger equations: iut + p:∇∇u + f(|u|2)u = 0 are reviewed. Conditions for existence, uniqueness, and stability of solitary wave solutions are presented, along with conditions for blow-up and global existence for the Cauchy problem....
A nonlinear Schroedinger equation with two symmetric point interactions in one dimension
Energy Technology Data Exchange (ETDEWEB)
Kovarik, Hynek [Dipartimento di Matematica, Politecnico di Torino, Torino (Italy); Sacchetti, Andrea [Facolta di Scienze, Universita di Modena e Reggio Emilia, Modena (Italy)], E-mail: Hynek.Kovarik@polito.it, E-mail: Andrea.Sacchetti@unimore.it
2010-04-16
We consider a time-dependent one-dimensional nonlinear Schroedinger equation with a symmetric double-well potential represented by two Dirac's {delta}. Among our results we give an explicit formula for the integral kernel of the unitary semigroup associated with the linear part of the Hamiltonian. Then we establish the corresponding Strichartz-type estimate and we prove local existence and uniqueness of the solution to the original nonlinear probl0008.
Protogenov, A P
2001-01-01
The brief review of events, conditioned by the nonlinear modes strong correlations in the planar systems is presented. The analysis is limited by the Schroedinger nonlinear equation model. The fields stationary distributions are determined. The dependence of the particles number on the parameter characterizing the degree of looking, of the universal oscillation lines, is obtained. It is shown that by small values of this parameter there exists on the two-dimensional lattice the universal gravitation, which may be the dynamic cause of transition to the coherent state. The connection of the chiral nonlinear boundary modes with the violations of the Galilean-invariance of the considered system is discussed
Numerical approximation on computing partial sum of nonlinear Schroedinger eigenvalue problems
Institute of Scientific and Technical Information of China (English)
JiachangSUN; DingshengWANG; 等
2001-01-01
In computing electronic structure and energy band in the system of multiparticles,quite a large number of problems are to obtain the partial sum of the densities and energies by using “First principle”。In the ordinary method,the so-called self-consistency approach,the procedure is limited to a small scale because of its high computing complexity.In this paper,the problem of computing the partial sum for a class of nonlinear Schroedinger eigenvalue equations is changed into the constrained functional minimization.By space decompostion and Rayleigh-Schroedinger method,one approximating formula for the minimal is provided.The numerical experiments show that this formula is more precise and its quantity of computation is smaller.
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.)
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Mihalache, D.; Panoiu, N.-C.; Moldoveanu, F.; Baboiu, D.-M. [Dept. of Theor. Phys., Inst. of Atomic Phys., Bucharest (Romania)
1994-09-21
We used the Riemann problem method with a 3*3 matrix system to find the femtosecond single soliton solution for a perturbed nonlinear Schroedinger equation which describes bright ultrashort pulse propagation in properly tailored monomode optical fibres. Compared with the Gel'fand-Levitan-Marchenko approach, the major advantage of the Riemann problem method is that it provides the general single soliton solution in a simple and compact form. Unlike the standard nonlinear Schroedinger equation, here the single soliton solution exhibits periodic evolution patterns. (author)
Yang, Jianke
2012-01-01
Linear stability of both sign-definite (positive) and sign-indefinite solitary waves near pitchfork bifurcations is analyzed for the generalized nonlinear Schroedinger equations with arbitrary forms of nonlinearity and external potentials in arbitrary spatial dimensions. Bifurcations of linear-stability eigenvalues associated with pitchfork bifurcations are analytically calculated. It is shown that the smooth solution branch switches stability at the bifurcation point. In addition, the two bifurcated solution branches and the smooth branch have the opposite (same) stability when their power slopes have the same (opposite) sign. One unusual feature on the stability of these pitchfork bifurcations is that the smooth and bifurcated solution branches can be both stable or both unstable, which contrasts such bifurcations in finite-dimensional dynamical systems where the smooth and bifurcated branches generally have opposite stability. For the special case of positive solitary waves, stronger and more explicit stab...
Yang, Jianke
2016-01-01
Stability of soliton families in one-dimensional nonlinear Schroedinger equations with non-parity-time (PT)-symmetric complex potentials is investigated numerically. It is shown that these solitons can be linearly stable in a wide range of parameter values both below and above phase transition. In addition, a pseudo-Hamiltonian-Hopf bifurcation is revealed, where pairs of purely-imaginary eigenvalues in the linear-stability spectra of solitons collide and bifurcate off the imaginary axis, creating oscillatory instability, which resembles Hamiltonian-Hopf bifurcations of solitons in Hamiltonian systems even though the present system is dissipative and non-Hamiltonian. The most important numerical finding is that, eigenvalues of linear-stability operators of these solitons appear in quartets $(\\lambda, -\\lambda, \\lambda^*, -\\lambda^*)$, similar to conservative systems and PT-symmetric systems. This quartet eigenvalue symmetry is very surprising for non-PT-symmetric systems, and it has far-reaching consequences ...
An Analog of the Fourier Transform Associated with a Nonlinear One-Dimensional Schroedinger Equation
Zhidkov, E P
2001-01-01
We consider an eigenvalue problem which includes a nonlinear Schroedinger equation on the half-line [0,\\infty) and certain boundary conditions. It is shown that the spectrum of this problem fills a half-line and that to each point of the spectrum there corresponds a unique eigenfunction. The main result of the paper is that an arbitrary infinitely differentiable function g(x) rapidly decaying as x\\to\\infty and satisfying suitable boundary conditions at the point x=0 can be uniquely expanded into an integral over eigenfunctions similar to the representation of functions by the Fourier transform (the latter is obviously associated with a linear self-adjoint eigenvalue problem).
Directory of Open Access Journals (Sweden)
G. Wunner
2011-01-01
Full Text Available The coalescence of two eigenfunctions with the same energy eigenvalue is not possible in Hermitian Hamiltonians. It is, however, a phenomenon well known from non-hermitian quantum mechanics. It can appear, e.g., for resonances in open systems, with complex energy eigenvalues. If two eigenvalues of a quantum mechanical system which depends on two or more parameters pass through such a branch point singularity at a critical set of parameters, the point in the parameter space is called an exceptional point. We will demonstrate that exceptional points occur not only for non-hermitean Hamiltonians but also in the nonlinear Schroedinger equations which describe Bose-Einstein condensates, i.e., the Gross-Pitaevskii equation for condensates with a short-range contact interaction, and with additional long-range interactions. Typically, in these condensates the exceptional points are also found to be bifurcation points in parameter space. For condensates with a gravity-like interaction between the atoms, these findings can be confirmed in an analytical way.
Institute of Scientific and Technical Information of China (English)
马正义; 马松华; 杨毅
2012-01-01
The nonlinear Schroedinger equation is one of the most important nonlinear models with widely applications in physics. Based on a similarity transformation, the (2+1)-dimensional nonlinear Schroedinger equation with distributed coefficients is transformed into a traceable nonlinear Schroedinger equation, and then two types of rational solutions and several spatial solitons are derived.%非线性Schroedinger方程是物理学中具有广泛应用的非线性模型之一．本文采用相似变换，将具有色散系数的（2＋1）维非线性Schrioedinger方程简化成熟知的Schroedinger方程，进而得到原方程的有理解和一些空间孤子．
Skokos, Ch; Bodyfelt, J D; Papamikos, G; Eggl, S
2013-01-01
While symplectic integration methods based on operator splitting are well established in many branches of science, high order methods for Hamiltonian systems that split in more than two parts have not yet been studied in detail. We demonstrate ways to construct high order symplectic integrators for Hamiltonian systems that can be split in three integrable parts. Using these techniques for the integration of the disordered, discrete nonlinear Schroedinger equation, we show that three part split symplectic integrators are more efficient than other numerical methods for the long time integration of multidimensional systems, with respect to both accuracy and computational time.
Energy Technology Data Exchange (ETDEWEB)
Kozlowski, K.K. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Terras, V. [CNRS, ENS Lyon (France). Lab. de Physique
2010-12-15
We present a new method allowing us to derive the long-time and large-distance asymptotic behavior of the correlations functions of quantum integrable models from their exact representations. Starting from the form factor expansion of the correlation functions in finite volume, we explain how to reduce the complexity of the computation in the so-called interacting integrable models to the one appearing in free fermion equivalent models. We apply our method to the time-dependent zero-temperature current-current correlation function in the non-linear Schroedinger model and compute the first few terms in its asymptotic expansion. Our result goes beyond the conformal field theory based predictions: in the time-dependent case, other types of excitations than the ones on the Fermi surface contribute to the leading orders of the asymptotics. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Kozlowski, K.K.
2010-12-15
Starting from the form factor expansion in finite volume, we derive the multidimensional generalization of the so-called Natte series for the zero-temperature, time and distance dependent reduced density matrix in the non-linear Schroedinger model. This representation allows one to read-off straightforwardly the long-time/large-distance asymptotic behavior of this correlator. Our method of analysis reduces the complexity of the computation of the asymptotic behavior of correlation functions in the so-called interacting integrable models, to the one appearing in free fermion equivalent models. We compute explicitly the first few terms appearing in the asymptotic expansion. Part of these terms stems from excitations lying away from the Fermi boundary, and hence go beyond what can be obtained by using the CFT/Luttinger liquid based predictions. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Romero, MarIa de los Angeles Sandoval; Weder, Ricardo [Instituto de Investigaciones en Matematicas Aplicadas y en Sistemas, Universidad Nacional Autonoma de Mexico, Apartado Postal 20-726, Mexico DF 01000 (Mexico)
2006-09-15
We consider nonlinear Schroedinger equations with a potential, and non-local nonlinearities, that are models in mesoscopic physics, for example of a quantum capacitor, and that are also models of molecular structure. We study in detail the initial value problem for these equations, in particular, existence and uniqueness of local and global solutions, continuous dependence on the initial data and regularity. We allow for a large class of unbounded potentials. We have no restriction on the growth at infinity of the positive part of the potential. We also construct the scattering operator in the case of potentials that go to zero at infinity. Furthermore, we give a method for the unique reconstruction of the potential from the small amplitude limit of the scattering operator. In the case of the quantum capacitor, our method allows us to uniquely reconstruct all the physical parameters from the small amplitude limit of the scattering operator.
Kis, Z.; Janszky, J.; Vinogradov, An. V.; Kobayashi, T.
1996-01-01
The optical Schroedinger cat states are simple realizations of quantum states having nonclassical features. It is shown that vibrational analogues of such states can be realized in an experiment of double pulse excitation of vibrionic transitions. To track the evolution of the vibrational wave packet we derive a non-unitary time evolution operator so that calculations are made in a quasi Heisenberg picture.
Blow-up in nonlinear Schroedinger equations. II. Similarity structure of the blow-up singularity
DEFF Research Database (Denmark)
Rypdal, K.; Juul Rasmussen, Jens
1986-01-01
invariance and generalizations of the latter. This generalized "quasi-invariance" reveals the nature of the blow-up singularity and resolves an old controversy. Most of the previous work has been done on the cubic nonlinearity. We generalize the results to an arbitrary power nonlinearity....
Energy Technology Data Exchange (ETDEWEB)
Su, Chuan-Qi; Gao, Yi-Tian; Yu, Xin [Beijing Univ. of Aeronautics and Astronautics (China). Ministry-of-Education Key Lab. of Fluid Mechanics and National Lab. for Computational Fluid Dynamics; Xue, Long [Beijing Univ. of Aeronautics and Astronautics (China). Ministry-of-Education Key Lab. of Fluid Mechanics and National Lab. for Computational Fluid Dynamics; Aviation Univ. of Air Force, Liaoning (China). Flight Training Base
2015-07-01
Under investigation in this article is a higher-order nonlinear Schroedinger-Maxwell-Bloch (HNLS-MB) system for the optical pulse propagation in an erbium-doped fiber. Lax pair, Darboux transformation (DT), and generalised DT for the HNLS-MB system are constructed. Soliton solutions and rogue wave solutions are derived based on the DT and generalised DT, respectively. Properties of the solitons and rogue waves are graphically presented. The third-order dispersion parameter, fourth-order dispersion parameter, and frequency detuning all influence the characteristic lines and velocities of the solitons. The frequency detuning also affects the amplitudes of solitons. The separating function has no effect on the properties of the first-order rogue waves, except for the locations where the first-order rogue waves appear. The third-order dispersion parameter affects the propagation directions and shapes of the rogue waves. The frequency detuning influences the rogue-wave types of the module for the measure of polarization of resonant medium and the extant population inversion. The fourth-order dispersion parameter impacts the rogue-wave interaction range and also has an effect on the rogue-wave type of the extant population inversion. The value of separating function affects the spatial-temporal separation of constituting elementary rogue waves for the second-order and third-order rogue waves. The second-order and third-order rogue waves can exhibit the triangular and pentagon patterns under different choices of separating functions.
Reduction of the equation for lower hybrid waves in a plasma to a nonlinear Schroedinger equation
Karney, C. F. F.
1977-01-01
Equations describing the nonlinear propagation of waves in an anisotropic plasma are rarely exactly soluble. However it is often possible to make approximations that reduce the exact equations into a simpler equation. The use of MACSYMA to make such approximations, and so reduce the equation describing lower hybrid waves into the nonlinear Schrodinger equation which is soluble by the inverse scattering method is demonstrated. MACSYMA is used at several stages in the calculation only because there is a natural division between calculations that are easiest done by hand, and those that are easiest done by machine.
Vortex Nucleation in a Dissipative Variant of the Nonlinear Schroedinger Equation Under Rotation
2014-12-01
Vortices in Nonlinear Fields (Clarendon, UK, 1999). [2] Yu.S. Kivshar and B. Luther -Davies, Physics Reports 298, 81–197 (1998). [3] Y.S. Kivshar, J...Christou, V. Tikhonenko, B. Luther -Davies and L. Pismen, Optics Comm. 152, 198–206 (1998). [4] H.J. Lugt, Vortex Flow in Nature and Technology (John
Yang, Yunqing; Malomed, Boris A
2015-01-01
We analytically study rogue-wave (RW) solutions and rational solitons of an integrable fifth-order nonlinear Schr\\"odinger (FONLS) equation with three free parameters. It includes, as particular cases, the usual NLS, Hirota, and Lakshmanan-Porsezian-Daniel (LPD) equations. We present continuous-wave (CW) solutions and conditions for their modulation instability in the framework of this model. Applying the Darboux transformation to the CW input, novel first- and second-order RW solutions of the FONLS equation are analytically found. In particular, trajectories of motion of peaks and depressions of profiles of the first- and second-order RWs are produced by means of analytical and numerical methods. The solutions also include newly found rational and W-shaped one- and two-soliton modes. The results predict the corresponding dynamical phenomena in extended models of nonlinear fiber optics and other physically relevant integrable systems.
Interfaces Supporting Surface Gap Soliton Ground States in the 1D Nonlinear Schroedinger Equation
Dohnal, Tomas; Plum, Michael; Reichel, Wolfgang
2012-01-01
We consider the problem of verifying the existence of $H^1$ ground states of the 1D nonlinear Schr\\"odinger equation for an interface of two periodic structures: $$-u" +V(x)u -\\lambda u = \\Gamma(x) |u|^{p-1}u \\ {on} \\R$$ with $V(x) = V_1(x), \\Gamma(x)=\\Gamma_1(x)$ for $x\\geq 0$ and $V(x) = V_2(x), \\Gamma(x)=\\Gamma_2(x)$ for $x1$. The article [T. Dohnal, M. Plum and W. Reichel, "Surface Gap Soliton Ground States for the Nonlinear Schr\\"odinger Equation," \\textit{Comm. Math. Phys.} \\textbf{308}, 511-542 (2011)] provides in the 1D case an existence criterion in the form of an integral inequality involving the linear potentials $V_{1},V_2$ and the Bloch waves of the operators $-\\tfrac{d^2}{dx^2}+V_{1,2}-\\lambda$. We choose here the classes of piecewise constant and piecewise linear potentials $V_{1,2}$ and check this criterion for a set of parameter values. In the piecewise constant case the Bloch waves are calculated explicitly and in the piecewise linear case verified enclosures of the Bloch waves are computed ...
Costiner, Sorin; Taasan, Shlomo
1994-01-01
This paper presents multigrid (MG) techniques for nonlinear eigenvalue problems (EP) and emphasizes an MG algorithm for a nonlinear Schrodinger EP. The algorithm overcomes the mentioned difficulties combining the following techniques: an MG projection coupled with backrotations for separation of solutions and treatment of difficulties related to clusters of close and equal eigenvalues; MG subspace continuation techniques for treatment of the nonlinearity; an MG simultaneous treatment of the eigenvectors at the same time with the nonlinearity and with the global constraints. The simultaneous MG techniques reduce the large number of self consistent iterations to only a few or one MG simultaneous iteration and keep the solutions in a right neighborhood where the algorithm converges fast.
Energy Technology Data Exchange (ETDEWEB)
Herbert, John M. [Kansas State Univ., Manhattan, KS (United States). Dept. of Chemistry
1997-01-01
Rayleigh-Schroedinger perturbation theory is an effective and popular tool for describing low-lying vibrational and rotational states of molecules. This method, in conjunction with ab initio techniques for computation of electronic potential energy surfaces, can be used to calculate first-principles molecular vibrational-rotational energies to successive orders of approximation. Because of mathematical complexities, however, such perturbation calculations are rarely extended beyond the second order of approximation, although recent work by Herbert has provided a formula for the nth-order energy correction. This report extends that work and furnishes the remaining theoretical details (including a general formula for the Rayleigh-Schroedinger expansion coefficients) necessary for calculation of energy corrections to arbitrary order. The commercial computer algebra software Mathematica is employed to perform the prohibitively tedious symbolic manipulations necessary for derivation of generalized energy formulae in terms of universal constants, molecular constants, and quantum numbers. As a pedagogical example, a Hamiltonian operator tailored specifically to diatomic molecules is derived, and the perturbation formulae obtained from this Hamiltonian are evaluated for a number of such molecules. This work provides a foundation for future analyses of polyatomic molecules, since it demonstrates that arbitrary-order perturbation theory can successfully be applied with the aid of commercially available computer algebra software.
Generalization of Schroedinger invariance. Applications to Bose-Einstein condensation
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Stoimenov, S. [Institute of Nuclear Research and Nuclear Energy, Sofia (Bulgaria)
2009-05-15
The symmetries of non-linear Schroedinger equations with power-law non-linearities are investigated. It is shown that Galilei invariance can be extended to Schroedinger invariance if the coupling constant(s) in non-linearity is treated as dimensionful quantity. This is used to find a new non-stationary solutions from given stationary ones. (Abstract Copyright [2009], Wiley Periodicals, Inc.)
Bertola, Marco
2010-01-01
The semiclassical (zero-dispersion) limit of the one-dimensional focusing Nonlinear Schroedinger equation (NLS) with decaying potentials is studied in a full scaling neighborhood D of the point of gradient catastrophe (x_0,t_0). This neighborhood contains the region of modulated plane wave (with rapid phase oscillations), as well as the region of fast amplitude oscillations (spikes). In this paper we establish the following universal behaviors of the NLS solutions near the point of gradient catastrophe: i) each spike has the height 3|q_0(x_0,t_0,epsilon)| and uniform shape of the rational breather solution to the NLS, scaled to the size O(epsilon); ii) the location of the spikes are determined by the poles of the tritronquee solution of the Painleve I (P1) equation through an explicit diffeomorphism between D and a region into the Painleve plane; iii) if (x,t) belongs to D but lies away from the spikes, the asymptotics of the NLS solution q(x,t,epsilon) is given by the plane wave approximation q_0(x,t,epsilon...
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Gao, Zhe; Gao, Yi-Tian; Su, Chuan-Qi; Wang, Qi-Min; Mao, Bing-Qing [Beijing Univ. of Aeronautics and Astronautics (China). Ministry-of-Education Key Lab. of Fluid Mechanics and National Lab. for Computational Fluid Dynamics
2016-04-01
Under investigation in this article is a generalised nonlinear Schroedinger-Maxwell-Bloch system for the picosecond optical pulse propagation in an inhomogeneous erbium-doped silica optical fibre. Lax pair, conservation laws, Darboux transformation, and generalised Darboux transformation for the system are constructed; with the one- and two-soliton solutions, the first- and second-order rogue waves given. Soliton propagation is discussed. Nonlinear tunneling effect on the solitons and rogue waves are investigated. We find that (i) the detuning of the atomic transition frequency from the optical pulse frequency affects the velocity of the pulse when the detuning is small, (ii) nonlinear tunneling effect does not affect the energy redistribution of the soliton interaction, (iii) dispersion barrier/well has an effect on the soliton velocity, whereas nonlinear well/barrier does not, (iv) nonlinear well/barrier could amplify/compress the solitons or rogue waves in a smoother manner than the dispersion barrier/well, and (v) dispersion barrier could ''attract'' the nearby rogue waves, whereas the dispersion well has a repulsive effect on them.
Variable Separation Solution for （1＋1）-Dimensional Nonlinear Models Related to Schroedinger Equation
Institute of Scientific and Technical Information of China (English)
XUChang-Zhi; ZHANGJie-Fang
2004-01-01
A variable separation approach is proposed and successfully extended to the (1+1)-dimensional physics models. The new exact solution of (1+1)-dimensional nonlinear models related to Schr6dinger equation by the entrance of three arbitrary functions is obtained. Some special types of soliton wave solutions such as multi-soliton wave solution,non-stable soliton solution, oscillating soliton solution, and periodic soliton solutions are discussed by selecting the arbitrary functions appropriately.
Effective Schroedinger equations on submanifolds
Energy Technology Data Exchange (ETDEWEB)
Wachsmuth, Jakob
2010-02-11
In this thesis the time dependent Schroedinger equation is considered on a Riemannian manifold A with a potential that localizes a certain class of states close to a fixed submanifold C, the constraint manifold. When the potential is scaled in the directions normal to C by a small parameter epsilon, the solutions concentrate in an epsilon-neighborhood of the submanifold. An effective Schroedinger equation on the submanifold C is derived and it is shown that its solutions, suitably lifted to A, approximate the solutions of the original equation on A up to errors of order {epsilon}{sup 3} vertical stroke t vertical stroke at time t. Furthermore, it is proved that, under reasonable conditions, the eigenvalues of the corresponding Hamiltonians below a certain energy coincide upto errors of order {epsilon}{sup 3}. These results holds in the situation where tangential and normal energies are of the same order, and where exchange between normal and tangential energies occurs. In earlier results tangential energies were assumed to be small compared to normal energies, and rather restrictive assumptions were needed, to ensure that the separation of energies is maintained during the time evolution. The most important consequence of this thesis is that now constraining potentials that change their shape along the submanifold can be treated, which is the typical situation in applications like molecular dynamics and quantum waveguides.
Schroedinger Equation and the Quantization of Celestial Systems
Directory of Open Access Journals (Sweden)
Smarandache F.
2006-04-01
Full Text Available In the present article, we argue that it is possible to generalize Schroedinger equation to describe quantization of celestial systems. While this hypothesis has been described by some authors, including Nottale, here we argue that such a macroquantization was formed by topological superfluid vortice. We also provide derivation of Schroedinger equation from Gross-Pitaevskii-Ginzburg equation, which supports this superfluid dynamics interpretation.
Schroedinger's radial equation - Solution by extrapolation
Goorvitch, D.; Galant, D. C.
1992-01-01
A high-accuracy numerical method for the solution of a 1D Schroedinger equation that is suitable for a diatomic molecule, obtained by combining a finite-difference method with iterative extrapolation to the limit, is presently shown to have several advantages over more conventional methods. Initial guesses for the term values are obviated, and implementation of the algorithm is straightforward. The method is both less sensitive to round-off error, and faster than conventional methods for equivalent accuracy. These advantages are illustrated through the solution of Schroedinger's equation for a Morse potential function suited for HCl and a numerically derived Rydberg-Klein-Rees potential function for the X 1Sigma(+) state of CO.
Schroedinger`s statistical physics and some related themes
Energy Technology Data Exchange (ETDEWEB)
Darrigol, O. [Centre National de la Recherche Scientifique (CNRS), 75 - Paris (France)
1992-12-31
This article is divided in two sections. One is about the origins and contents of Schroedinger`s works in statistical physics: kinetic theory and statistical thermodynamics (diamagnetism, melting, specific heats, quantum degeneracy, detailed balancing and quantized waves, entropy definitions, quantized matter waves. The other is about general themes elaborated in this context and brought to bear on quantum theory: holism, acausality, and the Bild-conception of physical theory. 108 refs.
Lie symmetries of semi-linear Schroedinger equations and applications
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Stoimenov, Stoimen [Laboratoire de Physique des Materiaux (CNRS UMR 7556), Universite Henri Poincare Nancy I, B.P.239, F-54506 Vandoeuvre les Nancy Cedex (France); Henkel, Malte [Laboratoire de Physique des Materiaux (CNRS UMR 7556), Universite Henri Poincare Nancy I, B.P.239, F-54506 Vandoeuvre les Nancy Cedex (France)
2006-05-15
Conditional Lie symmetries of semi-linear 1D Schroedinger and diffusion equations are studied in case the mass (or the diffusion constant) is considered as an additional variable and/or where the couplings of the non-linear part have a non-vanishing scaling dimension. In this way, dynamical symmetries of semi-linear Schroedinger equations become related to certain subalgebras of a three-dimensional conformal Lie algebra (conf{sub 3}){sub C}. The representations of these subalgebras are classified and the complete list of conditionally invariant semi-linear Schroedinger equations is obtained. Applications to the phase-ordering kinetics of simple magnets and to simple particle-reaction models are briefly discussed.
A life of Erwin Schroedinger; Erwin Schroedinger. Eine Biographie
Energy Technology Data Exchange (ETDEWEB)
Moore, Walter J.
2012-07-01
Erwin Schroedinger (1887-1961) was a pioneer of quantum physics, one of the most important scientists of the 20th century at all and - a charming Austrian. He was a man with a passionate interest in people and ideas. Mostly known he became by his representation of quantum theory in the form of wave mechanics, for which he got the Nobel prize for physics and naturally by the famous thought experiment ''Schroedinger's cat''. Walter Moore's biography is very close to the person of Schroedinger and presents his scientific work in the context of his private friendships, his interest in mysticism, and in front of the moving background of the political events in Germany and Austria.
Newton-Cartan supergravity with torsion and Schroedinger supergravity
Bergshoeff, Eric; Zojer, Thomas
2015-01-01
We derive a torsionfull version of three-dimensional N=2 Newton-Cartan supergravity using a non-relativistic notion of the superconformal tensor calculus. The "superconformal" theory that we start with is Schroedinger supergravity which we obtain by gauging the Schroedinger superalgebra. We present two non-relativistic N=2 matter multiplets that can be used as compensators in the superconformal calculus. They lead to two different off-shell formulations which, in analogy with the relativistic case, we call "old minimal" and "new minimal" Newton-Cartan supergravity. We find similarities but also point out some differences with respect to the relativistic case.
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Paul, Wolfgang; Koeppe, Jeanette [Institut fuer Physik, Martin Luther Universitaet, 06099 Halle (Germany); Grecksch, Wilfried [Institut fuer Mathematik, Martin Luther Universitaet, 06099 Halle (Germany)
2016-07-01
The standard approach to solve a non-relativistic quantum problem is through analytical or numerical solution of the Schroedinger equation. We show a way to go around it. This way is based on the derivation of the Schroedinger equation from conservative diffusion processes and the establishment of (several) stochastic variational principles leading to the Schroedinger equation under the assumption of a kinematics described by Nelson's diffusion processes. Mathematically, the variational principle can be considered as a stochastic optimal control problem linked to the forward-backward stochastic differential equations of Nelson's stochastic mechanics. The Hamilton-Jacobi-Bellmann equation of this control problem is the Schroedinger equation. We present the mathematical background and how to turn it into a numerical scheme for analyzing a quantum system without using the Schroedinger equation and exemplify the approach for a simple 1d problem.
Bondeson, A.; Ott, E.; Antonsen, T. M., Jr.
1985-01-01
Certain first-order nonlinear ordinary differential equations exemplified by strongly damped, quasiperiodically driven pendula and Josephson junctions are isomorphic to Schroedinger equations with quasiperiodic potentials. The implications of this equivalence are discussed. In particular, it is shown that the transition to Anderson localization in the Schroedinger problem corresponds to the occurrence of a novel type of strange attractor in the pendulum problem. This transition should be experimentally observable in the frequency spectrum of the pendulum of Josephson junction.
A new propagation method for the radial Schroedinger equation
Devries, P. L.
1979-01-01
A new method for propagating the solution of the radial Schroedinger equation is derived from a Taylor series expansion of the wavefunction and partial re-summation of the infinite series. Truncation of the series yields an approximation to the exact propagator which is applied to a model calculation and found to be highly convergent.
Schroedinger vs. Navier–Stokes
Directory of Open Access Journals (Sweden)
P. Fernández de Córdoba
2016-01-01
Full Text Available Quantum mechanics has been argued to be a coarse-graining of some underlying deterministic theory. Here we support this view by establishing a map between certain solutions of the Schroedinger equation, and the corresponding solutions of the irrotational Navier–Stokes equation for viscous fluid flow. As a physical model for the fluid itself we propose the quantum probability fluid. It turns out that the (state-dependent viscosity of this fluid is proportional to Planck’s constant, while the volume density of entropy is proportional to Boltzmann’s constant. Stationary states have zero viscosity and a vanishing time rate of entropy density. On the other hand, the nonzero viscosity of nonstationary states provides an information-loss mechanism whereby a deterministic theory (a classical fluid governed by the Navier–Stokes equation gives rise to an emergent theory (a quantum particle governed by the Schroedinger equation.
Magnetic virial identities and applications to blow-up for Schroedinger and wave equations
Energy Technology Data Exchange (ETDEWEB)
Garcia, Andoni, E-mail: andoni.garcia@ehu.es [Departamento de Matematicas, Universidad del Pais Vasco, Apartado 644, 48080 Bilbao (Spain)
2012-01-13
We prove blow-up results for the solution of the initial-value problem with negative energy of the focusing mass-critical and supercritical nonlinear Schroedinger and the focusing energy-subcritical nonlinear wave equations with electromagnetic potential. (paper)
Hamiltonian Formalism of the Derivative Nonlinear Schrodinger Equation
Institute of Scientific and Technical Information of China (English)
CAI Hao; LIU Feng-Min; HUANG Nian-Ning
2003-01-01
A particular form of poisson bracket is introduced for the derivative nonlinear Schrodinger (DNLS) equation.And its Hamiltonian formalism is developed by a linear combination method. Action-angle variables are found.
Advances in Derivative-Free State Estimation for Nonlinear Systems
DEFF Research Database (Denmark)
Nørgaard, Magnus; Poulsen, Niels Kjølstad; Ravn, Ole
In this paper we show that it involves considerable advantages to use polynomial approximations obtained with an interpolation formula for derivation of state estimators for nonlinear systems. The estimators become more accurate than estimators based on Taylor approximations, and yet...
Effect of ordering ambiguity in constructing the Schroedinger equation on perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Jaghoub, M.I. [Hashemite University, Physics Department, P.O. Box 150459, Zarka (Jordan)
2006-05-15
This work explores the application of perturbation formalism, developed for isotropic velocity-dependent potentials, to three-dimensional Schroedinger equations obtained using different orderings of the Hamiltonian. It is found that the formalism is applicable to Schroedinger equations corresponding to three possible ordering ambiguities. The validity of the derived expressions is verified by considering examples admitting exact solutions. The perturbative results agree quite well with the exactly obtained ones. (orig.)
Short pulse equations and localized structures in frequency band gaps of nonlinear metamaterials
Energy Technology Data Exchange (ETDEWEB)
Tsitsas, N.L. [School of Applied Mathematical and Physical Sciences, National Technical University of Athens, Zografos, Athens 15773 (Greece); Horikis, T.P. [Department of Mathematics, University of Ioannina, Ioannina 45110 (Greece); Shen, Y.; Kevrekidis, P.G.; Whitaker, N. [Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003-4515 (United States); Frantzeskakis, D.J., E-mail: dfrantz@phys.uoa.g [Department of Physics, University of Athens, Panepistimiopolis, Zografos, Athens 157 84 (Greece)
2010-03-01
We consider short pulse propagation in nonlinear metamaterials characterized by a weak Kerr-type nonlinearity in their dielectric response. Two short-pulse equations (SPEs) are derived for the high- and low-frequency 'band gaps' (where linear electromagnetic waves are evanescent) with linear effective permittivity epsilon<0 and permeability mu>0. The structure of the solutions of the SPEs is also briefly discussed, and connections with the soliton solutions of the nonlinear Schroedinger equation are made.
Nonlinear propagation of a wave packet in a hard-walled circular duct
Nayfeh, A. H.
1975-01-01
The method of multiple scales is used to derive a nonlinear Schroedinger equation for the temporal and spatial modulation of the amplitudes and the phases of waves propagating in a hard-walled circular duct. This equation is used to show that monochromatic waves are stable and to determine the amplitude dependance of the cutoff frequencies.
Large Enhancement of Optical Nonlinearities of New Organophosphorus Fullerene Derivative
Institute of Scientific and Technical Information of China (English)
刘智波; 田建国; 臧维平; 周文远; 张春平; 郑建禺; 周迎春; 徐华
2003-01-01
Optical nonlinearities of new organophosphorus fullerene derivative were determined by the Z-scan method with a pulsed Q-switch Nd:YAG laser at 532nm. The experimental results demonstrated that the derivative has much larger excited-states nonlinear absorption and nonlinear refraction than C60. A five-level model was utilized to fit the experimental data, and a good agreement is reached. Some parameters such as excited-state absorption cross and refraction cross were obtained. To our knowledge, the excited-state cross section of new organophosphorus fullerene derivative and its effective ratio to the ground-state cross section are the largest values among the fullerene derivatives reported to date.
Representations of the Schroedinger group and matrix orthogonal polynomials
Energy Technology Data Exchange (ETDEWEB)
Vinet, Luc [Centre de recherches mathematiques, Universite de Montreal, CP 6128, succ. Centre-ville, Montreal, QC H3C 3J7 (Canada); Zhedanov, Alexei, E-mail: luc.vinet@umontreal.ca, E-mail: zhedanov@fti.dn.ua [Donetsk Institute for Physics and Technology, Donetsk 83114 (Ukraine)
2011-09-02
The representations of the Schroedinger group in one space dimension are explicitly constructed in the basis of the harmonic oscillator states. These representations are seen to involve matrix orthogonal polynomials in a discrete variable that have Charlier and Meixner polynomials as building blocks. The underlying Lie-theoretic framework allows for a systematic derivation of the structural formulas (recurrence relations, difference equations, Rodrigues' formula, etc) that these matrix orthogonal polynomials satisfy. (paper)
The phase space of the focused cubic Schroedinger equation: A numerical study
Energy Technology Data Exchange (ETDEWEB)
Burlakov, Yuri O. [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
1998-05-01
In a paper of 1988 [41] on statistical mechanics of the nonlinear Schroedinger equation, it was observed that a Gibbs canonical ensemble associated with the nonlinear Schroedinger equation exhibits behavior reminiscent of a phase transition in classical statistical mechanics. The existence of a phase transition in the canonical ensemble of the nonlinear Schroedinger equation would be very interesting and would have important implications for the role of this equation in modeling physical phenomena; it would also have an important bearing on the theory of weak solutions of nonlinear wave equations. The cubic Schroedinger equation, as will be shown later, is equivalent to the self-induction approximation for vortices, which is a widely used equation of motion for a thin vortex filament in classical and superfluid mechanics. The existence of a phase transition in such a system would be very interesting and actually very surprising for the following reasons: in classical fluid mechanics it is believed that the turbulent regime is dominated by strong vortex stretching, while the vortex system described by the cubic Schroedinger equation does not allow for stretching. In superfluid mechanics the self-induction approximation and its modifications have been used to describe the motion of thin superfluid vortices, which exhibit a phase transition; however, more recently some authors concluded that these equations do not adequately describe superfluid turbulence, and the absence of a phase transition in the cubic Schroedinger equation would strengthen their argument. The self-induction approximation for vortices takes into account only very localized interactions, and the existence of a phase transition in such a simplified system would be very unexpected. In this thesis the authors present a numerical study of the phase transition type phenomena observed in [41]; in particular, they find that these phenomena are strongly related to the splitting of the phase space into
Schroedinger's Cat is not Alone
Gato, Beatriz
2010-01-01
We introduce the `Complete Wave Function' and deduce that all living beings, not just Schroedinger's cat, are actually described by a superposition of `alive' and `dead' quantum states; otherwise they would never die. Therefore this proposal provides a quantum mechanical explanation to the world-wide observation that we all pass away. Next we consider the Measurement problem in the framework of M-theory. For this purpose, together with Schroedinger's cat we also place inside the box Rasputin's cat, which is unaffected by poisson. We analyse the system identifying its excitations (catons and catinos) and we discuss its evolution: either to a classical fight or to a quantum entanglement. We also propose the $BSV\\Psi$ scenario, which implements the Complete Wave Function as well as the Big Bang and the String Landscape in a very (super)natural way. Then we test the gravitational decoherence of the entangled system applying an experimental setting due to Galileo. We also discuss the Information Loss paradox. For ...
Institute of Scientific and Technical Information of China (English)
ZHANGJin-Liang; WANGMing-Liang
2004-01-01
The complex tanh-function expansion method was presented recently, and it can be applied to derive exact solutions to the Schroedinger-type nonlinear evolution equations directly without transformation. In this paper,the complex tanh-function expansion method is applied to derive the exact solutions to the general coupled nonlinear evolution equations. Zakharov system and a long-short-wave interaction system are considered as examples, and the new applications of the complex tanh-function expansion method are shown.
Lifshitz Space-Times for Schroedinger Holography
Hartong, Jelle; Obers, Niels A
2014-01-01
We show that asymptotically locally Lifshitz space-times are holographically dual to field theories that exhibit Schroedinger invariance. This involves a complete identification of the sources, which describe torsional Newton-Cartan geometry on the boundary and transform under the Schroedinger algebra. We furthermore identify the dual vevs from which we define and construct the boundary energy-momentum tensor and mass current and show that these obey Ward identities that are organized by the Schroedinger algebra. We also point out that even though the energy flux has scaling dimension larger than z+2, it can be expressed in terms of computable vev/source pairs.
Erwin Schroedinger, Francis Crick and epigenetic stability.
Ogryzko, Vasily V
2008-04-17
Schroedinger's book 'What is Life?' is widely credited for having played a crucial role in development of molecular and cellular biology. My essay revisits the issues raised by this book from the modern perspective of epigenetics and systems biology. I contrast two classes of potential mechanisms of epigenetic stability: 'epigenetic templating' and 'systems biology' approaches, and consider them from the point of view expressed by Schroedinger. I also discuss how quantum entanglement, a nonclassical feature of quantum mechanics, can help to address the 'problem of small numbers' that led Schroedinger to promote the idea of a molecular code-script for explaining the stability of biological order.
Erwin Schroedinger, Francis Crick and epigenetic stability
Directory of Open Access Journals (Sweden)
Ogryzko Vasily V
2008-04-01
Full Text Available Abstract Schroedinger's book 'What is Life?' is widely credited for having played a crucial role in development of molecular and cellular biology. My essay revisits the issues raised by this book from the modern perspective of epigenetics and systems biology. I contrast two classes of potential mechanisms of epigenetic stability: 'epigenetic templating' and 'systems biology' approaches, and consider them from the point of view expressed by Schroedinger. I also discuss how quantum entanglement, a nonclassical feature of quantum mechanics, can help to address the 'problem of small numbers' that led Schroedinger to promote the idea of a molecular code-script for explaining the stability of biological order.
Erwin Schroedinger, Francis Crick and epigenetic stability
Ogryzko, Vasily
2007-01-01
Schroedinger's book 'What is Life?' is widely credited for having played a crucial role in development of molecular and cellular biology. My essay revisits the issues raised by this book from the modern perspective of epigenetics and systems biology. I contrast two classes of potential mechanisms of epigenetic stability: 'epigenetic templating' and 'systems biology' approaches, and consider them from the point of view expressed by Schroedinger. I also discuss how quantum entanglement, a nonclassical feature of quantum mechanics, can help to address the 'problem of small numbers' that lead Schroedinger to promote the idea of molecular code-script for explanation of stability of biological order.
Advances in Derivative-Free State Estimation for Nonlinear Systems
DEFF Research Database (Denmark)
Nørgaard, Magnus; Poulsen, Niels Kjølstad; Ravn, Ole
In this paper we show that it involves considerable advantages to use polynomial approximations obtained with an interpolation formula for derivation of state estimators for nonlinear systems. The estimators become more accurate than estimators based on Taylor approximations, and yet the implemen......In this paper we show that it involves considerable advantages to use polynomial approximations obtained with an interpolation formula for derivation of state estimators for nonlinear systems. The estimators become more accurate than estimators based on Taylor approximations, and yet...... the implementation is significantly simpler as no derivatives are required. Thus, it is believed that estimators derived in this way can replace well-known filters, such as the extended Kalman filter (EKF) and its higher order relatives, in most practical applications. In addition to proposing a new set of state...
Energy Technology Data Exchange (ETDEWEB)
Gogoi, R; Kalita, L; Devi, N, E-mail: runmoni_gogoi@rediffmail.co, E-mail: latikakalita@rediffmail.co, E-mail: nirupama_cotton@rediffmail.co [Department of Mathematics, Cotton College, Guwahati-781001, Assam (India)
2010-02-01
Much interest was shown towards the studies on nonlinear stability in the late sixties. Plasma instabilities play an important role in plasma dynamics. More attention has been given towards stability analysis after recognizing that they are one of the principal obstacles in the way of a successful resolution of the problem of controlled thermonuclear fusion. Nonlinearity and dispersion are the two important characteristics of plasma instabilities. Instabilities and nonlinearity are the two important and interrelated terms. In our present work, the continuity and momentum equations for both ions and electrons together with the Poisson equation are considered as cold plasma model. Then we have adopted the modified reductive perturbation technique (MRPT) from Demiray [1] to derive the higher order equation of the Nonlinear Schroedinger equation (NLSE). In this work, detailed mathematical expressions and calculations are done to investigate the changing character of the modulation of ion acoustic plasma wave through our derived equation. Thus we have extended the application of MRPT to derive the higher order equation. Both progressive wave solutions as well as steady state solutions are derived and they are plotted for different plasma parameters to observe dark/bright solitons. Interesting structures are found to exist for different plasma parameters.
Periodic Wave Solutions of Generalized Derivative Nonlinear Schr(o)dinger Equation
Institute of Scientific and Technical Information of China (English)
ZHA Qi-Lao; LI Zhi-Bin
2008-01-01
A Darboux transformation of the generalized derivative nonlinear Schr(o)dinger equation is derived. As an application, some new periodic wave solutions of the generalized derivative nonlinear Schr(o)dinger equation are explicitly given.
Similarities Derived from 3-D Nonlinear Psychophysics: Variance Distributions.
Gregson, Robert A. M.
1994-01-01
The derivation of the variance of similarity judgments is made from the 3-D process in nonlinear psychophysics. The idea of separability of dimensions in metric space theories of similarity is replaced by one parameter that represents the degree of a form of interdimensional cross-sampling. (SLD)
Asymptotical Stability of Nonlinear Fractional Differential System with Caputo Derivative
2011-01-01
This paper deals with the stability of nonlinear fractional differential systems equipped with the Caputo derivative. At first, a sufficient condition on asymptotical stability is established by using a Lyapunov-like function. Then, the fractional differential inequalities and comparison method are applied to the analysis of the stability of fractional differential systems. In addition, some other sufficient conditions on stability are also presented.
Spectral Target Detection using Schroedinger Eigenmaps
Dorado-Munoz, Leidy P.
Applications of optical remote sensing processes include environmental monitoring, military monitoring, meteorology, mapping, surveillance, etc. Many of these tasks include the detection of specific objects or materials, usually few or small, which are surrounded by other materials that clutter the scene and hide the relevant information. This target detection process has been boosted lately by the use of hyperspectral imagery (HSI) since its high spectral dimension provides more detailed spectral information that is desirable in data exploitation. Typical spectral target detectors rely on statistical or geometric models to characterize the spectral variability of the data. However, in many cases these parametric models do not fit well HSI data that impacts the detection performance. On the other hand, non-linear transformation methods, mainly based on manifold learning algorithms, have shown a potential use in HSI transformation, dimensionality reduction and classification. In target detection, non-linear transformation algorithms are used as preprocessing techniques that transform the data to a more suitable lower dimensional space, where the statistical or geometric detectors are applied. One of these non-linear manifold methods is the Schroedinger Eigenmaps (SE) algorithm that has been introduced as a technique for semi-supervised classification. The core tool of the SE algorithm is the Schroedinger operator that includes a potential term that encodes prior information about the materials present in a scene, and enables the embedding to be steered in some convenient directions in order to cluster similar pixels together. A completely novel target detection methodology based on SE algorithm is proposed for the first time in this thesis. The proposed methodology does not just include the transformation of the data to a lower dimensional space but also includes the definition of a detector that capitalizes on the theory behind SE. The fact that target pixels and
Direct Perturbation Method for Derivative Nonlinear Schrodinger Equation
Institute of Scientific and Technical Information of China (English)
CHENG Xue-Ping; LIN Ji; HAN Ping
2008-01-01
We extend Lou's direct perturbation method for solving the nonlinear SchrSdinger equation to the case of the derivative nonlinear Schrodinger equation (DNLSE). By applying this method, different types of perturbation solutions axe obtained. Based on these approximate solutions, the analytical forms of soliton parameters, such as the velocity, the width and the initial position, are carried out and the effects of perturbation on solitons are analyzed at the same time. A numerical simulation of perturbed DNLSE finally verifies the results of the perturbation method.
Asymptotical Stability of Nonlinear Fractional Differential System with Caputo Derivative
Directory of Open Access Journals (Sweden)
Fengrong Zhang
2011-01-01
Full Text Available This paper deals with the stability of nonlinear fractional differential systems equipped with the Caputo derivative. At first, a sufficient condition on asymptotical stability is established by using a Lyapunov-like function. Then, the fractional differential inequalities and comparison method are applied to the analysis of the stability of fractional differential systems. In addition, some other sufficient conditions on stability are also presented.
Initial study of Schroedinger eigenmaps for spectral target detection
Dorado-Munoz, Leidy P.; Messinger, David W.
2016-08-01
Spectral target detection refers to the process of searching for a specific material with a known spectrum over a large area containing materials with different spectral signatures. Traditional target detection methods in hyperspectral imagery (HSI) require assuming the data fit some statistical or geometric models and based on the model, to estimate parameters for defining a hypothesis test, where one class (i.e., target class) is chosen over the other classes (i.e., background class). Nonlinear manifold learning methods such as Laplacian eigenmaps (LE) have extensively shown their potential use in HSI processing, specifically in classification or segmentation. Recently, Schroedinger eigenmaps (SE), which is built upon LE, has been introduced as a semisupervised classification method. In SE, the former Laplacian operator is replaced by the Schroedinger operator. The Schroedinger operator includes by definition, a potential term V that steers the transformation in certain directions improving the separability between classes. In this regard, we propose a methodology for target detection that is not based on the traditional schemes and that does not need the estimation of statistical or geometric parameters. This method is based on SE, where the potential term V is taken into consideration to include the prior knowledge about the target class and use it to steer the transformation in directions where the target location in the new space is known and the separability between target and background is augmented. An initial study of how SE can be used in a target detection scheme for HSI is shown here. In-scene pixel and spectral signature detection approaches are presented. The HSI data used comprise various target panels for testing simultaneous detection of multiple objects with different complexities.
Nonlinear wave propagation in a rapidly-spun fiber.
McKinstrie, C J; Kogelnik, H
2006-09-04
Multiple-scale analysis is used to study linear wave propagation in a rapidly-spun fiber and its predictions are shown to be consistent with results obtained by other methods. Subsequently, multiple-scale analysis is used to derive a generalized Schroedinger equation for nonlinear wave propagation in a rapidly-spun fiber. The consequences of this equation for pulse propagation and four-wave mixing are discussed briefly.
Iterative Solutions for Low Lying Excited States of a Class of Schroedinger Equation
Friedberg, R; Zhao, W Q
2006-01-01
The convergent iterative procedure for solving the groundstate Schroedinger equation is extended to derive the excitation energy and the wave function of the low-lying excited states. The method is applied to the one-dimensional quartic potential problem. The results show that the iterative solution converges rapidly when the coupling $g$ is not too small.
EXISTENCE TIME FOR THE SEMILINEAR SCHROEDINGER EQUATION
Institute of Scientific and Technical Information of China (English)
WeiMingjun
2003-01-01
Based on the methods introduced by Klainerman and Ponce.and Cohn.a lower bounded estimate of the existence time for a kind of semilinear Schroedinger equation is obtained in this paper.The implemantation of this method depends on the Lp-Lq estimate and the energy estimate.
New Ways to Solve the Schroedinger Equation
Friedberg, R
2004-01-01
We discuss a new approach to solve the low lying states of the Schroedinger equation. For a fairly large class of problems, this new approach leads to convergent iterative solutions, in contrast to perturbative series expansions. These convergent solutions include the long standing difficult problem of a quartic potential with either symmetric or asymmetric minima.
Schroedinger's Wave Structure of Matter (WSM)
Wolff, Milo; Haselhurst, Geoff
2009-10-01
The puzzling electron is due to the belief that it is a discrete particle. Einstein deduced this structure was impossible since Nature does not allow the discrete particle. Clifford (1876) rejected discrete matter and suggested structures in `space'. Schroedinger, (1937) also eliminated discrete particles writing: What we observe as material bodies and forces are nothing but shapes and variations in the structure of space. Particles are just schaumkommen (appearances). He rejected wave-particle duality. Schroedinger's concept was developed by Milo Wolff and Geoff Haselhurst (SpaceAndMotion.com) using the Scalar Wave Equation to find spherical wave solutions in a 3D quantum space. This WSM, the origin of all the Natural Laws, contains all the electron's properties including the Schroedinger Equation. The origin of Newton's Law F=ma is no longer a puzzle; It originates from Mach's principle of inertia (1883) that depends on the space medium and the WSM. Carver Mead (1999) at CalTech used the WSM to design Intel micro-chips correcting errors of Maxwell's magnetic Equations. Applications of the WSM also describe matter at molecular dimensions: alloys, catalysts, biology and medicine, molecular computers and memories. See ``Schroedinger's Universe'' - at Amazon.com
The Universe according to Schroedinger and Milo
Wolff, Milo
2009-10-01
The puzzling electron is due to the belief that it is a discrete particle. Schroedinger, (1937) eliminated discrete particles writing: What we observe as material bodies and forces are nothing but shapes and variations in the structure of space. Particles are just schaumkommen (appearances). Thus he rejected wave-particle duality. Schroedinger's concept was developed by Milo Wolff using a Scalar Wave Equation in 3D quantum space to find wave solutions. The resulting Wave Structure of Matter (WSM) contains all the electron's properties including the Schroedinger Equation. Further, Newton's Law F=ma is no longer a puzzle; It originates from Mach's principle of inertia (1883) that depends on the space medium and the WSM. These the origin of all the Natural Laws. Carver Mead (1999) at CalTech used the WSM to design Intel micro-chips and to correct errors of Maxwell's Equations. Applications of the WSM describe matter at molecular dimensions: Industrial alloys, catalysts, biology and medicine, molecular computers and memories. See book ``Schroedinger's Universe'' - at Amazon.com. Pioneers of the WSM are growing rapidly. Some are: SpaceAndMotion.com, QuantumMatter.com, treeincarnation.com/audio/milowolff.htm, daugerresearch.com/orbitals/index.shtml, glafreniere.com/matter.html =A new Universe.
Ultrafast third-order nonlinear optical response of pyrene derivatives
Shi, Yufang; Li, Zhongguo; Fang, Yu; Sun, Jinyu; Zhao, Minggen; Song, Yinglin
2017-05-01
Two mono-substituted pyrene derivatives with delocalized electron system 1-(pyren-1-yl)-3-(4-Methyl thiophene-2-yl) acrylic ketone (13#) and 1-(pyren-1-yl)-3-(4-bromo thiophene-2-yl) acrylic ketone (15#) were successfully synthesized. The resultant compounds were characterized by nuclear magnetic resonance (NMR), infrared spectroscopy (IR), high resolution mass spectrum (HR-MS), and UV-vis spectra. The third-order nonlinear optical properties of the compounds were investigated using Z-scan technique with femtosecond laser pulses at 500 nm and 700 nm, respectively. Both of the compounds showed a decrease in transmittance about the focus, which are typical of two-photon absorption. It was found that the two-photon absorption behavior of the pyrene derivatives were modified by substituents on thiophene ring. These results indicate that both compounds can be promising candidates for future optoelectronic and bio-imaging applications.
Linear and nonlinear propagation of water wave groups
Pierson, W. J., Jr.; Donelan, M. A.; Hui, W. H.
1992-01-01
Results are presented from a study of the evolution of waveforms with known analytical group shapes, in the form of both transient wave groups and the cloidal (cn) and dnoidal (dn) wave trains as derived from the nonlinear Schroedinger equation. The waveforms were generated in a long wind-wave tank of the Canada Centre for Inland Waters. It was found that the low-amplitude transients behaved as predicted by the linear theory and that the cn and dn wave trains of moderate steepness behaved almost as predicted by the nonlinear Schroedinger equation. Some of the results did not fit into any of the available theories for waves on water, but they provide important insight on how actual groups of waves propagate and on higher-order effects for a transient waveform.
On the solution of the coupled Schroedinger-KdV equation by the decomposition method
Energy Technology Data Exchange (ETDEWEB)
Kaya, Dogan; El-Sayed, Salah M
2003-06-23
In this Letter, we consider a coupled Schroedinger-Korteweg-de Vries equation (or Sch-KdV) equation with appropriate initial values using the Adomian's decomposition method (or ADM). In this method, the solution is calculated in the form of a convergent power series with easily computable components. The method does not need linearization, weak nonlinearity assumptions or perturbation theory. The convergence of the method as applied to Sch-KdV is illustrated numerically.
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...
Nonlinear optical response of some Graphene oxide and Graphene fluoride derivatives
Liaros, Nikolaos; Orfanos, Ioannis; Papadakis, Ioannis; Couris, Stelios
2016-12-01
The nonlinear optical properties of two graphene derivatives, graphene oxide and graphene fluoride, are investigated by means of the Z-scan technique employing 35 ps and 4 ns, visible (532 nm) laser excitation. Both derivatives were found to exhibit significant third-order nonlinear optical response at both excitation regimes, with the nonlinear absorption being relatively stronger and concealing the presence of nonlinear refraction under ns excitation, while ps excitation reveals the presence of both nonlinear absorption and refraction. Both nonlinear properties are of great interest for several photonics, opto-fluidics, opto-electronics and nanotechnology applications.
Chen, Yong; Yan, Zhenya
2017-01-01
The effect of derivative nonlinearity and parity-time-symmetric (PT -symmetric) potentials on the wave propagation dynamics is explored in the derivative nonlinear Schrödinger equation, where the physically interesting Scarf-II and harmonic-Hermite-Gaussian potentials are chosen. We study numerically the regions of unbroken and broken linear PT -symmetric phases and find some stable bright solitons of this model in a wide range of potential parameters even though the corresponding linear PT -symmetric phases are broken. The semielastic interactions between particular bright solitons and exotic incident waves are illustrated such that we find that particular nonlinear modes almost keep their shapes after interactions even if the exotic incident waves have evidently been changed. Moreover, we exert the adiabatic switching on PT -symmetric potential parameters such that a stable nonlinear mode with the unbroken linear PT -symmetric phase can be excited to another stable nonlinear mode belonging to the broken linear PT -symmetric phase.
A life of Erwin Schroedinger. 2. ed.; Erwin Schroedinger. Eine Biographie
Energy Technology Data Exchange (ETDEWEB)
Moore, Walter J.
2015-07-01
Erwin Schroedinger (1887-1961) was a pioneer of quantum physics, one of the most important scientist of the 20th century at all and a charming Austrian. He was a man with a passionate interest for men and ideas. Mostly known he became by his representation of quantum theory in the form of wave mechanics, for which he obtained the Nobel prize for physics and naturally by the famous thought experiment ''Schroedingers cat''. Walter Moore's biography is quite near to the person of Schroedinger and presents his scientific work in the context of his friendships, his interset for mysticism, and in front of the moving background of the political events in Germany and Austria.
Nonlinear viscosity derived by means of Grad's moment method
Eu, Byung Chan
2002-03-01
In this paper we examine the stress tensor component evolution equations recently derived by Uribe and Garcia-Colin [Phys. Rev. E 60, 4052 (1999)] for unidirectional flow at uniform temperature under the assumption/approximation of vanishing transversal velocity gradients. By removing this assumption/approximation we derive the stress tensor evolution equation from the Boltzmann equation within the framework of the Grad moment expansion for the case of uniform temperature (the same condition as theirs). Specializing the evolution equation to the case of steady unidirectional flow in a square channel, we obtain a set of steady state evolution equations for the components of the stress tensor. Because the transversal velocity gradients are not assumed to vanish in this paper in contrast to their paper, the present result is more general than theirs. Its special case corresponding to the one-dimensional flow considered by Uribe and Garcia-Colin is at variance with theirs because of a missing term in their stress evolution equation for the xy component. The nonlinear viscosity formulas are also different. A general remark is given with regard to the relation of dimensionalities of hydrodynamic equations and the kinetic equation underlying the former. They are not necessarily the same.
Synthesis of Imidazole Derivatives for Their Second-order Nonlinear Optics
Institute of Scientific and Technical Information of China (English)
无
2003-01-01
The design and the synthesis of two conjugated donor-acceptor imidazole derivatives(1, 2) were carried out for second-order nonlinear optics. The thermal properties, the transparency and second-order nonlinear optical properties of the molecules were investigated. The experimental results indicate that a good nonlinearity-transparency-thermal stability trade-off is achieved for them.
From qubits and actions to the Pauli-Schroedinger equation
Mizrahi, Salomon S
2010-01-01
Here I show that a classical or quantum bit state plus one simple operation, an action, are sufficient ingredients to derive a quantum dynamical equation that rules the sequential changes of the state. Then, by assuming that a freely moving massive particle is the qubit carrier, it is found that both, the particle position in physical space and the qubit state, change in time according to the Pauli-Schroedinger equation. So, this approach suggests the following conjecture: because it carries one qubit of information the particle motion has its description enslaved by the very existence of the internal degree of freedom. It is compelled to be no more described classically but by a wavefunction. I also briefly discuss the Dirac equation in terms of qubits.
Generalized Nonlinear Proca Equation and its Free-Particle Solutions
Nobre, F D
2016-01-01
We introduce a non-linear extension of Proca's field theory for massive vector (spin $1$) bosons. The associated relativistic nonlinear wave equation is related to recently advanced nonlinear extensions of the Schroedinger, Dirac, and Klein-Gordon equations inspired on the non-extensive generalized thermostatistics. This is a theoretical framework that has been applied in recent years to several problems in nuclear and particle physics, gravitational physics, and quantum field theory. The nonlinear Proca equation investigated here has a power-law nonlinearity characterized by a real parameter $q$ (formally corresponding to the Tsallis entropic parameter) in such a way that the standard linear Proca wave equation is recovered in the limit $q \\rightarrow 1$. We derive the nonlinear Proca equation from a Lagrangian that, besides the usual vectorial field $\\Psi^{\\mu}(\\vec{x},t)$, involves an additional field $\\Phi^{\\mu}(\\vec{x},t)$. We obtain exact time dependent soliton-like solutions for these fields having the...
Nonlinear Optical Properties of Novel C60 Derivatives under Picosecond Laser Excitation
Institute of Scientific and Technical Information of China (English)
MAO Yan-Li; CHENG Yong-Guang; LIU Jun-Hui; LIN Bing-chen; HUO Yan-Ping; ZENG He-Ping
2007-01-01
We investigate the third-order nonlinear optical properties of six novel fullerene derivatives under picosecond laser excitation by Z-scan technique.The experimental results reveal that all the derivatives have very large nonlinear absorption coefficient under 532 nm pulses excitation and great third-order nonlinear refraction index under 1064 nm pulses excitation.The molecular second hyperpolarizabilities are obtained from the experimental results.
Schroedinger Eigenmaps for the analysis of biomedical data.
Czaja, Wojciech; Ehler, Martin
2013-05-01
We introduce Schroedinger Eigenmaps (SE), a new semi-supervised manifold learning and recovery technique. This method is based on an implementation of graph Schroedinger operators with appropriately constructed barrier potentials as carriers of labeled information. We use our approach for the analysis of standard biomedical datasets and new multispectral retinal images.
Stable explicit schemes for equations of Schroedinger type
Mickens, Ronald E.
1989-01-01
A method for constructing explicit finite-difference schemes which can be used to solve Schroedinger-type partial-differential equations is presented. A forward Euler scheme that is conditionally stable is given by the procedure. The results presented are based on the analysis of the simplest Schroedinger type equation.
Schroedinger Eigenmaps for the Analysis of Bio-Medical Data
Czaja, Wojciech
2011-01-01
We introduce Schroedinger Eigenmaps, a new semi-supervised manifold learning and recovery technique. This method is based on an implementation of graph Schroedinger operators with appropriately constructed barrier potentials as carriers of labeled information. We apply it to analyze two complex bio-medical datasets: multispectral retinal images and microarray gene expressions.
Solving the Schroedinger equation using Smolyak interpolants.
Avila, Gustavo; Carrington, Tucker
2013-10-07
In this paper, we present a new collocation method for solving the Schroedinger equation. Collocation has the advantage that it obviates integrals. All previous collocation methods have, however, the crucial disadvantage that they require solving a generalized eigenvalue problem. By combining Lagrange-like functions with a Smolyak interpolant, we device a collocation method that does not require solving a generalized eigenvalue problem. We exploit the structure of the grid to develop an efficient algorithm for evaluating the matrix-vector products required to compute energy levels and wavefunctions. Energies systematically converge as the number of points and basis functions are increased.
A Photonic Basis for Deriving Nonlinear Optical Response
Andrews, David L.; Bradshaw, David S.
2009-01-01
Nonlinear optics is generally first presented as an extension of conventional optics. Typically the subject is introduced with reference to a classical oscillatory electric polarization, accommodating correction terms that become significant at high intensities. The material parameters that quantify the extent of the nonlinear response are cast as…
Energy Technology Data Exchange (ETDEWEB)
Asselmeyer, T.
1997-12-22
First we introduce a simple model for the description of evolutionary algorithms, which is based on 2nd order partial differential equations for the distribution function of the individuals. Then we turn to the properties of Boltzmann's and Darwin's strategy. the next chapter is dedicated to the mathematical properties of Schroedinger operators. Both statements on the spectral density and their reproducibility during the simulation are summarized. The remaining of this chapter are dedicated to the analysis of the kernel as well as the dependence of the Schroedinger operator on the potential. As conclusion from the results of this chapter we obtain the classification of the strategies in dependence of the fitness. We obtain the classification of the evolutionary strategies, which are described by a 2nd order partial differential equation, in relation to their solution behaviour. Thereafter we are employed with the variation of the mutation distribution.
The Schroedinger-Virasoro algebra. Mathematical structure and dynamical Schroedinger symmetries
Energy Technology Data Exchange (ETDEWEB)
Unterberger, Jeremie [Henri Poincare Univ., Vandoeuvre-les-Nancy (France). Inst. Elie Cartan; Roger, Claude [Lyon I Univ., Villeurbanne (France). Dept. de Mathematiques
2012-07-01
This monograph provides the first up-to-date and self-contained presentation of a recently discovered mathematical structure the Schroedinger-Virasoro algebra. Just as Poincare invariance or conformal (Virasoro) invariance play a key role in understanding, respectively, elementary particles and two-dimensional equilibrium statistical physics, this algebra of non-relativistic conformal symmetries may be expected to apply itself naturally to the study of some models of non-equilibrium statistical physics, or more specifically in the context of recent developments related to the non-relativistic AdS/CFT correspondence. The study of the structure of this infinite-dimensional Lie algebra touches upon topics as various as statistical physics, vertex algebras, Poisson geometry, integrable systems and supergeometry as well as representation theory, the cohomology of infinite-dimensional Lie algebras, and the spectral theory of Schroedinger operators. (orig.)
Marchenko Equation for the Derivative Nonlinear Schr(o)dinger Equation
Institute of Scientific and Technical Information of China (English)
HUANG Nian-Ning
2007-01-01
A simple derivation of the Marchenko equation is given for the derivative nonlinear Schr(o)dinger equation.The kernel of the Marchenko equation is demanded to satisfy the conditions given by the compatibility equations.the soliton solutions to the Marchenko equation are verified.The derivation is not concerned with the revisions of Kaup and Newell.
Vector solitons in nonlinear isotropic chiral metamaterials
Energy Technology Data Exchange (ETDEWEB)
Tsitsas, N L [School of Applied Mathematical and Physical Sciences, National Technical University of Athens, Zografos, Athens 15773 (Greece); Lakhtakia, A [Department of Engineering Science and Mechanics, Pennsylvania State University, University Park, PA 16802-6812 (United States); Frantzeskakis, D J, E-mail: dfrantz@phys.uoa.gr [Department of Physics, University of Athens, Panepistimiopolis, Zografos, Athens 15784 (Greece)
2011-10-28
Starting from the Maxwell equations, we used the reductive perturbation method to derive a system of two coupled nonlinear Schroedinger (NLS) equations for the two Beltrami components of the electromagnetic field propagating along a fixed direction in an isotropic nonlinear chiral metamaterial. With single-resonance Lorentz models for the permittivity and permeability and a Condon model for the chirality parameter, in certain spectral regimes, one of the two Beltrami components exhibits a negative-real refractive index when nonlinearity is ignored and the chirality parameter is sufficiently large. We found that, inside such a spectral regime, there may exist a subregime wherein the system of the NLS equations can be approximated by the Manakov system. Bright-bright, dark-dark, and dark-bright vector solitons can be formed in that spectral subregime. (paper)
Institute of Scientific and Technical Information of China (English)
LIN Xiangguo; LIANG Yong
2005-01-01
The processing of nonlinear data was one of hot topics in surveying and mapping field in recent years.As a result, many linear methods and nonlinear methods have been developed.But the methods for processing generalized nonlinear surveying and mapping data, especially for different data types and including unknown parameters with random or nonrandom, are seldom noticed.A new algorithm model is presented in this paper for processing nonlinear dynamic multiple-period and multiple-accuracy data derived from deformation monitoring network.
Optimum sensitivity derivatives of objective functions in nonlinear programming
Barthelemy, J.-F. M.; Sobieszczanski-Sobieski, J.
1983-01-01
The feasibility of eliminating second derivatives from the input of optimum sensitivity analyses of optimization problems is demonstrated. This elimination restricts the sensitivity analysis to the first-order sensitivity derivatives of the objective function. It is also shown that when a complete first-order sensitivity analysis is performed, second-order sensitivity derivatives of the objective function are available at little additional cost. An expression is derived whose application to linear programming is presented.
Directory of Open Access Journals (Sweden)
Süleyman Öğrekçi
2015-01-01
Full Text Available We propose an efficient analytic method for solving nonlinear differential equations of fractional order. The fractional derivative is defined in the sense of modified Riemann-Liouville derivative. A new technique for calculating the generalized Taylor series coefficients (also known as “generalized differential transforms,” GDTs of nonlinear functions and a new approach of the generalized Taylor series method (GTSM are presented. This new method offers a simple algorithm for computing GDTs of nonlinear functions and avoids massive computational work that usually arises in the standard method. Several illustrative examples are demonstrated to show effectiveness of the proposed method.
Umezawa, Hirohito; Jackson, Matthew; Lebel, Olivier; Nunzi, Jean-Michel; Sabat, Ribal Georges
2016-10-01
The second-order nonlinear optical coefficients of thin films of mexylaminotriazine-functionalized azobenzene molecular glass derivatives were measured using second harmonic generation. The thin films were poled using a custom corona poling set-up and the second harmonic light from a pulsed 1064-nm laser was detected. Four out of the six tested compounds showed optical nonlinearity and a maximum coefficient of 75 pm/V was obtained. The time dependence of the nonlinear coefficients was studied under ambient light and under dark; the second harmonic generation intensity stayed constant for thiazole-containing derivatives while a significant decay was measured for the other compounds.
Chains of Darboux transformations for the matrix Schroedinger equation
Samsonov, B F; Samsonov, Boris F; Pecheritsin, AA
2004-01-01
Chains of Darboux transformations for the matrix Schroedinger equation are considered. Matrix generalization of the well-known for the scalar equation Crum-Krein formulas for the resulting action of such chains is given.
An Asymptotic Derivation of Weakly Nonlinear Ray Theory
Indian Academy of Sciences (India)
Phoolan Prasad
2000-11-01
Using a method of expansion similar to Chapman–Enskog expansion, a new formal perturbation scheme based on high frequency approximation has been constructed. The scheme leads to an eikonal equation in which the leading order amplitude appears. The transport equation for the amplitude has been deduced with an error (2) where is the small parameter appearing in the high frequency approximation. On a length scale over which Choquet–Bruhat's theory is valid, this theory reduces to the former. The theory is valid on a much larger length scale and the leading order terms give the weakly nonlinear ray theory (WNLRT) of Prasad, which has been very successful in giving physically realistic results and also in showing that the caustic of a linear theory is resolved when nonlinear effects are included. The weak shock ray theory with infinite system of compatibility conditions also follows from this theory.
Studies on third-order nonlinear optical properties of chalcone derivatives in polymer host
Shettigar, Seetharam; Umesh, G.; Chandrasekharan, K.; Sarojini, B. K.; Narayana, B.
2008-04-01
In this paper we present the experimental study of the third-order nonlinear optical properties of two chalcone derivatives, viz., 1-(4-methoxyphenyl)-3-(4-butyloxyphenyl)-prop-2-en-1-one and 1-(4-methoxyphenyl)-3-(4-propyloxyphenyl)-prop-2-en-1-one in PMMA host, with the prospective of reaching a compromise between good processability and high nonlinear optical properties. The nonlinear optical properties have been investigated by Z-scan technique using 7 ns laser pulses at 532 nm. The nonlinear refractive index, nonlinear absorption coefficient, magnitude of third-order susceptibility and the coupling factor have been determined. The values obtained are of the order of 10 -14 cm 2/W, 1 cm/GW, 10 -13 esu and 0.2, respectively. The molecular second hyperpolarizability for the chalcone derivatives in polymer is of the order of 10 -31 esu. Different guest/host concentrations have also been studied. The results suggest that the nonlinear properties of the chalcones have been improved when they are used as dopants in polymer matrix. The nonlinear parameters obtained are comparable with the reported values of II-VI compound semiconductors. Hence, these chalcons are a promising class of nonlinear optical dopant materials for optical device applications.
Institute of Scientific and Technical Information of China (English)
WANG Peng-Zhou; ZHANG Shun-Li
2008-01-01
We present basic theory of variable separation for (1 + 1)-dimensional nonlinear evolution equations with mixed partial derivatives. As an application, we classify equations uxt = A(u, ux)uxxx + B(u, ux) that admits derivative-dependent functional separable solutions (DDFSSs) and illustrate how to construct those DDFSSs with some examples.
Nonlinear Schroedinger excitations scattering on local barrier in one dimension
Kovrizhin, D L
2001-01-01
The task on the excitations scattering of the Bose condensate under consideration on the unidimensional barrier is nontrivial one even in the case of a low barrier because the barrier itself and change in the condensate density in its vicinity play the similar important role. It is shown that if any repulsive barrier for a bare particle within the range of the waves high lengths is impermeable, than the coefficient of the delta-functional transmission for the phonons within this range strives to the unity and the barrier becomes transparent
Directory of Open Access Journals (Sweden)
Jessada Tariboon
2014-01-01
Full Text Available We study existence and uniqueness of solutions for a problem consisting of nonlinear Langevin equation of Hadamard-Caputo type fractional derivatives with nonlocal fractional integral conditions. A variety of fixed point theorems are used, such as Banach’s fixed point theorem, Krasnoselskii’s fixed point theorem, Leray-Schauder’s nonlinear alternative, and Leray-Schauder’s degree theory. Enlightening examples illustrating the obtained results are also presented.
Positive Solution of a Nonlinear Fractional Differential Equation Involving Caputo Derivative
Directory of Open Access Journals (Sweden)
Changyou Wang
2012-01-01
Full Text Available This paper is concerned with a nonlinear fractional differential equation involving Caputo derivative. By constructing the upper and lower control functions of the nonlinear term without any monotone requirement and applying the method of upper and lower solutions and the Schauder fixed point theorem, the existence and uniqueness of positive solution for the initial value problem are investigated. Moreover, the existence of maximal and minimal solutions is also obtained.
Ramachandran, S.; Wells, W. R.
1974-01-01
This paper is concerned with the estimation of stability and control parameters of a high performance fighter aircraft from data obtained from high angle of attack flight. The estimation process utilizes a maximum likelihood algorithm derived for the case of a nonlinear aerodynamic force and moment model. The aircraft used was a high speed variable sweep heavy weight fighter with twin vertical tails. Comparisons of results from the nonlinear analysis are made with linear theory and wind tunnel results when available.
Institute of Scientific and Technical Information of China (English)
FU, Wei; FENG, Ji-Kang; YU, Kun-Qian; REN, Ai-Min; CUI, Meng
2000-01-01
On the basis of Z1NDO methods, according to the sum-overstates (SOS) expression, the progran for the calculation of the second-order nonlinear optical susceptibilities βuk and βμ ofmolecules was devised, and the structures and nonlinear optical properties of unsymmetric bis (phenylethynyl) benzene series derivatives were studied. The influence of the molecular conjugated chain lengths, the donor and the acceptor on βμwas examined.
Sudheesh, P.; Rao, D. Mallikharjuna; Chandrasekharan, K.
2014-01-01
The third-order nonlinear optical properties of newly synthesized phenylhydrazone derivatives and the influence of noble metal nanoparticles (Ag & Au) on their nonlinear optical responses were investigated by employing Degenerate Four wave Mixing (DFWM) technique with a 7 nanosecond, 10Hz Nd: YAG laser pulses at 532nm. Metal nanoparticles were prepared by laser ablation and the particle formation was confirmed using UV-Visible spectroscopy, Transmission Electron Microscopy (TEM). The nonlinear optical susceptibility were measured and found to be of the order 10-13esu. The results are encouraging and conclude that the materials are promising candidate for future optical device applications.
Kirilyuk, A P
2001-01-01
Following Max Planck's hypothesis of quanta (quant-ph/0012069) and the matter wave idea of Louis de Broglie (quant-ph/9911107), Erwin Schroedinger proposed, at the beginning of 1926, the concept of the wavefunction and the wave equation for it. Though endowed with a realistic undular interpretation by its farther, the wavefunction could not be considered as a real 'matter wave' and has been provided with the abstract, formally probabilistic interpretation. In this paper we show how the resulting 'mysteries' of the standard theory are resolved within the unreduced, dynamically multivalued description of the underlying, essentially nonlinear interaction process (quant-ph/9902015, quant-ph/9902016), without artificial modification of the Schroedinger equation. The causal, totally realistic wavefunction emerges as the dynamically probabilistic intermediate state of a simple system with interaction performing dynamically discrete transitions between its localised, incompatible 'realisations' ('corpuscular' states)...
Rigatos, Gerasimos
2016-07-01
The Derivative-free nonlinear Kalman Filter is used for developing a communication system that is based on a chaotic modulator such as the Duffing system. In the transmitter's side, the source of information undergoes modulation (encryption) in which a chaotic signal generated by the Duffing system is the carrier. The modulated signal is transmitted through a communication channel and at the receiver's side demodulation takes place, after exploiting the estimation provided about the state vector of the chaotic oscillator by the Derivative-free nonlinear Kalman Filter. Evaluation tests confirm that the proposed filtering method has improved performance over the Extended Kalman Filter and reduces significantly the rate of transmission errors. Moreover, it is shown that the proposed Derivative-free nonlinear Kalman Filter can work within a dual Kalman Filtering scheme, for performing simultaneously transmitter-receiver synchronisation and estimation of unknown coefficients of the communication channel.
Chen, Xiang-Jun; Lam, Wa Kun
2004-06-01
An inverse scattering transform for the derivative nonlinear Schrödinger equation with nonvanishing boundary conditions is derived by introducing an affine parameter to avoid constructing Riemann sheets. A one-soliton solution simpler than that in the literature is obtained, which is a breather and degenerates to a bright or dark soliton as the discrete eigenvalue becomes purely imaginary. The solution is mapped to that of the modified nonlinear Schrödinger equation by a gaugelike transformation, predicting some sub-picosecond solitons in optical fibers.
Mickens, Ronald E.
1989-01-01
A family of conditionally stable, forward Euler finite difference equations can be constructed for the simplest equation of Schroedinger type, namely u sub t - iu sub xx. Generalization of this result to physically realistic Schroedinger type equations is presented.
Ferroelectric nanofibers with an embedded optically nonlinear benzothiazole derivative
Baptista, Rosa M. F.; Isakov, Dmitry; Raposo, M. Manuela M.; Belsley, Michael; Bdikin, Igor; Kholkin, Andrei L.; Costa, Susana P. G.; de Matos Gomes, Etelvina
2014-07-01
We report measurements of the molecular first hyperpolarizability, thermal stability, photophysical, piezoelectric, and ferroelectric properties of a benzothiazole derivative bearing an arylthiophene π-conjugated bridge both in solution and when embedded into a poly ( l-lactic acid) matrix in the form of electrospun fibers with an average diameter of roughly 500 nm. The embedded nanocrystalline phenylthienyl-benzothiazole with crystal sizes of about 1.4 nm resulted in a good piezoelectric response from these functionalized electrospun fibers, indicative of a polar crystalline structure.
Some Exact Results for the Schroedinger Wave Equation with a Time Dependent Potential
Campbell, Joel
2009-01-01
The time dependent Schroedinger equation with a time dependent delta function potential is solved exactly for many special cases. In all other cases the problem can be reduced to an integral equation of the Volterra type. It is shown that by knowing the wave function at the origin, one may derive the wave function everywhere. Thus, the problem is reduced from a PDE in two variables to an integral equation in one. These results are used to compare adiabatic versus sudden changes in the potential. It is shown that adiabatic changes in the p otential lead to conservation of the normalization of the probability density.
A Simple Method to Obtain Exact Soliton Solutions for a Nonlinear Equation in a Loss Fibre System
Institute of Scientific and Technical Information of China (English)
YANGXiao－Xue; WUYing; 等
2002-01-01
We show that the nonlinear equation governing wave propagation in a loss fibre system considered by Nakkerian in J.Phys.A34(2001) 5111 can be brought into the standard nonlinear schroedinger equation by a simple transformation.
García, Santiago; Vázquez, Juan L.; Rentería, Marvin; Aguilar-Garduño, Isis G.; Delgado, Francisco; Trejo-Durán, Mónica; García-Revilla, Marco A.; Alvarado-Méndez, Edgar; Vázquez, Miguel A.
2016-12-01
A series of novel 3-(2,2a,3-triazacyclopenta[jk]fluoren-1-yl)-2H-chromen-2-one derivatives 5a-c have been synthesized by [8 + 2] cycloaddition reaction between the corresponding 3-(imidazo[1,2-a]pyrimidines)-2-yl)-2H-chromen-2-one 4a-c with 2-(trimethylsilyl)phenyl triflates as benzyne precursor in 65-80% yields. The strategic incorporation of triazacyclopentafluorene group at the 3-position of the coumarin molecules resulted in dyes with excellent nonlinear optical properties. The nonlinear optical properties of third order (compounds 5a-c) were studied using Z-scan technique. The high nonlinear response is of 10-7 cm2/W order. The nonlinearity of the compounds is an indication of a promising material for applications at low power, such as optical switching, waveguides, nonlinear contrast phase, among others. Theoretical results of HOMO-LUMO gaps and oscillator strengths are used to rationalize the high efficiency of the novel compound in the nonlinear optical behavior. In particular, 5b displays the best nonlinear optical properties and at the same time the smaller HOMO-LUMO gap and the highest oscillator strength.
Highway traffic estimation of improved precision using the derivative-free nonlinear Kalman Filter
Rigatos, Gerasimos; Siano, Pierluigi; Zervos, Nikolaos; Melkikh, Alexey
2015-12-01
The paper proves that the PDE dynamic model of the highway traffic is a differentially flat one and by applying spatial discretization its shows that the model's transformation into an equivalent linear canonical state-space form is possible. For the latter representation of the traffic's dynamics, state estimation is performed with the use of the Derivative-free nonlinear Kalman Filter. The proposed filter consists of the Kalman Filter recursion applied on the transformed state-space model of the highway traffic. Moreover, it makes use of an inverse transformation, based again on differential flatness theory which enables to obtain estimates of the state variables of the initial nonlinear PDE model. By avoiding approximate linearizations and the truncation of nonlinear terms from the PDE model of the traffic's dynamics the proposed filtering methods outperforms, in terms of accuracy, other nonlinear estimators such as the Extended Kalman Filter. The article's theoretical findings are confirmed through simulation experiments.
Substituent Dependence of Third-Order Optical Nonlinearity in Chalcone Derivatives
Kiran, Anthony John; Satheesh Rai, Nooji; Chandrasekharan, Keloth; Kalluraya, Balakrishna; Rotermund, Fabian
2008-08-01
The third-order nonlinear optical properties of derivatives of dibenzylideneacetone were investigated using the single beam z-scan technique at 532 nm. A strong dependence of third-order optical nonlinearity on electron donor and acceptor type of substituents was observed. An enhancement in χ(3)-value of one order of magnitude was achieved upon the substitution of strong electron donors compared to that of the molecule substituted with an electron acceptor. The magnitude of nonlinear refractive index of these chalcones is as high as of 10-11 esu. Their nonlinear optical coefficients are larger than those of widely used thiophene oligomers and trans-1-[p-(p-dimethylaminobenzyl-azo)-benzyl]-2-(N-methyl-4-pyridinium)-ethene iodide (DABA-PEI) organic compounds.
Second-order Nonlinear Optical Properties of a Series of Benzothiazole Derivatives
Institute of Scientific and Technical Information of China (English)
LIU,Xiao-Juan; LENG,Wei-Nan; FENG,Ji-Kang; REN,Ai-Min; ZHOU,Xin
2003-01-01
The second- order nonlinear optical ( NLO ) properties of a series of benzothiazole derivatives were studied by use of the ZINDO-SOS method. These chromphores are formed by a donor-π-bridge-acceptor system, based on a nitro group connected with benzothiazole as the acceptor and a hydroxyl-functional amino group as the donor. For the purpose of comparison, we also designed molecules in which nitrobenzene is an acceptor. The calculation results indicate that benzothiazole derivatives exhibit larger second-order polarizabilities than nitrobenzene derivatives. In order to clarify the origin of the NLO response of these chromophores, their electron properties were investigated as well. The benzothiazole derivatives are good candidates for application in electro-optical device due to their high optical nonlinearities, good thermla and photonic stability.
Random discrete Schroedinger operators from random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Breuer, Jonathan [Institute of Mathematics, Hebrew University of Jerusalem, Jerusalem 91904 (Israel); Forrester, Peter J [Department of Mathematics and Statistics, University of Melbourne, Parkville, Vic 3010 (Australia); Smilansky, Uzy [Department of Physics of Complex Systems, Weizmann Institute, Rehovot 76100 (Israel)
2007-02-02
We investigate random, discrete Schroedinger operators which arise naturally in the theory of random matrices, and depend parametrically on Dyson's Coulomb gas inverse temperature {beta}. They are similar to the class of 'critical' random Schroedinger operators with random potentials which diminish as vertical bar x vertical bar{sup -1/2}. We show that as a function of {beta} they undergo a transition from a regime of (power-law) localized eigenstates with a pure point spectrum for {beta} < 2 to a regime of extended states with a singular continuous spectrum for {beta} {>=} 2. (fast track communication)
Energy Technology Data Exchange (ETDEWEB)
D' silva, E.D., E-mail: deepak.dsilva@gmail.com [Department of Studies in Physics, Mangalore University, Mangalagangotri, Mangalore 574199 (India); Podagatlapalli, G. Krishna [Advanced Centre of Research in High Energy Materials (ACRHEM), University of Hyderabad, Hyderabad 500046 (India); Venugopal Rao, S., E-mail: soma_venu@yahoo.com [Advanced Centre of Research in High Energy Materials (ACRHEM), University of Hyderabad, Hyderabad 500046 (India); Dharmaprakash, S.M. [Department of Studies in Physics, Mangalore University, Mangalagangotri, Mangalore 574199 (India)
2012-11-15
Graphical abstract: Photograph and schematic representation of Z-scan experimental setup used to investigate third order nonlinear properties of the chalcone materials. Highlights: ► Br and NO{sub 2} substituted chalcone derivatives were exposed to picosecond laser pulses. ► Third-order nonlinear optical (NLO) properties were investigated. ► Compounds show promising third-order and optical limiting properties. ► These materials found suitable for electrical and optical applications. -- Abstract: In this paper we present results from the experimental study of third-order nonlinear optical (NLO) properties of three molecules of Br and NO{sub 2} substituted chalcone derivatives namely (2E)-1-(4-bromophenyl)-3-[4(methylsulfanyl)phenyl]prop-2-en-1-one (4Br4MSP), (2E)-1-(3-bromophenyl)-3-[4-(methylsulfanyl) phenyl]prop-2-en-1-one (3Br4MSP) and (2E)-3[4(methylsulfanyl) phenyl]-1-(4-nitrophenyl)prop-2-en-1-one (4N4MSP). The NLO properties have been investigated by Z-scan technique using 2 ps laser pulses at 800 nm. The nonlinear refractive indices, nonlinear absorption coefficient, and the magnitude of third-order susceptibility have been determined. The values obtained are of the order of 10{sup −7} cm{sup 2}/GW, 10{sup −3} cm/GW and 10{sup −14} esu respectively. The molecular second hyperpolarizability for the chalcone derivatives is of the order of 10{sup −32} esu. The coupling factor, excited state cross section, ground state cross section etc. were determined. The optical limiting (OL) property was studied. The results suggest that the nonlinear properties investigated for present chalcones are comparable with some of the reported chalcone derivatives and can be desirable for NLO applications.
Institute of Scientific and Technical Information of China (English)
FAN Eh-Gui
2001-01-01
An explicit N-fold Darboux transformation for a coupled of derivative nonlinear Schrodinger equations is constructed with the help of a gauge transformation of spectral problems. As a reduction, the Darboux transformation for well-known Gerdjikov-Ivanov equation is further obtained, from which a general form of N-soliton solutions for Gerdjikov-Ivanov equation is given.``
Institute of Scientific and Technical Information of China (English)
陶华学; 郭金运
2002-01-01
Using difference quotient instead of derivative, the paper presents the solution method and procedure of the nonlinear least square estimation containing different classes of measurements. In the meantime, the paper shows several practical cases, which indicate the method is very valid and reliable.
A Critical Centre-Stable Manifold for the Schroedinger Equation in Three Dimensions
Beceanu, Marius
2009-01-01
Consider the H^{1/2}-critical Schroedinger equation with a cubic nonlinearity in R^3, i \\partial_t \\psi + \\Delta \\psi + |\\psi|^2 \\psi = 0. It admits an eight-dimensional manifold of periodic solutions called solitons e^{i(\\Gamma + vx - t|v|^2 + \\alpha^2 t)} \\phi(x-2tv-D, \\alpha), where \\phi(x, \\alpha) is a positive ground state solution of the semilinear elliptic equation -\\Delta \\phi + \\alpha^2\\phi = \\phi^3. We prove that in the neighborhood of the soliton manifold there exists a H^{1/2} real analytic manifold N of asymptotically stable solutions of the Schroedinger equation, meaning they are the sum of a moving soliton and a dispersive term. Furthermore, a solution starting on N remains on N for all positive time and for some finite negative time and N can be identified as the centre-stable manifold for this equation. The proof is based on the method of modulation, introduced by Soffer and Weinstein and adapted by Schlag to the L^2-supercritical case. Novel elements include a different linearization and a S...
Energy Technology Data Exchange (ETDEWEB)
Guasti, M Fernandez [Depto de Fisica, CBI, Universidad A Metropolitana - Iztapalapa, 09340 Mexico, DF, Apdo Postal 55-534 (Mexico); Moya-Cessa, H [INAOE, Coordinacion de Optica, Apdo Postal 51 y 216, 72000 Puebla, Pue. (Mexico)
2003-02-28
An extension of the classical orthogonal functions invariant to the quantum domain is presented. This invariant is expressed in terms of the Hamiltonian. Unitary transformations which involve the auxiliary function of this quantum invariant are used to solve the time-dependent Schroedinger equation for a harmonic oscillator with time-dependent parameter. The solution thus obtained is in agreement with the results derived using other methods which invoke the Lewis invariant in their procedures.
Theoretical Study on Second-order Nonlinear Optical Properties of Substituted Thiazole Derivatives
Institute of Scientific and Technical Information of China (English)
LIU, Yong-Juna; LIU, Yong-Jun; LIU, Ying; ZHANG, Dong-Ju; ZHAO, Xan; LIU, Cheng-Bu; HU,Hai-Quan
2001-01-01
On the basis of ZINDO program, we have designed a program to calculate the nonlinear second-order polarizability βijk and βμ according to the SOS expression. The second-order nonlinear optical properties of 4-nitro-4′-dimethylamino-stilbene and a series of its thiazole derivatives were studied. The calculated results were that: When replacing a benzene ring in 4-nitro-4′-dimethylamino-stilbene by a thiazole ring, the influence on β values depends on the position of thiazole ring.When the thiazole ring connects with nitro group (acceptor),the β values increase significantly compared with corresponding stilbene derivatives. The β values of 2-(p-donor-β-styryl)-5-nitro-thiazole derivatives (2－7) are larger than those of 2-(p-nitro- β- styryl)-5-donor-thiazole derivatives (8－13) and 2-(p-donor-phenyl)-azo-5-nitro-thiazole derivatives (14－19).The 2-(p-donor-β-styryl)-5-nitro-thiazole derivatives (2－7)are good candidates as chromophores duo to their high nonlin-earities and potential good thermal stability.
Institute of Scientific and Technical Information of China (English)
CHEN Xiang-Jun; HOU Li-Jie; LAM Wa Kun
2005-01-01
@@ Conservation laws for the derivative nonlinear Schr(o)dinger equation with non-vanishing boundary conditions are derived, based on the recently developed inverse scattering transform using the affine parameter technique.
A technique using a nonlinear helicopter model for determining trims and derivatives
Ostroff, A. J.; Downing, D. R.; Rood, W. J.
1976-01-01
A technique is described for determining the trims and quasi-static derivatives of a flight vehicle for use in a linear perturbation model; both the coupled and uncoupled forms of the linear perturbation model are included. Since this technique requires a nonlinear vehicle model, detailed equations with constants and nonlinear functions for the CH-47B tandem rotor helicopter are presented. Tables of trims and derivatives are included for airspeeds between -40 and 160 knots and rates of descent between + or - 10.16 m/sec (+ or - 200 ft/min). As a verification, the calculated and referenced values of comparable trims, derivatives, and linear model poles are shown to have acceptable agreement.
Bar, D
2002-01-01
Using the Gell-Mann-Hartle-Griffiths formalism in the framework of the Flesia-Piron form of the Lax-Phillips theory we show that the Schr\\"oedinger equation may be derived as a condition of stability of histories. This mechanism is realized in a mathematical structure closely related to the Zeno effect.
Schroedinger operators with the q-ladder symmetry algebras
Skorik, Sergei; Spiridonov, Vyacheslav
1994-01-01
A class of the one-dimensional Schroedinger operators L with the symmetry algebra LB(+/-) = q(+/-2)B(+/-)L, (B(+),B(-)) = P(sub N)(L), is described. Here B(+/-) are the 'q-ladder' operators and P(sub N)(L) is a polynomial of the order N. Peculiarities of the coherent states of this algebra are briefly discussed.
Intertwining operator method and supersymmetry for effective mass Schroedinger equations
Energy Technology Data Exchange (ETDEWEB)
Suzko, A.A. [Joint Institute for Nuclear Research, 141980 Dubna (Russian Federation); JIPENP, National Academy of Sciences of Belarus, Minsk (Belarus)], E-mail: suzko@cv.jinr.ru; Schulze-Halberg, A. [Mathematics Department, University of Colima, Bernal Diaz del Castillo 340, Colima 28045 (Mexico)], E-mail: xbat@ucol.mx
2008-09-08
By application of the intertwining operator method to Schroedinger equations with position-dependent (effective) mass, we construct Darboux transformations, establish the supersymmetry factorization technique and show equivalence of both formalisms. Our findings prove equivalence of the intertwining technique and the method of point transformations.
Studying the gradient flow coupling in the Schroedinger functional
Energy Technology Data Exchange (ETDEWEB)
Fritzsch, P. [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Ramos, A. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC
2013-08-15
We discuss the setup and features of a new definition of the running coupling in the Schroedinger functional scheme based on the gradient flow. Its suitability for a precise continuum limit in QCD is demonstrated on a set of N{sub f}=2 gauge field ensembles in a physical volume of L{proportional_to}0.4 fm.
On the chirally rotated Schroedinger functional with Wilson fermions
Energy Technology Data Exchange (ETDEWEB)
Gonzalez Lopez, Jenifer
2011-05-25
There are many phenomena in nature, which are closely linked to the low energy regime of QCD. From a theoretical point of view, these low energy phenomena can be dealt with only by means of non-perturbative methods. It is the central goal of this thesis to provide a framework for such a nonperturbative renormalization. For that purpose, we employ a 4-dimensional lattice as a regulator of QCD. As a renormalization scheme, we propose a finite volume Schroedinger functional scheme and here in particular, the chirally rotated Schroedinger functional ({chi}SF). We first perform analytical studies of the {chi}SF at tree-level of perturbation theory, in the continuum and on the lattice. We study the eigenvalue spectrum of the continuum Dirac operator, equipped with chirally rotated SF boundary conditions, and derive the corresponding quark propagator. We then determine the tree-level quark propagator on the lattice, employing massless Wilson fermions as a regulator of the theory. Beyond tree-level, all studies are performed in the quenched approximation of QCD, as a first, computationally much simpler step to understand the properties of the newly proposed {chi}SF scheme. One of the main targets of the present work, has been to perform the non-perturbative tuning of the two required coefficients of the {chi}SF scheme, such that a well defined continuum limit can be reached. We demonstrate, as the first main result of this thesis, that the tuning is feasible and that, moreover, physical quantities are insensitive to the particular tuning condition. As in any lattice regularization with SF-like boundary conditions, there are also in the {chi}SF a couple of counterterms at the boundaries, whose coefficients need to be tuned in order to remove the O(a) discretization effects originated at the boundaries. However, besides these boundary O(a) effects, the {chi}SF is expected to be compatible with bulk automatic O(a)-improvement. We show here that, indeed, the scaling behavior
Bai, Cheng; Huang, Jin
2015-07-01
Fast settling, accurate positioning, and a large tilt angle range are important for MEMS mirrors. Here, residual vibration and the pull-in phenomenon-both major problems affecting the performance of an electrostatically actuated mirror-are investigated. Based on the analysis of a nonlinear proportional-derivative (PD) control with parametric uncertainties, a closed-loop feedback control strategy with a combined control scheme is proposed. This method, combining nonlinear PD control and sliding mode control (SMC), not only inherits the virtue of a good dynamic performance from the nonlinear PD control, but also further improves the robustness with SMC for such MEMS mirrors. Furthermore, this method can be convenient when tuning design gains of the controller to obtain a faster error convergence rate. Numerical simulation results show that with this combined control scheme not only the transient response of the MEMS mirror is improved but the influence of parametric uncertainties and external disturbance is also reduced.
Nonlinear analysis and analog simulation of a piezoelectric buckled beam with fractional derivative
Mokem Fokou, I. S.; Buckjohn, C. Nono Dueyou; Siewe Siewe, M.; Tchawoua, C.
2017-08-01
In this article, an analog circuit for implementing fractional-order derivative and a harmonic balance method for a vibration energy harvesting system under pure sinusoidal vibration source is proposed in order to predict the system response. The objective of this paper is to discuss the performance of the system with fractional derivative and nonlinear damping (μb). Bifurcation diagram, phase portrait and power spectral density (PSD) are provided to deeply characterize the dynamics of the system. These results are corroborated by the 0-1 test. The appearance of the chaotic vibrations reduces the instantaneous voltage. The pre-experimental investigation is carried out through appropriate software electronic circuit (Multisim). The corresponding electronic circuit is designed, exhibiting periodic and chaotic behavior, in accord with numerical simulations. The impact of fractional derivative and nonlinear damping is presented with detail on the output voltage and power of the system. The agreement between numerical and analytical results justifies the efficiency of the analytical technique used. In addition, by combining the harmonic excitation with the random force, the stochastic resonance phenomenon occurs and improves the harvested energy. It emerges from these results that the order of fractional derivative μ and nonlinear damping μb play an important role in the response of the system.
Anderson Localization in Nonlocal Nonlinear Media
Folli, Viola; 10.1364/OL.37.000332
2012-01-01
The effect of focusing and defocusing nonlinearities on Anderson localization in highly nonlocal media is theoretically and numerically investigated. A perturbative approach is developed to solve the nonlocal nonlinear Schroedinger equation in the presence of a random potential, showing that nonlocality stabilizes Anderson states.
Institute of Scientific and Technical Information of China (English)
顾绍泉; 向新民
2005-01-01
Nonlinear Schroedinger equation arises in many physical problems. There are many works in which properties of the solution are studied. In this paper we use fully discrete Fourier spectral method to get an approximation solution of nonlinear weakly dissipative Schroedinger equation with quintic term. We give a large-time error estimate and obtain the existence of the approximate attractor A Nk.
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.
Control of underactuated robotic systems with the use of the derivative-free nonlinear Kalman filter
Rigatos, Gerasimos G.; Siano, Pierluigi
2013-10-01
The Derivative-free nonlinear Kalman Filter is used for developing a robust controller which can be applied to underactuated MIMO robotic systems. Using differential flatness theory it is shown that the model of a closed-chain 2-DOF robotic manipulator can be transformed to linear canonical form. For the linearized equivalent of the robotic system it is shown that a state feedback controller can be designed. Since certain elements of the state vector of the linearized system can not be measured directly, it is proposed to estimate them with the use of a novel filtering method, the so-called Derivative-free nonlinear Kalman Filter. Moreover, by redesigning the Kalman Filter as a disturbance observer, it is is shown that one can estimate simultaneously external disturbances terms that affect the robotic model or disturbance terms which are associated with parametric uncertainty.
Kinetic treatment of nonlinear magnetized plasma motions - General geometry and parallel waves
Khabibrakhmanov, I. KH.; Galinskii, V. L.; Verheest, F.
1992-01-01
The expansion of kinetic equations in the limit of a strong magnetic field is presented. This gives a natural description of the motions of magnetized plasmas, which are slow compared to the particle gyroperiods and gyroradii. Although the approach is 3D, this very general result is used only to focus on the parallel propagation of nonlinear Alfven waves. The derivative nonlinear Schroedinger-like equation is obtained. Two new terms occur compared to earlier treatments, a nonlinear term proportional to the heat flux along the magnetic field line and a higher-order dispersive term. It is shown that kinetic description avoids the singularities occurring in magnetohydrodynamic or multifluid approaches, which correspond to the degenerate case of sound speeds equal to the Alfven speed, and that parallel heat fluxes cannot be neglected, not even in the case of low parallel plasma beta. A truly stationary soliton solution is derived.
Lyapunov functions for a class of nonlinear systems using Caputo derivative
Fernandez-Anaya, G.; Nava-Antonio, G.; Jamous-Galante, J.; Muñoz-Vega, R.; Hernández-Martínez, E. G.
2017-02-01
This paper presents an extension of recent results that allow proving the stability of Caputo nonlinear and time-varying systems, by means of the fractional order Lyapunov direct method, using quadratic Lyapunov functions. This article introduces a new way of building polynomial Lyapunov functions of any positive integer order as a way of determining the stability of a greater variety of systems when the order of the derivative is 0 < α < 1. Some examples are given to validate these results.
Well-posedness for a generalized derivative nonlinear Schrödinger equation
Hayashi, Masayuki; Ozawa, Tohru
2016-11-01
We study the Cauchy problem for a generalized derivative nonlinear Schrödinger equation with the Dirichlet boundary condition. We establish the local well-posedness results in the Sobolev spaces H1 and H2. Solutions are constructed as a limit of approximate solutions by a method independent of a compactness argument. We also discuss the global existence of solutions in the energy space H1.
Gencoglu, Muharrem Tuncay; Baskonus, Haci Mehmet; Bulut, Hasan
2017-01-01
The main aim of this manuscript is to obtain numerical solutions for the nonlinear model of interpersonal relationships with time fractional derivative. The variational iteration method is theoretically implemented and numerically conducted only to yield the desired solutions. Numerical simulations of desired solutions are plotted by using Wolfram Mathematica 9. The authors would like to thank the reviewers for their comments that help improve the manuscript.
Nonlinear first order PDEs reducible to autonomous form polynomially homogeneous in the derivatives
Gorgone, Matteo; Oliveri, Francesco
2017-03-01
It is proved a theorem providing necessary and sufficient conditions enabling one to map a nonlinear system of first order partial differential equations, polynomial in the derivatives, to an equivalent autonomous first order system polynomially homogeneous in the derivatives. The result is intimately related to the symmetry properties of the source system, and the proof, involving the use of the canonical variables associated to the admitted Lie point symmetries, is constructive. First order Monge-Ampère systems, either with constant coefficients or with coefficients depending on the field variables, where the theorem can be successfully applied, are considered.
Energy Technology Data Exchange (ETDEWEB)
Kravchenko, Vladislav V [Departmento de Telecomunicaciones, SEPI, Escuela Superior de IngenierIa Mecanica y Electrica, Instituto Politecnico Nacional, CP 07738 Mexico DF (Mexico)
2005-01-28
Given a particular solution of a one-dimensional stationary Schroedinger equation this equation of second order can be reduced to a first-order linear ordinary differential equation. This is done with the aid of an auxiliary Riccati differential equation. In the present work we show that the same fact is true in a multidimensional situation also. For simplicity we consider the case of two or three independent variables. One particular solution of the stationary Schroedinger equation allows us to reduce this second-order equation to a linear first-order quaternionic differential equation. As in the one-dimensional case this is done with the aid of an auxiliary quaternionic Riccati equation. The resulting first-order quaternionic equation is equivalent to the static Maxwell system and is closely related to the Dirac equation. In the case of two independent variables it is the well-known Vekua equation from theory of pseudoanalytic (or generalized analytic) functions. Nevertheless, we show that even in this case it is very useful to consider not only complex valued functions, solutions of the Vekua equation, but complete quaternionic functions. In this way the first-order quaternionic equation represents two separate Vekua equations, one of which gives us solutions of the Schroedinger equation and the other one can be considered as an auxiliary equation of a simpler structure. Moreover for the auxiliary equation we always have the corresponding Bers generating pair (F, G), the base of the Bers theory of pseudoanalytic functions, and what is very important, the Bers derivatives of solutions of the auxiliary equation give us solutions of the main Vekua equation and as a consequence of the Schroedinger equation. Based on this fact we obtain an analogue of the Cauchy integral theorem for solutions of the stationary Schroedinger equation. Other results from theory of pseudoanalytic functions can be written for solutions of the Schroedinger equation. Moreover, for an ample
Bell's theorem and quantum realism. Reassessment in light of the Schroedinger paradox
Energy Technology Data Exchange (ETDEWEB)
Shakur, Asif M. [Salisbury Univ., MD (United States). Dept. of Physics; Hemmick, Douglas L.
2012-07-01
Quantum theory presents a strange picture of the world, offering no real account of physical properties apart from observation. Neils Bohr felt that this reflected a core truth of nature: ''There is no quantum world. There is only an abstract mathematical description.'' Among the most significant developments since Bohr's day has been the theorem of John S. Bell. It is important to consider whether Bell's analysis supports such a denial of microrealism. In this book, we evaluate the situation in terms of an early work of Erwin Schroedinger. Doing so, we see how Bell's theorem is conceptually related to the Conway and Kochen Free Will theorem and also to all the major anti-realism efforts. It is easy to show that none of these analyses imply the impossibility of objective realism. We find that Schroedinger's work leads to the derivation of a new series of theoretical proofs and potential experiments, each involving ''entanglement,'' the link between particles in some quantum systems. (orig.)
A new fundamental model of moving particle for reinterpreting Schroedinger equation
Energy Technology Data Exchange (ETDEWEB)
Umar, Muhamad Darwis [Laboratorium Fisika Material dan Komputasi, Jurusan Fisika, Universitas Gadjah Mada Sekip Utara BLS 21 Yogyakarta 55281 (Indonesia)
2012-06-20
The study of Schroedinger equation based on a hypothesis that every particle must move randomly in a quantum-sized volume has been done. In addition to random motion, every particle can do relative motion through the movement of its quantum-sized volume. On the other way these motions can coincide. In this proposed model, the random motion is one kind of intrinsic properties of the particle. The every change of both speed of randomly intrinsic motion and or the velocity of translational motion of a quantum-sized volume will represent a transition between two states, and the change of speed of randomly intrinsic motion will generate diffusion process or Brownian motion perspectives. Diffusion process can take place in backward and forward processes and will represent a dissipative system. To derive Schroedinger equation from our hypothesis we use time operator introduced by Nelson. From a fundamental analysis, we find out that, naturally, we should view the means of Newton's Law F(vector sign) = ma(vector sign) as no an external force, but it is just to describe both the presence of intrinsic random motion and the change of the particle energy.
Another Simple Way of Deriving Several Iterative Functions to Solve Nonlinear Equations
Directory of Open Access Journals (Sweden)
Ramandeep Behl
2012-01-01
Full Text Available We present another simple way of deriving several iterative methods for solving nonlinear equations numerically. The presented approach of deriving these methods is based on exponentially fitted osculating straight line. These methods are the modifications of Newton's method. Also, we obtain well-known methods as special cases, for example, Halley's method, super-Halley method, Ostrowski's square-root method, Chebyshev's method, and so forth. Further, new classes of third-order multipoint iterative methods free from a second-order derivative are derived by semidiscrete modifications of cubically convergent iterative methods. Furthermore, a simple linear combination of two third-order multipoint iterative methods is used for designing new optimal methods of order four.
Schroedinger functional formalism with Ginsparg-Wilson fermion
Taniguchi, Y
2005-01-01
The Schroedinger functional formalism is given as a field theory in a finite volume with a Dirichlet boundary condition in temporal direction. When one tries to construct this formalism with the Ginsparg-Wilson fermion including the overlap Dirac operator and the domain-wall fermion one easily runs into difficulties. The reason is that if the Dirichlet boundary condition is simply imposed on the Wilson Dirac operator $DW$ inside of the overlap Dirac operator an exponentially small eigenvalue appears in $DW$, which affects the locality properties of the operator. In this paper we propose a new procedure to impose the Schroedinger functional Dirichlet boundary condition on the overlap Dirac operator using an orbifolding projection.
Asymptotic Value Distribution for Solutions of the Schroedinger Equation
Energy Technology Data Exchange (ETDEWEB)
Breimesser, S. V., E-mail: s.v.breimesser@maths.hull.ac.uk; Pearson, D. B. [University of Hull, Department of Mathematics (United Kingdom)], E-mail: d.b.pearson@maths.hull.ac.uk
2000-12-15
We consider the Dirichlet Schroedinger operator T=-(d{sup 2}/d x{sup 2})+V, acting in L{sup 2}(0,{infinity}), where Vis an arbitrary locally integrable potential which gives rise to absolutely continuous spectrum. Without any other restrictive assumptions on the potential V, the description of asymptotics for solutions of the Schroedinger equation is carried out within the context of the theory of value distribution for boundary values of analytic functions. The large x asymptotic behaviour of the solution v(x,{lambda}) of the equation Tf(x,{lambda})={lambda}f(x,{lambda}), for {lambda} in the support of the absolutely continuous part {mu}{sub a.c.} of the spectral measure {mu}, is linked to the spectral properties of this measure which are determined by the boundary value of the Weyl-Titchmarsh m-function. Our main result (Theorem 1) shows that the value distribution for v'(N,{lambda})/v(N,{lambda}) approaches the associated value distribution of the Herglotz function m{sup N}(z) in the limit N{sup {yields}}{infinity}, where m{sup N}(z) is the Weyl-Titchmarsh m-function for the Schroedinger operator -(d{sup 2}/d x{sup 2})+Vacting in L{sup 2}(N,{infinity}), with Dirichlet boundary condition at x=N. We will relate the analysis of spectral asymptotics for the absolutely continuous component of Schroedinger operators to geometrical properties of the upper half-plane, viewed as a hyperbolic space.
Non-Schroedinger forces and pilot waves in quantum cosmology
Energy Technology Data Exchange (ETDEWEB)
Tipler, F.J.
1987-09-01
The author argues that the version of the pilot wave interpretation of quantum mechanics which uses a non-local non-Schroedinger force is inconsistent when applied to distributions with small numbers of particles. Thus, no version of the pilot wave interpretation (some-times called the de Broglie-Bohm, or causal, interpretation) can be applied to the wavefunction of quantum cosmology because in any version of this interpretation, there is only one particle, the universe.
Non-Linear Back-propagation: Doing Back-Propagation withoutDerivatives of the Activation Function
DEFF Research Database (Denmark)
Hertz, John; Krogh, Anders Stærmose; Lautrup, Benny
1997-01-01
The conventional linear back-propagation algorithm is replaced by a non-linear version, which avoids the necessity for calculating the derivative of the activation function. This may be exploited in hardware realizations of neural processors. In this paper we derive the non-linear back-propagatio......-propagation algorithms in the framework of recurrent back-propagation and present some numerical simulations of feed-forward networks on the NetTalk problem. A discussion of implementation in analog VLSI electronics concludes the paper.......The conventional linear back-propagation algorithm is replaced by a non-linear version, which avoids the necessity for calculating the derivative of the activation function. This may be exploited in hardware realizations of neural processors. In this paper we derive the non-linear back...
Proportional-integral-derivative control of nonlinear half-car electro-hydraulic suspension systems
Institute of Scientific and Technical Information of China (English)
John E.D.EKORU; Jimoh O.PEDRO
2013-01-01
This paper presents the development of a proportional-integral-derivative (PID)-based control method for application to active vehicle suspension systems (AVSS).This method uses an inner PID hydraulic actuator force control loop,in combination with an outer PID suspension travel control loop,to control a nonlinear half-car AVSS.Robustness to model uncertainty in the form of variation in suspension damping is tested,comparing performance of the AVSS with a passive vehicle suspension system (PVSS),with similar model parameters.Spectral analysis of suspension system model output data,obtained by performing a road input disturbance frequency sweep,provides frequency response plots for both nonlinear vehicle suspension systems and time domain vehicle responses to a sinusoidal road input disturbance on a smooth road.The results show the greater robustness of the AVSS over the PVSS to parametric uncertainty in the frequency and time domains.
Directory of Open Access Journals (Sweden)
Wolfgang Witteveen
2014-01-01
Full Text Available The mechanical response of multilayer sheet structures, such as leaf springs or car bodies, is largely determined by the nonlinear contact and friction forces between the sheets involved. Conventional computational approaches based on classical reduction techniques or the direct finite element approach have an inefficient balance between computational time and accuracy. In the present contribution, the method of trial vector derivatives is applied and extended in order to obtain a-priori trial vectors for the model reduction which are suitable for determining the nonlinearities in the joints of the reduced system. Findings show that the result quality in terms of displacements and contact forces is comparable to the direct finite element method but the computational effort is extremely low due to the model order reduction. Two numerical studies are presented to underline the method’s accuracy and efficiency. In conclusion, this approach is discussed with respect to the existing body of literature.
Evaluation of bias associated with capture maps derived from nonlinear groundwater flow models
Nadler, Cara; Allander, Kip K.; Pohll, Greg; Morway, Eric; Naranjo, Ramon C.; Huntington, Justin
2017-01-01
The impact of groundwater withdrawal on surface water is a concern of water users and water managers, particularly in the arid western United States. Capture maps are useful tools to spatially assess the impact of groundwater pumping on water sources (e.g., streamflow depletion) and are being used more frequently for conjunctive management of surface water and groundwater. Capture maps have been derived using linear groundwater flow models and rely on the principle of superposition to demonstrate the effects of pumping in various locations on resources of interest. However, nonlinear models are often necessary to simulate head-dependent boundary conditions and unconfined aquifers. Capture maps developed using nonlinear models with the principle of superposition may over- or underestimate capture magnitude and spatial extent. This paper presents new methods for generating capture difference maps, which assess spatial effects of model nonlinearity on capture fraction sensitivity to pumping rate, and for calculating the bias associated with capture maps. The sensitivity of capture map bias to selected parameters related to model design and conceptualization for the arid western United States is explored. This study finds that the simulation of stream continuity, pumping rates, stream incision, well proximity to capture sources, aquifer hydraulic conductivity, and groundwater evapotranspiration extinction depth substantially affect capture map bias. Capture difference maps demonstrate that regions with large capture fraction differences are indicative of greater potential capture map bias. Understanding both spatial and temporal bias in capture maps derived from nonlinear groundwater flow models improves their utility and defensibility as conjunctive-use management tools.
A Note on Lifshitz and Schroedinger Solutions in Pure Lovelock theories
Jatkar, Dileep P
2015-01-01
We look for Lifshitz and Schroedinger solutions in Lovelock gravity. We span the entire parameter space and determine parametric relations under which Lifshitz and Schroedinger solution exists. We find that in arbitrary dimensions pure Lovelock theories have Lifshitz and Schroedinger solutions on a co-dimension two locus in the Lovelock parameter space. This co-dimension two locus precisely corresponds to the subspace over which the Lovelock gravity can be written in the Chern-Simons form. While Lifshitz and Schroedinger solutions do not exist outside this locus, on this locus these solutions exist for arbitrary dynamical exponent z.
Remarks on the solution of the position-dependent mass Schroedinger equation
Energy Technology Data Exchange (ETDEWEB)
Koc, Ramazan; Sayin, Seda, E-mail: koc@gantep.edu.t, E-mail: ssayin@gantep.edu.t [Faculty of Engineering, Department of Physics, Gaziantep University, 27310 Gaziantep (Turkey)
2010-11-12
An approximate method is proposed to solve the position-dependent mass (PDM) Schroedinger equation. The procedure suggested here leads to the solution of the PDM Schroedinger equation without transforming the potential function to the mass space or vice versa. The method based on the asymptotic Taylor expansion of the function produces an approximate analytical expression for eigenfunction and numerical results for eigenvalues of the PDM Schroedinger equation. The results show that the PDM and constant mass Schroedinger equations are not isospectral. The calculations are carried out with the aid of a computer system of symbolic or numerical calculation by constructing a simple algorithm.
A derivative-free distributed filtering approach for sensorless control of nonlinear systems
Rigatos, Gerasimos G.
2012-09-01
This article examines the problem of sensorless control for nonlinear dynamical systems with the use of derivative-free Extended Information Filtering (EIF). The system is first subject to a linearisation transformation and next state estimation is performed by applying the standard Kalman Filter to the linearised model. At a second level, the standard Information Filter is used to fuse the state estimates obtained from local derivative-free Kalman filters running at the local information processing nodes. This approach has significant advantages because unlike the EIF (i) is not based on local linearisation of the nonlinear dynamics (ii) does not assume truncation of higher order Taylor expansion terms thus preserving the accuracy and robustness of the performed estimation and (iii) does not require the computation of Jacobian matrices. As a case study a robotic manipulator is considered and a cameras network consisting of multiple vision nodes is assumed to provide the visual information to be used in the control loop. A derivative-free implementation of the EIF is used to produce the aggregate state vector of the robot by processing local state estimates coming from the distributed vision nodes. The performance of the considered sensorless control scheme is evaluated through simulation experiments.
A GLOBALLY DERIVATIVE-FREE DESCENT METHOD FOR NONLINEAR COMPLEMENTARITY PROBLEMS
Institute of Scientific and Technical Information of China (English)
Hou-duo Qi; Yu-zhong Zhang
2000-01-01
Based on a class of functions. which generalize the squared Fischer-Burmeister NCP function and have many desirable properties as the latter function has, we reformulate nonlinear complementarity problem (NCP for short) as an equivalent unconstrained optimization problem, for which we propose a derivative-free descent method in monotone case. We show its global convergence under some mild conditions. If F, the function involved in NCP, is Ro－function, the optimization problem has bounded level sets. A local property of the merit function is discussed. Finally, we report some numerical results.
OBLIQUE DERIVATIVE PROBLEMS FOR SECOND ORDER NONLINEAR MIXED EQUATIONS WITH DEGENERATE LINE
Institute of Scientific and Technical Information of China (English)
Wen Guochun
2008-01-01
The present article deals with oblique derivative problems for some nonlin-ear mixed equations with parabolic degeneracy, which include the Tricomi problem as a special case. First, the formulation of the problems for the equations is given; next, the representation and estimates of solutions for the above problems are obtained; finally, the existence of solutions for the problems is proved by the successive iteration and the com-pactness principle of solutions of the problems. In this article, the author uses the complex method, namely, the complex functions in the elliptic domain and the hyperbolic complex functions in hyperbolic domain are used.
Directory of Open Access Journals (Sweden)
Abdon Atangana
2014-01-01
Full Text Available A novel approach is proposed to deal with a class of nonlinear partial equations including integer and noninteger order derivative. This class of equations cannot be handled with any other commonly used analytical technique. The proposed method is based on the multi-Laplace transform. We solved as an example some complicated equations. Three illustrative examples are presented to confirm the applicability of the proposed method. We have presented in detail the stability, the convergence and the uniqueness analysis of some examples.
A Derivative-Free Method of Eighth-Order For Finding Simple Root of Nonlinear Equations
Directory of Open Access Journals (Sweden)
Neha Choubey
2015-06-01
Full Text Available In this paper we have constructed an optimal eighth-order method with four function evaluations to solve the non-linear equations. The proposed method is a three-step method in which no derivative is required. Our scheme is optimal in the sense of Kung and Traub. Moreover, some test functions have been also included to confirm the superiority of the proposed method. At the end, we have presented the basins of attraction of some existing methods along with our proposed method to illustrate their performances.
Rigatos, Gerasimos G
2016-06-01
It is proven that the model of the p53-mdm2 protein synthesis loop is a differentially flat one and using a diffeomorphism (change of state variables) that is proposed by differential flatness theory it is shown that the protein synthesis model can be transformed into the canonical (Brunovsky) form. This enables the design of a feedback control law that maintains the concentration of the p53 protein at the desirable levels. To estimate the non-measurable elements of the state vector describing the p53-mdm2 system dynamics, the derivative-free non-linear Kalman filter is used. Moreover, to compensate for modelling uncertainties and external disturbances that affect the p53-mdm2 system, the derivative-free non-linear Kalman filter is re-designed as a disturbance observer. The derivative-free non-linear Kalman filter consists of the Kalman filter recursion applied on the linearised equivalent of the protein synthesis model together with an inverse transformation based on differential flatness theory that enables to retrieve estimates for the state variables of the initial non-linear model. The proposed non-linear feedback control and perturbations compensation method for the p53-mdm2 system can result in more efficient chemotherapy schemes where the infusion of medication will be better administered.
Analytical solitons for Langmuir waves in plasma physics with cubic nonlinearity and perturbations
Energy Technology Data Exchange (ETDEWEB)
Zhou, Qin [Wuhan Donghu Univ. (China). School of Electronics and Information Engineering; Mirzazadeh, M. [Guilan Univ. (Iran, Islamic Republic of). Dept. of Engineering Sciences
2016-07-01
We presented an analytical study on dynamics of solitons for Langmuir waves in plasma physics. The mathematical model is given by the perturbed nonlinear Schroedinger equation with full nonlinearity and Kerr law nonlinearity. There are three techniques of integrability were employed to extract exact solutions along with the integrability conditions. The topological 1-soliton solutions, singular 1-soliton solutions, and plane wave solution were reported by Ricatti equation expansion approach and then the bright 1-soliton solution, singular 1-soliton solution, periodic singular solutions, and plane wave solution were derived with the help of trial solution method. Finally, based on the G'/G-expansion scheme, we obtained the hyperbolic function travelling wave solution, trigonometric function travelling wave solution, and plane wave solution.
Directory of Open Access Journals (Sweden)
Marilú Chávez-Castillo
2015-01-01
Full Text Available Two copolymers of 3-alkylthiophene (alkyl = hexyl, octyl and a thiophene functionalized with disperse red 19 (TDR19 as chromophore side chain were synthesized by oxidative polymerization. The synthetic procedure was easy to perform, cost-effective, and highly versatile. The molecular structure, molecular weight distribution, film morphology, and optical and thermal properties of these polythiophene derivatives were determined by NMR, FT-IR, UV-Vis GPC, DSC-TGA, and AFM. The third-order nonlinear optical response of these materials was performed with nanosecond and femtosecond laser pulses by using the third-harmonic generation (THG and Z-scan techniques at infrared wavelengths of 1300 and 800 nm, respectively. From these experiments it was observed that although the TRD19 incorporation into the side chain of the copolymers was lower than 5%, it was sufficient to increase their nonlinear response in solid state. For instance, the third-order nonlinear electric susceptibility (χ3 of solid thin films made of these copolymers exhibited an increment of nearly 60% when TDR19 incorporation increased from 3% to 5%. In solution, the copolymers exhibited similar two-photon absorption cross sections σ2PA with a maximum value of 8545 GM and 233 GM (1 GM = 10−50 cm4 s per repeated monomeric unit.
Indian Academy of Sciences (India)
Basudeb Sahu; Bidubhusan Sahu; Santosh K Agarwalla
2008-01-01
In a one-dimensional quantal solution of Schroedinger equation, the general expressions for reflection and transmission coefficients are derived for a potential constituting n number of rectangular wells and barriers. These expressions are readily used for the estimation of eigenvalues of a smooth potential which is simulated by a multi-step potential. The applicability of this method is demonstrated with success in potentials with different forms including the most versatile Ginocchio potential where the widely used numerical method like Runge–Kutta integration algorithm fails to yield the result. Accurate evaluation of eigenvalues free from numerical problem for any form of potentials, whether analytically solvable or not, is the highlight of the present multi-step approximation method in the theory of potential scattering.
Non-relativistic Schroedinger theory on q-deformed quantum spaces III, Scattering theory
Wachter, H
2007-01-01
This is the third part of a paper about non-relativistic Schroedinger theory on q-deformed quantum spaces like the braided line or the three-dimensional q-deformed Euclidean space. Propagators for the free q-deformed particle are derived and their basic properties are discussed. A time-dependent formulation of scattering is proposed. In this respect, q-analogs of the Lippmann-Schwinger equation are given. Expressions for their iterative solutions are written down. It is shown how to calculate S-matrices and transition probabilities. Furthermore, attention is focused on the question what becomes of unitarity of S-matrices in a q-deformed setting. The examinations are concluded by a discussion of the interaction picture and its relation to scattering processes.
Degenerate RS perturbation theory. [Rayleigh-Schroedinger energies and wave functions
Hirschfelder, J. O.; Certain, P. R.
1974-01-01
A concise, systematic procedure is given for determining the Rayleigh-Schroedinger energies and wave functions of degenerate states to arbitrarily high orders even when the degeneracies of the various states are resolved in arbitrary orders. The procedure is expressed in terms of an iterative cycle in which the energy through the (2n + 1)-th order is expressed in terms of the partially determined wave function through the n-th order. Both a direct and an operator derivation are given. The two approaches are equivalent and can be transcribed into each other. The direct approach deals with the wave functions (without the use of formal operators) and has the advantage that it resembles the usual treatment of nondegenerate perturbations and maintains close contact with the basic physics. In the operator approach, the wave functions are expressed in terms of infinite-order operators which are determined by the successive resolution of the space of the zeroth-order functions.
Yang, Yongge; Xu, Wei; Sun, Yahui; Xiao, Yanwen
2017-01-01
This paper aims to investigate the stochastic bifurcations in the nonlinear vibroimpact system with fractional derivative under random excitation. Firstly, the original stochastic vibroimpact system with fractional derivative is transformed into equivalent stochastic vibroimpact system without fractional derivative. Then, the non-smooth transformation and stochastic averaging method are used to obtain the analytical solutions of the equivalent stochastic system. At last, in order to verify the effectiveness of the above mentioned approach, the van der Pol vibroimpact system with fractional derivative is worked out in detail. A very satisfactory agreement can be found between the analytical results and the numerical results. An interesting phenomenon we found in this paper is that the fractional order and fractional coefficient of the stochastic van der Pol vibroimpact system can induce the occurrence of stochastic P-bifurcation. To the best of authors' knowledge, the stochastic P-bifurcation phenomena induced by fractional order and fractional coefficient have not been found in the present available literature which studies the dynamical behaviors of stochastic system with fractional derivative under Gaussian white noise excitation.
Islam, Nasarul; Pandith, Altaf Hussain
2017-07-01
Density functional theory at CAM-B3LYP/6-311G++ (2d, 2p) level was employed to study the Triphenylboroxine derivatives (TB) containing electron donating and electron substituents, for their charge transfer and nonlinear optical properties. The results reveal that electron donating groups facilitate the rapid electron injection as compared to unsubstituted TB. It was observed that upon substitution with electron donating groups, the TB derivatives show an increased double bond character in the B3-C18 bond indicating an increase in the degree of conjugation. The Frontier molecular orbital studies indicate that highest occupied molecular orbitals of the neutral molecules delocalize primarily over the three phenyl rings and bridging oxygen atoms, whereas the lowest unoccupied molecular orbitals localize largely on the two phenyl rings and the boron atoms. Further, the TD-DFT studies indicate that the maximum absorption band results from the electron transitions from the initial states that are contributed by the HOMO and HOMO-1 to the final states that are mainly contributed by the LUMOs. In addition, we have observed that the introduction of electron donating group to the TB-7 leads to more active nonlinear performance.
Nieto, L M; Suzko, A A
2003-01-01
The intertwining operator technique is applied to difference Schroedinger equations with operator-valued coefficients. It is shown that these equations appear naturally when a discrete basis is used for solving a multichannel Schroedinger equation. New families of exactly solvable multichannel Hamiltonians are found.
Revised Iterative Solution for Groundstate of Schroedinger Equation
Institute of Scientific and Technical Information of China (English)
ZHAOWei-Qin
2004-01-01
A revised iterative method based on Green function defined by quadratures along a single trajectory is proposed to solve the low-lying quantum wave function for Schroedinger equation. Specially a new expression of the perturbed energy is obtained, which is much simpler than the traditional one. The method is applied to solve the unharmonic oscillator potential. The revised iteration procedure gives exactly the same result as those based on the single trajectory quadrature method. A comparison of the revised iteration method to the old one is made using the example of Stark effect. The obtained results are consistent to each other after making power expansion.
A new method for the solution of the Schroedinger equation
Energy Technology Data Exchange (ETDEWEB)
Amore, Paolo [Facultad de Ciencias, Universidad de Colima, Bernal DIaz del Castillo 340, Colima, Colima (Mexico); Aranda, Alfredo [Facultad de Ciencias, Universidad de Colima, Bernal DIaz del Castillo 340, Colima, Colima (Mexico); De Pace, Arturo [Istituto Nazionale di Fisica Nucleare, Sezione di Torino, Via P Giuria 1, I-10125, Torino (Italy)
2004-03-12
We present a new method for the solution of the Schroedinger equation applicable to problems of a non-perturbative nature. The method works by identifying three different scales in the problem, which then are treated independently: an asymptotic scale, which depends uniquely on the form of the potential at large distances; an intermediate scale, still characterized by an exponential decay of the wavefunction; and, finally, a short distance scale, in which the wavefunction is sizable. The notion of optimized perturbation is then used in the last two regimes. We apply the method to the quantum anharmonic oscillator and find it suitable to treat both energy eigenvalues and wavefunctions, even for strong couplings.
Non-Schroedinger forces and pilot waves in quantum cosmology
Tipler, Frank J.
1987-09-01
The version of the pilot wave interpretation of quantum mechanics using a nonlocal non-Schroedinger force is found to be inconsistent when applied to distributions with small numbers of particles. Any version of the pilot wave interpretation is shown to require the universe to move along a single trajectory. It is suggested that no version of the pilot wave interpretation can be applied to the wavefunction of quantum cosmology, because in any version of this interpretation there is only one particle, the universe.
Numerical stochastic perturbation theory in the Schroedinger functional
Energy Technology Data Exchange (ETDEWEB)
Brambilla, Michele; Di Renzo, Francesco; Hesse, Dirk [Parma Univ. (Italy); INFN, Parma (Italy); Dalla Brida, Mattia [Trinity College Dublin (Ireland). School of Mathematics; Sint, Stefan [Trinity College Dublin (Ireland). School of Mathematics; Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC
2013-11-15
The Schroedinger functional (SF) is a powerful and widely used tool for the treatment of a variety of problems in renormalization and related areas. Albeit offering many conceptual advantages, one major downside of the SF scheme is the fact that perturbative calculations quickly become cumbersome with the inclusion of higher orders in the gauge coupling and hence the use of an automated perturbation theory framework is desirable. We present the implementation of the SF in numerical stochastic perturbation theory (NSPT) and compare first results for the running coupling at two loops in pure SU(3) Yang-Mills theory with the literature.
Schroedinger invariant solutions of type IIB with enhanced supersymmetry
Energy Technology Data Exchange (ETDEWEB)
Donos, Aristomenis [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Gauntlett, Jerome P. [Imperial College, London (United Kingdom). Theoretical Physics Group; Imperial College, London (United Kingdom). Inst. for Mathematical Sciences
2009-07-15
We construct the Killing spinors for a class of supersymmetric solutions of type IIB supergravity that are invariant under the non-relativistic Schroedinger algebra. The solutions depend on a five-dimensional Sasaki- Einstein space and it has been shown that they admit two Killing spinors. Here we will show that, for generic Sasaki-Einstein space, there are special subclasses of solutions which admit six Killing spinors and we determine the corresponding superisometry algebra. We also show that for the special case that the Sasaki-Einstein space is the round five-sphere, the number of Killing spinors can be increased to twelve. (orig.)
Energy Density of Vortices in the Schroedinger Picture
Laenge, J D; Reinhardt, H
2003-01-01
The one-loop energy density of an infinitely thin static magnetic vortex in SU(2) Yang-Mills theory is evaluated using the Schroedinger picture. Both the gluonic fluctuations as well as the quarks in the vortex background are included. The energy density of the magnetic vortex is discussed as a function of the magnetic flux. The center vortices correspond to local minima in the effective potential. These minima are degenerated with the perturbative vacuum if the fermions are ignored. Inclusion of fermions lifts this degeneracy, raising the vortex energy above the energy of the perturbative vacuum.
Comparison theorems for the position-dependent mass Schroedinger equation
Kulikov, D A
2011-01-01
The following comparison rules for the discrete spectrum of the position-dependent mass (PDM) Schroedinger equation are established. (i) If a constant mass $m_0$ and a PDM $m(x)$ are ordered everywhere, that is either $m_0\\leq m(x)$ or $m_0\\geq m(x)$, then the corresponding eigenvalues of the constant-mass Hamiltonian and of the PDM Hamiltonian with the same potential and the BenDaniel-Duke ambiguity parameters are ordered. (ii) The corresponding eigenvalues of PDM Hamiltonians with the different sets of ambiguity parameters are ordered if $\
Dark Spatial Soliton Interaction in Nonlinear Kerr Medium
Institute of Scientific and Technical Information of China (English)
LuchuanWANG; QinliangFAN
1998-01-01
The dark spatial soliton interaction in nonlinear Kerr medium has been studied in this paper.The problem has been solved by the use of the slowly varying envelope approximation in solving coupled nonlinear Schroedinger equations.The perturbation nature of dark spatial soliton interaction has been described and some of their key properties has been discussed as well in the paper.
A new LES model derived from generalized Navier-Stokes equations with nonlinear viscosity
Rodríguez, José M
2015-01-01
Large Eddy Simulation (LES) is a very useful tool when simulating turbulent flows if we are only interested in its "larger" scales. One of the possible ways to derive the LES equations is to apply a filter operator to the Navier-Stokes equations, obtaining a new equation governing the behavior of the filtered velocity. This approach introduces in the equations the so called subgrid-scale tensor, that must be expressed in terms of the filtered velocity to close the problem. One of the most popular models is that proposed by Smagorinsky, where the subgrid-scale tensor is modeled by introducing an eddy viscosity. In this work, we shall propose a new approximation to this problem by applying the filter, not to the Navier-Stokes equations, but to a generalized version of them with nonlinear viscosity. That is, we shall introduce a nonlinear viscosity, not as a procedure to close the subgrid-scale tensor, but as part of the model itself (see below). Consequently, we shall need a different method to close the subgri...
Target tracking by distributed autonomous vessels using the derivative-free nonlinear Kalman filter
Rigatos, Gerasimos; Siano, Pierluigi; Raffo, Guilerme
2015-12-01
In this paper a distributed control problem for unmanned surface vessels (USVs) is formulated as follows: there are N USVs which pursue another vessel (moving target). At each time instant each USV can obtain measurements of the target's cartesian coordinates. The objective is to make the USVs converge in a synchronized manner towards the target, while avoiding collisions between them and avoiding collisions with obstacles in their motion plane. A distributed control law is developed for the USVs which enables not only convergence of the USVs to the goal position, but also makes possible to maintain the cohesion of the USVs fleet. Moreover, distributed filtering is performed, so as to obtain an estimate of the target vessel's state vector. This provides the desirable state vector to be tracked by each one of the USVs. To this end, a new distributed nonlinear filtering method of improved accuracy and computation speed is introduced. This filtering approach, under the name Derivative-free distributed nonlinear Kalman Filter is based on differential flatness theory and on an exact linearization of the target vessel's dynamic/kinematic model.
Wang, Jun-Wei; Wu, Huai-Ning; Li, Han-Xiong
2012-06-01
In this paper, a distributed fuzzy control design based on Proportional-spatial Derivative (P-sD) is proposed for the exponential stabilization of a class of nonlinear spatially distributed systems described by parabolic partial differential equations (PDEs). Initially, a Takagi-Sugeno (T-S) fuzzy parabolic PDE model is proposed to accurately represent the nonlinear parabolic PDE system. Then, based on the T-S fuzzy PDE model, a novel distributed fuzzy P-sD state feedback controller is developed by combining the PDE theory and the Lyapunov technique, such that the closed-loop PDE system is exponentially stable with a given decay rate. The sufficient condition on the existence of an exponentially stabilizing fuzzy controller is given in terms of a set of spatial differential linear matrix inequalities (SDLMIs). A recursive algorithm based on the finite-difference approximation and the linear matrix inequality (LMI) techniques is also provided to solve these SDLMIs. Finally, the developed design methodology is successfully applied to the feedback control of the Fitz-Hugh-Nagumo equation.
A numerical study of the Schroedinger-Newton equations
Harrison, R I
2001-01-01
and added perturbations oscillate at frequencies determined by the linear perturbation theory. The higher states are shown to be unstable, emitting scatter and leaving a rescaled ground state. The rate at which they decay is controlled by the complex eigenvalues of the linear perturbation. Next we consider adding another dimension in two different ways: by considering the axisymmetric case and the 2-D equations. The stationary solutions are found. We modify the evolution method and find that the higher states are unstable. In 2-D case we consider rigidly rotating solutions and show they exist and are unstable. The Schroedinger-Newton (S-N) equations were proposed by Penrose [18] as a model for gravitational collapse of the wave-function. The potential in the Schroedinger equation is the gravity due to the density of vertical bar psi vertical bar sup 2 , where psi is the wave-function. As with normal Quantum Mechanics the probability, momentum and angular momentum are conserved. We first consider the spherical...
A general derivation of the subharmonic threshold for non-linear bubble oscillations.
Prosperetti, Andrea
2013-06-01
The paper describes an approximate but rather general derivation of the acoustic threshold for a subharmonic component to be possible in the sound scattered by an insonified gas bubble. The general result is illustrated with several specific models for the mechanical behavior of the surface coating of bubbles used as acoustic contrast agents. The approximate results are found to be in satisfactory agreement with fully non-linear numerical results in the literature. The amplitude of the first harmonic is also found by the same method. A fundamental feature identified by the analysis is that the subharmonic threshold can be considerably lowered with respect to that of an uncoated free bubble if the mechanical response of the coating varies rapidly in the neighborhood of certain specific values of the bubble radius, e.g., because of buckling.
Derivation of second-order nonlinear optical conductivity by the projection-diagram method
Directory of Open Access Journals (Sweden)
Nam Lyong Kang
2012-03-01
Full Text Available A projection-diagram method is introduced for optical conductivity with lineshape functions, which takes into account the population criterion that the electron and phonon distribution functions are multiplicatively combined along with the energy conservation factors for proper interpretation of emission and absorption of phonons and photons in all the processes of electron transitions. It is further shown that the second order nonlinear optical conductivity of the system of electrons interacting with phonons, obtained using this method, is identical with that derived by using the state dependent projectors and the KC reduction identities [J. Phys. A: Math. Theor. 43, 165203 (2010]. We expect that this method can reduce the amount of many-body calculation and can be of help in providing physical intuition into solid state quantum dynamics and representing perturbation expressions for such systems.
Dwivedi, Y.; de Boni, L.; Gonçalves, P. J.; Mairink, L. M.; Menegatti, R.; Fonseca, T. L.; Zilio, S. C.
2013-03-01
This work reports on the optical nonlinearities of a newly synthesized pyrazole derivative, namely (E)-1-(4-chlorophenyl)-4-(2-nitrovinyl)-1H-pyrazole. The Z-scan technique with femtosecond laser pulses was used to determine the two-photon absorption (2PA) cross-section spectrum, which presents a maximum of 67 GM at 690 nm. We have combined hyper-Rayleigh scattering (HRS) experiments and second-order Møller-Plesset perturbation theory (MP2) calculations to study the first hyperpolarizability (βHRS). It was found that the MP2/6-311+G(d) model, taking into account solvent and dispersion effects, provides the βHRS value of 40 × 10-30 cm5/esu for the compound, in good agreement with the experimental result of 45 ± 2 × 10-30 cm5/esu.
Sunil Kumar Reddy, N.; Badam, Rajashekar; Sattibabu, Romala; Molli, Muralikrishna; Sai Muthukumar, V.; Siva Sankara Sai, S.; Rao, G. Nageswara
2014-11-01
We report here the nonlinear optical (NLO) properties of eight bis-chalcones of D-π-A-π-D type. These dibenzylideneacetone (DBA) derivatives are synthesized by Claisen-Schmidt reaction. The compounds are characterized by UV-vis, FTIR, 1H NMR, 13C NMR, mass spectroscopy and powder XRD. By substituting different groups (electron withdrawing and electron donating) at 'para' and 'meta' positions of the aromatic ring, we observed an enhancement in second harmonic generation with substitution at 'para' position. These compounds have also showed higher two-photon absorption compared to other chalcones reported in literature. These compounds, exhibiting both second and third order NLO effects, are plausible candidate materials in photonic devices.
Wachter, H
2007-01-01
This is the second part of a paper about a q-deformed analog of non-relativistic Schroedinger theory. It applies the general ideas of part I and tries to give a description of one-particle states on q-deformed quantum spaces like the braided line or the q-deformed Euclidean space in three dimensions. Hamiltonian operators for the free q-deformed particle in one as well as three dimensions are introduced. Plane waves as solutions to the corresponding Schroedinger equations are considered. Their completeness and orthonormality relations are written down. Expectation values of position and momentum observables are taken with respect to one-particle states and their time-dependence is discussed. A potential is added to the free-particle Hamiltonians and q-analogs of the Ehrenfest theorem are derived from the Heisenberg equations of motion. The conservation of probability is proved.
Chaotic synchronization of two complex nonlinear oscillators
Energy Technology Data Exchange (ETDEWEB)
Mahmoud, Gamal M. [Department of Mathematics, Faculty of Science, Assiut University, Assiut 71516 (Egypt)], E-mail: gmahmoud@aun.edu.eg; Mahmoud, Emad E. [Department of Mathematics, Faculty of Science, Sohag University (Egypt)], E-mail: emad_eluan@yahoo.com; Farghaly, Ahmed A. [Department of Mathematics, Faculty of Science, Assiut University, Assiut 71516 (Egypt)], E-mail: ahmed_1_66@yahoo.com; Aly, Shaban A. [Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut 71511 (Egypt)], E-mail: shhaly12@yahoo.com
2009-12-15
Synchronization is an important phenomenon commonly observed in nature. It is also often artificially induced because it is desirable for a variety of applications in physics, applied sciences and engineering. In a recent paper [Mahmoud GM, Mohamed AA, Aly SA. Strange attractors and chaos control in periodically forced complex Duffing's oscillators. Physica A 2001;292:193-206], a system of periodically forced complex Duffing's oscillators was introduced and shown to display chaotic behavior and possess strange attractors. Such complex oscillators appear in many problems of physics and engineering, as, for example, nonlinear optics, deep-water wave theory, plasma physics and bimolecular dynamics. Their connection to solutions of the nonlinear Schroedinger equation has also been pointed out. In this paper, we study the remarkable phenomenon of chaotic synchronization on these oscillator systems, using active control and global synchronization techniques. We derive analytical expressions for control functions and show that the dynamics of error evolution is globally stable, by constructing appropriate Lyapunov functions. This means that, for a relatively large set initial conditions, the differences between the drive and response systems vanish exponentially and synchronization is achieved. Numerical results are obtained to test the validity of the analytical expressions and illustrate the efficiency of these techniques for inducing chaos synchronization in our nonlinear oscillators.
Beyond single stream with the Schroedinger method - Closing the Vlasov hierarchy
Energy Technology Data Exchange (ETDEWEB)
Uhlemann, Cora; Kopp, Michael; Haugg, Thomas [Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-University, Theresienstr. 37, D-80333 Munich (Germany)
2014-07-01
We investigate large scale structure formation of dark matter in the phase-space description based on the Vlasov equation whose nonlinearity is induced by gravitational interaction according to the Poisson equation. Determining the time-evolution of density and peculiar velocity demands solving the full Vlasov hierarchy for the moments of the phase-space distribution function. In the presence of long-range interaction no consistent truncation of the hierarchy is known apart from the pressureless fluid (dust) model which is incapable of describing virialization due to the occurrence of shell-crossing singularities and the inability to generate higher cumulants like vorticity and velocity dispersion. Our goal is to find a phase-space distribution function that is able to describe regions of multi-streaming and therefore can serve as theoretical N-body double. We use the coarse-grained Wigner probability distribution obtained from a wavefunction fulfilling the Schroedinger equation and show that its evolution equation bears strong resemblance to the Vlasov equation but cures the shell-crossing singularities. This feature was already employed in cosmological simulations of large-scale structure formation by Widrow and Kaiser '93. We are able to show that the coarse-grained Wigner ansatz automatically closes the corresponding hierarchy while incorporating nonzero higher cumulants which are determined self-consistently from density and velocity.
Prieur, Fabrice; Vilenskiy, Gregory; Holm, Sverre
2012-10-01
A corrected derivation of nonlinear wave propagation equations with fractional loss operators is presented. The fundamental approach is based on fractional formulations of the stress-strain and heat flux definitions but uses the energy equation and thermodynamic identities to link density and pressure instead of an erroneous fractional form of the entropy equation as done in Prieur and Holm ["Nonlinear acoustic wave equations with fractional loss operators," J. Acoust. Soc. Am. 130(3), 1125-1132 (2011)]. The loss operator of the obtained nonlinear wave equations differs from the previous derivations as well as the dispersion equation, but when approximating for low frequencies the expressions for the frequency dependent attenuation and velocity dispersion remain unchanged.
Abbasbandy, S.
2007-10-01
In this article, an application of He's variational iteration method is proposed to approximate the solution of a nonlinear fractional differential equation with Riemann-Liouville's fractional derivatives. Also, the results are compared with those obtained by Adomian's decomposition method and truncated series method. The results reveal that the method is very effective and simple.
The solution of coupled Schroedinger equations using an extrapolation method
Goorvitch, D.; Galant, D. C.
1992-01-01
In this paper, extrapolation to the limit in a finite-difference method is applied to solve a system of coupled Schroedinger equations. This combination results in a method that only requires knowledge of the potential energy functions for the system. This numerical procedure has several distinct advantages over the more conventional methods. Namely, initial guesses for the term values are not needed; assumptions need be made about the behavior of the wavefunctions, such as the slope or magnitude in the nonclassical region; and the algorithm is easy to implement, has a firm mathematical foundation, and provides error estimates. Moreover, the method is less sensitive to round-off error than other methods since a small number of mesh points is used and it can be implemented on small computers. A comparison of the method with another numerical method shows results agreeing within 1 part in 10 exp 4.
Schroedinger Invariance from Lifshitz Isometries in Holography and Field Theory
Hartong, Jelle; Obers, Niels A
2014-01-01
We study non-relativistic field theory coupled to a torsional Newton-Cartan geometry both directly as well as holographically. The latter involves gravity on asymptotically locally Lifshitz space-times. We define an energy-momentum tensor and a mass current and study the relation between conserved currents and conformal Killing vectors for flat Newton-Cartan backgrounds. It is shown that this involves two different copies of the Lifshitz algebra together with an equivalence relation that joins these two Lifshitz algebras into a larger Schroedinger algebra (without the central element). In the holographic setup this reveals a novel phenomenon in which a large bulk diffeomorphism is dual to a discrete gauge invariance of the boundary field theory.
Soliton-like solutions to the ordinary Schroedinger equation
Energy Technology Data Exchange (ETDEWEB)
Zamboni-Rached, Michel [Universidade Estadual de Campinas (DMO/FEEC/UNICAMP), Campinas, SP (Brazil). Fac. de Engenharia Eletrica e de Computacao. Dept. de Microondas e Optica; Recami, Erasmo, E-mail: recami@mi.infn.i [Universita Statale di Bergamo, Bergamo (Italy). Facolta di Ingegneria
2011-07-01
In recent times it has been paid attention to the fact that (linear) wave equations admit of soliton-like solutions, known as Localized Waves or Non-diffracting Waves, which propagate without distortion in one direction. Such Localized Solutions (existing also for K-G or Dirac equations) are a priori suitable, more than Gaussian's, for describing elementary particle motion. In this paper we show that, mutatis mutandis, Localized Solutions exist even for the ordinary Schroedinger equation within standard Quantum Mechanics; and we obtain both approximate and exact solutions, also setting forth for them particular examples. In the ideal case such solutions bear infinite energy, as well as plane or spherical waves: we show therefore how to obtain nite-energy solutions. At last, we briefly consider solutions for a particle moving in the presence of a potential. (author)
Comment on "Fractional quantum mechanics" and "Fractional Schroedinger equation"
Wei, Yuchuan
2016-01-01
In this comment, we point out some shortcomings in two papers "Fractional quantum mechanics" [Phys. Rev. E 62, 3135 (2000)] and "Fractional Schroedinger equation" [Phys. Rev. E 66, 056108 (2002)]. We prove that the fractional uncertainty relation does not hold generally. The probability continuity equation in fractional quantum mechanics has a missing source term, which leads to particle teleportation, i.e., a particle can teleport from one place to another. Since the relativistic kinetic energy can be viewed as an approximate realization of the fractional kinetic energy, the particle teleportation should be an observable relativistic effect in quantum mechanics. With the help of this concept, superconductivity could be viewed as the teleportation of electrons from one side of a superconductor to another and superfluidity could be viewed as the teleportation of helium atoms from one end of a capillary tube to the other. We also point out how to teleport a particle to a destination.
The gradient flow coupling in the Schroedinger functional
Energy Technology Data Exchange (ETDEWEB)
Fritzsch, Patrick [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Ramos, Alberto [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC
2013-01-15
We study the perturbative behavior of the Yang-Mills gradient flow in the Schroedinger Functional, both in the continuum and on the lattice. The energy density of the flow field is used to define a running coupling at a scale given by the size of the finite volume box. From our perturbative computation we estimate the size of cutoff effects of this coupling to leading order in perturbation theory. On a set of N{sub f}=2 gauge field ensembles in a physical volume of L{proportional_to}0.4 fm we finally demonstrate the suitability of the coupling for a precise continuum limit due to modest cutoff effects and high statistical precision.
Bound states for non-symmetric evolution Schroedinger potentials
Energy Technology Data Exchange (ETDEWEB)
Corona, Gulmaro Corona [Area de Analisis Matematico y sus Aplicaciones, Universidad Autonoma Metropolitana-Azcapotalco, Atzcapotzalco, DF (Mexico)). E-mail: ccg@correo.azc.uam.mx
2001-09-14
We consider the spectral problem associated with the evolution Schroedinger equation, (D{sup 2}+ k{sup 2}){phi}=u{phi}, where u is a matrix-square-valued function, with entries in the Schwartz class defined on the real line. The solution {phi}, called the wavefunction, consists of a function of one real variable, matrix-square-valued with entries in the Schwartz class. This problem has been dealt for symmetric potentials u. We found for the present case that the bound states are localized similarly to the scalar and symmetric cases, but by the zeroes of an analytic matrix-valued function. If we add an extra condition to the potential u, we can determine these states by an analytic scalar function. We do this by generalizing the scalar and symmetric cases but without using the fact that the Wronskian of a pair of wavefunction is constant. (author)
The chirally rotated Schroedinger functional. Theoretical expectations and perturbative tests
Energy Technology Data Exchange (ETDEWEB)
Dalla Brida, Mattia [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Sint, Stefan [Trinity College Dublin (Ireland). School of Mathematics; Vilaseca, Pol [Istituto Nazionale di Fisica Nucleare, Sezione di Roma (Italy)
2016-03-15
The chirally rotated Schroedinger functional (χSF) with massless Wilson-type fermions provides an alternative lattice regularization of the Schroedinger functional (SF), with different lattice symmetries and a common continuum limit expected from universality. The explicit breaking of flavour and parity symmetries needs to be repaired by tuning the bare fermion mass and the coefficient of a dimension 3 boundary counterterm. Once this is achieved one expects the mechanism of automatic O(a) improvement to be operational in the χSF, in contrast to the standard formulation of the SF. This is expected to significantly improve the attainable precision for step-scaling functions of some composite operators. Furthermore, the χSF offers new strategies to determine finite renormalization constants which are traditionally obtained from chiral Ward identities. In this paper we consider a complete set of fermion bilinear operators, define corresponding correlation functions and explain the relation to their standard SF counterparts. We discuss renormalization and O(a) improvement and then use this set-up to formulate the theoretical expectations which follow from universality. Expanding the correlation functions to one-loop order of perturbation theory we then perform a number of non-trivial checks. In the process we obtain the action counterterm coefficients to one-loop order and reproduce some known perturbative results for renormalization constants of fermion bilinears. By confirming the theoretical expectations, this perturbative study lends further support to the soundness of the χSF framework and prepares the ground for non-perturbative applications.
The Schroedinger functional for Gross-Neveu models
Energy Technology Data Exchange (ETDEWEB)
Leder, B.
2007-04-18
Gross-Neveu type models with a finite number of fermion flavours are studied on a two-dimensional Euclidean space-time lattice. The models are asymptotically free and are invariant under a chiral symmetry. These similarities to QCD make them perfect benchmark systems for fermion actions used in large scale lattice QCD computations. The Schroedinger functional for the Gross-Neveu models is defined for both, Wilson and Ginsparg-Wilson fermions, and shown to be renormalisable in 1-loop lattice perturbation theory. In two dimensions four fermion interactions of the Gross-Neveu models have dimensionless coupling constants. The symmetry properties of the four fermion interaction terms and the relations among them are discussed. For Wilson fermions chiral symmetry is explicitly broken and additional terms must be included in the action. Chiral symmetry is restored up to cut-off effects by tuning the bare mass and one of the couplings. The critical mass and the symmetry restoring coupling are computed to second order in lattice perturbation theory. This result is used in the 1-loop computation of the renormalised couplings and the associated beta-functions. The renormalised couplings are defined in terms of suitable boundary-to-boundary correlation functions. In the computation the known first order coefficients of the beta-functions are reproduced. One of the couplings is found to have a vanishing betafunction. The calculation is repeated for the recently proposed Schroedinger functional with exact chiral symmetry, i.e. Ginsparg-Wilson fermions. The renormalisation pattern is found to be the same as in the Wilson case. Using the regularisation dependent finite part of the renormalised couplings, the ratio of the Lambda-parameters is computed. (orig.)
Institute of Scientific and Technical Information of China (English)
Liang Li; Yiqun Wu; Yang Wang
2012-01-01
Two novel anthracene derivatives containing 4-vinylpyridine (FPEA) and 2-vinylpyridine (TPEA) poly(methyl methacrylate) films are prepared on quartz glass substrates.Their nonlinear absorption properties are investigated by using a 120-fs,800-am Ti:sapphire femtosecond pulsed laser operating at a 1-kHz repetition rate.The unique nonlinear absorption properties of these new compounds are observed by utilizing a Z-scan system.These two-photon absorption (TPA) properties are proven by the two-photon fluorescence excited at 800 nm.The FPEA and TPEA films have nonlinear TPA coefficients of 0.164 and 0.148 cm/GW and the TPA cross sections of 3.345 × 10-48 and 3.081 × 10-48 cm4.s/photon,respectively.The influence of the chemical structures on the nonlinear TPA properties of the compounds is also discussed.The highly nonlinear TPA activities of the films implied that the new anthracene derivatives are suitable materials with promising applications in super-high-density three-dimensional data storage and nano- or microstructure fabrication.
Existence of the time periodic solution for damped Schroedinger-Boussinesq equation
Institute of Scientific and Technical Information of China (English)
BolingGUO; XianyunDU
2000-01-01
In this paper, we study the time priodic solution for the weakly damped Schroedinger-Boussinesq equation, by Galerkin method, and prove the existence and uniqueness of the equations under some appropriate conditions.
Finite-difference scheme for the numerical solution of the Schroedinger equation
Mickens, Ronald E.; Ramadhani, Issa
1992-01-01
A finite-difference scheme for numerical integration of the Schroedinger equation is constructed. Asymptotically (r goes to infinity), the method gives the exact solution correct to terms of order r exp -2.
Energy Technology Data Exchange (ETDEWEB)
Amore, Paolo [Facultad de Ciencias, Universidad de Colima, Bernal Diaz del Castillo 340, Colima, Colima (Mexico)], E-mail: paolo.amore@gmail.com; Fernandez, Francisco M. [INIFTA (Conicet, UNLP), Division Quimica Teorica, Diag. 113 y 64 (S/N), Sucursal 4, Casilla de Correo 16, 1900 La Plata (Argentina)], E-mail: fernande@quimica.unlp.edu.ar
2008-04-28
We show that the Riccati-Pade method is suitable for the calculation of the complex eigenvalues of the Schroedinger equation with a repulsive exponential potential. The accuracy of the results is remarkable for realistic potential parameters.
Directory of Open Access Journals (Sweden)
Smarandache F.
2010-04-01
Full Text Available In this article, we find out some analytical and numerical solutions to the problem of barrier tunneling for cluster deuterium, in particular using Langevin method to solve the time-independent Schroedinger equation.
Directory of Open Access Journals (Sweden)
Azita Yazdanpanah
2014-04-01
Full Text Available Continuum robot manipulators are optimized to meet best trajectory requirements. Closed loop control is a key technology that is used to optimize the system output process to achieve this goal. In order to conduct research in the area of closed loop control, a control oriented cycle-to-cycle continuum robot model, containing dynamic model information for each individual continuum robot manipulator, is a necessity. In this research, the continuum robot manipulator is modeled according to information between joint variable and torque, which is represented by the nonlinear dynamic equation. After that, a multi-input-multi-output baseline computed torque control scheme is used to simultaneously control the torque load of system to regulate the joint variables to desired levels. One of the most important challenge in control theory is on-line tuning therefore fuzzy supervised optimization is used to tune the modified baseline and computed torque control coefficient. The performance of the modified baseline computed torque controller is compared with that of a baseline proportional, integral, and derivative (PID controller.
Optimal heat kernel estimates for Schroedinger operators with magnetic fields in two dimensions
Energy Technology Data Exchange (ETDEWEB)
Loss, M. [Georgia Inst. of Tech., Atlanta (United States). School of Mathematics; Thaller, B. [Institut fuer Mathematik, Universitaet Graz, A-8010 Graz (Austria)
1997-06-01
Sharp smoothing estimates are proven for magnetic Schroedinger semigroups in two dimensions under the assumption that the magnetic field is bounded below by some positive constant B{sub 0}. As a consequence the L{sup {infinity}} norm of the associated integral kernel is bounded by the L{sup {infinity}} norm of the Mehler kernel of the Schroedinger semigroup with the constant magnetic field B{sub 0}. (orig.)
Perturbative analysis of the Neuberger-Dirac operator in the Schroedinger functional
Takeda, S
2008-01-01
I examine some properties of the overlap operator in the Schroedinger functional formulated by Luescher at perturbative level. By investigating spectra of the free operator and one-loop coefficient of the Schroedinger functional coupling, I confirm the universality at tree and one-loop level. Furthermore, I address cutoff effects of the step scaling function and it turns out that the lattice artifacts for the overlap operator are comparable with those of the clover actions.
New Chiral Bis-Dipolar 6,6'-Disubstituted-Binaphthol Derivatives for Second-Order Nonlinear Optics
DEFF Research Database (Denmark)
Deussen, Heinz-Josef; Boutton, Carlo; Thorup, Niels;
1998-01-01
(S)everal chiral molecules with C-2 symmetry derived from two geometries of the binaphthol (BN) system substituted with different accepters have been synthesized in order to study the possibility of producing noncentrosymmetric crystals formed from these chiral structures. All the molecules possess...... cancel out exactly despite the noncentrosymmetry. The crystal structure of racemic 9,14-dicyanodinaphtho[2,1-d:1',2'-f][1,3]-dioxepin (2b) was found to be centrosymmetric. The new compounds were investigated for second-harmonic generation (including BN derivatives reported earlier) by the Kurtz......-Perry powder test to evaluate the second-order nonlinear optical (NLO) properties of polycrystalline samples. Although chirality ensures noncentrosymmetric crystals, only modest (approximate to 2-methyl-4-nitroaniline) or no nonlinearities were observed in the powder test, For a representative selection...
Directory of Open Access Journals (Sweden)
Kohei Arai
2013-01-01
Full Text Available Method for image prediction with nonlinear control lines which are derived from extracted feature points from the previously acquired imagery data based on Kriging method and morphing method is proposed. Through comparisons between the proposed method and the conventional linear interpolation and widely used Cubic Spline interpolation methods, it is found that the proposed method is superior to the conventional methods in terms of prediction accuracy.
Kerasidou, A. P.; Khammar, F.; Iliopoulos, K.; Ayadi, A.; El-Ghayoury, A.; Zouari, N.; Mhiri, T.; Sahraoui, B.
2014-03-01
The third order nonlinearities of two azobenzene-iminopyridine molecular systems have been investigated employing the Z-scan technique at 532 nm, 30 ps. The objective of the work has been to study and to compare the nonlinearity of two iminopyridine based ligands substituted with one (NO2AzoIminoPy, A) and two azobenzene units ((NO2Azo)2IminoPy, B). The ligand B exhibits an extended conjugated structure and higher charge transfer within the molecule. Our results show high dependence of the nonlinearity on both the conjugation length within the molecule and on the number of the electron accepting units.
Institute of Scientific and Technical Information of China (English)
REN, Ai-Min(任爱民); FENG, Ji-Kang(封继康); LIU, Xiao-Juan(刘孝娟)
2004-01-01
Different types of stilbene derivatives (D-π-D, A-π-A, D-π-A) were investigated with AM1, and specially, equilibrium geometries of symmetrical stilbene derivatives (D-π-D) were studied using of PM3. With the same method INDO/CI, the UV-vis spectra were explored and the position and strength of the two-photon absorption were predicated by Sum-Over-States expression. The relationships of the structures, spectra and nonlinear optical properties have been examined. The influence of various substituents on two photon absorption cross-sections was discussed micromechanically.
Exact bright and dark spatial soliton solutions in saturable nonlinear media
Energy Technology Data Exchange (ETDEWEB)
Calvo, Gabriel F. [Departamento de Matematicas, E.T.S. de Ingenieros Industriales, Instituto de Matematica Aplicada a la Ciencia y la Ingenieria (IMACI), E.T.S.I. Industriales, Avda. Camilo Jose Cela, 3, Universidad de Castilla-La Mancha, 13071 Ciudad Real (Spain); Belmonte-Beitia, Juan [Departamento de Matematicas, E.T.S. de Ingenieros Industriales, Instituto de Matematica Aplicada a la Ciencia y la Ingenieria (IMACI), E.T.S.I. Industriales, Avda. Camilo Jose Cela, 3, Universidad de Castilla-La Mancha, 13071 Ciudad Real (Spain)], E-mail: Juan.Belmonte@uclm.es; Perez-Garcia, Victor M. [Departamento de Matematicas, E.T.S. de Ingenieros Industriales, Instituto de Matematica Aplicada a la Ciencia y la Ingenieria (IMACI), E.T.S.I. Industriales, Avda. Camilo Jose Cela, 3, Universidad de Castilla-La Mancha, 13071 Ciudad Real (Spain)
2009-08-30
We present exact analytical bright and dark (black and grey) solitary wave solutions of a nonlinear Schroedinger-type equation describing the propagation of spatial beams in media exhibiting a saturable nonlinearity (such as centrosymmetric photorefractive materials). A qualitative study of the stationary equation is carried out together with a discussion of the stability of the solutions.
Nonlinear wave mechanics from classical dynamics and scale covariance
Energy Technology Data Exchange (ETDEWEB)
Hammad, F. [Departement TC-SETI, Universite A.Mira de Bejaia, Route Targa Ouzemmour, 06000 Bejaia (Algeria)], E-mail: fayhammad@yahoo.fr
2007-10-29
Nonlinear Schroedinger equations proposed by Kostin and by Doebner and Goldin are rederived from Nottale's prescription for obtaining quantum mechanics from classical mechanics in nondifferentiable spaces; i.e., from hydrodynamical concepts and scale covariance. Some soliton and plane wave solutions are discussed.
Generalized nonlinear Proca equation and its free-particle solutions
Energy Technology Data Exchange (ETDEWEB)
Nobre, F.D. [Centro Brasileiro de Pesquisas Fisicas and National Institute of Science and Technology for Complex Systems, Rio de Janeiro, RJ (Brazil); Plastino, A.R. [Universidad Nacional Buenos Aires-Noreoeste, CeBio y Secretaria de Investigacion, Junin (Argentina)
2016-06-15
We introduce a nonlinear extension of Proca's field theory for massive vector (spin 1) bosons. The associated relativistic nonlinear wave equation is related to recently advanced nonlinear extensions of the Schroedinger, Dirac, and Klein-Gordon equations inspired on the non-extensive generalized thermostatistics. This is a theoretical framework that has been applied in recent years to several problems in nuclear and particle physics, gravitational physics, and quantum field theory. The nonlinear Proca equation investigated here has a power-law nonlinearity characterized by a real parameter q (formally corresponding to the Tsallis entropic parameter) in such a way that the standard linear Proca wave equation is recovered in the limit q → 1. We derive the nonlinear Proca equation from a Lagrangian, which, besides the usual vectorial field Ψ{sup μ}(vector x,t), involves an additional field Φ{sup μ}(vector x,t). We obtain exact time-dependent soliton-like solutions for these fields having the form of a q-plane wave, and we show that both field equations lead to the relativistic energy-momentum relation E{sup 2} = p{sup 2}c{sup 2} + m{sup 2}c{sup 4} for all values of q. This suggests that the present nonlinear theory constitutes a new field theoretical representation of particle dynamics. In the limit of massless particles the present q-generalized Proca theory reduces to Maxwell electromagnetism, and the q-plane waves yield localized, transverse solutions of Maxwell equations. Physical consequences and possible applications are discussed. (orig.)
Song, Jia; Wang, Lun; Cai, Guobiao; Qi, Xiaoqiang
2015-06-01
Near space hypersonic vehicle model is nonlinear, multivariable and couples in the reentry process, which are challenging for the controller design. In this paper, a nonlinear fractional order proportion integral derivative (NFOPIλDμ) active disturbance rejection control (ADRC) strategy based on a natural selection particle swarm (NSPSO) algorithm is proposed for the hypersonic vehicle flight control. The NFOPIλDμ ADRC method consists of a tracking-differentiator (TD), an NFOPIλDμ controller and an extended state observer (ESO). The NFOPIλDμ controller designed by combining an FOPIλDμ method and a nonlinear states error feedback control law (NLSEF) is to overcome concussion caused by the NLSEF and conversely compensate the insufficiency for relatively simple and rough signal processing caused by the FOPIλDμ method. The TD is applied to coordinate the contradiction between rapidity and overshoot. By attributing all uncertain factors to unknown disturbances, the ESO can achieve dynamic feedback compensation for these disturbances and thus reduce their effects. Simulation results show that the NFOPIλDμ ADRC method can make the hypersonic vehicle six-degree-of-freedom nonlinear model track desired nominal signals accurately and fast, has good stability, dynamic properties and strong robustness against external environmental disturbances.
Gong, Weixiang; Yang, Junyi; Qin, Yuan-cheng; Wu, Xing-zhi; Jin, Xiao; Song, Yinglin
2016-10-01
The third-order nonlinear optical properties of benzothiadiazole copolymer with triphenylamine derivative side chain (BCT) dissolved in chloroform are investigated by top-hat Z-scan and time-resolved pump-probe techniques with a picoseconds pulses laser at wavelength of 532nm. Organic polymers of triphenylamine have been widely applied to optoelectronic devices owing to its outstanding physics and chemistry characteristic. So its nonlinear optical characteristic is worth studying. The sample's excited-state dynamics can be detected by the pump-probe with phase object device with/without an aperture in the far field. We can determine the sample's nonlinear absorptive and refractive coefficient by the top-hot Z-scan device with/without an aperture in the far field. The experimental results show that the BCT has a good reverse saturation absorption and negative refraction. At the same time, the BCT showed up long excited-state lifetimes. By means of a five-level model and analyzing the experimental curves, all nonlinear optical parameters are obtained. With the proper lifetime and intersystem crossing time, this sample can be a candidate for optical limiting.
Synthesis, growth and characterization of π conjugated organic nonlinear optical chalcone derivative
Energy Technology Data Exchange (ETDEWEB)
Prabhu, A.N., E-mail: ashwatha.prabhu@manipal.edu [Department of Physics, Manipal Institute of Technology, Manipal University, Manipal 576 104 (India); Upadhyaya, V. [Department of Physics, Manipal Institute of Technology, Manipal University, Manipal 576 104 (India); Jayarama, A., E-mail: jayaram@mite.ac.in [Department of Physics, Mangalore Institute of Technology and Engineering (MITE), Moodabidri 574225 (India); Subrahmanya Bhat, K. [Department of Chemistry, Manipal Institute of Technology, Manipal University, Manipal 576 104 (India)
2013-02-15
A new potentially useful nonlinear optical organic material, 1-(5-chlorothiophen-2-yl)-3-(2,3-dimethoxyphenyl)prop-2-en-1-one, has been synthesized and grown as a high-quality single crystal by the slow evaporation technique. The grown crystals were characterized by FT-IR, NMR, thermal analysis, and UV–visible spectroscopy. The material is thermally stabile up to 111 °C. The mechanical property of the grown crystals was studied using Vickers microhardness tester and the load dependence hardness was observed. The third order nonlinear optical properties of the material such as real and imaginary part of χ{sup (3)}, nonlinear absorption coefficient and nonlinear refractive index were determined using nanosecond laser pulses at 532 nm wavelength by employing Z-scan technique. The nonlinear refractive index is found to be of the order of 10{sup −11} cm{sup 2} W{sup −1}. The magnitude of third order susceptibility is of the order of 10{sup −13} esu. The observed increase in the third order nonlinearity in these molecules clearly indicates the electronic origin. The compounds exhibit good optical limiting at 532 nm. The best optical limiting behavior of this molecule is due to the substituted strong electron donor. - Highlights: ► A novel thiophene substituted NLO crystal has been grown using methanol as solvent. ► The crystals were characterized by using FTIR, TGA/DTA and UV–visible spectroscopy. ► The n{sub 2} and χ{sup (3)} values is of the order of 10{sup −11} cm{sup 2} W{sup −1} and 10{sup −13} esu respectively. ► The crystals show better optical limiting behavior.
Wei, Song; Chen, Wen; Hon, Y. C.
2016-11-01
This paper investigates the temporal effects in the modeling of flows through porous media and particles transport. Studies will be made among the time fractional diffusion model and two classical nonlinear diffusion models. The effects of the parameters upon the mentioned models have been studied. By simulating the sub-diffusion processes and comparing the numerical results of these models under different boundary conditions, we can conclude that the time fractional diffusion model is more suitable for simulating the sub-diffusion with steady diffusion rate; whereas the nonlinear models are more appropriate for depicting the sub-diffusion under changing diffusion rate.
Vlaykov, Dimitar G; Schmidt, Wolfram; Schleicher, Dominik R G
2016-01-01
Compressible magnetohydrodynamic (MHD) turbulence is ubiquitous in astrophysical phenomena ranging from the intergalactic to the stellar scales. In studying them, numerical simulations are nearly inescapable, due to the large degree of nonlinearity involved. However the dynamical ranges of these phenomena are much larger than what is computationally accessible. In large eddy simulations (LES), the resulting limited resolution effects are addressed explicitly by introducing to the equations of motion additional terms associated with the unresolved, subgrid-scale (SGS) dynamics. This renders the system unclosed. We derive a set of nonlinear structural closures for the ideal MHD LES equations with particular emphasis on the effects of compressibility. The closures are based on a gradient expansion of the finite-resolution operator (W.K. Yeo CUP 1993, ed. Galperin & Orszag) and require no assumptions about the nature of the flow or magnetic field. Thus the scope of their applicability ranges from the sub- to ...
DEFF Research Database (Denmark)
Nielsen, Mogens Brønsted; Petersen, Jan Conrad; Thorup, Niels
2005-01-01
A selection of donor-acceptor chromophores containing the redox-active dithiafulvene unit about acetylenic and aryl scaffolds has been synthesized. The molecules were studied for their optical, redox and structural properties. Moreover, third-order non-linear optical properties were investigated ...
Nonlinear localized modes in PT-symmetric Rosen-Morse potential well
Midya, Bikashkali
2013-01-01
We report the existence and properties of localized modes described by nonlinear Schroedinger equation with complex PT-symmetric Rosen-Morse potential well. Exact analytical expressions of the localized modes are found in both one dimensional and two-dimensional geometry with self-focusing and self-defocusing Kerr nonlinearity. Linear stability analysis reveals that these localized modes are unstable for all real values of the potential parameters although corresponding linear Schroedinger eigenvalue problem possesses unbroken PT-symmetry. This result has been verified by the direct numerical simulation of the governing equation. The transverse power flow density associated with these localized modes has also been examined.
Naik, Vasant S.; Vinitha, G.; Pragasam, A.; Shettigar, V.
2017-08-01
A new organic nonlinear optical single crystal of chalcone derivative, 1-(5-chlorothiophene-2-yl)-3-(4-methoxyphenyl) prop-2-en-1-one (5CT4MP) has been synthesized by slow evaporation technique. The structure of the sample has been determined by CHN analysis, FTIR and H1 NMR. The thermal stability of the grown crystal has been determined from DSC, DSC-TGA. The grown crystal has been characterized for their optical transmission. Second harmonic generation efficiency of the crystals obtained by classical powder technique using Nd:YAG laser is found out to be 1.6 times that of urea. The third order nonlinear optical parameters such as nonlinear optical susceptibility, nonlinear refractive index and nonlinear absorption coefficient have been determined by employing the Z-scan technique. The nonlinearity exhibited by these crystals is used to study the optical limiting behaviour.
A New Derivation of the Time-Dependent Schr\\"odinger Equation from Wave and Matrix Mechanics
Nanni, Luca
2015-01-01
An alternative method is proposed for deriving the time dependent Schroedinger equation from the pictures of wave and matrix mechanics. The derivation is of a mixed classical quantum character, since time is treated as a classical variable, thus avoiding any controversy over its meaning in quantum mechanics. The derivation method proposed in this paper requires no ad hoc assumption and avoids going through a second-order differential equation that can be reduced to the well known time-dependent Schroedinger equation only postulating a complex wavefunction with an exponential time dependence, as did by Schroedinger in its original paper of 1926.
Institute of Scientific and Technical Information of China (English)
LIU Zheng-Feng; WANG Xiao-Hong
2008-01-01
Adopting Yoshizawa's two-scale expansion technique,the fluctuating field is expanded around the isotropic field.The renormalization group method is applied for calculating the covariance of the fluctuating field at the lower order expansion,A nonlinear Reynolds stress model is derived and the turbulent constants inside are evaluated analytically.Compared with the two-scale direct interaction approximation analysis for turbulent shear flows proposed by Yoshizawa,the calculation is much more simple.The analytical model presented here is close to the Speziale model,which is widely applied in the numerical simulations for the complex turbulent flows.
Cheng, Wanyou; Xiao, Yunhai; Hu, Qing-Jie
2009-02-01
In this paper, we propose a family of derivative-free conjugate gradient methods for large-scale nonlinear systems of equations. They come from two modified conjugate gradient methods [W.Y. Cheng, A two term PRP based descent Method, Numer. Funct. Anal. Optim. 28 (2007) 1217-1230; L. Zhang, W.J. Zhou, D.H. Li, A descent modified Polak-Ribiére-Polyak conjugate gradient method and its global convergence, IMA J. Numer. Anal. 26 (2006) 629-640] recently proposed for unconstrained optimization problems. Under appropriate conditions, the global convergence of the proposed method is established. Preliminary numerical results show that the proposed method is promising.
Nonlinear waves described by a fifth-order equation derived from the Fermi-Pasta-Ulam system
Volkov, A. K.; Kudryashov, N. A.
2016-04-01
Nonlinear wave processes described by a fifth-order generalized KdV equation derived from the Fermi-Pasta-Ulam (FPU) model are considered. It is shown that, in contrast to the KdV equation, which demonstrates the recurrence of initial states and explains the FPU paradox, the fifthorder equation fails to pass the Painlevé test, is not integrable, and does not exhibit the recurrence of the initial state. The results of this paper show that the FPU paradox occurs only at an initial stage of a numerical experiment, which is explained by the existence of KdV solitons only on a bounded initial time interval.
Institute of Scientific and Technical Information of China (English)
YE Cheng; WANG Jiafu; FENG Zhiming
1993-01-01
In this paper,the poling properties of (PS)O-DCV,a derivative of poly (p-hydroxystyrene),was reported.The investigations showed that the thermochromism correction,which was neglected in the literatures,should be considered in the measurements of order parameter of poled films with electrochromism technique Here,another linear optical method,IR and polarized IR spectra for characterizing of poled films was suggested first time.The bulk second nonlinear optical coefficient d33 of poled films could be estimated by measured order parameter semi-qualitatively.
Directory of Open Access Journals (Sweden)
Tatar Nasser-eddine
2011-01-01
Full Text Available Abstract A second-order abstract problem of neutral type with derivatives of non-integer order in the nonlinearity as well as in the nonlocal conditions is investigated. This model covers many of the existing models in the literature. It extends the integer order case to the fractional case in the sense of Caputo. A fixed point theorem is used to prove existence of mild solutions. AMS Subject Classification 26A33, 34K40, 35L90, 35L70, 35L15, 35L07
Simulation of non-linear rf losses derived from characteristic Nb topography
Energy Technology Data Exchange (ETDEWEB)
Reece, Charles E. [JLAB; Xu, Chen; Kelley, Michael [W& M. JLAB
2013-09-01
A simplified model has been developed to simulate non-linear RF losses on Nb surfaces exclusively due to topographical enhancement of surface magnetic fields. If local sharp edges are small enough, at locations where local surface fields exceed Hc, small volumes of material may become normal conducting without thermal leading to quench. These small volumes of normal material yield increases in the effective surface resistance of the Nb. Using topographic data from typical BCP?d and EP?d fine grain niobium surfaces, we have simulated field-dependent losses and found that when extrapolated to resulting cavity performance, these losses correspond well to characteristic BCP/EP high field Q0 performance differences for fine grain Nb. We describe the structure of the model, its limitations, and the effects of this type of non-linear loss contribution on SRF cavities.
Kamath, Laxminarayana; Manjunatha, K. B.; Shettigar, Seetharam; Umesh, G.; Narayana, B.; Samshuddin, S.; Sarojini, B. K.
2014-03-01
A series of new chalcones containing terphenyl as a core and with different functional groups has been successfully synthesized by Claisen-Schmidt condensation method in search of new nonlinear optical (NLO) materials. Molecular structural characterization for the compounds was achieved by FTIR and single crystal X-ray diffraction. The third-order NLO absorption and refraction coefficients were simultaneously determined by Z-scan technique. The measurements were performed at 532 nm with 7 ns laser pulses using a Nd:YAG laser in solution form. The Z-scan experiments reveal that the compounds exhibit strong nonlinear refraction coefficient of the order 10-11 esu and the molecular two photon absorption cross section is 10-46 cm4 s/photon. The results also show that the structures of the compounds have great impact on NLO properties. The compounds show optical power limiting behavior due to two-photon absorption (TPA).
Nonlinear pulse propagation in birefringent fiber Bragg gratings.
Pereira, S; Sipe, J
1998-11-23
We present two sets of equations to describe nonlinear pulse propagation in a birefringent fiber Bragg grating. The first set uses a coupled-mode formalism to describe light in or near the photonic band gap of the grating. The second set is a pair of coupled nonlinear Schroedinger equations. We use these equations to examine viable switching experiments in the presence of birefringence. We show how the birefringence can both aid and hinder device applications.
Center for Analysis of Heterogeneous and Nonlinear Media
1989-10-14
computation of singular solutions of the nonlinear Schroedinger equation) Xue Xin (nonlinear homogenization) Jing-Yi Zhu (Ph.D. 1989, adaptive vortex method...numerical analysis of the vortex method for vortex sheets were carried out by Krasny and by Caflisch and Lowengrub. 2. Exact singular solutions of the...restriction to analytic functions. - 18- Singularities - Examples and the Generic Form of Singularities Singular solutions of the Birkhoff-Rott equation (1
Souza, Talita Evelyn; Rosa, Iara Maria Landre; Legendre, Alexandre Oliveira; Paschoal, Diego; Maia, Lauro J Q; Dos Santos, Hélio F; Matins, Felipe Terra; Doriguetto, Antonio Carlos
2015-08-01
Three new N-benzylideneaniline derivatives [p-nitrobenzylidene-p-phenylamineaniline (I), 2,4-dinitrobenzylidene-p-phenylamineaniline (II) and p-dinitrobenzylidene-p-diethylamineaniline (III)] containing electron-push-pull groups have been prepared. They present a planar N-benzylideneaniline core and neighbouring functional atoms, which are related through an efficient intramolecular charge transfer (CT). Two of the derivatives crystallize in non-centrosymmetric space groups, a necessary condition for non-linear optical (NLO) responses. The NLO properties were calculated for the molecular conformations determined by single-crystal X-ray diffraction as well as for the four molecules packed into each corresponding unit cell, using a quantum-chemical method at the cam-B3LYP/NLO-V level of theory. As expected from antiparallel face-to-face stacking through centrosymmetry, the main NLO descriptors - namely, the first hyperpolarizability (βtot) and its projection on the dipole moment direction (βvec) - are almost zero for the tetramer of derivative III. Interestingly, the calculated first hyperpolarizability decreases in the non-centrosymmetric unit-cell content of derivative II when compared to its single molecule, which may be related to its molecular pillaring, similar to that observed in derivative III. On the other hand, a desirable magnification of the NLO properties was found for packed units of derivative I, which may be a consequence of its parallel face-to-tail stacking with the CT vectors of all molecules pointing in the same direction. Moreover, the CT vector of compound I makes an angle of θ = 33.6° with its crystal polar axis, resulting in a higher-order parameter (cos(3)θ = 0.6) compared with the other derivatives. This is in line with the higher macroscopic second-order NLO response predicted for derivative I, βtot = 120.4 × 10(-30) e.s.u.
Nonlinear Maps Satisfying Derivability on the Parabolic Subalgebras of the Full Matrix Algebras
Institute of Scientific and Technical Information of China (English)
Zheng Xin CHEN; Yu E ZHAO
2011-01-01
Let F be a field of characteristic O,Mn(F) the full matrix algebra over F,t the subalgebra of Mn(F) consisting of all upper triangular matrices.Any subalgebra of Mn(F) containing t is called a parabolic subalgebra of Mn(F).Let P be a parabolic subalgebra of Mn(F).A map φ on P is said to satisfy derivability if φ(x·y) =φ(x).y+x·φ(y) for all x,y ∈ P,where φ is not necessarily linear.Note that a map satisfying derivability on P is not necessarily a derivation on P.In this paper,we prove that a map φ on P satisfies derivability if and only if φ is a sum of an inner derivation and an additive quasi-derivation on P.In particular,any derivation of parabolic subalgebras of Mn (F) is an inner derivation.
Synthesis and Non-linear Optical(NLO) Properties of a Series of Alkoxysilane Derivative Chromophores
Institute of Scientific and Technical Information of China (English)
SHI Zuo-sen; ZHANG Xiao-long; WANG Shi-wei; ZHAO Li-sha; CUI Zhan-chen
2009-01-01
@@ 1 Introduction Nonlinear optical materials(NLO) have drawn a great intrest of some scholars and scientists in the last dacades because of their tremendous potential application in optoelectronic~[1]. The fabrication of efficient optoelectron devices is a challenging task because such systems need to meet the stringentable requirements for high optical quality and large and sustainable electro-optical(EO) response[2]. In pursuit of NLO materials with excellent optoelectronic property, a number of organic and inorganic materials have been investigated. Among them, organic-inorganic hybrid materials have drawn a great interest due to their good thermal stabilities, low optical loss and convenience in fabricating their thin films[3-6].
Helffer, Bernard
2008-01-01
The two-dimensional Schroedinger operator with a uniform magnetic field and a periodic zero-range potential is considered. For weak magnetic fields we reduce the spectral problem to the semiclassical analysis of one-dimensional Harper-like operators. This shows the existence of parts of Cantor structure in the spectrum for special values of the magnetic flux.
Monte Carlo solution of the Schroedinger equation in Fock space representation
Energy Technology Data Exchange (ETDEWEB)
Szybisz, L.; Zabolitzky, J.G. (Koeln Univ. (Germany, F.R.). Inst. fuer Theoretische Physik)
1984-09-03
A new Monte Carlo method to solve the Schroedinger equation when expressed in Fock space is presented. The procedure is applied to two soluble many-body hamiltonians, the quasispin model of Lipkin-Meshkov-Glick and the so-called 'static source' limit of the nucleon-scalar-meson interaction in the discrete one-dimensional space.
Solutions of type IIB and D=11 supergravity with Schroedinger(z) symmetry
Energy Technology Data Exchange (ETDEWEB)
Donos, Aristomenis [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Gauntlett, Jerome P. [Imperial College, London (United Kingdom). Theoretical Physics Group; Imperial College, London (United Kingdom). Inst. for Mathematical Sciences
2009-05-15
We construct families of supersymmetric solutions of type IIB and D=11 supergravity that are invariant under the non-relativistic Schroedinger(z) algebra for various values of the dynamical exponent z. The new solutions are based on five- and seven-dimensional Sasaki-Einstein manifolds, respectively, and include supersymmetric solutions with z=2. (orig.)
Owolabi, Kolade M.; Atangana, Abdon
2016-09-01
In this paper, dynamics of time-dependent fractional-in-space nonlinear Schrödinger equation with harmonic potential V(x),x in R in one, two and three dimensions have been considered. We approximate the Riesz fractional derivative with the Fourier pseudo-spectral method and advance the resulting equation in time with both Strang splitting and exponential time-differencing methods. The Riesz derivative introduced in this paper is found to be so convenient to be applied in models that are connected with applied science, physics, and engineering. We must also report that the Riesz derivative introduced in this work will serve as a complementary operator to the commonly used Caputo or Riemann-Liouville derivatives in the higher-dimensional case. In the numerical experiments, one expects the travelling wave to evolve from such an initial function on an infinite computational domain (-∞, &infty); , which we truncate at some large, but finite values L. It is important that the value of L is chosen large enough to give enough room for the wave function to propagate. We observe a different distribution of complex wave functions for the focusing and defocusing cases.
Institute of Scientific and Technical Information of China (English)
Liu YANG; Zongmin QIAO
2012-01-01
In this paper,the existence and multiplicity of positive solutions for Robin type boundary value problem of differential equation involving the Riemann-Liouville fractional order derivative are established.
A new application of Riccati equation to some nonlinear evolution equations
Energy Technology Data Exchange (ETDEWEB)
Geng Tao [School of Science, PO Box 122, Beijing University of Posts and Telecommunications, Beijing 100876 (China)], E-mail: taogeng@yahoo.com.cn; Shan Wenrui [School of Science, PO Box 122, Beijing University of Posts and Telecommunications, Beijing 100876 (China)
2008-03-03
By means of symbolic computation, a new application of Riccati equation is presented to obtain novel exact solutions of some nonlinear evolution equations, such as nonlinear Klein-Gordon equation, generalized Pochhammer-Chree equation and nonlinear Schroedinger equation. Comparing with the existing tanh methods and the proposed modifications, we obtain the exact solutions in the form as a non-integer power polynomial of tanh (or tan) functions by using this method, and the availability of symbolic computation is demonstrated.
Mishurov, Dmytro; Voronkin, Andrii; Roshal, Alexander; Brovko, Oleksandr
2016-07-01
Cross-linked polymers on the basis of di-, tri and tetraglycidyl ethers of quercetin (3,3‧,4‧,5,7-pentahydroxyflavone) were synthesized, and then, poled in electrical field of corona discharge. Investigations of structural, thermal and optical parameters of the polymer films were carried out. It was found that the polymers obtained from di- and triglycidyl quercetin ethers had high values of macroscopic quadratic susceptibilities and substantial stability of nonlinear optical (NLO) properties after the poling. Tetraglycidyl ether of quercetin forms the polymer of lower quadratic susceptibility, which demonstrates noticeable relaxation process resulting in decrease of the NLO effect. It is supposed that the difference of the NLO properties is due to peculiarities of physical network of the polymers, namely to the ratio between numbers of hydrogen bonds formed by hydroxyl groups of chromophore fragments and by the ones of interfragmental parts of the polymeric chains.
A limit analysis approach to derive a thermodynamic damage potential for non-linear geomaterials
Karrech, A.; Poulet, T.; Regenauer-Lieb, K.
2012-10-01
This paper introduces a mathematical model which describes the continuum damage of non-linear geo-materials. The model accounts for full thermo-mechanical coupling as well as irreversible failure and its effect on shear heating. It involves multi-mechanisms creep to describe the material rheology depending on time, temperature, pressure and water content. This coupled thermo-mechanical model combined with the upper bound theory is used to formulate a potential capable of predicting the damage evolution. The model is implemented and applied to a cross-sectional geological layer subjected to extension. It reveals that damage accelerates the creation of faults and accentuates the localization of shear zones, thereby competing with the increase in material rigidity due to rate dependency, especially at high temperature.
Convexity of effective Lagrangian in nonlinear electrodynamics as derived from causality
Shabad, Anatoly E
2009-01-01
In nonlinear electrodynamics, by implementing the causality principle as the requirement that the group velocity of elementary excitations over a background field should not exceed unity, and the unitarity principle as the requirement that the residue of the propagator should be nonnegative, we find restrictions on the behavior of massive and massless dispersion curves and establish the convexity of the effective Lagrangian on the class of constant fields, also the positivity of all characteristic dielectric and magnetic permittivity constants. Violation of the general principles by the one-loop approximation in QED at exponentially large magnetic field is analyzed resulting in complex energy tachyons and super-luminal ghosts that signal the instability of the magnetized vacuum. General grounds for kinematical selection rules in the process of photon splitting/merging are discussed.
Classification of kink type solutions to the extended derivative nonlinear Schrödinger equation
DEFF Research Database (Denmark)
Wyller, J.; Fla, T.; Juul Rasmussen, J.
1998-01-01
The Raman Extended Derivative Non Linear Schrodinger (R-EDNLS) equation which models single mode propagation in optical fibers, is shown to possess travelling and stationary kink envelope solutions of monotonic and oscillatory type. These structures have been called optical shocks in analogy...... with hydrodynamical shocks or optical double layers in analogy with electrostatic double layers in plasma physics. Hydrodynamical equations for the action density and local wave number are derived and shock wave solutions of the Rankine-Hugionot type are constructed. They are consistent with the kink structures when...
A general derivation of the subharmonic threshold for non-linear bubble oscillations
Prosperetti, A.
2013-01-01
The paper describes an approximate but rather general derivation of the acoustic threshold for a subharmonic component to be possible in the sound scattered by an insonified gas bubble. The general result is illustrated with several specific models for the mechanical behavior of the surface coating
Energy Technology Data Exchange (ETDEWEB)
Zuniga S, A. [Instituto Politecnico Nacional, Departamento de Fisica, Escuela Superior de Fisica y Matematicas, Edificio 9, Unidad Profesional Adolfo Lopez Mateos, 07738 Mexico D.F. (Mexico)
2003-07-01
Employing canonical transformations defined in the coherent-state representation of quantum mechanics, we introduce Schroedinger-Cat- Like-States. The squeezed displaced number states with real squeezing parameter are contained in these states. (Author)
Directory of Open Access Journals (Sweden)
Nam Lyong Kang
2013-07-01
Full Text Available The projection-reduction method introduced by the present authors is known to give a validated theory for optical transitions in the systems of electrons interacting with phonons. In this work, using this method, we derive the linear and first order nonlinear optical conductivites for an electron-impurity system and examine whether the expressions faithfully satisfy the quantum mechanical philosophy, in the same way as for the electron-phonon systems. The result shows that the Fermi distribution function for electrons, energy denominators, and electron-impurity coupling factors are contained properly in organized manners along with absorption of photons for each electron transition process in the final expressions. Furthermore, the result is shown to be represented properly by schematic diagrams, as in the formulation of electron-phonon interaction. Therefore, in conclusion, we claim that this method can be applied in modeling optical transitions of electrons interacting with both impurities and phonons.
Directory of Open Access Journals (Sweden)
Cheng-Dong Yang
2014-01-01
Full Text Available This paper addresses the problem of robust H∞ control design via the proportional-spatial derivative (P-sD control approach for a class of nonlinear distributed parameter systems modeled by semilinear parabolic partial differential equations (PDEs. By using the Lyapunov direct method and the technique of integration by parts, a simple linear matrix inequality (LMI based design method of the robust H∞ P-sD controller is developed such that the closed-loop PDE system is exponentially stable with a given decay rate and a prescribed H∞ performance of disturbance attenuation. Moreover, a suboptimal H∞ controller is proposed to minimize the attenuation level for a given decay rate. The proposed method is successfully employed to address the control problem of the FitzHugh-Nagumo (FHN equation, and the achieved simulation results show its effectiveness.
Energy Technology Data Exchange (ETDEWEB)
Kouno, H.; Kakuta, N.; Noda, N.; Koide, K.; Mitsumori, T.; Hasegawa, A.; Nakano, M. (Department of Physics, Saga University, Saga 840 (Japan))
1995-04-01
We have studied the equations of state of nuclear matter using the nonlinear [sigma]-[omega] model. At the normal density, there is a strong correlation among the effective nucleon mass [ital M][sub 0][sup *], the incompressibility, [ital K] and the third derivative [ital K][prime] of binding energy. The results are compared with the empirical analysis of the giant isoscalar monopole resonances data. It is difficult to fit the data when [ital K][approx lt]200 MeV, using the model. It is also found that [ital K]=300[plus minus]50 MeV is favorable to account for the volume-symmetry properties of nuclear matter.
Solitons supported by singular spatial modulation of the Kerr nonlinearity
Borovkova, Olga V; Malomed, Boris A
2012-01-01
We introduce a setting based on the one-dimensional (1D) nonlinear Schroedinger equation (NLSE) with the self-focusing (SF) cubic term modulated by a singular function of the coordinate, |x|^{-a}. It may be additionally combined with the uniform self-defocusing (SDF) nonlinear background, and with a similar singular repulsive linear potential. The setting, which can be implemented in optics and BEC, aims to extend the general analysis of the existence and stability of solitons in NLSEs. Results for fundamental solitons are obtained analytically and verified numerically. The solitons feature a quasi-cuspon shape, with the second derivative diverging at the center, and are stable in the entire existence range, which is 0 < a < 1. Dipole (odd) solitons are found too. They are unstable in the infinite domain, but stable in the semi-infinite one. In the presence of the SDF background, there are two subfamilies of fundamental solitons, one stable and one unstable, which exist together above a threshold value ...
Institute of Scientific and Technical Information of China (English)
PENG,Qiang(彭强); HUANG,Yan(黄艳); LU,Zhi-Yun(卢志云); QIN,Sheng-Ying(秦圣英); XIE,Ming-Gui(谢明贵); GAO,Wei-Xianb(高维先); PENG,Jun-Biao(彭俊彪); CAO,Yong(曹镛)
2004-01-01
Two novel fluorene-based copolymers (PFSD and PFMD) containing squaric acid or maleimide unit in the main chain were synthesized in good yields by Suzuki coupling reaction. The resulting polymers possess excellent thermal stability, high electron affinity and high photoluminescence (PL) quantum yields. They can fluoresce in yellow-light range due to either the charge transfer between a fluorene segment and an electron-deficient containing squaric acid/maleimide segment of the polymers or the Forster energy transfer between different polymer chains.The results from PL measurements of the isothermally heated polymer thin films show that the commonly observed aggregate excimer formation in polyfluorenes is very effectively suppressed in these two polymers due to the nonlinear structures of maleimide and squaric acid moieties. Double-layer polymer light-emitting diodes (PLED)were fabricated using the resulting polymers as the emitting layers and Ba or Mg :Ag (V :V= 10 :1) as cathodes.All the devices show bright yellow emission (562-579 nm) with different maximum external quantum efficiencies (0.006%-1.13%). Compared with the other devices, indium-tin oxide (ITO)/polyethylenedioxythiophene (PEDOT):polystyrene sulfonic acid (PSS)/PFMD/Mg:Ag has the higher maximum external quantum efficiency of 1.13% at 564 cd/m2 with a bias of 8.4 V.
Gayvoronsky, V. Ya.; Uklein, A. V.; Gerasov, A. O.; Garashchenko, V. V.; Kovtun, Yu. P.; Shandura, M. P.; Kachkovsky, O. D.
2013-08-01
A series of the merocyanines containing the aminocoumarin as an acceptor terminal group and typical donor residues with different length of the polymethine chain were studied in detail. Joint spectral and quantum-chemical analysis of their molecular geometries and electronic structures as well as origin of their lowest electron transitions have been performed. It was shown that the electronic and spectral properties of the neutral merocyanines are similar to the well-known cationic cyanine dyes, being determined by the same structure of the lowest electron transitions in molecule. The elongation of the chromophore chain of the studied merocyanines leads to the significant bathochromic shift of the long wavelength band in their absorption spectra, approximately to that in the symmetrical cyanines. The calculated third hyperpolarizability increases for the higher merocyanine vinylog due to the dependence of the energy of the excited state on the elongation of the conjugated chain. It was confirmed by nonlinear optical (NLO) study performed within the picosecond range pulsed laser excitation at 532 nm.
Energy Technology Data Exchange (ETDEWEB)
Sakmann, Kaspar
2010-07-21
In this thesis, the physics of trapped, interacting Bose-Einstein condensates is analyzed by solving the many-body Schroedinger equation. Particular emphasis is put on coherence, fragmentation and reduced density matrices. First, the ground state of a trapped Bose-Einstein condensate and its correlation functions are obtained. Then the dynamics of a bosonic Josephson junction is investigated by solving the time-dependent many-body Schroedinger equation numerically exactly. These are the first exact results in literature in this context. It is shown that the standard approximations of the field, Gross-Pitaevskii theory and the Bose-Hubbard model fail at weak interaction strength and within their range of expected validity. For stronger interactions the dynamics becomes strongly correlated and a new equilibration phenomenon is discovered. By comparison with exact results it is shown that a symmetry of the Bose- Hubbard model between attractive and repulsive interactions must be considered an artefact of the model. A conceptual innovation of this thesis are time-dependent Wannier functions. Equations of motion for time-dependent Wannier functions are derived from the variational principle. By comparison with exact results it is shown that lattice models can be greatly improved at little computational cost by letting the Wannier functions of a lattice model become time-dependent. (orig.)
Relativistic regimes for dispersive shock-waves in non-paraxial nonlinear optics
Gentilini, Silvia; Conti, Claudio
2014-01-01
We investigate the effect of non-paraxiality in the dynamics of dispersive shock waves in the defocusing nonlinear Schroedinger equation. We show that the problem can be described in terms of a relativistic particle moving in a potential. Lowest order corrections enhance the wave-breaking and impose a limit to the highest achievable spectrum in an amount experimentally testable.
Derivation of amplitude equations for nonlinear oscillators subject to arbitrary forcing.
Mayol, Catalina; Toral, Raúl; Mirasso, Claudio R
2004-06-01
By using a generalization of the multiple scales technique we develop a method to derive amplitude equations for zero-dimensional forced systems. The method allows to consider either additive or multiplicative forcing terms and can be straightforwardly applied to the case that the forcing is white noise. We give examples of the use of this method to the case of the van der Pol-Duffing oscillator. The writing of the amplitude equations in terms of a Lyapunov potential allow us to obtain an analytical expression for the probability distribution function which reproduces reasonably well the numerical simulation results.
Non-iterative solution of the Schroedinger Eq. in the presence of exchange terms.
Rawitscher, George H.; Kang, S.-Y.; Koltracht, I.
2000-06-01
In the Hartree-Fock approximation the Pauli exclusion principle leads to a Schroedinger Eq. of an integro-differential form. We show that this equation can be solved non-iteratively by the same integral equation algorithm developed previously [1] for local potentials. This holds for non-localities of the exchange type, since a) the corresponding integration kernel is semi-separable, b) the convolution of the semi-separable exchange kernel with the semi-separable Green's function kernel is also of semi-separable form, and c) the integral equation method works well with semi-separable kernels. Numerical examples for electron-hydrogen scattering will be presented, and comparisons with existing iterative methods will be given. [1] R. A. Gonzales et. al., ''Integral Equation Method for Coupled Schroedinger Equations'', J. Comput. Phys., 153, 160 (1999).
Kar, Swayamsiddha; Adithya, K. S.; Shankar, Pruthvik; Jagadeesh Babu, N.; Srivastava, Sailesh; Nageswara Rao, G.
2017-07-01
Nine chalcones were prepared via Claisen-Schmidt condensation, and characterized by UV-vis, IR, 1H NMR, 13C NMR and mass spectrometry. One of the representative member 4-NDM-TC has been studied via single crystal XRD and the TGA/DTA technique. SHG efficiency and NLO susceptibilities of the chalcones have been evaluated by the Kurtz and Perry method and Degenerate Four Wave Mixing techniques respectively. 3-Cl-4‧-HC was noted to possess SHG efficiency 1.37 times that of urea while 4-NDM-TC returned the highest third order NLO susceptibilities with respect to CS2. In silico studies help evaluate various physical parameters, in correlating the observed activities. In conclusion, the structure-activity relationship was derived based on the in silico and experimental results for the third order NLO susceptibilities.
Quantum Nonlocality and Generation of Multi-mode Schroedinger Cat States
Institute of Scientific and Technical Information of China (English)
ZHENGShi-Biao
2004-01-01
We describe the Greenberger-Horne-Zeilinger (GHZ) paradox in the multi-mode Schroedinger cat states.We also show that the multi-mode cat states violate the Bell's inequality by an amount that grows exponentially with number of modes. The test of quantum nonlocality is based on parity measurement and displacement operation, which are experimentally feasible. We also describe a scheme for the generation of the cat states in cavity QED.
Efficient Scheme for the Generation of Atomic Schroedinger Cat States in an Optical Cavity
Institute of Scientific and Technical Information of China (English)
ZHENGShi-Biao; LINLi-Hua; JIANGYun-Kun
2003-01-01
An efficient scheme is proposed for the generation of atomic Schroedinger cat states in an optical cavity. In the scheme N three-level atoms are loaded in the optical cavity. Raman coupling of two ground states is achieved via a laser tield and the cavity mode. The cavity mode is always in the vacuum state and the atoms have no probability of being populated in the excited state. Thus, the scheme is insensitive to both the cavity decay and spontaneous emission.
Remarks on the Schroedinger operator with singular complex potentials. Technical summary report
Energy Technology Data Exchange (ETDEWEB)
Brezis, H.; Kato, T.
1978-08-01
Schroedinger operators of the form A = delta + V(x), where delta is the Laplacian and V is a scalar potential, arise in quantum mechanics and other areas. Delicate questions concerning what domain should be assigned to A must be settled in order to have a good theory. These questions are answered here for a very general class of potentials V which may even have complex values.
Rigatos, Gerasimos
2014-12-01
A synchronizing control scheme for coupled neural oscillators of the FitzHugh-Nagumo type is proposed. Using differential flatness theory the dynamical model of two coupled neural oscillators is transformed into an equivalent model in the linear canonical (Brunovsky) form. A similar linearized description is succeeded using differential geometry methods and the computation of Lie derivatives. For such a model it becomes possible to design a state feedback controller that assures the synchronization of the membrane's voltage variations for the two neurons. To compensate for disturbances that affect the neurons' model as well as for parametric uncertainties and variations a disturbance observer is designed based on Kalman Filtering. This consists of implementation of the standard Kalman Filter recursion on the linearized equivalent model of the coupled neurons and computation of state and disturbance estimates using the diffeomorphism (relations about state variables transformation) provided by differential flatness theory. After estimating the disturbance terms in the neurons' model their compensation becomes possible. The performance of the synchronization control loop is tested through simulation experiments.
Muhammad, Shabbir; Al-Sehemi, Abdullah G; Irfan, Ahmad; Chaudhry, Aijaz R
2016-07-01
Using the density functional theory methods, we effectively tune the second-order nonlinear optical (NLO) properties in some chalcone derivatives. Various unique push-pull configurations are used to efficiently enhance the intramolecular charge transfer process over the designed derivatives, which result in significantly larger amplitudes of the first hyperpolarizability as compared to their parent molecule. The ground state molecular geometries have been optimized using B3LYP/6-311G** level of theory. A variety of methods including B3LYP, CAM-B3LYP, PBE0, M06, BHandHLYP and MP2 are tested with 6-311G** basis set to calculate the first hyperpolarizability of parent system 1. The results of M06 are found closer to highly correlated MP2 method, which has been selected to calculate static and frequency dependent first hyperpolarizability amplitudes of all selected systems. At M06/6-311G** level of theory, the permanent electronic dipole moment (μtot), polarizability (α0) and static first hyperpolarizability (βtot) amplitudes for parent system 1 are found to be 5.139 Debye, 274a. u. and 24.22×10(-30)esu, respectively. These amplitudes have been significantly enhanced in designed derivatives 2 and 3. More importantly, the (βtot) amplitudes of systems 2 and 3 mount to 75.78×10(-30) and 128.51×10(-30)esu, respectively, which are about 3 times and 5 times larger than that of their parent system 1. Additionally, we have extended the structure-NLO property relationship to several newly synthesized chalcone derivatives. Interestingly, the amplitudes of dynamic frequency dependent hyperpolarizability μβω (SHG) are also significantly larger having values of 366.72×10(-48), 856.32×10(-48) and 1913.46×10(-48)esu for systems 1-3, respectively, at 1400nm of incident laser wavelength. The dispersion behavior over a wide range of change in wavelength has also been studied adopting a range of wavelength from 1907 to 544nm. Thus, the present work realizes the potential of
Institute of Scientific and Technical Information of China (English)
SUN,Gang(孙刚); QIU,Yong-Qing(仇永清); SUN,Hai-Zhu(孙海珠); SU,Zhong-Min(苏忠民); FENG,Jing-Dong(冯静东); ZHU,Yu-Lan(朱玉兰)
2004-01-01
The structures of barbituric acid derivatives substituted with Schiff base were optimized using ab initio HF method at 6-31G basis set.Based on the optimized structures,the electronic spectra were obtained by INDO/CI method.The second-order nonlinear optical (NLO) coefficients βu were calculated according to the sum-over-states (SOS) formula.In addition,the effect of conjugation on electronic spectra and second-order NLO coefficients was investigated.The influence of exchange between C and N atoms as well as the substituted effect on the barbituric acid was discussed.It was indicated that the exchange between C and N atoms on Schiff base is important for enhancing the NLO coefficient of the whole molecule with donor and acceptor (D-A).Meanwhile significant changes in electron donation and acception were observed as substituents changes positions.Among the designed models,molecule 1b has maximal βμ value of 124.65 × 10-30 esu.About molecule 1b,barbituric acid is considered as an accepted electronic group and the position of N atom on Schiff base is close to it.
Institute of Scientific and Technical Information of China (English)
刘岩; 饧国春; 孙世玲; 苏忠民
2012-01-01
The structures and second-order nonlinear optical (NLO) properties of a series of chlorobenzyl-o-carboranes derivatives (1 12) containing different push-pull groups have been studied by density functional theory (DFT) cal- culation. Our theoretical calculations show that the static first hyperpolarizability (fltot) values gradually increase with increasing the π-conjugation length and the strength of electron donor group. Especially, compound 12 exhibits the largest βtot (62.404 × 10^-30 esu) by introducing tetrathiafulvalene (TTF), which is about 76 times larger than that of compound 1 containing aryl. This means that the appropriate structural modification can substantially increase the first hyperpolarizabilities of the studied compounds. For the sake of understanding the origin of these large NLO responses, the frontier molecular orbitals (FMOs), electron density difference maps (EDDMs), orbital energy and electronic transition energy of the studied compounds are analyzed. According to the two-state model, the lower transition energy plays an important role in increasing the first hyperpolarizability values. This study may evoke possible ways to design preferable NLO materials.
Alqaraleh, Sahar Mubarak
2006-04-01
We study in this paper the effective energy potential of nonlinear composites in terms of the corresponding energy potential for linear material. We study this for power law material using Suquet's variational principle, for bilinear material using Ponte Castaneda variational principle, and we studied the yield behavior as limiting cases of both. We show that three established variational principles can be derived from the Cauchy-Buniakowski-Schwartz inequality; these variational principles (bounds) are: (a) bounds on yield behavior of mixtures, (b) The Hashin-Shtrikman variational principle for linear materials, (c) The Debotton and Ponte Castaneda bound for power-law polycrystals. We also compute the actual stress and strain fields for laminate material for two choices of the average strain, and compute a bound on the effective potential for spherical inclusions using Hashin's linear bound, as well as for spheroidal inclusions using Willis's linear bound. We obtained bounds sharper than the established bounds for both laminate and aligned ellipsoids geometry, and we investigate also how the bound depends on the specified geometry and on specific parameters of the problem.
Instability and dynamics of two nonlinearly coupled laser beams in a plasma
Shukla, P K; Marklund, M; Stenflo, L; Kourakis, I; Parviainen, M; Dieckmann, M E
2006-01-01
We investigate the nonlinear interaction between two laser beams in a plasma in the weakly nonlinear and relativistic regime. The evolution of the laser beams is governed by two nonlinear Schroedinger equations that are coupled with the slow plasma density response. We study the growth rates of the Raman forward and backward scattering instabilities as well of the Brillouin and self-focusing/modulational instabilities. The nonlinear evolution of the instabilities is investigated by means of direct simulations of the time-dependent system of nonlinear equations.
Variational principles for some nonlinear partial differential equations with variable coefficients
Energy Technology Data Exchange (ETDEWEB)
He Jihuan E-mail: jhhe@dhu.edu.cn
2004-03-01
Variational principles for generalized Korteweg-de Vries equation and nonlinear Schroedinger's equation are obtained by the semi-inverse method. The most interesting features of the proposed method are its extreme simplicity and concise forms of variational functionals for a wide range of nonlinear problems. Comparison with the results obtained by the Noether's theorem is made, revealing the present theorem is a straightforward and attracting mathematical tool.
Muhammad, Shabbir
2015-06-01
Using density functional theory (DFT) methods, the nonlinear optical (NLO) properties have been calculated with strong donor-π-conjugation-acceptor configurations. The static first hyperpolarizability (β0) and dynamic (frequency dependent) electric field induced second harmonic generation (EFISHG) first hyperpolarizability (μβ) are calculated for all designed systems. Our DFT calculations show dithienophenazine merged TTF (2) holds larger β0 amplitudes (β0=21.04×10(3)a.u.) as compared to its corresponding compounds of TTF merged-difurophenazine (1), dicyclopentaphenazine (3) and dipyrrolophenazine (4) derivatives having β0 amplitudes of 16.25×10(3), 12.69×10(3), and 18.38×10(3)a.u., respectively. Furthermore, substitution of dimalononitrile [C(CN)2]2 groups at acceptor end of these compounds results in new derivatives 1a-4a, respectively. Interestingly, a butterfly effect on first hyperpolarizability of all systems 1a-4a has been spotted, which not only results in their robustly larger β0 amplitudes but also changes the increasing order of β0 amplitudes from systems 3systems 1a, 2a, 3a and 4a are 3, 3, 5, and 19 times as compared with their corresponding non dimalononitrile derivatives at PBE0/6-31G* level of theory, respectively. Remarkably, unlike the static first hyperpolarizability, the dynamic EFISHG hyperpolarizability (μβω) has the largest value for system 4a with its amplitudes of 1378.59×10(-46) and 1349.40×10(-46)esu, at PBE0/6-31G* and CAM-B3LYP/6-31+G* levels of theory, respectively. TD-DFT calculations have been performed to trace the origin of first hyperpolarizability. It has been found that the lower transition energy and higher oscillator strengths cause robustly large amplitudes especially in systems 3a and 4a, which consequently stems in strong donor-π-conjugation-acceptor configuration of these systems. Thus the present results intrigue the butterfly effect of a two-step substitution on NLO properties of TTF merged
The thermal-wave model: A Schroedinger-like equation for charged particle beam dynamics
Fedele, Renato; Miele, G.
1994-01-01
We review some results on longitudinal beam dynamics obtained in the framework of the Thermal Wave Model (TWM). In this model, which has recently shown the capability to describe both longitudinal and transverse dynamics of charged particle beams, the beam dynamics is ruled by Schroedinger-like equations for the beam wave functions, whose squared modulus is proportional to the beam density profile. Remarkably, the role of the Planck constant is played by a diffractive constant epsilon, the emittance, which has a thermal nature.
THE LONG-TIME BEHAVIOR OF SPECTRAL APPROXIMATE FOR KLEIN-GORDON-SCHROEDINGER EQUATIONS
Institute of Scientific and Technical Information of China (English)
Xin-minXiang
2004-01-01
Klein-Gordon-Schroedinger (KGS) equations are very important in physics. Some papers studied their well-posedness and numerical solution [1-4], and another works investigated the existence of global attractor in Rn and Ω包含于Rn (n≤3) [5-6,11-12]. In this paper, we discuss the dynamical behavior when we apply spectral method to find numerical approximation for periodic initial value problem of KGS equations. It includes the existence of approximate attractor AN, the upper semi-continuity on A which is a global attractor of initial problem and the upper bounds of Hausdorff and fractal dimensions for A and AN,etc.
A New Approach to Solve the Low-lying States of the Schroedinger Equation
Lee Tsung Dao
2005-01-01
We review a new iterative procedure to solve the low-lying states of the Schroedinger equation, done in collaboration with Richard Friedberg. For the groundstate energy, the $n^{th}$ order iterative energy is bounded by a finite limit, independent of $n$; thereby it avoids some of the inherent difficulties faced by the usual perturbative series expansions. For a fairly large class of problems, this new procedure can be proved to give convergent iterative solutions. These convergent solutions include the long standing difficult problem of a quartic potential with either symmetric or asymmetric minima.
Trajectory length and autocorrelation times. N{sub f} = 2 simulations in the Schroedinger functional
Energy Technology Data Exchange (ETDEWEB)
Meyer, H. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Witzel, O. [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik
2006-09-15
A status report is presented on the large-volume simulations in the Schroedinger functional with two flavours of O(a) improved Wilson quarks performed by the ALPHA collaboration. The physics goal is to set the scale for the computation of the fundamental parameters of QCD. In this talk the emphasis is on aspects of the Hybrid Monte-Carlo algorithm, which we use with (symmetric) even-odd and Hasenbusch preconditioning. We study the dependence of aucorrelation times on the trajectory length. The latter is found to be significant for fermionic correlators, the trajectories longer than unity performing better than the shorter ones. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Lopez, J. Gonzalez [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Jansen, K. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Renner, D.B. [Jefferson Lab, Newport News, VA (United States); Shindler, A. [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik
2012-08-23
The use of chirally rotated boundary conditions provides a formulation of the Schroedinger functional that is compatible with automatic O(a) improvement of Wilson fermions up to O(a) boundary contributions. The elimination of bulk O(a) effects requires the non-perturbative tuning of the critical mass and one additional boundary counterterm. We present the results of such a tuning in a quenched setup for several values of the renormalized gauge coupling, from perturbative to nonperturbative regimes, and for a range of lattice spacings. We also check that the correct boundary conditions and symmetries are restored in the continuum limit. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Lopez, J. Gonzalez [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Jansen, K. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Renner, D.B. [Jefferson Lab, Newport News, VA (United States); Shindler, A. [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik
2012-08-23
The use of chirally rotated boundary conditions provides a formulation of the Schroedinger functional that is compatible with automatic O(a) improvement of Wilson fermions up to O(a) boundary contributions. The elimination of bulk O(a) effects requires the non-perturbative tuning of the critical mass and one additional boundary counterterm. We present the results of such a tuning in a quenched setup for several values of the renormalized gauge coupling, from perturbative to nonperturbative regimes, and for a range of lattice spacings. We also check that the correct boundary conditions and symmetries are restored in the continuum limit. (orig.)
Klein-Gordon-Wheeler-DeWitt-Schroedinger Equation
Pavsic, Matej
2011-01-01
We start from the Einstein-Hilbert action for the gravitational field in the presence of a point particle source, and cast the action into the corresponding phase space form. The dynamical variables of such a system satisfy the point particle mass shell constraint, the Hamilton and the momentum constraints of the canonical gravity. In the quantized theory, those constraints become operators that annihilate a state. A state can be represented by a wave functional $\\Psi$ that simultaneously satisfies the Klein-Gordon and the Wheeler-DeWitt-Schr\\"odinger equation. The latter equation, besides the term due to gravity, also contains the Schr\\"odinger like term, namely the derivative of $\\Psi$ with respect to time, that occurs because of the presence of the point particle. The particle's time coordinate, $X^0$, serves the role of time. Next, we generalize the system to $p$-branes, and find out that for a quantized spacetime filling brane there occurs an effective cosmological constant, proportional to the expectati...
Energy Technology Data Exchange (ETDEWEB)
Arvieu, R.; Carbonell, J.; Gignoux, C.; Mangin-Brinet, M. [Inst. des Sciences Nucleaires, Grenoble-1 Univ., 38 (France); Rozmej, P. [Uniwersytet Marii Curie-Sklodowskiej, Lublin (Poland)
1997-12-31
The time evolution of coherent rotational wave packets associated to a diatomic molecule or to a deformed nucleus has been studied. Assuming a rigid body dynamics the J(J+1) law leads to a mechanism of cloning: the way function is divided into wave packets identical to the initial one at specific time. Applications are studied for a nuclear wave packed formed by Coulomb excitation. Exact boundary conditions at finite distance for the solution of the time-dependent Schroedinger equation are derived. A numerical scheme based on Crank-Nicholson method is proposed to illustrate its applicability in several examples. (authors) 3 refs.
Energy Technology Data Exchange (ETDEWEB)
Fenili, André; Lopes Rebello da Fonseca Brasil, Reyolando Manoel [Universidade Federal do ABC (UFABC), Centro de Engenharia, Modelagem e Ciências Sociais Aplicadas (CECS) / Aerospace Engineering Santo André, São Paulo (Brazil); Balthazar, José M., E-mail: jmbaltha@gmail.com [Universidade Federal do ABC (UFABC), Centro de Engenharia, Modelagem e Ciências Sociais Aplicadas (CECS) / Aerospace Engineering Santo André, São Paulo, Brazil and Universidade Estadual Paulista, Faculdade de Engenharia Mec and #x00E (Brazil); Francisco, Cayo Prado Fernandes [Universidade Federal do ABC (UFABC), Centro de Engenharia, Modelagem e Ciências Sociais Aplicadas (CECS) / Aerospace Engineering Santo André, São Paulo, Brazil and Instituto de Aeronáutica e Espaço, Departamento de (Brazil)
2014-12-10
We derive nonlinear governing equations without assuming that the beam is inextensible. The derivation couples the equations that govern a weak electric motor, which is used to rotate the base of the beam, to those that govern the motion of the beam. The system is considered non-ideal in the sense that the response of the motor to an applied voltage and the motion of the beam must be obtained interactively. The moment that the motor exerts on the base of the beam cannot be determined without solving for the motion of the beam.
Energy Technology Data Exchange (ETDEWEB)
Kravchenko, Viktor G [Faculdade de Ciencias y Tecnologia, Universidade do Algarve, Campus de Gambelas, 8000 Faro (Portugal); Kravchenko, Vladislav V [Depto de Telecomunicaciones, SEPI ESIME Zacatenco, Instituto Politecnico Nacional, Av. IPN S/N, Edif. 1 CP 07738, DF (Mexico)
2003-11-07
We show that an ample class of physically meaningful partial differential systems of first order such as the Dirac equation with different one-component potentials, static Maxwell's system and the system describing the force-free magnetic fields are equivalent to a single quaternionic equation which in its turn reduces in general to a Schroedinger equation with quaternionic potential, and in some situations this last can be diagonalized. The rich variety of methods developed for different problems corresponding to the Schroedinger equation can be applied to the systems considered in the present work.
Institute of Scientific and Technical Information of China (English)
Bai Cheng-Lin; Zhang Xia; Zhang Li-Hua
2009-01-01
This paper presents a new and efficient approach for constructing exact solutions to nonlinear differential-differenceequations (NLDDEs) and lattice equation. By using this method via symbolic computation system MAPLE, we obtained abundant soliton-like and/or period-form solutions to the (2+l)-dimensional Toda equation. It seems that solitary wave solutions are merely special cases in one family. Furthermore, the method can also be applied to other nonlinear differential-difference equations.
Energy Technology Data Exchange (ETDEWEB)
Hesse, Dirk
2012-07-13
The author developed the pastor software package for automated lattice perturbation theory calculations in the Schroedinger functional scheme. The pastor code consists of two building blocks, dealing with the generation of Feynman rules and Feynman diagrams respectively. Accepting a rather generic class of lattice gauge and fermion actions, passed to the code in a symbolic form as input, a low level part of pastor will generate Feynman rules to an arbitrary order in the bare coupling with a trivial or an Abelian background field. The second, high level part of pastor is a code generator whose output relies on the vertex generator. It writes programs that evaluate Feynman diagrams for a class of Schroedinger functional observables up to one loop order automatically, the relevant O(a) improvement terms are taken into account. We will describe the algorithms used for implementation of both parts of the code in detail, and provide cross checks with perturbative and non-perturbative data to demonstrate the correctness of our code. We demonstrate the usefulness of the pastor package through various applications taken from the matching process of heavy quark effective theory with quantum chromodynamics. We have e.g. completed a one loop analysis for new candidates for matching observables timely and with rather small effort, highlighting two advantages of an automated software setup. The results that were obtained so far will be useful as a guideline for further non-perturbative studies.
Institute of Scientific and Technical Information of China (English)
张燕; 陈增强; 杨鹏; 袁著祉
2004-01-01
A nonlinear proportional-integral-derivative (PID) controller is constructed based on recurrent neural networks. In the control process of nonlinear multivariable systems, several nonlinear PID controllers have been adopted in parallel. Under the decoupling cost function, a decoupling control strategy is proposed. Then the stability condition of the controller is presented based on the Lyapunov theory. Simulation examples are given to show effectiveness of the proposed decoupling control.
Indian Academy of Sciences (India)
ANUJ KUMAR; MAHESH PAL SINGH YADAV
2017-07-01
We have reported a theoretical investigation on nonlinear optical behaviour, electronic and optical properties and other molecular properties of the organic nonlinear optical crystal 2-aminopyridinium ptoluenesulphonate(APPTS). The computation has been done using density functional theory (DFT) methodemploying 6-31G(d) basis set and Becke’s three-parameter hybrid functional (B3LYP). Calculated values of static hyperpolarizability confirm the good nonlinear behaviour of the molecule. Electronic behaviour and global reactivity descriptor parameters are calculated and analysed using HOMO–LUMO analysis. Energy band gap and simulated UV–visible spectrum show good agreement with experimental results. Other important molecular properties like rotational constant, zero-point vibrational energy, total energy at room temperature and pressure have also beencalculated in the ground state.
Kumar, Anuj; Yadav, Mahesh Pal Singh
2017-07-01
We have reported a theoretical investigation on nonlinear optical behaviour, electronic and optical properties and other molecular properties of the organic nonlinear optical crystal 2-aminopyridinium p-toluenesulphonate (APPTS). The computation has been done using density functional theory (DFT) method employing 6-31G(d) basis set and Becke's three-parameter hybrid functional (B3LYP). Calculated values of static hyperpolarizability confirm the good nonlinear behaviour of the molecule. Electronic behaviour and global reactivity descriptor parameters are calculated and analysed using HOMO-LUMO analysis. Energy band gap and simulated UV-visible spectrum show good agreement with experimental results. Other important molecular properties like rotational constant, zero-point vibrational energy, total energy at room temperature and pressure have also been calculated in the ground state.
Institute of Scientific and Technical Information of China (English)
FANHong-Yi; XUXue-Fen; LIChao
2004-01-01
A newly transparent approach for determining energy eigenvalues is proposed, which is finding the ‘eigen-operator' of the square of the Schroedinger operator. As three examples, we discuss the energy level of a nondegenerate parametric amplifier, an angular momentum system and a ring shape of coupled oscillators.
Energy Technology Data Exchange (ETDEWEB)
Cobian, Hector [Facultad de Ciencias, Universidad de Colima, Bernal DIaz del Castillo 340, 28045 Colima, Colima (Mexico); Schulze-Halberg, Axel, E-mail: horus.cobian@gmail.com, E-mail: xbataxel@gmail.com, E-mail: axgeschu@iun.edu [Department of Mathematics and Actuarial Science, Indiana University Northwest, 3400 Broadway, Gary, IN 46408 (United States)
2011-07-15
We construct Darboux transformations for time-dependent Schroedinger equations with position-dependent mass in (2 + 1) dimensions. Several examples illustrate our results, which complement and generalize former findings for the constant mass case in two spatial variables (Schulze-Halberg 2010 J. Math. Phys. 51 033521).
Muhammad, Shabbir; Al-Sehemi, Abdullah G; Irfan, Ahmad; Chaudhry, Aijaz R; Gharni, Hamid; AlFaify, S; Shkir, Mohd; Asiri, Abdullah M
2016-04-01
Using the state-of-art computational techniques, we limelight a structure-property relationship for the position and number of methoxy group(s) to tune the optical and nonlinear optical (NLO) properties (first hyperpolarizability) of chalcone derivatives. Based on our previously synthesized chalcones [system 1 ((E)-1-(2,5-dimethylthiophen-3-yl)-3-(2-methoxyphenyl)prop-2-en-1-one and system 4 (E)-1-(2,5-dimethylthiophen-3-yl)-3-(2,4,5-trimethoxyphenyl)prop-2-en-1-one)], we systematically design several novel derivatives with tuned optical and NLO properties. For instance, the rotation of methoxy group substitutions at three different possible ortho, meta, and para positions on phenyl ring show significant changes in NLO properties of these chalcones derivatives. The system 3 has shown β tot amplitude of 1776 a.u. with terminal 4-methoxyphenyl group (para-methoxy substitution), which is ~2.2 and 2.4 times larger than that of ortho- and meta-methoxyphenyl systems 1 and 2, respectively. Additionally, systems 3a and 4a, which are cyano derivatives of the systems 3 and 4 show significantly large β tot amplitudes of 3280 and 4388 a.u., respectively, which are about 3 and 4 times larger than that of para-nitro aniline (PNA) molecule (a typical donor-acceptor molecule) at the same LC-wPBE/6-311G** level of theory. The origin of larger β tot amplitudes has been traced in lower transition energies and higher oscillator strengths for crucial transitions of designed derives. Thus, our investigation reveals that the chalcones derivatives with para-methoxyphenyl groups possess reasonably large amplitudes of their first hyperpolarizability and good optical transparency (3.0-4.7 eV), which can make them attractive candidates for nonlinear optical applications.
Institute of Scientific and Technical Information of China (English)
Bin-bin LEI; Xue-chao DUAN; Hong BAO; Qian XU
2016-01-01
Type-2 fuzzy controllers have been mostly viewed as black-box function generators. Revealing the analytical struc-ture of any type-2 fuzzy controller is important as it will deepen our understanding of how and why a type-2 fuzzy controller functions and lay a foundation for more rigorous system analysis and design. In this study, we derive and analyze the analytical structure of an interval type-2 fuzzy controller that uses the following identical elements: two nonlinear interval type-2 input fuzzy sets for each variable, four interval type-2 singleton output fuzzy sets, a Zadeh AND operator, and the Karnik-Mendel type reducer. Through dividing the input space of the interval type-2 fuzzy controller into 15 partitions, the input-output relationship for each local region is derived. Our derivation shows explicitly that the controller is approximately equivalent to a nonlinear proportional integral or proportional differential controller with variable gains. Furthermore, by comparing with the analytical structure of its type-1 counterpart, potential advantages of the interval type-2 fuzzy controller are analyzed. Finally, the reliability of the analysis results and the effectiveness of the interval type-2 fuzzy controller are verified by a simulation and an experiment.
Zhu, Shengyang; Cai, Chengbiao; Spanos, Pol D.
2015-01-01
A nonlinear and fractional derivative viscoelastic (FDV) model is used to capture the complex behavior of rail pads. It is implemented into the dynamic analysis of coupled vehicle-slab track (CVST) systems. The vehicle is treated as a multi-body system with 10 degrees of freedom, and the slab track is represented by a three layer Bernoulli-Euler beam model. The model for the rail pads is one dimensional, and the force-displacement relation is based on a superposition of elastic, friction, and FDV forces. This model takes into account the influences of the excitation frequency and of the displacement amplitude through a fractional derivative element, and a nonlinear friction element, respectively. The Grünwald representation of the fractional derivatives is employed to numerically solve the fractional and nonlinear equations of motion of the CVST system by means of an explicit integration algorithm. A dynamic analysis of the CVST system exposed to excitations of rail harmonic irregularities is carried out, pointing out the stiffness and damping dependence on the excitation frequency and the displacement amplitude. The analysis indicates that the dynamic stiffness and damping of the rail pads increase with the excitation frequency while they decrease with the displacement amplitude. Furthermore, comparisons between the proposed model and ordinary Kelvin model adopted for the CVST system, under excitations of welded rail joint irregularities and of random track irregularities, are conducted in the time domain as well as in the frequency domain. The proposed model is shown to possess several modeling advantages over the ordinary Kelvin element which overestimates both the stiffness and damping features at high frequencies.
Midya, Bikashkali; Roychoudhury, Rajkumar
2010-01-01
Here we have studied first and second-order intertwining approach to generate isospectral partner potentials of position-dependent (effective) mass Schroedinger equation. The second-order intertwiner is constructed directly by taking it as second order linear differential operator with position depndent coefficients and the system of equations arising from the intertwining relationship is solved for the coefficients by taking an ansatz. A complete scheme for obtaining general solution is obtained which is valid for any arbitrary potential and mass function. The proposed technique allows us to generate isospectral potentials with the following spectral modifications: (i) to add new bound state(s), (ii) to remove bound state(s) and (iii) to leave the spectrum unaffected. To explain our findings with the help of an illustration, we have used point canonical transformation (PCT) to obtain the general solution of the position dependent mass Schrodinger equation corresponding to a potential and mass function. It is...
Exact solution of Schroedinger equation in the case of reduction to Riccati type of ODE
Ershkov, Sergey V
2011-01-01
Here is presented a new type of exact solution of Schroedinger equation in the case of it's reduction to Riccati type of ordinary differential equations. Due to a very special character of Riccati's type equation, it's general solution is proved to have a proper gap of components of the particle wavefunction (which is known to be determining a proper quantum state of the particle). It means a possibility of sudden transformation or transmutation of quantum state of the particle (from one meaning of wavefunction to another), at definite moment of parametrical time. Besides, in the case of spherical symmetry of particle potential V in position space, as well as spherical symmetry of quantum system E total energy, such a solution is proved to be a multiplying of Bessel function (for radial component) & Legendre spherical function (for angle component), in spherical coordinate system.
A dynamical study of the chirally rotated Schroedinger functional in QCD
Energy Technology Data Exchange (ETDEWEB)
Dalla Brida, Mattia; Sint, Stefan [Trinity College, Dublin (Ireland). School of Mathematics; Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC
2014-12-15
The chirally rotated Schroedinger functional for Wilson-fermions allows for finite-volume, mass-independent renormalization schemes compatible with automatic O(a) improvement. So far, in QCD, the set-up has only been studied in the quenched approximation. Here we present first results for N{sub f}=2 dynamical quark-flavours for several renormalization factors of quark-bilinears. We discuss how these renormalization factors can be easily obtained from simple ratios of two-point functions, and show how automatic O(a) improvement is at work. As a by-product of this investigation the renormalization of the non-singlet axial current, Z{sub A}, is determined very precisely.
Beyond the Dirac phase factor: Dynamical Quantum Phase-Nonlocalities in the Schroedinger Picture
Moulopoulos, Konstantinos
2011-01-01
Generalized solutions of the standard gauge transformation equations are presented and discussed in physical terms. They go beyond the usual Dirac phase factors and they exhibit nonlocal quantal behavior, with the well-known Relativistic Causality of classical fields affecting directly the phases of wavefunctions in the Schroedinger Picture. These nonlocal phase behaviors, apparently overlooked in path-integral approaches, give a natural account of the dynamical nonlocality character of the various (even static) Aharonov-Bohm phenomena, while at the same time they seem to respect Causality. Indeed, for particles passing through nonvanishing magnetic or electric fields they lead to cancellations of Aharonov-Bohm phases at the observation point, generalizing earlier semiclassical experimental observations (of Werner & Brill) to delocalized (spread-out) quantum states. This leads to a correction of previously unnoticed sign-errors in the literature, and to a natural explanation of the deeper reason why certa...
Institute of Scientific and Technical Information of China (English)
蒋利华; 徐安农
2007-01-01
基于NCP(F)的约束极小化变形,构造了一种新的merit函数,将原始的NCP(F)问题转化为约束极小化问题,并构造了相应的derivative-free下降算法,并在merit函数严格单调的条件下证明了derivative-free算法的合理性以及整体收敛性.
Bielawa, R. L.
1976-01-01
The differential equations of motion for the lateral and torsional deformations of a nonlinearly twisted rotor blade in steady flight conditions together with those additional aeroelastic features germane to composite bearingless rotors are derived. The differential equations are formulated in terms of uncoupled (zero pitch and twist) vibratory modes with exact coupling effects due to finite, time variable blade pitch and, to second order, twist. Also presented are derivations of the fully coupled inertia and aerodynamic load distributions, automatic pitch change coupling effects, structural redundancy characteristics of the composite bearingless rotor flexbeam - torque tube system in bending and torsion, and a description of the linearized equations appropriate for eigensolution analyses. Three appendixes are included presenting material appropriate to the digital computer program implementation of the analysis, program G400.
Ekbote, Anusha; Patil, P. S.; Maidur, Shivaraj R.; Chia, Tze Shyang; Quah, Ching Kheng
2017-02-01
In this paper, we present the structure and nonlinear optical (NLO) studies of a D-π-A-π-D type chalcone derivative, (E)-1-(4-aminophenyl)-3-(3-chlorophenyl) prop-2-en-1-one (abbreviated as 3CAMC). The compound was synthesized by Claisen-Schmidt condensation and single crystals were grown by slow evaporation solution growth technique. The structure was confirmed by FT-IR, 1H NMR and single-crystal X-ray diffraction techniques. The 3CAMC crystal is crystallized in the monoclinic crystal system with non-centrosymmetric space group P21 with the unit cell parameters a = 8.0013 (19) Å, b = 4.6630 (11) Å, c = 16.883 (4) Å, β = 95.568 (3)° and Z = 2. The optical absorption spectrum was recorded using UV-Vis-NIR spectrophotometer and the band gap was calculated. The title crystal has a direct band gap of 2.96 eV. TGA/DTA thermal analysis revealed that the crystal has a good thermal stability. The second harmonic generation (SHG) efficiency was investigated using the modified Kurtz-Perry powder test at 1064 nm wavelength with nanosecond (ns) laser pulses. The SHG efficiency is found to be 7 times higher than the well-studied urea. The third-order nonlinear optical properties of 3CAMC at different concentrations were investigated in DMF using Z-scan technique with continuous wave (CW) DPSS laser at 532 nm wavelength. The molecule shows a strong two-photon absorption (2PA) and significant negative nonlinear refraction characteristic (self-defocusing) in the CW regime. Further, we observed the optical limiting behavior in the compound, and evaluated the one-photon and two-photon figures of merit. The encouraging results of NLO studies suggest that the 3CAMC crystal is a promising material for photonics devices, optical switches, and optical power limiting applications.
Droghei, Riccardo; Salusti, Ettore
2013-04-01
Control of drilling parameters, as fluid pressure, mud weight, salt concentration is essential to avoid instabilities when drilling through shale sections. To investigate shale deformation, fundamental for deep oil drilling and hydraulic fracturing for gas extraction ("fracking"), a non-linear model of mechanic and chemo-poroelastic interactions among fluid, solute and the solid matrix is here discussed. The two equations of this model describe the isothermal evolution of fluid pressure and solute density in a fluid saturated porous rock. Their solutions are quick non-linear Burger's solitary waves, potentially destructive for deep operations. In such analysis the effect of diffusion, that can play a particular role in fracking, is investigated. Then, following Civan (1998), both diffusive and shock waves are applied to fine particles filtration due to such quick transients , their effect on the adjacent rocks and the resulting time-delayed evolution. Notice how time delays in simple porous media dynamics have recently been analyzed using a fractional derivative approach. To make a tentative comparison of these two deeply different methods,in our model we insert fractional time derivatives, i.e. a kind of time-average of the fluid-rocks interactions. Then the delaying effects of fine particles filtration is compared with fractional model time delays. All this can be seen as an empirical check of these fractional models.
Directory of Open Access Journals (Sweden)
F. Kwasniok
2012-11-01
Full Text Available A stochastic Duffing-type oscillator model, i.e noise-driven motion with inertia in a potential landscape, is considered for glacial millennial-scale climate transitions. The potential and noise parameters are estimated from a Greenland ice-core record using a nonlinear Kalman filter. For the period from 60 to 20 ky before present, a bistable potential with a deep well corresponding to a cold stadial state and a shallow well corresponding to a warm interstadial state is found. The system is in the strongly dissipative regime and can be very well approximated by an effective one-dimensional Langevin equation.
Beretta, G P
2001-01-01
In view of the recent quest for well-behaved nonlinear extensions of the traditional Schroedinger-von Neumann unitary dynamics that could provide fundamental explanations of recent experimental evidence of loss of quantum coherence at the microscopic level, in this paper, together with a review of the general features of the nonlinear quantum (thermo)dynamics I proposed in a series of papers [see references in G.P. Beretta, Found.Phys. 17, 365 (1987)], I show its exact equivalence with the maximal-entropy-production variational-principle formulation recently derived in S. Gheorghiu-Svirschevski, Phys.Rev. A 63, 022105 (2001). In addition, based on the formalism of general interest I developed for the analysis of composite systems, I show how the variational derivation can be extended to the case of a composite system to obtain the general form of my equation of motion, that turns out to be consistent with the demanding requirements of strong separability. Moreover, I propose a new intriguing fundamental ansat...
Energy Technology Data Exchange (ETDEWEB)
Kravchenko, Vladislav V [Seccion de Posgrado e Investigacion, Escuela Superior de IngenierIa Mecanica y Electrica, Instituto Politecnico Nacional, C.P.07738 Mexico DF (Mexico)
2005-05-06
We consider the real stationary two-dimensional Schroedinger equation. With the aid of any of its particular solutions, we construct a Vekua equation possessing the following special property. The real parts of its solutions are solutions of the original Schroedinger equation and the imaginary parts are solutions of an associated Schroedinger equation with a potential having the form of a potential obtained after the Darboux transformation. Using Bers' theory of Taylor series for pseudoanalytic functions, we obtain a locally complete system of solutions of the original Schroedinger equation which can be constructed explicitly for an ample class of Schroedinger equations. For example it is possible when the potential is a function of one Cartesian, spherical, parabolic or elliptic variable. We give some examples of application of the proposed procedure for obtaining a locally complete system of solutions of the Schroedinger equation. The procedure is algorithmically simple and can be implemented with the aid of a computer system of symbolic or numerical calculation.
Tanev, George; Saadi, Dorthe B; Hoppe, Karsten; Sorensen, Helge B D
2014-01-01
Chronic stress detection is an important factor in predicting and reducing the risk of cardiovascular disease. This work is a pilot study with a focus on developing a method for detecting short-term psychophysiological changes through heart rate variability (HRV) features. The purpose of this pilot study is to establish and to gain insight on a set of features that could be used to detect psychophysiological changes that occur during chronic stress. This study elicited four different types of arousal by images, sounds, mental tasks and rest, and classified them using linear and non-linear HRV features from electrocardiograms (ECG) acquired by the wireless wearable ePatch® recorder. The highest recognition rates were acquired for the neutral stage (90%), the acute stress stage (80%) and the baseline stage (80%) by sample entropy, detrended fluctuation analysis and normalized high frequency features. Standardizing non-linear HRV features for each subject was found to be an important factor for the improvement of the classification results.
Mi, Yongsheng; Liang, Pengxia; Yang, Zhou; Wang, Dong; Cao, Hui; He, Wanli; Yang, Huai; Yu, Lian
2016-02-01
Recently, third-order nonlinear properties of porphyrins and porphyrin polymers and coordination compounds have been extensively studied in relation to their use in photomedicine and molecular photonics. A new functionalized porphyrin dye containing electron-rich alkynes was synthesized and further modified by formal [2+2] click reactions with click reagents tetracyanoethylene (TCNE) and 7, 7, 8, 8-tetracyanoquinodimethane (TCNQ). The photophysical properties of these porphyrin dyes, as well as the click reaction, were studied by UV/Vis spectroscopy. In particular, third-order nonlinear optical properties of the dyes, which showed typical d-π-A structures, were characterized by Z-scan techniques. In addition, the self-assembly properties were investigated through the phase-exchange method, and highly organized morphologies were observed by scanning electron microscopy (SEM). The effects of the click post-functionalization on the properties of the porphyrins were studied, and these functionalized porphyrin dyes represent an interesting set of candidates for optoelectronic device components.
Mi, Yongsheng; Liang, Pengxia; Cao, Hui; He, Wanli
2015-01-01
Abstract Recently, third‐order nonlinear properties of porphyrins and porphyrin polymers and coordination compounds have been extensively studied in relation to their use in photomedicine and molecular photonics. A new functionalized porphyrin dye containing electron‐rich alkynes was synthesized and further modified by formal [2+2] click reactions with click reagents tetracyanoethylene (TCNE) and 7, 7, 8, 8‐tetracyanoquinodimethane (TCNQ). The photophysical properties of these porphyrin dyes, as well as the click reaction, were studied by UV/Vis spectroscopy. In particular, third‐order nonlinear optical properties of the dyes, which showed typical d‐π‐A structures, were characterized by Z‐scan techniques. In addition, the self‐assembly properties were investigated through the phase‐exchange method, and highly organized morphologies were observed by scanning electron microscopy (SEM). The effects of the click post‐functionalization on the properties of the porphyrins were studied, and these functionalized porphyrin dyes represent an interesting set of candidates for optoelectronic device components. PMID:27308215
Energy Technology Data Exchange (ETDEWEB)
Herbert, J.M.
1997-02-01
Perturbation theory has long been utilized by quantum chemists as a method for approximating solutions to the Schroedinger equation. Perturbation treatments represent a system`s energy as a power series in which each additional term further corrects the total energy; it is therefore convenient to have an explicit formula for the nth-order energy correction term. If all perturbations are collected into a single Hamiltonian operator, such a closed-form expression for the nth-order energy correction is well known; however, use of a single perturbed Hamiltonian often leads to divergent energy series, while superior convergence behavior is obtained by expanding the perturbed Hamiltonian in a power series. This report presents a closed-form expression for the nth-order energy correction obtained using Rayleigh-Schroedinger perturbation theory and a power series expansion of the Hamiltonian.
Wachter, H
2007-01-01
The aim of these three papers (I, II, and III) is to develop a q-deformed version of non-relativistic Schroedinger theory. Paper I introduces the fundamental mathematical and physical concepts. The braided line and the three-dimensional q-deformed Euclidean space play the role of position space. For both cases the algebraic framework is extended by a time element. A short review of the elements of q-deformed analysis on the spaces under consideration is given. The time evolution operator is introduced in a consistent way and its basic properties are discussed. These reasonings are continued by proposing q-deformed analogs of the Schroedinger and the Heisenberg picture.
B0-B0bar mixing in the static approximation from the Schroedinger Functional and twisted mass QCD
Palombi, F.; Papinutto, M.; Pena., C; Wittig, H.
2005-01-01
We discuss the renormalisation properties of parity-odd Delta B=2 operators with the heavy quark treated in the static approximation. Via twisted mass QCD (tmQCD), these operators provide the matrix elements relevant for the B0-B0bar mixing amplitude. The layout of a non-perturbative renormalisation programme for the operator basis, using Schroedinger Functional techniques, is described. Finally, we report our results for a one-loop perturbative study of various renormalisation schemes with W...
Hemmateenejad, Bahram; Shamsipur, Mojtaba; Miri, Ramin; Elyasi, Maryam; Foroghinia, Farzaneh; Sharghi, Hashem
2008-03-03
A quantitative structure-property relation (QSPR) study was conducted on the solubility in supercritical fluid carbon dioxide (SCF-CO2) of some recently synthesized anthraquinone, anthrone and xanthone derivatives. The data set consisted of 29 molecules in various temperatures and pressures, which form 1190 solubility data. The combined data splitting-feature selection (CDFS) strategy, which previously developed in our research group, was used as descriptor selection and model development method. Modeling of the relationship between selected molecular descriptors and solubility data was achieved by linear (multiple linear regression; MLR) and nonlinear (artificial neural network; ANN) methods. The QSPR models were validated by cross-validation as well as application of the models to predict the solubility of three external set compounds, which did not have contribution in model development steps. Both linear and nonlinear methods resulted in accurate prediction whereas more accurate results were obtained by ANN model. The respective root mean square error of prediction obtained by MLR and ANN models were 0.284 and 0.095 in the term of logarithm of g solute m(-3) of SCF-CO2. A comparison was made between the models selected by CDFS method and the conventional stepwise feature selection method. It was found that the latter produced models with higher number of descriptors and lowered prediction ability, thus it can be considered as an over-fitted model.
Moustafa, H.; Elshakre, Mohamed E.; Elramly, Salwa
2017-05-01
The electronic structure of and NLO of 2,4-di-aryl-1,5-benzothiazepine and some of its derivatives are investigated theoretically at the B3LYP/6-311G**level of theory. The extent of delocalization and intramolecular charge transfer are estimated and discussed in terms of natural bond orbital analysis (NBO) and second order perturbation interactions between donor and acceptor MOs. The calculated EHOMO and ELUMO energies of the studied compounds can be used to calculate the global properties; chemical hardness (η), softness (S) and electronegativity (χ). The equilibrium geometries of the studied compounds are determined, and it was found that these geometries are non plannar. The choice of these substituents aims at creating a push- pull system on the 1,5-thiazepine basic structure which pave the way to understand their nonlinear optical properties. The calculated nonlinear optical parameters (NLO); polarizability (α), anisotropy of the polarizibility (Δα) and first order hyperpolarizibility (β) of the studied compounds show promising optical properties. 3D-plots of the molecular electrostatic potential (MEP) for some selected molecules are investigated and analyzed showing the distribution of electronic density of orbitals describing the electrophilic and nucleophilic sites of the selected molecules.
Kong, Ming; Liu, Yanqiu; Wang, Hui; Luo, Junshan; Li, Dandan; Zhang, Shengyi; Li, Shengli; Wu, Jieying; Tian, Yupeng
2015-01-01
Four novel Zn(II) terpyridine complexes (ZnLCl2, ZnLBr2, ZnLI2, ZnL(SCN)2) based on carbazole derivative group were designed, synthesized and fully characterized. Their photophysical properties including absorption and one-photon excited fluorescence, two-photon absorption (TPA) and optical power limiting (OPL) were further investigated systematically and interpreted on the basis of theoretical calculations (TD-DFT). The influences of different solvents on the absorption and One-Photon Excited Fluorescence (OPEF) spectral behavior, quantum yields and the lifetime of the chromophores have been investigated in detail. The third-order nonlinear optical (NLO) properties were investigated by open/closed aperture Z-scan measurements using femtosecond pulse laser in the range from 680 to 1080 nm. These results revealed that ZnLCl2 and ZnLBr2 exhibited strong two-photon absorption and ZnLCl2 showed superior optical power limiting property.
Energy Technology Data Exchange (ETDEWEB)
Narain, R; Kara, A H, E-mail: Abdul.Kara@wits.ac.z [School of Mathematics, University of the Witwatersrand, Wits 2050, Johannesburg (South Africa)
2010-02-26
The construction of conserved vectors using Noether's theorem via a knowledge of a Lagrangian (or via the recently developed concept of partial Lagrangians) is well known. The formulas to determine these for higher order flows are somewhat cumbersome but peculiar and become more so as the order increases. We carry out these for a class of high-order partial differential equations from mathematical physics and then consider some specific ones with mixed derivatives. In the latter set of examples, our main focus is that the resultant conserved flows display some previously unknown interesting 'divergence properties' owing to the presence of the mixed derivatives. Overall, we consider a large class of equations of interest and construct some new conservation laws.
Liu, Chuang; Lam, Hak-Keung; Fernando, Tyrone; Iu, Herbert Ho-Ching
2016-05-02
In this paper, we investigate the stability of Takagi-Sugeno fuzzy-model-based (FMB) functional observer-control system. When system states are not measurable for state-feedback control, a fuzzy functional observer is designed to directly estimate the control input instead of the system states. Although the fuzzy functional observer can reduce the order of the observer, it leads to a number of observer gains to be determined. Therefore, a new form of fuzzy functional observer is proposed to facilitate the stability analysis such that the observer gains can be numerically obtained and the stability can be guaranteed simultaneously. The proposed form is also in favor of applying separation principle to separately design the fuzzy controller and the fuzzy functional observer. To design the fuzzy controller with the consideration of system stability, higher order derivatives of Lyapunov function (HODLF) are employed to reduce the conservativeness of stability conditions. The HODLF generalizes the commonly used first-order derivative. By exploiting the properties of membership functions and the dynamics of the FMB control system, convex and relaxed stability conditions can be derived. Simulation examples are provided to show the relaxation of the proposed stability conditions and the feasibility of designed fuzzy functional observer-controller.
Energy Technology Data Exchange (ETDEWEB)
Yan, D; Kevrekidis, P G [Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003-4515 (United States); Frantzeskakis, D J, E-mail: kevrekid@math.umass.edu [Department of Physics, University of Athens, Panepistimiopolis, Zografos, Athens 157 84 (Greece)
2011-10-14
In this work, we consider a model of a defocusing nonlinear Schroedinger equation with a variable nonlinearity exponent. This is motivated by the study of a superfluid Fermi gas in the Bose-Einstein condensation (BEC)-Bardeen-Cooper-Schrieffer crossover. In particular, we focus on the relevant mean-field model in the regime from BEC to unitarity and especially consider the modification of the nearly black soliton oscillation frequency due to the variation in the nonlinearity exponent in a harmonic trapping potential. The analytical expressions given as a function of the relevant nonlinearity exponent are corroborated by numerical computations and also extended past the BEC limit. (paper)
Energy Technology Data Exchange (ETDEWEB)
Aslan, Ismail, E-mail: ismailaslan@iyte.edu.t [Department of Mathematics, Izmir Institute of Technology, Urla, Izmir 35430 (Turkey)
2010-10-01
In this paper, a discrete extension of the (G'/G)-expansion method is applied to a relativistic Toda lattice system and a discrete nonlinear Schroedinger equation in order to obtain discrete traveling wave solutions. Closed form solutions with more arbitrary parameters, which reduce to solitary and periodic waves, are exhibited. New rational solutions are also obtained. The method is straightforward and concise, and its applications in physical sciences are promising.
Extension of the homotopy pertubation method for solving nonlinear differential-difference equations
Energy Technology Data Exchange (ETDEWEB)
Mousa, Mohamed Medhat [Benha Univ. (Egypt). Benha High Inst. of Technology; Al-Farabi Kazakh National Univ., Almaty (Kazakhstan); Kaltayev, Aidarkan [Al-Farabi Kazakh National Univ., Almaty (Kazakhstan); Bulut, Hasan [Firat Univ., Elazig (Turkey). Dept. of Mathematics
2010-12-15
In this paper, we have extended the homotopy perturbation method (HPM) to find approximate analytical solutions for some nonlinear differential-difference equations (NDDEs). The discretized modified Korteweg-de Vries (mKdV) lattice equation and the discretized nonlinear Schroedinger equation are taken as examples to demonstrate the validity and the great potential of the HPM in solving such NDDEs. Comparisons are made between the results of the presented method and exact solutions. The obtained results reveal that the HPM is a very effective and convenient tool for solving such kind of equations. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Helffer, B. [Paris-11 Univ., 91 - Orsay (France). Dept. de Mathematiques; Hoffmann-Ostenhof, M. [Institut fuer Mathematik, Universitaet Wien, Strudthofgasse 4, A-1090 Wien (Austria); Hoffmann-Ostenhof, T. [Institut fuer Theoretische Chemie, Universitaet Wien, Waehringerstrasse 17, A-1090 Wien (Austria)]|[International Erwin Schroedinger Inst. for Mathematical Physics, Vienna (Austria); Owen, M.P. [International Erwin Schroedinger Inst. for Mathematical Physics, Vienna (Austria)
1999-05-01
We investigate nodal sets of magnetic Schroedinger operators with zero magnetic field, acting on a non-simply connected domain in R{sup 2}. For the case of circulation 1/2 of the magnetic vector potential around each hole in the region, we obtain a characterisation of the nodal set, and use this to obtain bounds on the multiplicity of the ground state. For the case of one hole and a fixed electric potential, we show that the first eigenvalue takes its highest value for circulation 1/2. (orig.) With 8 figs., 20 refs.
Energy Technology Data Exchange (ETDEWEB)
Serafini, Thomas; Bertoni, Andrea, E-mail: andrea.bertoni@unimore.i [S3 National Research Center, INFM-CNR, 41125 Modena (Italy)
2009-11-15
In this work we present TDStool, a general-purpose easy-to-use software tool for the solution of the time-dependent Schroedinger equation in 2D and 3D domains with arbitrary time-dependent potentials. The numerical algorithms adopted in the code, namely Fourier split-step and box-integration methods, are sketched and the main characteristics of the tool are illustrated. As an example, the dynamics of a single electron in systems of two and three coupled quantum dots is obtained. The code is released as an open-source project and has a build-in graphical interface for the visualization of the results.
Rodriguez-Toro, Victor A; Velasco-Medina, Jaime
2011-01-01
This paper presents a first approach in order to design an optimal architecture to implement the Numerov method, which solves the time-independent Schroedinger equation (TISE) for one dimension. The design and simulation have been performed by using 64-bits floating-point megafunctions available in Quartus II (Version 9.0). The verification of these results was done by using Matlab. According to these results, it is possible to extend this design to parallel structures, which would be able to calculate several TISE solutions.
Compressible hydromagnetic nonlinearities in the predecoupling plasma
Giovannini, Massimo
2012-01-01
The adiabatic inhomogeneities of the scalar curvature lead to a compressible flow affecting the dynamics of the hydromagnetic nonlinearities. The influence of the plasma on the evolution of a putative magnetic field is explored with the aim of obtaining an effective description valid for sufficiently large scales. The bulk velocity of the plasma, computed in the framework of the LambdaCDM scenario, feeds back into the evolution of the magnetic power spectra leading to a (nonlocal) master equation valid in Fourier space and similar to the ones discussed in the context of wave turbulence. Conversely, in physical space, the magnetic power spectra obey a Schroedinger-like equation whose effective potential depends on the large-scale curvature perturbations. Explicit solutions are presented both in physical space and in Fourier space. It is argued that curvature inhomogeneities, compatible with the WMAP 7yr data, shift to lower wavenumbers the magnetic diffusivity scale.
Fuss, Franz Konstantin
2013-01-01
Standard methods for computing the fractal dimensions of time series are usually tested with continuous nowhere differentiable functions, but not benchmarked with actual signals. Therefore they can produce opposite results in extreme signals. These methods also use different scaling methods, that is, different amplitude multipliers, which makes it difficult to compare fractal dimensions obtained from different methods. The purpose of this research was to develop an optimisation method that computes the fractal dimension of a normalised (dimensionless) and modified time series signal with a robust algorithm and a running average method, and that maximises the difference between two fractal dimensions, for example, a minimum and a maximum one. The signal is modified by transforming its amplitude by a multiplier, which has a non-linear effect on the signal's time derivative. The optimisation method identifies the optimal multiplier of the normalised amplitude for targeted decision making based on fractal dimensions. The optimisation method provides an additional filter effect and makes the fractal dimensions less noisy. The method is exemplified by, and explained with, different signals, such as human movement, EEG, and acoustic signals.
Directory of Open Access Journals (Sweden)
Franz Konstantin Fuss
2013-01-01
Full Text Available Standard methods for computing the fractal dimensions of time series are usually tested with continuous nowhere differentiable functions, but not benchmarked with actual signals. Therefore they can produce opposite results in extreme signals. These methods also use different scaling methods, that is, different amplitude multipliers, which makes it difficult to compare fractal dimensions obtained from different methods. The purpose of this research was to develop an optimisation method that computes the fractal dimension of a normalised (dimensionless and modified time series signal with a robust algorithm and a running average method, and that maximises the difference between two fractal dimensions, for example, a minimum and a maximum one. The signal is modified by transforming its amplitude by a multiplier, which has a non-linear effect on the signal’s time derivative. The optimisation method identifies the optimal multiplier of the normalised amplitude for targeted decision making based on fractal dimensions. The optimisation method provides an additional filter effect and makes the fractal dimensions less noisy. The method is exemplified by, and explained with, different signals, such as human movement, EEG, and acoustic signals.
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.
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
derivative nonlinear Schroedinger (DNLS) equation. Ragnisco and Zullo [18] construct Backlund transformations for the trigonometric classical Gaudin magnet in the partially anisotropic (xxz) case, identifying the subcase of transformations that preserve the real character of the variables. The recently discovered exceptional polynomials are complete polynomial systems that satisfy Sturm-Liouville problems but differ from the classical families of Hermite, Laguerre and Jacobi. Gomez-Ullate et al [19] prove that the families of exceptional orthogonal polynomials known to date can be obtained from the classical ones via a Darboux transformation, which becomes a useful tool to derive some of their properties. Integrability in the context of classical mechanics is associated to the existence of a sufficient number of conserved quantities, which allows sometimes an explicit integration of the equations of motion. This is the case for the motion of the Chaplygin sleigh, a rigid body motion on a fluid with nonholonomic constraints studied in the paper by Fedorov and Garcia-Naranjo [20], who derive explicit solutions and study their asymptotic behaviour. In connection with classical mechanics, some techniques of KAM theory have been used by Procesi [21] to derive normal forms for the NLS equation in its Hamiltonian formulation and prove existence and stability of quasi-periodic solutions in the case of periodic boundary conditions. Algebraic and group theoretic aspects of integrability are covered in a number of papers in the issue. The quest for symmetries of a system of differential equations usually allows us to reduce the order or the number of equations or to find special solutions possesing that symmetry, but algebraic aspects of integrable systems encompass a wide and rich spectrum of techniques, as evidenced by the following contributions. Muriel and Romero [22] perform a systematic study of all second order nonlinear ODEs that are linearizable by generalized Sundman and
Energy Technology Data Exchange (ETDEWEB)
de Swiniarski, R.; Beatty, D.; Donoghue, E.; Fergerson, R.W.; Franey, M.; Gazzaly, M.; Glashausser, C.; Hintz, N.; Jones, K.W.; McClelland, J.B.; Nanda, S.; Plum, M. (Institut des Sciences Nucleaires, 53, avenue des Martyrs, F-38026 Grenoble CEDEX (France) Serin Physics Laboratory, Rutgers University, Piscataway, NJ (USA) School of Physics and Astronomy, University of Minnesota, Minneapolis, MN (USA) Los Alamos Meson Physics Facility, Los Alamos National Laboratory, Los Alamos, NM (USA))
1990-09-01
Analyzing powers have been measured for elastic and inelastic scattering of 500-MeV protons from {sup 28}Si. These data for the first 0{sup +}, 2{sup +}, and 4{sup +} states and the corresponding cross-section data have been analyzed with both Schroedinger and Dirac equation phenomenological coupled-channels methods. Good, qualitatively similar, results are achieved with the two methods.
Modulational development of nonlinear gravity-wave groups
Chereskin, T. K.; Mollo-Christensen, E.
1985-01-01
Observations of the development of nonlinear surface gravity-wave groups are presented, and the amplitude and phase modulations are calculated using Hilbert-transform techniques. With increasing propagation distance and wave steepness, the phase modulation develops local phase reversals whose locations correspond to amplitude minima or nodes. The concomitant frequency modulation develops jumps or discontinuities. The observations are compared with recent similar results for wavetrains. The observations are modelled numerically using the cubic nonlinear Schroedinger equation. The motivation is twofold: to examine quantitatively the evolution of phase as well as amplitude modulation, and to test the inviscid predictions for the asymptotic behavior of groups versus long-time observations. Although dissipation rules out the recurrence, there is a long-time coherence of the groups. The phase modulation is found to distinguish between dispersive and soliton behavior.
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 q-Generalizations of Quantum Equations: Homogeneous and Nonhomogeneous Cases—An Overview
Directory of Open Access Journals (Sweden)
Fernando D. Nobre
2017-01-01
Full Text Available Recent developments on the generalizations of two important equations of quantum physics, namely the Schroedinger and Klein–Gordon equations, are reviewed. These generalizations present nonlinear terms, characterized by exponents depending on an index q, in such a way that the standard linear equations are recovered in the limit q → 1 . Interestingly, these equations present a common, soliton-like, traveling solution, which is written in terms of the q-exponential function that naturally emerges within nonextensive statistical mechanics. In both cases, the corresponding well-known Einstein energy-momentum relations, as well as the Planck and the de Broglie ones, are preserved for arbitrary values of q. In order to deal appropriately with the continuity equation, a classical field theory has been developed, where besides the usual Ψ ( x → , t , a new field Φ ( x → , t must be introduced; this latter field becomes Ψ * ( x → , t only when q → 1 . A class of linear nonhomogeneous Schroedinger equations, characterized by position-dependent masses, for which the extra field Φ ( x → , t becomes necessary, is also investigated. In this case, an appropriate transformation connecting Ψ ( x → , t and Φ ( x → , t is proposed, opening the possibility for finding a connection between these fields in the nonlinear cases. The solutions presented herein are potential candidates for applications to nonlinear excitations in plasma physics, nonlinear optics, in structures, such as those of graphene, as well as in shallow and deep water waves.
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...
Kypraios, Ioannis; Young, Rupert C. D.; Birch, Philip M.; Chatwin, Christopher R.
2003-08-01
The various types of synthetic discriminant function (sdf) filter result in a weighted linear superposition of the training set images. Neural network training procedures result in a non-linear superposition of the training set images or, effectively, a feature extraction process, which leads to better interpolation properties than achievable with the sdf filter. However, generally, shift invariance is lost since a data dependant non-linear weighting function is incorporated in the input data window. As a compromise, we train a non-linear superposition filter via neural network methods with the constraint of a linear input to allow for shift invariance. The filter can then be used in a frequency domain based optical correlator. Simulation results are presented that demonstrate the improved training set interpolation achieved by the non-linear filter as compared to a linear superposition filter.
Isaacson, D.; Isaacson, E. L.; Paes-Leme, P. J.; Marchesin, D.
1981-01-01
Several methods for computing many eigenvalues and eigenfunctions of a single anharmonic oscillator Schroedinger operator whose potential may have one or two minima are described. One of the methods requires the solution of an ill-conditioned generalized eigenvalue problem. This method has the virtue of using a bounded amount of work to achieve a given accuracy in both the single and double well regions. Rigorous bounds are given, and it is proved that the approximations converge faster than any inverse power of the size of the matrices needed to compute them. The results of computations for the g:phi(4):1 theory are presented. These results indicate that the methods actually converge exponentially fast.
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Hoang-Do, Ngoc-Tram; Hoang, Van-Hung; Le, Van-Hoang [Department of Physics, Ho Chi Minh City University of Pedagogy, 280 An Duong Vuong Street, District 5, Ho Chi Minh City (Viet Nam)
2013-05-15
The Feranchuk-Komarov operator method is developed by combining with the Levi-Civita transformation in order to construct analytical solutions of the Schroedinger equation for a two-dimensional exciton in a uniform magnetic field of arbitrary strength. As a result, analytical expressions for the energy of the ground and excited states are obtained with a very high precision of up to four decimal places. Especially, the precision is uniformly stable for the whole range of the magnetic field. This advantage appears due to the consideration of the asymptotic behaviour of the wave-functions in strong magnetic field. The results could be used for various physical analyses and the method used here could also be applied to other atomic systems.
Non-perturbative renormalization of quark mass in Nf=2+1 QCD with the Schroedinger functional scheme
Taniguchi, Yusuke
2010-01-01
We present an evaluation of the quark mass renormalization factor for Nf=2+1 QCD. The Schroedinger functional scheme is employed as the intermediate scheme to carry out non-perturbative running from the low energy to deep in the high energy perturbative region. The regularization independent step scaling function of the quark mass is obtained in the continuum limit. Renormalization factors for the pseudo scalar density and the axial vector current are also evaluated for the same action and the bare couplings as two recent large scale Nf=2+1 simulations; previous work of the CP-PACS/JLQCD collaboration, which covered the up-down quark mass range heavier than m_pi=500 MeV and that of PACS-CS collaboration on the physical point using the reweighting technique.
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.
Arun, N K; Mohan, B M
2017-09-01
The mathematical models reported in the literature so far have been found using Center of Sums (CoS) defuzzification method only. It appears that no one has found models using Center of Area (CoA) or Center of Gravity (CoG) defuzzification method. Although there have been some works reported to deal with modeling of fuzzy controllers via Centroid method, all of them have in fact used CoS method only. In this paper, for the first time mathematical models of the simplest Mamdani type fuzzy Proportional Integral (PI)/Proportional Derivative (PD) controllers via CoG defuzzification are presented. L-type and Γ-type membership functions over different Universes of Discourse (UoDs) are considered for the input variables. L-type, Π-type and Γ-type membership functions are considered for the output variable. Three linear fuzzy control rules relating all four input fuzzy sets to three output fuzzy sets are chosen. Two triangular norms namely Algebraic Product (AP) and Minimum (Min), Maximum (Max) triangular co-norm, and two inference methods, Larsen Product (LP) and Mamdani Minimum (MM), are used. Properties of the models are studied. Stability analysis of closed-loop systems containing one of these controller models in the loop is done using the Small Gain theorem. Since digital controllers are implemented using digital processors, computational and memory requirements of these fuzzy controllers and conventional (nonfuzzy) controllers are compared. A rough estimate of the computational time taken by the digital computer while implementing any of these discrete-time fuzzy controllers is given. Two nonlinear plants are considered to show the superiority of the simplest fuzzy controller obtained using CoA or CoG defuzzification method over the simplest fuzzy controller obtained using CoS method and reported recently. Real-time implementation of one of the developed controller models is done on coupled tank experimental setup to show the feasibility of the developed model
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)
The time-dependent Schroedinger equation, Riccati equation and Airy functions
Lanfear, Nathan
2009-01-01
We construct the Green functions (or Feynman's propagators) for the Schr\\"odinger equations of the form $i\\psi_{t}+{1/4}\\psi_{xx}\\pm tx^{2}\\psi =0$ in terms of Airy functions and solve the Cauchy initial value problem in the coordinate and momentum representations. Particular solutions of the corresponding nonlinear Schr\\"odinger equations with variable coefficients are also found.
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.
Sudheesh, P.; Siji Narendran, N. K.; Chandrasekharan, K.
2013-12-01
Here we report a study on the third-order nonlinear optical properties of a new class of phenylhydrazones and the influence of silver and gold metal nanoparticles on their nonlinear response. Metal nanoparticles were prepared by laser ablation method. Single beam Z-scan technique with a 7 ns, 10 Hz Nd: YAG laser pulses at 532 nm were employed for the measurements. The compounds exhibit well optical limiting properties. Hence, these compounds are a promising class of materials for the optical device applications.
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.
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...
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.
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Davies, C.L.; Maslen, E.N.
1983-12-21
A procedure for solving the few-particle Schroedinger equation exactly is applied to a model system consisting of two identical particles and a massive third particle. The type of interaction potential is not specified except that it should not diverge more rapidly than r/sup -2/ at the particle positions. Allowable interactions include the Coulomb and the harmonic oscillator potentials. The principles are illustrated by reference to the spatially symmetric states of the system.
Nakamura, Yousuke; Taniguchi, Yusuke; Collaboration, for CP-PACS
2007-01-01
We present non-perturbative renormalization factors for $\\Delta S=2$ four-quark operators in quenched domain-wall QCD using the Schroedinger functional method. Non-perturbative renormalization factor for $B_K$ is evaluated at hadronic scale. Combined with the non-perturbative RG running obtained by the Alpha collaboration, our result yields renormalization factor which converts lattice bare $B_K$ to the renormalization group invariant one. We apply the renormalization factor to bare $B_K$ pre...
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Dembinski, S.T.; Wolniewicz, L. [Institute of Physics, Nicholas Copernicus University, Torun (Poland)
1996-01-21
It is shown that the 1 D Hamiltonian, which is a sum of operators which generate a finite nilpotent Lie algebra and depends explicitly on time existing closed form solutions of the time-dependent Schroedinger equation, cannot fulfil in general boundary and normalization conditions on a positive semi-axis. An explanation of the controversy surrounding the solutions of the quantum bouncer model, which appeared recently in the literature, is given. (author)
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Nguyen, Ba Phi [Central University of Construction, Tuy Hoa (Viet Nam); Kim, Ki Hong [Ajou University, Suwon (Korea, Republic of)
2014-06-15
We study theoretically the influence of nonlinear gain effects on the transmission and the Anderson localization of waves in both uniform and random one-dimensional amplifying media by using the discrete nonlinear Schroedinger equation. In uniform amplifying media with nonlinear gain, we find that the strong oscillatory behavior of the transmittance and the reflectance for odd and even values of the sample length disappears for large nonlinearities. The exponential decay rate of the transmittance in the asymptotic limit is found to be independent of nonlinear gain. In random amplifying media, we find that the maximum values of the disorder-averaged logarithmic transmittance and reflectance depend nonmonotonically on the strength of nonlinear gain. We also find that the localization length is independent of nonlinear gain. In other words, the Anderson localization is neither enhanced nor weakened due to nonlinear gain. In both the uniform and the random cases, the crossover length, which is the critical length for the amplification to be efficient, is strongly reduced by the nonlinear nature of the gain.
Carrillo, J. A.
2009-10-30
Weak solutions of the spatially inhomogeneous (diffusive) Aizenmann-Bak model of coagulation-breakup within a bounded domain with homogeneous Neumann boundary conditions are shown to converge, in the fast reaction limit, towards local equilibria determined by their mass. Moreover, this mass is the solution of a nonlinear diffusion equation whose nonlinearity depends on the (size-dependent) diffusion coefficient. Initial data are assumed to have integrable zero order moment and square integrable first order moment in size, and finite entropy. In contrast to our previous result [5], we are able to show the convergence without assuming uniform bounds from above and below on the number density of clusters. © Taylor & Francis Group, LLC.
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
Directory of Open Access Journals (Sweden)
Parovik Roman I.
2016-09-01
Full Text Available The paper deals with the model of variable-order nonlinear hereditary oscillator based on a numerical finite-difference scheme. Numerical experiments have been carried out to evaluate the stability and convergence of the difference scheme. It is argued that the approximation, stability and convergence are of the first order, while the scheme is stable and converges to the exact solution.
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.
Institute of Scientific and Technical Information of China (English)
陈盈盈; 韩奎; 李海鹏; 李明雪; 唐刚; 沈晓鹏
2015-01-01
Organic nonlinear optical materials have attracted considerable attention in recent years because of their potential applications in photonic devices and optical information processing. Recent studies have shown that annulene derivatives exhibit good second-order nonlinear optical properties, but their third-order nonlinear optical properties are studied little. In this paper, the values of molecular static linear polarizabilityαand second hyperpolarizabilityγ of substituted annulenes have been investigated with different levels of HF, B3LYP, BHandHLYP and CAM-B3LYP at different basis sets, respectively. Their ultraviolet spectra have also been calculated by using the TD-B3LYP method. It is found that the quality of the basis set is important for the hyperpolarizability calculations, and diffuse functions are important to obtain accurate results for the second hyperpolarizability. We also study the structure-optical property relationship for annulene. It is found that annulene molecular structure has a significant influence on third-order nonlinear optical response. Increasing the conjugation length and introducing push-pull electronic groups can enhance the second hyperpolarizability. But the introduction of push-pull electronic groups can enhance the hyperpolarizability more remarkably than increasing the conjugation length dose, which may be due to the fact that the introduction of push-pull electronic groups can provide a large number of polarizable electrons whereas increasing the conjugation length can only enhance the electron delocalization. Meanwhile the push-pull electronic group substituted annulenes can also exhibit high transparency in visible region. Thus, this work has a good reference for designing nonlinear optical material with high, nonlinear optical coeﬃcient and good transparency. In addition, for the same push-pull electronic groups, the higher conjugation degree and the longerπ-conjugated bridge result in the decrease of HOMO-LUMO energy
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.
Non-perturbative renormalization of quark mass in Nf=2+1 QCD with the Schroedinger functional scheme
Aoki, S; Ishizuka, N; Izubuchi, T; Kanaya, K; Kuramashi, Y; Murano, K; Namekawa, Y; Okawa, M; Taniguchi, Y; Ukawa, A; Ukita, N; Yoshié, T
2010-01-01
We present an evaluation of the quark mass renormalization factor for Nf=2+1 QCD. The Schroedinger functional scheme is employed as the intermediate scheme to carry out non-perturbative running from the low energy region, where renormalization of bare mass is performed on the lattice, to deep in the high energy perturbative region, where the conversion to the renormalization group invariant mass or the MS-bar scheme is safely carried out. For numerical simulations we adopted the Iwasaki gauge action and non-perturbatively improved Wilson fermion action with the clover term. Seven renormalization scales are used to cover from low to high energy regions and three lattice spacings to take the continuum limit at each scale. The regularization independent step scaling function of the quark mass for the Nf=2+1 QCD is obtained in the continuum limit. Renormalization factors for the pseudo scalar density and the axial vector current are also evaluated for the same action and the bare couplings as two recent large sca...
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.
Solitons in quadratic nonlinear photonic crystals
DEFF Research Database (Denmark)
Corney, Joel Frederick; Bang, Ole
2001-01-01
We study solitons in one-dimensional quadratic nonlinear photonic crystals with modulation of both the linear and nonlinear susceptibilities. We derive averaged equations that include induced cubic nonlinearities, which can be defocusing, and we numerically find previously unknown soliton families...
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...
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.
Ho, K. K.; Moody, G. B.; Peng, C. K.; Mietus, J. E.; Larson, M. G.; Levy, D.; Goldberger, A. L.
1997-01-01
BACKGROUND: Despite much recent interest in quantification of heart rate variability (HRV), the prognostic value of conventional measures of HRV and of newer indices based on nonlinear dynamics is not universally accepted. METHODS AND RESULTS: We have designed algorithms for analyzing ambulatory ECG recordings and measuring HRV without human intervention, using robust methods for obtaining time-domain measures (mean and SD of heart rate), frequency-domain measures (power in the bands of 0.001 to 0.01 Hz [VLF], 0.01 to 0.15 Hz [LF], and 0.15 to 0.5 Hz [HF] and total spectral power [TP] over all three of these bands), and measures based on nonlinear dynamics (approximate entropy [ApEn], a measure of complexity, and detrended fluctuation analysis [DFA], a measure of long-term correlations). The study population consisted of chronic congestive heart failure (CHF) case patients and sex- and age-matched control subjects in the Framingham Heart Study. After exclusion of technically inadequate studies and those with atrial fibrillation, we used these algorithms to study HRV in 2-hour ambulatory ECG recordings of 69 participants (mean age, 71.7+/-8.1 years). By use of separate Cox proportional-hazards models, the conventional measures SD (Psurvival over a mean follow-up period of 1.9 years; other measures, including ApEn (P>.3), were not. In multivariable models, DFA was of borderline predictive significance (P=.06) after adjustment for the diagnosis of CHF and SD. CONCLUSIONS: These results demonstrate that HRV analysis of ambulatory ECG recordings based on fully automated methods can have prognostic value in a population-based study and that nonlinear HRV indices may contribute prognostic value to complement traditional HRV measures.
Robertson-Schroedinger type formulation of Ozawa's noise-disturbance uncertainty principle
Bastos, Catarina; Bertolami, Orfeu; Dias, Nuno Costa; Prata, Joao Nuno
2013-01-01
In this work we derive a matrix formulation of a noise-disturbance uncertainty relation, which is akin to the Robertson-Schr\\"odinger uncertainty principle. Our inequality is stronger than Ozawa's uncertainty principle and takes noise-disturbance correlations into account. Moreover, we show that, for certain types of measurement interactions, it is covariant with respect to linear symplectic transformations of the noise and disturbance operators.
2011-03-01
Schrödinger’s equation in dual power law media,” Physics Letters A, Vol. 372, 5941–5943, 2008. 29. Biswas, A., “Optical solitons in a parabolic law media...Agranovich, V. M., V. S. Babichenko, and V. Ya Chernyak, “Nonlinear surface polaritons,” Soviet Physics . JETP Letters , Vol. 32, 512–515, 1980. 33. Stegeman...Fibers to Photonic Crystals, Academic Press, 2003. 2. Stegeman, G. I., L. Jankovic, H. Kim, S. Polyakov , S. Carrasco, L. Torner, C. Bosshard, P. Gunter
Nonlinearity and trapping in excitation transfer Dimers and Trimers.
Barvik, I; Schanz, H; Barvik, Ivan; Esser, Bernd; Schanz, Holger
1995-01-01
We study the interplay between nonlinearity in exciton transport and trapping due to a sink site for the dimer and the trimer with chain configuration by a numerical integration of the discrete nonlinear Schroedinger equation. Our results for the dimer show, that the formation of a self trapped state due to the nonlinear coupling increases the life time of the exciton substantially. Self trapping can be enhanced by the sink for short times, but for long times it disappears. In the trimer consisting of a subdimer extended by a sink site exists a transition between states localized on the two sites of the subdimer before for larger nonlinear coupling self trapping on one site of the subdimer is observed. For large trapping rates the fear of death effect leads to an increasing life time of the excitation on both, the dimer and the trimer. The sink site is then effectively decoupled. We explain this effect using an asymptotic theory for strong trapping and demonstrate it by direct numerical computation.
Robustness analysis for a class of nonlinear descriptor systems
Institute of Scientific and Technical Information of China (English)
吴敏; 张凌波; 何勇
2004-01-01
The robustness analysis problem of a class of nonlinear descriptor systems is studied. Nonlinear matrix inequality which has the good computation property of convex feasibility is employed to derive some sufficient conditions to guarantee that the nonlinear descriptor systems have robust disturbance attenuation performance, which avoids the computational difficulties in conversing nonlinear matrix and Hamilton-Jacobi inequality. The computation property of convex feasibility of nonlinear matrix inequality makes it possible to apply the results of nonlinear robust control to practice.
Exponential ergodicity and Raleigh-Schroedinger series for infinite dimensional diffusions
Ramirez, Alejandro F
2009-01-01
We consider an infinite dimensional diffusion on $T^{\\mathbb Z^d}$, where $T$ is the circle, defined by an infinitesimal generator of the form $L=\\sum_{i\\in\\mathbb Z^d}(\\frac{a_i(\\eta)}{2}\\partial^2_i +b_i(\\eta)\\partial_i)$, with $\\eta\\in T^{\\mathbb Z^d}$, where the coefficients $a_i,b_i$ are finite range, bounded with bounded second order partial derivatives and the ellipticity assumption $\\inf_{i,\\eta}a_i(\\eta)>0$ is satisfied. We prove that whenever $\
Zhu, Hong-Ming; Pen, Ue-Li; Chen, Xuelei; Yu, Hao-Ran
2016-01-01
We present a direct approach to non-parametrically reconstruct the linear density field from an observed non-linear map. We solve for the unique displacement potential consistent with the non-linear density and positive definite coordinate transformation using a multigrid algorithm. We show that we recover the linear initial conditions up to $k\\sim 1\\ h/\\mathrm{Mpc}$ with minimal computational cost. This reconstruction approach generalizes the linear displacement theory to fully non-linear fields, potentially substantially expanding the BAO and RSD information content of dense large scale structure surveys, including for example SDSS main sample and 21cm intensity mapping.
Boyd, Robert W
2013-01-01
Nonlinear Optics is an advanced textbook for courses dealing with nonlinear optics, quantum electronics, laser physics, contemporary and quantum optics, and electrooptics. Its pedagogical emphasis is on fundamentals rather than particular, transitory applications. As a result, this textbook will have lasting appeal to a wide audience of electrical engineering, physics, and optics students, as well as those in related fields such as materials science and chemistry.Key Features* The origin of optical nonlinearities, including dependence on the polarization of light* A detailed treatment of the q
Nonlinear 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.
Bastos, Catarina; Bertolami, Orfeu; Dias, Nuno Costa; Prata, João Nuno
2014-01-01
We revisit Ozawa's uncertainty principle (OUP) in the framework of noncommutative (NC) quantum mechanics. We derive a matrix version of OUP accommodating any NC structure in the phase-space, and compute NC corrections to lowest order for two measurement interactions, namely the Backaction Evading Quadrature Amplifier and Noiseless Quadrature Transducers. These NC corrections alter the nature of the measurement interaction, as a noiseless interaction may acquire noise, and an interaction of independent intervention may become dependent of the object system. However the most striking result is that noncommutativity may lead to a violation of the OUP itself. The NC corrections for the Backaction Evading Quadrature Amplifier reveal a new term which may potentially be amplified in such a way that the violation of the OUP becomes experimentally testable. On the other hand, the NC corrections to the Noiseless Quadrature Transducer shows an incompatibility of this model with NC quantum mechanics. We discuss the impli...
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
Energy Technology Data Exchange (ETDEWEB)
Griffin, J. J.; Lichtner, P. C.; Dworzecka, M.; Kan, K. K.
1979-01-01
The restrictions implied for the time dependent many-body reaction theory by the (TDHF) single determinantal assumption are explored by constructive analysis. A restructured TD-S-HF reaction theory is modelled, not after the initial-value form of the Schroedinger reaction theory, but after the (fully equivalent) S-matrix form, under the conditions that only self-consistent TDHF solutions occur in the theory, every wave function obeys the fundamental statistical interpretation of quantum mechanics, and the theory reduces to the exact Schroedinger theory for exact solutions which are single determinantal. All of these conditions can be accomodated provided that the theory is interpreted on a time-averaged basis, i.e., physical constants of the Schroedinger theory which are time-dependent in the TDHF theory, are interpreted in TD-S-HF in terms of their time averaged values. The resulting reaction theory, although formulated heuristically, prescribes a well defined and unambiguous calculational program which, although somewhat more demanding technically than the conventional initial-value TDHF method, is nevertheless more consonant with first principles, structurally and mechanistically. For its physical predictions do not depend upon the precise location of the distant measuring apparatus, and are in no way influenced by the spurious cross channel correlations which arise whenever the description of many reaction channels is imposed upon one single-determinantal solution. For nuclear structure physics, the TDHF-eigenfunctions provide the first plausible description of exact eigenstates in the time-dependent framework; moreover, they are unencumbered by any restriction to small amplitudes. 14 references.
Energy Technology Data Exchange (ETDEWEB)
Palombi, F.; Wittig, H. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Papinutto, M. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Pena, C. [European Organization for Nuclear Research, Geneva (Switzerland)
2005-09-01
We discuss the renormalisation properties of parity-odd {delta}B = 2 operators with the heavy quark treated in the static approximation. Via twisted mass QCD, these operators provide the matrix elements relevant for the B{sup 0} - B{sup 0} mixing amplitude. The layout of a non-perturbative renormalisation programme for the operator basis, using Schroedinger Functional techniques, is described. Finally, we report our results for a one-loop perturbative study of various renormalisation schemes with Wilson-type lattice regularisations, which allows, in particular, to compute the NLO anomalous dimensions of the operators in the SF schemes of interest. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Barik, N.; Barik, B.K. (Utkal Univ., Bhubaneswar (India). Dept. of Physics)
1981-12-01
It is shown that a non-relativistic power-law potential model for the heavy quarks in the form V(r) = Arsup(..nu..) + V/sub 0/, (A,..nu..>0) acquires relativistic consistency in generating Dirac bound states of Q anti Q-system in agreement with the Schroedinger spectroscopy if the interaction is modelled by equally mixed scalar and vector parts as suggested by the phenomenology of fine-hyperfine splittings of heavy quarkonium systems in a non-relativistic perturbative approach.
Energy Technology Data Exchange (ETDEWEB)
Kurth, S.
2002-09-04
The renormalised quark mass in the Schroedinger functional is studied perturbatively with a non-vanishing background field. The framework in which the calculations are done is the Schroedinger functional. Its definition and basic properties are reviewed and it is shown how to make the theory converge faster towards its continuum limit by O(a) improvement. It is explained how the Schroedinger functional scheme avoids the implications of treating a large energy range on a single lattice in order to determine the scale dependence of renormalised quantities. The description of the scale dependence by the step scaling function is introduced both for the renormalised coupling and the renormalised quark masses. The definition of the renormalised coupling in the Schroedinger functional is reviewed, and the concept of the renormalised mass being defined by the axial current and density via the PCAC-relation is explained. The running of the renormalised mass described by its step scaling function is presented as a consequence of the fact that the renormalisation constant of the axial density is scale dependent. The central part of the thesis is the expansion of several correlation functions up to 1-loop order. The expansion coefficients are used to compute the critical quark mass at which the renormalised mass vanishes, as well as the 1-loop coefficient of the renormalisation constant of the axial density. Using the result for this renormalisation constant, the 2-loop anomalous dimension is obtained by conversion from the MS-scheme. Another important application of perturbation theory carried out in this thesis is the determination of discretisation errors. The critical quark mass at 1-loop order is used to compute the deviation of the coupling's step scaling function from its continuum limit at 2-loop order. Several lattice artefacts of the current quark mass, defined by the PCAC relation with the unrenormalised axial current and density, are computed at 1-loop order
[Regular and chaotic dynamics with applications in nonlinear optics]. Final report
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Kovacic, G.
1998-10-12
The following major pieces of work were completed under the sponsorship of this grant: (1) singular perturbation theory for dynamical systems; (2) homoclinic orbits and chaotic dynamics in second-harmonic generating, optically pumped, passive optical cavities; (3) chaotic dynamics in short ring-laser cavities; (4) homoclinic orbits in moderately-long ring-laser cavities; (5) finite-dimensional attractor in ring-laser cavities; (6) turbulent dynamics in long ring-laser cavities; (7) bifurcations in a model for a free-boundary problem for the heat equation; (8) weakly nonlinear dynamics of interface propagation; (9) slowly periodically forced planar Hamiltonian systems; and (10) soliton spectrum of the solutions of the nonlinear Schroedinger equation. A brief summary of the research is given for each project.
Nonlinear Gamow vectors, shock waves and irreversibility in optically nonlocal media
Gentilini, Silvia; Marcucci, Giulia; DelRe, Eugenio; Conti, Claudio
2015-01-01
Dispersive shock waves dominate wave-breaking phenomena in Hamiltonian systems. In the absence of loss, these highly irregular and disordered waves are potentially reversible. However, no experimental evidence has been given about the possibility of inverting the dynamics of a dispersive shock wave and turn it into a regular wave-front. Nevertheless, the opposite scenario, i.e., a smooth wave generating turbulent dynamics is well studied and observed in experiments. Here we introduce a new theoretical formulation for the dynamics in a highly nonlocal and defocusing medium described by the nonlinear Schroedinger equation. Our theory unveils a mechanism that enhances the degree of irreversibility. This mechanism explains why a dispersive shock cannot be reversed in evolution even for an arbitrarirly small amount of loss. Our theory is based on the concept of nonlinear Gamow vectors, i.e., power dependent generalizations of the counter-intuitive and hereto elusive exponentially decaying states in Hamiltonian sys...
Quantum physics in the nanoworld. Schroedinger's cat and the dwarfs
Energy Technology Data Exchange (ETDEWEB)
Lueth, Hans [Forschungszentrum Juelich GmbH (Germany). PGI-9 Semiconductor Nanoelectronics and Juelich Aachen Research Alliance (JARA)
2013-07-01
Gives a step-by-step derivation of the physical basis of quantum mechanics without using complex mathematics. Provides a close linking of experiment and theory. Describes most modern experiments related to nanoscience and to the foundation of quantum theory. Provides appendices describing the preparation of nanostructures and the importance of interface physics for nanoscience. Contains more than 40 problems to deepen the understanding. English language version of a successful German textbook. The book deals with all essential aspects of non-relativistic quantum physics up to the quantization of fields. In contrast to common textbooks of quantum mechanics, modern experiments are described both for the purpose of foundation of the theory and in relation to recent applications. In this respect applications to nano-electronics as well as the realization of quantum-bits are presented and discussed. Furthermore, links are made to other important research fields and applications, such as elementary particle physics, solid state physics and nuclear magnetic resonance tomography in medicine. Even though the representation of the topics is largely performed in terms of Dirac's bra-ket notation and by use of commutator algebra, the concrete description of the physical basis and the corresponding theoretical concepts are emphasized. Because of little requirement of complex mathematics, the book is suitable as an introduction into quantum physics, not only for physicists but also for chemists, biologists, engineers, computer scientists and even for philosophers as far as they are interested in natural philosophy and epistomology.
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.-
Institute of Scientific and Technical Information of China (English)
田玉鹏; 吴杰颖; 张胜义; 马文; 李胜利; 谢复新
2000-01-01
设计合成了三种含三种不同取代基(-N(CH3)2，-OCH3，-NO2)氨基硫脲衍生物配体及其ⅡB族配合物M(Ⅱ)X2L2(M=Zn，Cd；X=Cl，Br，I)，并通过元素分析和IR光谱进行了表征。测试了它们的粉末SHG效应。在此基础上结合理论计算和以前的工作，讨论了该类配合物产生SHG效应的微观原因。最后，对NLO(nonlinear optical)配合物的分子设计及配合物产生宏观微观NLO效应的联系进行了探讨。%Three kinds of ligands were designed. The ligands are derivatives from thiosemicarbazone, and with different benzaldehyde containing - N(CH3)2, - OCH3, - NO2 group, which abbreviated as L1, L2, L3, respectively. The three new thiosemicarbazone derivative ligands and their ⅡB group complexes M(Ⅱ)X2 L2(M=Zn, Cd;X=Cl, Br, I) were also synthesized in this work. The complexes have been characterized by spectroscopic techniques and elemental analysis. At last, general guidance for the molecular design of metal complexes for nonlinear optics was postulated based on second harmonic generation powder determination and theoretical calculation.
Institute of Scientific and Technical Information of China (English)
刘英; 刘永军
2001-01-01
On the basis of ZINDO program, a program to calculate the nonlinear second_order polarizabilities βijk and βμ according to the SOS equation was designed. The second_order nonlinear optical properties of diazadistyrene derivatives were studied. The calculated results reveal that the introduction of pyrimidine does not influence the transparency but give rise to large values of β. For the corresponding stilbene derivatives, the effect of the location of pyrimidine on the values of β is greater.%以ZINDO方法为基础, 按完全态求和(SOS)公式自编了计算分子二阶非线性光学系数βijk和βμ的程序，研究了氮杂联苯乙烯系列衍生物的电子光谱和二阶非线性光学性质,考察了嘧啶环位置对βμ的影响. 结果表明：通过引入嘧啶环使共轭链长增加对材料的透明性影响很小，而二阶非线性系数有较大提高，嘧啶环位置对β值有较大影响. 这类化合物由于具有较大的非线性极化率和较好的透明性,是一类很有前途的非线性光学候选材料.
Lespinats, Sylvain; Pinker-Domenig, Katja; Meyer-Bäse, Uwe; Meyer-Bäse, Anke
2015-05-01
Chromosome 19 is known to be linked to neurodegeneration and many cancers. Glioma-derived cancer stem cells (GSCs) are tumor-initiating cells and may be refractory to radiation and chemotherapy and thus have important implications for tumor biology and therapeutics. The analysis and interpretation of large proteomic data sets requires the development of new data mining and visualization approaches. Traditional techniques are insufficient to interpret and visualize these resulting experimental data. The emphasis of this paper lies in the presentation of novel approaches for the visualization, clustering and projection representation to unveil hidden data structures relevant for the accurate interpretation of biological experiments. These qualitative and quantitative methods are applied to the proteomic analysis of data sets derived from the GSCs. The achieved clustering and visualization results provide a more detailed insight into the expression patterns for chromosome 19 proteins.
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.
Supersymmetric quantum mechanics approach to a nonlinear lattice
Energy Technology Data Exchange (ETDEWEB)
Ricotta, Regina Maria [Faculdade de Tecnologia de Sao Paulo (FATEC), SP (Brazil); Drigo Filho, Elso [Universidade Estadual Paulista Julio de Mesquita Filho (UNESP), SP (Brazil)
2011-07-01
Full text: DNA is one of the most important macromolecules of all biological system. New discoveries about it have open a vast new field of research, the physics of nonlinear DNA. A particular feature that has attracted a lot of attention is the thermal denaturation, i.e., the spontaneous separation of the two strands upon heating. In 1989 a simple lattice model for the denaturation of the DNA was proposed, the Peyrard-Bishop model, PB. The bio molecule is described by two chains of particles coupled by nonlinear springs, simulating the hydrogen bonds that connect the two basis in a pair. The potential for the hydrogen bonds is usually approximated by a Morse potential. The Hamiltonian system generates a partition function which allows the evaluation of the thermodynamical quantities such as mean strength of the basis pairs. As a byproduct the Hamiltonian system was shown to be a NLSE (nonlinear Schroedinger equation) having soliton solutions. On the other hand, a reflectionless potential with one bound state, constructed using supersymmetric quantum mechanics, SQM, can be shown to be identical to a soliton solution of the KdV equation. Thus, motivated by this Hamiltonian problem and inspired by the PB model, we consider the Hamiltonian of a reflectionless potential through SQM, in order to evaluate thermodynamical quantities of a unidimensional lattice with possible biological applications. (author)
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
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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.
Energy Technology Data Exchange (ETDEWEB)
Yin, Hongyao [Department of Chemistry, Shanghai Normal University, Shanghai 200234 (China); Xiao, Haibo, E-mail: xiaohb@shnu.edu.cn [Department of Chemistry, Shanghai Normal University, Shanghai 200234 (China); Ding, Lei [Department of Chemistry, Shanghai Normal University, Shanghai 200234 (China); Zhang, Chun; Ren, Aiming [State Key Laboratory of Theoretical and Computational Chemistry, Institute of Theoretical Chemistry, Jilin University, Changchun 130023 (China); Li, Bo [Key Laboratory of Polar Materials and Devices, Ministry of Education, East China Normal University, Shanghai 200241 (China)
2015-02-01
A spirobifluorene-bridged donor/donor chromophore, 2,7-bis-(4-(N,N-diphenylamino)phen-1-yl)-9,9′-spirobifluorene (SPF-TP), was found to combine excellent transparency in the near UV–visible region (λ{sub cut-off} ≤ 420 nm), large two-photon absorption cross-section (4.5 × 10{sup 3}GM) and high thermal stability (T{sub d} = 501 °C). In comparison to the reported two-photon absorption molecules, SPF-TP represents the best thermal stability so far described in the literature. The main electronic factors explaining the high two-photon absorption activities of SPF-TP were analyzed by theoretical calculations. Cyclic voltammograms were employed to explore the causes of the excellent transparency of SPF-TP. It was found that the spiroconjugation effect is responsible for the excellent nonlinearity/transparency/thermal stability trade-off in SPF-TP. In addition, SPF-TP is also a good two-photon induced blue fluorescent material with high fluorescence quantum yield (Φ = 0.90, in THF). - Highlights: • We report a molecule exhibiting excellent transparency. • The two-photon absorption cross-section is as large as 4.5 × 10{sup 3}GM. • The molecule exhibits excellent thermal stability. • The molecule is a good two-photon induced blue fluorescent material. • The spiroconjugation effect explains the excellent properties.
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.
The nonlinear piezoelectric tuned vibration absorber
Soltani, P.; Kerschen, G.
2015-07-01
This paper proposes a piezoelectric vibration absorber, termed the nonlinear piezoelectric tuned vibration absorber (NPTVA), for the mitigation of nonlinear resonances of mechanical systems. The new feature of the NPTVA is that its nonlinear restoring force is designed according to a principle of similarity, i.e., the NPTVA should be an electrical analog of the nonlinear host system. Analytical formulas for the NPTVA parameters are derived using the homotopy perturbation method. Doing so, a nonlinear generalization of Den Hartog’s equal-peak tuning rule is developed for piezoelectric vibration absorbers.
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…
Energy Technology Data Exchange (ETDEWEB)
Sarlet, W, E-mail: Willy.Sarlet@ugent.b [Department of Mathematics, Ghent University, Krijgslaan 281, B-9000 Ghent (Belgium); Department of Mathematics and Statistics, La Trobe University, Bundoora, Victoria 3086 (Australia)
2010-11-12
In a recent paper (R Narain and A H Kara 2010 J. Phys. A: Math. Theor. 43 085205), the authors claim to be applying Noether's theorem to higher-order partial differential equations and state that in a large class of examples 'the resultant conserved flows display some previously unknown interesting 'divergence properties' owing to the presence of the mixed derivatives' (citation from their abstract). It turns out that what this obscure sentence is meant to say is that the vector whose divergence must be zero (according to Noether's theorem), turns out to have non-zero divergence and subsequently must be modified to obtain a true conservation law. Clearly this cannot be right: we explain in detail the main source of the error. (comment)
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.
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.
Institute of Scientific and Technical Information of China (English)
林海军; 王震宇; 林亚平; 汪鲁才
2013-01-01
电阻应变式称重传感器存在严重的非线性误差,直接影响称重结果的准确度。本文首先阐述了称重传感器的非线性误差机理与误差补偿原理,提出了一种基于导数约束的称重传感器非线性误差补偿方法。该方法根据称重传感器输入-输出特性曲线的单调递增性,构造神经网络补偿模型训练的约束条件,完成神经网络优化设计,弥补了因训练样本不足导致的网络泛化误差大的缺陷,同时讨论了惩罚因子对网络性能的影响。实验表明,采用这种基于导数约束神经网络补偿方法( DCNN方法)的称重传感器的非线性误差远小于补偿前的误差；同时当训练样本不足时,DCNN方法比传统训练方法(仅利用数据样本训练神经网络,DINN)具有更好的泛化能力,称重准确度更高。%The nonlinear error of the resistance strain gauge load cell has heavy nonlinear error,which will lead to the low accuracy of weighing results. In this paper,the mechanism of the load cell's nonlinear error is introduced and a method for compensation on the load cell's nonlinear error based on derivatives constraints neural network ( DCNN) is proposed. In this method,the monotonically increasing characteristic of load cell's input-output function is used to construct the constraint conditions of training and optimizing the error compensation model with neural network,which can decrease the model's generalization error because of the lack of its training samples. On the other hand,the model's performance affected by the punishing factor is discussed. The experimental results show that the nonlinear error of load cell with this proposed method is far less than that without compensation,and the DCNN's generalization ability is more advantageous than the DINN( i. e. training neural network by only using data samples and not any constraint condition) ,and the weighing results of load cell with DCNN are more accurate.
Exact solutions for nonlinear partial fractional differential equations
Institute of Scientific and Technical Information of China (English)
Khaled A.Gepreel; Saleh Omran
2012-01-01
In this article,we use the fractional complex transformation to convert nonlinear partial fractional differential equations to nonlinear ordinary differential equations.We use the improved (G’/G)-expansion function method to calculate the exact solutions to the time-and space-fractional derivative foam drainage equation and the time-and space-fractional derivative nonlinear KdV equation.This method is efficient and powerful for solving wide classes of nonlinear evolution fractional order equations.
Boundary control of long waves in nonlinear dispersive systems
DEFF Research Database (Denmark)
Hasan, Agus; Foss, Bjarne; Aamo, Ole Morten
2011-01-01
Unidirectional propagation of long waves in nonlinear dispersive systems may be modeled by the Benjamin-Bona-Mahony-Burgers equation, a third order partial differential equation incorporating linear dissipative and dispersive terms, as well as a term covering nonlinear wave phenomena. For higher...... orders of the nonlinearity, the equation may have unstable solitary wave solutions. Although it is a one dimensional problem, achieving a global result for this equation is not trivial due to the nonlinearity and the mixed partial derivative. In this paper, two sets of nonlinear boundary control laws...... that achieve global exponential stability and semi-global exponential stability are derived for both linear and nonlinear cases....
Energy Technology Data Exchange (ETDEWEB)
Martinez, D [Universidad Autonoma de la Ciudad de Mexico, Plantel Cuautepec, Av. La Corona 320, Col. Loma la Palma, Delegacion Gustavo A. Madero, 07160, Mexico DF (Mexico); Flores-Urbina, J C; Mota, R D [Unidad Profesional Interdisciplinaria de Ingenieria y Tecnologias Avanzadas, IPN. Av. Instituto Politecnico Nacional 2580, Col. La Laguna Ticoman, Delegacion Gustavo A. Madero, 07340 Mexico DF (Mexico); Granados, V D [Escuela Superior de Fisica y Matematicas, Instituto Politecnico Nacional, Ed. 9, Unidad Profesional Adolfo Lopez Mateos, 07738 Mexico DF (Mexico)], E-mail: dmartinezs77@yahoo.com.mx
2010-04-02
We apply the Schroedinger factorization to construct the ladder operators for the hydrogen atom, Mie-type potential, harmonic oscillator and pseudo-harmonic oscillator in arbitrary dimensions. By generalizing these operators we show that the dynamical algebra for these problems is the su(1, 1) Lie algebra.
EINSTEIN, SCHROEDINGER, AND ATOM
Directory of Open Access Journals (Sweden)
Trunev A. P.
2014-03-01
Full Text Available In this paper, we consider gravitation theory in multidimensional space. The model of the metric satisfying the basic requirements of quantum theory is proposed. It is shown that gravitational waves are described by the Liouville equation and the Schrodinger equation as well. The solutions of the Einstein equations describing the stationary states of arbitrary quantum and classical systems with central symmetry have been obtained. Einstein’s atom model has been developed, and proved that atoms and atomic nuclei can be represented as standing gravitational waves
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...
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...
Fast Stiffness Matrix Calculation for Nonlinear Finite Element Method
Directory of Open Access Journals (Sweden)
Emir Gülümser
2014-01-01
Full Text Available We propose a fast stiffness matrix calculation technique for nonlinear finite element method (FEM. Nonlinear stiffness matrices are constructed using Green-Lagrange strains, which are derived from infinitesimal strains by adding the nonlinear terms discarded from small deformations. We implemented a linear and a nonlinear finite element method with the same material properties to examine the differences between them. We verified our nonlinear formulation with different applications and achieved considerable speedups in solving the system of equations using our nonlinear FEM compared to a state-of-the-art nonlinear FEM.
Boundary controllability for a nonlinear beam equation
Directory of Open Access Journals (Sweden)
Xiao-Min Cao
2015-09-01
Full Text Available This article concerns a nonlinear system modeling the bending vibrations of a nonlinear beam of length $L>0$. First, we derive the existence of long time solutions near an equilibrium. Then we prove that the nonlinear beam is locally exact controllable around the equilibrium in $H^4(0,L$ and with control functions in $H^2(0,T$. The approach we used are open mapping theorem, local controllability established by linearization, and the induction.
Quantum Dynamics of Nonlinear Cavity Systems
Nation, Paul D.
2010-01-01
We investigate the quantum dynamics of three different configurations of nonlinear cavity systems. To begin, we carry out a quantum analysis of a dc superconducting quantum interference device (SQUID) mechanical displacement detector comprised of a SQUID with a mechanically compliant loop segment. The SQUID is approximated by a nonlinear current-dependent inductor, inducing a flux tunable nonlinear Duffing term in the cavity equation of motion. Expressions are derived for the detector signal ...
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.
New developments in state estimation for Nonlinear Systems
DEFF Research Database (Denmark)
Nørgård, Peter Magnus; Poulsen, Niels Kjølstad; Ravn, Ole
2000-01-01
Based on an interpolation formula, accurate state estimators for nonlinear systems can be derived. The estimators do not require derivative information which makes them simple to implement.; State estimators for nonlinear systems are derived based on polynomial approximations obtained with a multi...
Energy Technology Data Exchange (ETDEWEB)
Kirman, C R.; Sweeney, Lisa M.; Corley, Rick A.; Gargas, M L.
2005-04-01
Reference values, including an oral reference dose (RfD) and an inhalation reference concentration (RfC), were derived for propylene glycol methyl ether (PGME), and an oral RfD was derived for its acetate (PGMEA). These values were based upon transient sedation observed in F344 rats and B6C3F1 mice during a two-year inhalation study. The dose-response relationship for sedation was characterized using internal dose measures as predicted by a physiologically based pharmacokinetic (PBPK) model for PGME and its acetate. PBPK modeling was used to account for changes in rodent physiology and metabolism due to aging and adaptation, based on data collected during weeks 1, 2, 26, 52, and 78 of a chronic inhalation study. The peak concentration of PGME in richly perfused tissues was selected as the most appropriate internal dose measure based upon a consideration of the mode of action for sedation and similarities in tissue partitioning between brain and other richly perfused tissues. Internal doses (peak tissue concentrations of PGME) were designated as either no-observed-adverse-effect levels (NOAELs) or lowest-observed-adverse-effect levels (LOAELs) based upon the presence or absence of sedation at each time-point, species, and sex in the two year study. Distributions of the NOAEL and LOAEL values expressed in terms of internal dose were characterized using an arithmetic mean and standard deviation, with the mean internal NOAEL serving as the basis for the reference values, which was then divided by appropriate uncertainty factors. Where data were permitting, chemical-specific adjustment factors were derived to replace default uncertainty factor values of ten. Nonlinear kinetics are were predicted by the model in all species at PGME concentrations exceeding 100 ppm, which complicates interspecies and low-dose extrapolations. To address this complication, reference values were derived using two approaches which differ with respect to the order in which these extrapolations
Energy Technology Data Exchange (ETDEWEB)
Dartora, C.A., E-mail: cadartora@eletrica.ufpr.b [Electrical Engineering Department, Federal University of Parana (UFPR) (Brazil); Cabrera, G.G., E-mail: cabrera@ifi.unicamp.b [Instituto de Fisica ' Gleb Wataghin' , Universidade Estadual de Campinas (UNICAMP), C.P. 6165, Campinas 13.083-970 SP (Brazil)
2010-05-31
The non-relativistic Pauli-Schroedinger theory has a richer gauge structure than usually expected, being invariant under the U(1)xSU(2) gauge group, which allows to define spin-current density vectors and obtains the relevant conserved quantities from Noether's theorem. The electromagnetic fields E and B play the role of the gauge potentials for the SU(2) sector of the gauge group and can possibly contribute with a corresponding invariant curvature self-energy term in the Lagrangian density. From the dynamics of the U(1) and SU(2) gauge fields we show that electric fields can be induced by spin-currents originated from the SU(2) gauge symmetry.
Nakamura, Y
2007-01-01
We present non-perturbative renormalization factors for $\\Delta S=2$ four-quark operators in quenched domain-wall QCD using the Schroedinger functional method. Non-perturbative renormalization factor for $B_K$ is evaluated at hadronic scale. Combined with the non-perturbative RG running obtained by the Alpha collaboration, our result yields renormalization factor which converts lattice bare $B_K$ to the renormalization group invariant one. We apply the renormalization factor to bare $B_K$ previously obtained by the CP-PACS collaboration with the quenched domain-wall QCD(DWQCD). We compare our result with previous ones obtained by perturbative renormalization factors, different renormalization schemes or different quark actions. We also show that chiral symmetry breaking effects in the renormalization factor are numerically small.
Kovarik, M. D.; Barnes, T.
We describe a Monte Carlo simulation of a dynamical fermion problem in two spatial dimensions on an Intel iPSC/860 hypercube. The problem studied is the determination of the dispersion relation of a dynamical hole in the t-J model of the high temperature superconductors. Since this problem involves the motion of many fermions in more than one spatial dimension, it is representative of the class of systems that suffer from the 'minus sign problem' of dynamical fermions which has made Monte Carlo simulation very difficult. We demonstrate that for small values of the hole hopping parameter one can extract the entire hole dispersion relation using the GRW Monte Carlo algorithm, which is a simulation of the Euclidean time Schroedinger equation, and present results on 4 x 4 and 6 x 6 lattices. Generalization to physical hopping parameter values will only require use of an improved trial wavefunction for importance sampling.
Energy Technology Data Exchange (ETDEWEB)
Kovarik, M.D.; Barnes, T. [Oak Ridge National Lab., TN (United States)]|[Tennessee Univ., Knoxville, TN (United States). Dept. of Physics
1993-10-01
We describe a Monte Carlo simulation of a dynamical fermion problem in two spatial dimensions on an Intel iPSC/860 hypercube. The problem studied is the determination of the dispersion relation of a dynamical hole in the t-J model of the high temperature superconductors. Since this problem involves the motion of many fermions in more than one spatial dimensions, it is representative of the class of systems that suffer from the ``minus sign problem`` of dynamical fermions which has made Monte Carlo simulation very difficult. We demonstrate that for small values of the hole hopping parameter one can extract the entire hole dispersion relation using the GRW Monte Carlo algorithm, which is a simulation of the Euclidean time Schroedinger equation, and present results on 4 {times} 4 and 6 {times} 6 lattices. Generalization to physical hopping parameter values wig only require use of an improved trial wavefunction for importance sampling.
The Nonlinearity of Sum and Product for Boolean Functions
Directory of Open Access Journals (Sweden)
Huang Jinglian
2016-01-01
Full Text Available In this paper, we study the relationship between the nonlinearity of Boolean function and the nonlinearity of the sum and product of Boolean function, while derivative and e-derivative are used to study the problem further. We obtain that the sum of two functions’ nonlinearity is not less than the nonlinearity of the sum of two functions. The relationship between the nonlinearity of function and the nonlinearity of the sum and product of two functions are also obtained. Furthermore, we also get the relationship between the nonlinearity of the product of functions, and the derivative and e-derivative of function. Moreover, we also deduced some important applications on the basis of the above work.
A principle of similarity for nonlinear vibration absorbers
Habib, G.; Kerschen, G.
2016-10-01
This paper develops a principle of similarity for the design of a nonlinear absorber, the nonlinear tuned vibration absorber (NLTVA), attached to a nonlinear primary system. Specifically, for effective vibration mitigation, we show that the NLTVA should feature a nonlinearity possessing the same mathematical form as that of the primary system. A compact analytical formula for the nonlinear coefficient of the absorber is then derived. The formula, valid for any polynomial nonlinearity in the primary system, is found to depend only on the mass ratio and on the nonlinear coefficient of the primary system. When the primary system comprises several polynomial nonlinearities, we demonstrate that the NLTVA obeys a principle of additivity, i.e., each nonlinear coefficient can be calculated independently of the other nonlinear coefficients using the proposed formula.
Muhammad, Shabbir; Xu, Hongliang; Su, Zhongmin
2011-02-10
We present the design of fluoro derivatives of B(10)H(14) and Li@B(10)H(14) baskets. A synergistic effect of conical push and inward pull (reported independently in previous lithium nonlinear optical (NLO) complexes) has been explored in these derivatives to achieve a robustly large NLO response and a higher vertical ionization potential. Li@1,3,6,9-F(4)B(10)H(10), Li@6,9-F(2)B(10)H(12), and Li@2,4,6,9-F(4)B(10)H(10) exhibit first hyperpolarizability (β(0)) values as large as 181 624, 133 199, and 32 314 au; their vertical ionization potentials are 6.45, 6.30, and 6.78 eV, respectively. These values are significantly higher than those previously reported in Li-doped fluorocarbon chains at the same MP2/6-31+G* level of theory (Xu, H. L.; Li, Z. R.; Wu, D.; Wang, B. Q.; Li, Y.; Gu, F. L.; Aoki, Y. J. Am. Chem. Soc. 2007, 129, 2967). They also exceed those from our earlier designed Li@B(10)H(14) basket (Muhammad, S.; Xu, H. L.; Liao, Y.; Kan, Y. H.; Su , Z. M. J. Am. Chem. Soc. 2009, 131, 2967). In addition, new quantum chemical calculations of enthalpies of reaction (Δ(r)H°) at 298 K for B(10)H(14) and its lithium/fluoro derivatives highlight the changes in their thermodynamical aspects. The calculated enthalpies of lithiation reactions are -10.04, -11.29, and -13.18 kcal/mol for B(10)H(14), 6,9-F(2)B(10)H(12), and 2,4-F(2)B(10)H(12), respectively, demonstrating a higher probability of fluoro decaboranes for reaction with lithium. The obtained results not only explain the effect of position and number dependence of substituted fluoro atom(s) in B(10)H(14) and Li@B(10)H(14) but also elucidate a synergistic behavior to polarize a lithium excess electron for high NLO responses and vertical ionization potentials.
Nonlinear Electron Waves in Strongly Magnetized Plasmas
DEFF Research Database (Denmark)
Pécseli, Hans; Juul Rasmussen, Jens
1980-01-01
dynamics in the analysis is also demonstrated. As a particular case the authors investigate nonlinear waves in a strongly magnetized plasma filled wave-guide, where the effects of finite geometry are important. The relevance of this problem to laboratory experiments is discussed.......Weakly nonlinear dispersive electron waves in strongly magnetized plasma are considered. A modified nonlinear Schrodinger equation is derived taking into account the effect of particles resonating with the group velocity of the waves (nonlinear Landau damping). The possibility of including the ion...
Waveguide quantum electrodynamics - nonlinear physics at the few-photon level
Energy Technology Data Exchange (ETDEWEB)
Schneider, Michael; Sproll, Tobias; Martens, Christoph [Max-Born-Institut, Max-Born-Str. 2A, 12489 Berlin (Germany); Schmitteckert, Peter [Institut fuer Nanotechnologie, Karlsruher Institut fuer Technologie (KIT), 76344 Eggenstein-Leopoldshafen (Germany); Busch, Kurt [Max-Born-Institut, Max-Born-Str. 2A, 12489 Berlin (Germany); Humboldt-Universitaet zu Berlin, Institut fuer Physik, AG Theoretische Optik und Photonik, Newtonstr. 15, 12489 Berlin (Germany)
2014-07-01
The transport of few photons in 1D structures coupled to a fermionic impurity gives rise to a set of non-linear effects, induced by an effective interaction due to Pauli blocking such as photon bunching and the formation of atom-photon bound states. We analyze a specific example of such systems, namely a 1-D waveguide coupled to a 2-level system, for the case of one and two-photon transport. Therefore we have developed a general theoretical framework, which contains analytic approaches originating in methods of quantum field theory, like path integrals and Feynman diagrams as well as powerful numerical tools based on solving the time-dependent Schroedinger equation. Owing its generality, our approach is also applicable to more involved setups, including disorder and dissipation as well as more complicated impurities such as driven and undriven 3-level systems.
Exploring the performance of a nonlinear tuned mass damper
DEFF Research Database (Denmark)
Alexander, Nicholas A.; Schilder, Frank
2009-01-01
We explore the performance of a nonlinear tuned mass damper (NTMD), which is modeled as a two degree of freedom system with a cubic nonlinearity. This nonlinearity is physically derived from a geometric configuration of two pairs of springs. The springs in one pair rotate as they extend, which re...
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 magnetohydrodynamics of edge localized mode precursors
Energy Technology Data Exchange (ETDEWEB)
Guo, Z. B., E-mail: guozhipku@gmail.com [State Key Laboratory of Nuclear Physics and Technology, School of Physics, Peking University, Beijing (China); WCI Center for Fusion Theory, NFRI, Gwahangno 113, Yusung-gu, Daejeon 305-333 (Korea, Republic of); Wang, Lu [SEEE, Huazhong University of Science and Technology, Wuhan, Hubei 430074 (China); Wang, X. G. [State Key Laboratory of Nuclear Physics and Technology, School of Physics, Peking University, Beijing (China)
2015-02-15
A possible origin of edge-localized-mode (ELM) precursors based on nonlinear ideal peeling-ballooning mode is reported. Via nonlinear variational principle, a nonlinear evolution equation of the radial displacement is derived and solved, analytically. Besides an explosive growth in the initial nonlinear phase, it is found that the local displacement evolves into an oscillating state in the developed nonlinear phase. The nonlinear frequency of the ELM precursors scales as ω{sub pre}∼x{sup 1/3}ξ{sup ^}{sub ψ,in}{sup 2/3}n, with x position in radial direction, ξ{sup ^}{sub ψ,in} strength of initial perturbation, and n toroidal mode number.
Optical bistability in nonlinear composites with coated ellipsoidal nanoparticles
Pinchuk, A
2003-01-01
Nonlinear composite structures show great promise for use in optical switching, signal processing, etc. We derive an effective nonlinear dielectric permittivity of composite structures where coated ellipsoidal nonlinear particles are imbedded in a linear host medium. The derived expression for the effective dielectric permittivity tensor follows the Clasius-Mossotti approximation. We observe conditions for the existence of the optical bistability effect in a coated ellipsoidal particle with a nonlinear core and a metallic shell. Our numerical results show stronger bistability effects in more dense suspensions of nonlinear heterogeneous ellipsoids.
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.
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 Materials Characterization Facility
Federal Laboratory Consortium — The Nonlinear Materials Characterization Facility conducts photophysical research and development of nonlinear materials operating in the visible spectrum to protect...
Nonlinear approach to ternary scission
Kartavenco, V G
2002-01-01
Description of three-center configuration within mean-field approaches meets uncertainties to select a peculiar set of constraints. We suggest to use the inverse mean field method to solve single-particle Schroedinger equation, instead of constrained selfconsistent Hartree-Fock equations. It is shown, that it is possible to simulate one-dimensional three-center system in the approximation of reflectless single- particle potentials (authors)
Local scale invariances in the bosonic contact and pair-contact processes
Energy Technology Data Exchange (ETDEWEB)
Baumann, Florian [Institut fuer Theoretische Physik I, Universitaet Erlangen-Nuernberg, Staudtstrasse 7B3, D-91058 Erlangen (Germany); Laboratoire de Physique des Materiaux , Universite Henri Poincare Nancy I, BP 239, F-54506 Vandoeuvre les Nancy Cedex (France); Stoimenov, Stoimen [Laboratoire de Physique des Materiaux , Universite Henri Poincare Nancy I, BP 239, F-54506 Vandoeuvre les Nancy Cedex (France); Institute of Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 1784 Sofia (Bulgaria); Henkel, Malte [Laboratoire de Physique des Materiaux , Universite Henri Poincare Nancy I, BP 239, F-54506 Vandoeuvre les Nancy Cedex (France); Isaac Newton Institute of Mathematical Sciences, 20 Clarkson Road, Cambridge CB3 0EH (United Kingdom)
2006-04-21
Local scale invariance for ageing systems without detailed balance is tested through studying the dynamical symmetries of the critical bosonic contact process and the critical bosonic pair-contact process. Their field-theoretical actions can be split into a Schroedinger-invariant term and a pure noise term. It is shown that the two-time response and correlation functions are reducible to certain multipoint response functions which depend only on the Schroedinger-invariant part of the action. For the bosonic contact process, the representation of the Schroedinger group can be derived from the free diffusion equation, whereas for the bosonic pair-contact process, a new representation of the Schroedinger group related to a nonlinear Schroedinger equation with dimensionful couplings is constructed. The resulting predictions of local scale invariance for the two-time responses and correlators are completely consistent with the exactly-known results in both models.
Liu, Chang
2015-01-01
The nonlinear frequency shift is derived in a transparent asymptotic form for intense Langmuir waves in general collisionless plasma. The formula describes both fluid and kinetic effects simultaneously. The fluid nonlinearity is expressed, for the ?first time, through the plasma dielectric function, and the kinetic nonlinearity accounts for both smooth distributions and trapped-particle beams. Various known limiting scalings are reproduced as special cases. The calculation avoids differential equations and can be extended straightforwardly to other nonlinear plasma waves.
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 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.
Collapse in a forced three-dimensional nonlinear Schrodinger equation
DEFF Research Database (Denmark)
Lushnikov, P.M.; Saffman, M.
2000-01-01
We derive sufficient conditions for the occurrence of collapse in a forced three-dimensional nonlinear Schrodinger equation without dissipation. Numerical studies continue the results to the case of finite dissipation.......We derive sufficient conditions for the occurrence of collapse in a forced three-dimensional nonlinear Schrodinger equation without dissipation. Numerical studies continue the results to the case of finite dissipation....
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.
NONLINEAR APPROXIMATION WITH GENERAL WAVE PACKETS
Institute of Scientific and Technical Information of China (English)
L. Borup; M. Nielsen
2005-01-01
We study nonlinear approximation in the Triebel-Lizorkin spaces with dictionaries formed by dilating and translating one single function g. A general Jackson inequality is derived for best m-term approximation with such dictionaries. In some special cases where g has a special structure, a complete characterization of the approximation spaces is derived.
Nonlinear approximation with general wave packets
DEFF Research Database (Denmark)
Borup, Lasse; Nielsen, Morten
2005-01-01
We study nonlinear approximation in the Triebel-Lizorkin spaces with dictionaries formed by dilating and translating one single function g. A general Jackson inequality is derived for best m-term approximation with such dictionaries. In some special cases where g has a special structure, a complete...... characterization of the approximation spaces is derived....
NONLINEAR RESPONSES OF A FLUID-CONVEYING PIPE EMBEDDED IN NONLINEAR ELASTIC FOUNDATIONS
Institute of Scientific and Technical Information of China (English)
Qin Qian; Lin Wang; Qiao Ni
2008-01-01
The nonlinear responses of planar motions of a fluid-conveying pipe embedded in nonlinear elastic foundations are investigated via the differential quadrature method diseretization (DQMD) of the governing partial differential equation. For the analytical model, the effect of the nonlinear elastic foundation is modeled by a nonlinear restraining force. By using an iterative algorithm, a set of ordinary differential dynamical equations derived from the equation of motion of the system are solved numerically and then the bifurcations are analyzed. The numerical results, in which the existence of chaos is demonstrated, are presented in the form of phase portraits of the oscillations. The intermittency transition to chaos has been found to arise.
Analysis on the effect of nonlinear polarization evolution in nonlinear amplifying loop mirror
Institute of Scientific and Technical Information of China (English)
Feng Qu; Xiaoming Liu; Pu Zhang; Xubiao Jiang; Hongming Zhang; Minyu Yao
2005-01-01
By considering the cross phase modulation (XPM) between the two orthogonal poparization components,the nonlinear birefringence and nonlinear polarization evolution (NPE) in highly-nonlinear fiber (HNLF),as well as the unequal evolutions of the state of polarization (SOP) between the clockwise (CW) and counter-clockwise (CCW) waves in a nonlinear amplifying loop mirror (NALM) are analyzed. It is pointed out that the traditional cosine expression is no longer valid for the power transmission of NALM due to uncompleted interference under the high power condition. The analytical expression considering NPE effect is derived, and the experimental result is presented.
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.
Institute of Scientific and Technical Information of China (English)
张旭; 于宪伟; 齐美美; 张继明
2011-01-01
A subalgerbra A 1,which is equivalent to the subalgebra of the Loop algebra A2 in [4], is constructed by making use of algebraic transformation, and then a high - dimensional Loop alegebra G is presented in terms of A1. An isospectral problem is established following G by using direct sum operators and isomorphic relations among subalgebras. It is concluded that a class of expanding integrable system for generalized Schrodinger hierarchy of evolution equations is obtained. As in reduction cases, the integrable coupling of the famous generalized Schroedinger e -quation is presented.%利用代数变换，构造了与文献[4]中的Loop代数A2的子代数等价的Loop代数A1的一个子代数A1。再将A1扩展为一个高维的Loop代数G，利用G设计了一个等谱问题，结合子代数间直和运算和同构关系，得到了广义Schroedinger方程族的一类扩展可积系统。作为约化情形，求得了著名的广义Schroedinger方程的可积耦合系统。
Completely integrable models of nonlinear optics
Indian Academy of Sciences (India)
Andrey I Maimistov
2001-11-01
The models of the nonlinear optics in which solitons appeared are considered. These models are of paramount importance in studies of nonlinear wave phenomena. The classical examples of phenomena of this kind are the self-focusing, self-induced transparency and parametric interaction of three waves. At present there are a number of theories based on completely integrable systems of equations, which are, both, generations of the original known models and new ones. The modiﬁed Korteweg-de Vries equation, the nonlinear Schrödinger equation, the derivative nonlinear Schrödinger equation, Sine–Gordon equation, the reduced Maxwell–Bloch equation, Hirota equation, the principal chiral ﬁeld equations, and the equations of massive Thirring model are some soliton equations, which are usually to be found in nonlinear optics theory.
Effective ac response in weakly nonlinear composites
Energy Technology Data Exchange (ETDEWEB)
Wei Enbo [Institute of Oceanology, Chinese Academy of Sciences, Qingdao 266071 (China); Yang Zidong [College of Power Engineering, University of Shanghai Science and Technology, Shanghai 200093 (China); Gu Guoqing [Information College of Science and Technology, East China Normal University, Shanghai 200062 (China)
2004-01-07
The perturbation method is developed to deal with the problem of determining the effective nonlinear conductivity of Kerr-like nonlinear media under an external ac electric field. As an example, we have considered the cylindrical inclusion embedded in a host under the sinusoidal external field E{sub 1} sin (<{omega}t) + E{sub 3} sin (3<{omega}t) with frequencies{omega} and 3{omega}. The potentials of composites at higher harmonics are derived in both local inclusion particle and host regions. The effective responses of bulk nonlinear composites at basic frequency and harmonics are given for cylindrical composites in the dilute limit. Moreover, the relationships between the nonlinear effective responses at the basic frequency and the third harmonics are derived.
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.
Analytic approach to nonlinear hydrodynamic instabilities driven by time-dependent accelerations
Energy Technology Data Exchange (ETDEWEB)
Mikaelian, K O
2009-09-28
We extend our earlier model for Rayleigh-Taylor and Richtmyer-Meshkov instabilities to the more general class of hydrodynamic instabilities driven by a time-dependent acceleration g(t) . Explicit analytic solutions for linear as well as nonlinear amplitudes are obtained for several g(t)'s by solving a Schroedinger-like equation d{sup 2}{eta}/dt{sup 2} - g(t)kA{eta} = 0 where A is the Atwood number and k is the wavenumber of the perturbation amplitude {eta}(t). In our model a simple transformation k {yields} k{sub L} and A {yields} A{sub L} connects the linear to the nonlinear amplitudes: {eta}{sup nonlinear} (k,A) {approx} (1/k{sub L})ln{eta}{sup linear} (k{sub L}, A{sub L}). The model is found to be in very good agreement with direct numerical simulations. Bubble amplitudes for a variety of accelerations are seen to scale with s defined by s = {integral} {radical}g(t)dt, while spike amplitudes prefer scaling with displacement {Delta}x = {integral}[{integral}g(t)dt]dt.
CMOS current amplifiers : speed versus nonlinearity
2000-01-01
This work deals with analogue integrated circuit design using various types of current-mode amplifiers. These circuits are analysed and realised using modern CMOS integration technologies. The dynamic nonlinearities of these circuits are discussed in detail as in the literature only linear nonidealities and static nonlinearities are conventionally considered. For the most important open-loop current-mode amplifier, the second-generation current-conveyor (CCII), a macromodel is derived tha...
Parametrically Driven Nonlinear Oscillators with an Impurity
Institute of Scientific and Technical Information of China (English)
张卓; 唐翌
2002-01-01
By virtue of the method of multiple scales, we study a chain of parametrically driven nonlinear oscillators with a mass impurity. An equation is presented to describe the nonlinear wave of small amplitude in the chain.In our derivation, the equation is applicable to any eigenmode of coupled pendulum. Our result shows that a nonpropagation soliton emerges as the lowest or highest eigenmode of coupled pendulum is excited, and the impurity tends to pin the nonpropagation soliton excitation.
The nonlinear fixed gravimetric boundary value problem
Institute of Scientific and Technical Information of China (English)
于锦海; 朱灼文
1995-01-01
The properly-posedness of the nonlinear fixed gravimetric boundary value problem is shown with the help of nonlinear functional analysis and a new iterative method to solve the problem is also given, where each step of the iterative program is reduced to solving one and the same kind of oblique derivative boundary value problem with the same type. Furthermore, the convergence of the iterative program is proved with Schauder estimate of elliptic differential equation.
NONLINEAR DYNAMIC ANALYSIS OF FLEXIBLE MULTIBODY SYSTEM
Institute of Scientific and Technical Information of China (English)
A.Y.T.Leung; WuGuorong; ZhongWeifang
2004-01-01
The nonlinear dynamic equations of a multibody system composed of flexible beams are derived by using the Lagrange multiplier method. The nonlinear Euler beam theory with inclusion of axial deformation effect is employed and its deformation field is described by exact vibration modes. A numerical procedure for solving the dynamic equations is presented based on the Newmark direct integration method combined with Newton-Raphson iterative method. The results of numerical examples prove the correctness and efficiency of the method proposed.
Curvatures for Parameter Subsets in Nonlinear Regression
1986-01-01
The relative curvature measures of nonlinearity proposed by Bates and Watts (1980) are extended to an arbitrary subset of the parameters in a normal, nonlinear regression model. In particular, the subset curvatures proposed indicate the validity of linearization-based approximate confidence intervals for single parameters. The derivation produces the original Bates-Watts measures directly from the likelihood function. When the intrinsic curvature is negligible, the Bates-Watts parameter-effec...
APPROXIMATE OUTPUT REGULATION FOR AFFINE NONLINEAR SYSTEMS
Institute of Scientific and Technical Information of China (English)
Yali DONG; Daizhan CHENG; Huashu QIN
2003-01-01
Output regulation for affine nonlinear systems driven by an exogenous signal is investigated in this paper. In the absence of the standard exosystem hypothesis, we assume availability of the instantaneous values of the exogenous signal and its first time-derivative for use in the control law.For affine nonlinear systems, the necessary and sufficient conditions of the solvability of approximate output regulation problem are obtained. The precise form of the control law is presented under some suitable assumptions.
Nonlinear identification of power electronic systems
Chau, KT; Chan, CC
1995-01-01
This paper presents a new approach to modelling power electronic systems using nonlinear system identification. By employing the nonlinear autoregressive moving average with exogenous input (NARMAX) technique, the parametric model of power electronic systems can be derived from the time-domain data. This approach possesses some advantages over available circuit-oriented modelling approaches, such as no small-signal approximation, no circuit idealization and no detailed knowledge of system ope...
Nonlinear predictive control in the LHC accelerator
Blanco, E; Cristea, S; Casas, J
2009-01-01
This paper describes the application of a nonlinear model-based control strategy in a real challenging process. A predictive controller based on a nonlinear model derived from physical relationships, mainly heat and mass balances, has been developed and commissioned in the inner triplet heat exchanger unit (IT-HXTU) of the large hadron collider (LHC) particle accelerator at European Center for Nuclear Research (CERN). The advanced regulation\\ maintains the magnets temperature at about 1.9 K. The development includes a constrained nonlinear state estimator with a receding horizon estimation procedure to improve the regulator predictions.
Nonlinear wave interactions in quantum magnetoplasmas
Shukla, P K; Marklund, M; Stenflo, L
2006-01-01
Nonlinear interactions involving electrostatic upper-hybrid (UH), ion-cyclotron (IC), lower-hybrid (LH), and Alfven waves in quantum magnetoplasmas are considered. For this purpose, the quantum hydrodynamical equations are used to derive the governing equations for nonlinearly coupled UH, IC, LH, and Alfven waves. The equations are then Fourier analyzed to obtain nonlinear dispersion relations, which admit both decay and modulational instabilities of the UH waves at quantum scales. The growth rates of the instabilities are presented. They can be useful in applications of our work to diagnostics in laboratory and astrophysical settings.
Nonlinear cumulative damage model for multiaxial fatigue
Institute of Scientific and Technical Information of China (English)
SHANG De-guang; SUN Guo-qin; DENG Jing; YAN Chu-liang
2006-01-01
On the basis of the continuum fatigue damage theory,a nonlinear uniaxial fatigue cumulative damage model is first proposed.In order to describe multiaxial fatigue damage characteristics,a nonlinear multiaxial fatigue cumulative damage model is developed based on the critical plane approach,The proposed model can consider the multiaxial fatigue limit,mean hydrostatic pressure and the unseparated characteristic for the damage variables and loading parameters.The recurrence formula of fatigue damage model was derived under multilevel loading,which is used to predict multiaxial fatigue life.The results showed that the proposed nonlinear multiaxial fatigue cumulative damage model is better than Miner's rule.
Correlations and Non-Linear Probability Models
DEFF Research Database (Denmark)
Breen, Richard; Holm, Anders; Karlson, Kristian Bernt
2014-01-01
the dependent variable of the latent variable model and its predictor variables. We show how this correlation can be derived from the parameters of non-linear probability models, develop tests for the statistical significance of the derived correlation, and illustrate its usefulness in two applications. Under......Although the parameters of logit and probit and other non-linear probability models are often explained and interpreted in relation to the regression coefficients of an underlying linear latent variable model, we argue that they may also be usefully interpreted in terms of the correlations between...... certain circumstances, which we explain, the derived correlation provides a way of overcoming the problems inherent in cross-sample comparisons of the parameters of non-linear probability models....
A Hierarchy of New Nonlinear Evolution Equations Associated with a 3 × 3 Matrix Spectral Problem
Institute of Scientific and Technical Information of China (English)
GENG Xian-Guo; LI Fang
2009-01-01
A 3 × 3 matrix spectral problem with three potentials and the corresponding hierarchy of new nonlinear evolution equations are proposed. Generalized Hamiltonian structures for the hierarchy of nonlinear evolution equations are derived with the aid of trace identity.
The First Integral Method to the Nonlinear Schrodinger Equations in Higher Dimensions
Directory of Open Access Journals (Sweden)
Shoukry Ibrahim Atia El-Ganaini
2013-01-01
Full Text Available The first integral method introduced by Feng is adopted for solving some important nonlinear partial differential equations, including the (2 + 1-dimensional hyperbolic nonlinear Schrodinger (HNLS equation, the generalized nonlinear Schrodinger (GNLS equation with a source, and the higher-order nonlinear Schrodinger equation in nonlinear optical fibers. This method provides polynomial first integrals for autonomous planar systems. Through the established first integrals, exact traveling wave solutions are formally derived in a concise manner.
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
Extended models of nonlinear waves in liquid with gas bubbles
Kudryashov, Nikolay A
2016-01-01
In this work we generalize the models for nonlinear waves in a gas--liquid mixture taking into account an interphase heat transfer, a surface tension and a weak liquid compressibility simultaneously at the derivation of the equations for nonlinear waves. We also take into consideration high order terms with respect to the small parameter. Two new nonlinear differential equations are derived for long weakly nonlinear waves in a liquid with gas bubbles by the reductive perturbation method considering both high order terms with respect to the small parameter and the above mentioned physical properties. One of these equations is the perturbation of the Burgers equation and corresponds to main influence of dissipation on nonlinear waves propagation. The other equation is the perturbation of the Burgers--Korteweg--de Vries equation and corresponds to main influence of dispersion on nonlinear waves propagation.
Nonlinear effects in asymmetric catalysis.
Satyanarayana, Tummanapalli; Abraham, Susan; Kagan, Henri B
2009-01-01
There is a need for the preparation of enantiomerically pure compounds for various applications. An efficient approach to achieve this goal is asymmetric catalysis. The chiral catalyst is usually prepared from a chiral auxiliary, which itself is derived from a natural product or by resolution of a racemic precursor. The use of non-enantiopure chiral auxiliaries in asymmetric catalysis seems unattractive to preparative chemists, since the anticipated enantiomeric excess (ee) of the reaction product should be proportional to the ee value of the chiral auxiliary (linearity). In fact, some deviation from linearity may arise. Such nonlinear effects can be rich in mechanistic information and can be synthetically useful (asymmetric amplification). This Review documents the advances made during the last decade in the use of nonlinear effects in the area of organometallic and organic catalysis.
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.
Directory of Open Access Journals (Sweden)
Miguel A.V. Ferreira
2007-03-01
Full Text Available In the present work it is exposed synthetically part of an empirical investigation in the field of the sociology of scientific knowledge. From the sociological perspective that assumes the (social activity producing scientific knowledge as one of the epistemological components of this knowledge, it is exposed as, from an autobservational methodology, it has been possible to state the constituently reflexive nature of this activity. A reflexivity in which the formal and formalizeable it is intermingled very indisociably with the existential and informalizable. We present, from these methodologic foundations a (sociological vision of Schroedinger equation that reveals it in its social nataure: beyond its neutral appearance, formal and mathematical, it shows one agencial and active potentiality, shows all the dimensions of an authentic social subject.En el presente trabajo se expone sintéticamente parte de lo que ha sido una investigación empírica en el campo de la sociología del conocimiento científico. Desde la perspectiva sociológica que asume la actividad (social productora de conocimiento científico como uno de los constituyentes epistemológicos de dicho conocimiento, se expone cómo a partir de una metodología autobservacional se ha podido constatar la naturaleza constitutivamente reflexiva de dicha actividad. Una reflexividad en la que lo formal y formalizable se entremezcla indisociablemente con lo informal y vivencial. Presentamos, a partir de estos fundamentos metodológicos, una visión (sociológica de la ecuación de Schroedinger que la revela en su naturaleza social: más allá de su apariencia neutra, formal y matemática, muestra una virtualidad agencial y activa, muestra todas las dimensiones de un auténtico sujeto social. Proponemos, para culminar, que el tipo de reflexividad que entendemos constitutivo de la práctica científica y, por extensión, de cualquier práctica social, se distancia de lo que ha venido defini
On the Improved Nonlinear Tracking Differentiator based Nonlinear PID Controller Design
Directory of Open Access Journals (Sweden)
Ibraheem Kasim Ibraheem
2016-10-01
Full Text Available This paper presents a new improved nonlinear tracking differentiator (INTD with hyperbolic tangent function in the state-space system. The stability and convergence of the INTD are thoroughly investigated and proved. Through the error analysis, the proposed INTD can extract differentiation of any piecewise smooth nonlinear signal to reach a high accuracy. The improved tracking differentiator (INTD has the required filtering features and can cope with the nonlinearities caused by the noise. Through simulations, the INTD is implemented as a signal’s derivative generator for the closed-loop feedback control system with a nonlinear PID controller for the nonlinear Mass-Spring-Damper system and showed that it could achieve the signal tracking and differentiation faster with a minimum mean square error.
Energy Method to Obtain Approximate Solutions of Strongly Nonlinear Oscillators
Directory of Open Access Journals (Sweden)
Alex Elías-Zúñiga
2013-01-01
Full Text Available We introduce a nonlinearization procedure that replaces the system potential energy by an equivalent representation form that is used to derive analytical solutions of strongly nonlinear conservative oscillators. We illustrate the applicability of this method by finding the approximate solutions of two strongly nonlinear oscillators and show that this procedure provides solutions that follow well the numerical integration solutions of the corresponding equations of motion.
Block Monotone Iterative Algorithms for Variational Inequalities with Nonlinear Operators
Institute of Scientific and Technical Information of China (English)
Ming-hui Ren; Jin-ping Zeng
2008-01-01
Some block iterative methods for solving variational inequalities with nonlinear operators are proposed. Monotone convergence of the algorithms is obtained. Some comparison theorems are also established.Compared with the research work in given by Pao in 1995 for nonlinear equations and research work in given by Zeng and Zhou in 2002 for elliptic variational inequalities, the algorithms proposed in this paper are independent of the boundedness of the derivatives of the nonlinear operator.
Geometrically nonlinear behavior of piezoelectric laminated plates
Rabinovitch, Oded
2005-08-01
The geometrically nonlinear behavior of piezo-laminated plates actuated with isotropic or anisotropic piezoelectric layers is analytically investigated. The analytical model is derived using the variational principle of virtual work along with the lamination and plate theories, the von Karman large displacement and moderate rotation kinematic relations, and the anisotropic piezoelectric constitutive laws. A solution strategy that combines the approach of the method of lines, the advantages of the finite element concept, and the variational formulation is developed. This approach yields a set of nonlinear ordinary differential equations with nonlinear boundary conditions, which are solved using the multiple-shooting method. Convergence and verification of the model are examined through comparison with linear and nonlinear results of other approximation methods. The nonlinear response of two active plate structures is investigated numerically. The first plate is actuated in bending using monolithic piezoceramic layers and the second one is actuated in twist using macro-fiber composites. The results quantitatively reveal the complicated in-plane stress state associated with the piezoelectric actuation and the geometrically nonlinear coupling of the in-plane and out-of-plane responses of the plate. The influence of the nonlinear effects ranges from significant stiffening in certain combinations of electrical loads and boundary conditions to amplifications of the induced deflections in others. The paper closes with a summary and conclusions.
Nonlinear amplitude dynamics in flagellar beating
Oriola, David; Casademunt, Jaume
2016-01-01
The physical basis of flagellar and ciliary beating is a major problem in biology which is still far from completely understood. The fundamental cytoskeleton structure of cilia and flagella is the axoneme, a cylindrical array of microtubule doublets connected by passive crosslinkers and dynein motor proteins. The complex interplay of these elements leads to the generation of self-organized bending waves. Although many mathematical models have been proposed to understand this process, few attempts have been made to assess the role of dyneins on the nonlinear nature of the axoneme. Here, we investigate the nonlinear dynamics of flagella by considering an axonemal sliding control mechanism for dynein activity. This approach unveils the nonlinear selection of the oscillation amplitudes, which are typically either missed or prescribed in mathematical models. The explicit set of nonlinear equations are derived and solved numerically. Our analysis reveals the spatiotemporal dynamics of dynein populations and flagell...
Nonlinear theory of kinetic instabilities near threshold
Energy Technology Data Exchange (ETDEWEB)
Berk, H.L.; Pekker, M.S. [Univ. of Texas, Austin, TX (United States). Inst. for Fusion Studies; Breizman, B.N. [Texas Univ., Austin, TX (United States). Inst. for Fusion Studies]|[Budker Inst. of Nuclear Physics, Novosibirsk (Russian Federation)
1997-05-01
A new nonlinear equation has been derived and solved for the evolution of an unstable collective mode in a kinetic system close to the threshold of linear instability. The resonant particle response produces the dominant nonlinearity, which can be calculated iteratively in the near-threshold regime as long as the mode doe snot trap resonant particles. With sources and classical relaxation processes included, the theory describes both soft nonlinear regimes, where the mode saturation level is proportional to an increment above threshold, and explosive nonlinear regimes, where the mode grows to a level that is independent of the closeness to threshold. The explosive solutions exhibit mode frequency shifting. For modes that exist in the absence of energetic particles, the frequency shift is both upward and downward. For modes that require energetic particles for their existence, there is a preferred direction of the frequency shift. The frequency shift continues even after the mode traps resonant particles.
Nonlinear model predictive control theory and algorithms
Grüne, Lars
2017-01-01
This book offers readers a thorough and rigorous introduction to nonlinear model predictive control (NMPC) for discrete-time and sampled-data systems. NMPC schemes with and without stabilizing terminal constraints are detailed, and intuitive examples illustrate the performance of different NMPC variants. NMPC is interpreted as an approximation of infinite-horizon optimal control so that important properties like closed-loop stability, inverse optimality and suboptimality can be derived in a uniform manner. These results are complemented by discussions of feasibility and robustness. An introduction to nonlinear optimal control algorithms yields essential insights into how the nonlinear optimization routine—the core of any nonlinear model predictive controller—works. Accompanying software in MATLAB® and C++ (downloadable from extras.springer.com/), together with an explanatory appendix in the book itself, enables readers to perform computer experiments exploring the possibilities and limitations of NMPC. T...
Mode matching for optimal plasmonic nonlinear generation
O'Brien, Kevin; Suchowski, Haim; Rho, Jun Suk; Kante, Boubacar; Yin, Xiaobo; Zhang, Xiang
2013-03-01
Nanostructures and metamaterials have attracted interest in the nonlinear optics community due to the possibility of engineering their nonlinear responses; however, the underlying physics to describe nonlinear light generation in nanostructures and the design rules to maximize the emission are still under debate. We study the geometry dependence of the second harmonic and third harmonic emission from gold nanostructures, by designing arrays of nanostructures whose geometry varies from bars to split ring resonators. We fix the length (and volume) of the nanostructure on one axis, and change the morphology from a split ring resonator on the other axis. We observed that the optimal second harmonic generation does not occur at the morphology indicated by a nonlinear oscillator model with parameters derived from the far field transmission and is not maximized by a spectral overlap of the plasmonic modes; however, we find a near field overlap integral and mode matching considerations accurately predict the optimal geometry.
Localized Turing patterns in nonlinear optical cavities
Kozyreff, G.
2012-05-01
The subcritical Turing instability is studied in two classes of models for laser-driven nonlinear optical cavities. In the first class of models, the nonlinearity is purely absorptive, with arbitrary intensity-dependent losses. In the second class, the refractive index is real and is an arbitrary function of the intracavity intensity. Through a weakly nonlinear analysis, a Ginzburg-Landau equation with quintic nonlinearity is derived. Thus, the Maxwell curve, which marks the existence of localized patterns in parameter space, is determined. In the particular case of the Lugiato-Lefever model, the analysis is continued to seventh order, yielding a refined formula for the Maxwell curve and the theoretical curve is compared with recent numerical simulation by Gomila et al. [D. Gomila, A. Scroggie, W. Firth, Bifurcation structure of dissipative solitons, Physica D 227 (2007) 70-77.
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).
On absolute stability of nonlinear systems with small delays
Directory of Open Access Journals (Sweden)
M. I. Gil
1998-01-01
Full Text Available Nonlinear nonautonomous retarded systems with separated autonomous linear parts and continuous nonlinear ones are considered. It is assumed that deviations of the argument are sufficiently small. Absolute stability conditions are derived. They are formulated in terms of eigenvalues of auxiliary matrices.
Extension of Variable Separable Solutions for Nonlinear Evolution Equations
Institute of Scientific and Technical Information of China (English)
JIA Hua-Bing; ZHANG Shun-Li; XU Wei; ZHU Xiao-Ning; WANG Yong-Mao; LOU Sen-Yue
2008-01-01
We give the generalized definitions of variable separable solutions to nonlinear evolution equations, and characterize the relation between the functional separable solution and the derivative-dependent functional separablecation, we classify the generalized nonlinear diffusion equations that admit special functional separable solutions and obtain some exact solutions to the resulting equations.
Solutions of some class of nonlinear PDEs in mathematical physics
Directory of Open Access Journals (Sweden)
Shoukry El-Ganaini
2016-04-01
As a result, exact traveling wave solutions involving parameters have been obtained for the considered nonlinear equations in a concise manner. When these parameters are chosen as special values, the solitary wave solutions are derived. It is shown that the proposed technique provides a more powerful mathematical tool for constructing exact solutions for a broad variety of nonlinear PDEs in mathematical physics.
A NEW SOLUTION MODEL OF NONLINEAR DYNAMIC LEAST SQUARE ADJUSTMENT
Institute of Scientific and Technical Information of China (English)
陶华学; 郭金运
2000-01-01
The nonlinear least square adjustment is a head object studied in technology fields. The paper studies on the non-derivative solution to the nonlinear dynamic least square adjustment and puts forward a new algorithm model and its solution model. The method has little calculation load and is simple. This opens up a theoretical method to solve the linear dynamic least square adjustment.
Temperature effects in a nonlinear model of monolayer Scheibe aggregates
DEFF Research Database (Denmark)
Bang, Ole; Christiansen, Peter Leth; If, F.
1994-01-01
A nonlinear dynamical model of molecular monolayers arranged in Scheibe aggregates is derived from a proper Hamiltonian. Thermal fluctuations of the phonons are included. The resulting equation for the excitons is the two dimensional nonlinear Schrodinger equation with noise. Two limits...
ABSOLUTE STABILITY OF GENERAL LURIE DISCRETE NONLINEAR CONTROL SYSTEMS
Institute of Scientific and Technical Information of China (English)
GAN Zuoxin; HAN Jingqing; ZHAO Suxia; WU Yongxian
2002-01-01
In the present paper, the absolute stability of general Lurie discrete nonlinear control systems has been discussed by Lyapunov function approach. A sufficient condition of absolute stability for the general Lurie discrete nonlinear control systems is derived, and some necessary and sufficient conditions are obtained in special cases. Meanwhile, we give a simple example to illustrate the effectiveness of the results.
Nonlinear propagation of short wavelength drift-Alfven waves
DEFF Research Database (Denmark)
Shukla, P. K.; Pecseli, H. L.; Juul Rasmussen, Jens
1986-01-01
Making use of a kinetic ion and a hydrodynamic electron description together with the Maxwell equation, the authors derive a set of nonlinear equations which governs the dynamics of short wavelength ion drift-Alfven waves. It is shown that the nonlinear drift-Alfven waves can propagate as two...
Energy Technology Data Exchange (ETDEWEB)
Chevriaux, D
2007-06-15
We study wave scattering in different nonlinear media possessing a natural forbidden band gap. In particular, we show the existence of a bistable behavior in media governed by the sine-Gordon equation (short pendular chain, Josephson junction array, quantum Hall bilayer), or the nonlinear Schroedinger equation (Kerr and Bragg media), in discrete and continuous models. These different media are submitted to periodic boundary conditions with a frequency in the forbidden band gap and an amplitude that determines their stability states. Indeed, for a sufficient amplitude (supra-transmission), the medium switches from reflector to transmitter, hence allowing the output signal to jump from evanescent to large values. We give a complete analytical description of the bistability that allows to understand the different stationary states observed and to predict the switch of one state to the other. (author)
Nonlinear waves in waveguides with stratification
Leble, Sergei B
1991-01-01
S.B. Leble's book deals with nonlinear waves and their propagation in metallic and dielectric waveguides and media with stratification. The underlying nonlinear evolution equations (NEEs) are derived giving also their solutions for specific situations. The reader will find new elements to the traditional approach. Various dispersion and relaxation laws for different guides are considered as well as the explicit form of projection operators, NEEs, quasi-solitons and of Darboux transforms. Special points relate to: 1. the development of a universal asymptotic method of deriving NEEs for guide propagation; 2. applications to the cases of stratified liquids, gases, solids and plasmas with various nonlinearities and dispersion laws; 3. connections between the basic problem and soliton- like solutions of the corresponding NEEs; 4. discussion of details of simple solutions in higher- order nonsingular perturbation theory.
Nonlinear behavior of Helmholtz resonators
Hersh, A. S.
1990-10-01
A semi-empirical fluid mechanical model has been derived to predict the nonlinear acoustic behavior of thin-walled, single-orifice Helmholtz resonators. The model assumed that the sound particle velocity field approaches the resonator in a spherically symmetric manner. The incident and cavity sound pressure fields are connected in terms of an orifice discharge coefficient and an end correction parameter whose values are determined empirically. The accuracy of the model was verified by comparing predicted with measured impedance over a wide range of sound amplitudes and frequencies for two different resonator geometries and with measurements conducted by Ingard and Ising.